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PAGE 1 1 EFFECTS OF MATHEMATI CS INTEGRATION ON MA THEMATICAL ABILITY A ND EFFICACY OF PRESERVI CE TEACHERS By CHRISTOPHER T. STRIPLING A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012 PAGE 2 2 2012 Christopher T. Stripling PAGE 3 3 To Papa Smith PAGE 4 4 ACKNOWLEDGMENTS I am so grateful for the help and support of many people during the process of completing my doctoral degree. First of all, I thank my Lord and Savior Jesus Christ for giving me a great future and hope (Jeremiah 29:11). Secondly, I thank my wife, Mindi, my parents, my sister, and my in laws for their love and support during my e ducational endeavors. I am also indebted to Dr. T. Grady Roberts for all of his support, advice, and guidance during my research and few short years at the University of Florida. Next, I thank the other members of my committee Dr. Myers, Dr. Stedman and Dr. Gunderson for volunteering their time and for also providing advice and guidance Last but not least, I thank Chris Estepp, Kate Shoulders, Dr. Thoron, Dr. Strong, and my Westside Baptist Church Sunday School class for being very supportive and such g reat friends! PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 11 ABSTRACT ................................ ................................ ................................ ................... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 14 Educational Reform in the United States ................................ ................................ 15 Educational Reform in the1980s ................................ ................................ ...... 15 Educational Reform in the 1990s ................................ ................................ ..... 17 Educational Reform in the 2000s to the Present ................................ .............. 22 Educational Reform: Career and Technical Education ................................ ..... 28 Statement of the Problem ................................ ................................ ....................... 32 Purpose of the Study ................................ ................................ .............................. 33 Statement of Objectives ................................ ................................ .......................... 33 Statement of Hypotheses ................................ ................................ ........................ 34 Sign ificance of the Study ................................ ................................ ........................ 34 Definition of Terms ................................ ................................ ................................ .. 36 Limitations of the Study ................................ ................................ ........................... 37 Assumptions of the Study ................................ ................................ ....................... 37 Chap ter 1 Summary ................................ ................................ ................................ 37 2 REVIEW OF LITERATURE ................................ ................................ .................... 41 Constructivism ................................ ................................ ................................ ........ 41 Theoretical Framework ................................ ................................ ........................... 43 Triadi c Reciprocality ................................ ................................ ................................ 44 Behavior: Teaching Contextualized Mathematics ................................ ............. 45 Personal Factors ................................ ................................ .............................. 51 Demographic variables ................................ ................................ .............. 51 Self e fficacy ................................ ................................ ............................... 53 Mathematics ability/content knowledge ................................ ...................... 64 Environment ................................ ................................ ................................ ..... 71 Teacher education program ................................ ................................ ....... 72 Te aching methods course ................................ ................................ .......... 77 Chapter 2 Summary ................................ ................................ ................................ 84 PAGE 6 6 3 METHODOLOGY ................................ ................................ ................................ ... 90 Research Design ................................ ................................ ................................ .... 91 Procedures ................................ ................................ ................................ ............. 92 Population and Sample ................................ ................................ ........................... 93 Instrumentation ................................ ................................ ................................ ....... 94 Data Collection ................................ ................................ ................................ ....... 97 Analysis of Data ................................ ................................ ................................ ...... 98 Chapter 3 Summary ................................ ................................ .............................. 100 4 RESULTS ................................ ................................ ................................ ............. 103 Descriptive Statistics of Variables in this Study ................................ .................... 105 Mathematics Ability ................................ ................................ ........................ 105 Personal Mathematics Efficacy ................................ ................................ ...... 106 Mathematics Teaching Efficacy ................................ ................................ ...... 107 Personal Teaching Efficacy ................................ ................................ ............ 109 Relationships Between Variables ................................ ................................ ... 110 Antecedent Variables ................................ ................................ ............................ 112 Hypothesis Tests ................................ ................................ ................................ .. 112 Hypothesis Related to Mathematics Ability ................................ ..................... 113 Hypothesis Related to Personal Mathematics Efficacy ................................ .. 113 Hypothesis Related to Mathematics Teaching Efficacy ................................ .. 114 Hypothesis Related to Personal Teaching Efficacy ................................ ........ 114 Chapter 4 Summary ................................ ................................ .............................. 115 5 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS ................................ 140 Objectives ................................ ................................ ................................ ............. 140 Hypotheses ................................ ................................ ................................ ........... 140 Methodology ................................ ................................ ................................ ......... 141 Summary of Findings ................................ ................................ ............................ 143 Descript ive Statistics of Variables in this Study ................................ .............. 143 Mathematics ability ................................ ................................ .................. 143 Personal mathematics efficacy ................................ ................................ 144 Mathematics teaching efficacy ................................ ................................ 145 Personal teaching efficacy ................................ ................................ ....... 146 Hypothesis One ................................ ................................ .............................. 147 Hypothesis Two ................................ ................................ .............................. 147 Hypothesis Three ................................ ................................ ........................... 147 Hypothesis Four ................................ ................................ ............................. 148 Conclusions ................................ ................................ ................................ .......... 148 Discussion and Implications ................................ ................................ .................. 148 Hypothesis Related to Mathematics Ability ................................ ..................... 148 Hypothesis Related to Personal Mathematics Efficacy ................................ .. 150 Hypothesis Related to Mathematics Teaching Efficacy ................................ .. 152 Hypothesis Related to Personal Teaching Efficacy ................................ ........ 153 PAGE 7 7 Recommendations for Teacher Education ................................ ............................ 154 Recommendations for Future Research ................................ ............................... 154 Reflections ................................ ................................ ................................ ............ 155 APPENDIX A TREAT MENT MATERIALS ................................ ................................ ................... 159 B MATHEMATICS ABILITY TEST ................................ ................................ ........... 175 C MATHEMATICS ENHANCEMENT TEACHING EFFICACY INSTRUMENT ......... 184 D IRB APPROVAL AND INFORMED CONSENT ................................ .................... 187 E SCRIPT ................................ ................................ ................................ ................. 189 F DEMOGRAPHIC INSTRUMENT ................................ ................................ .......... 190 G EXPERTS ................................ ................................ ................................ ............. 192 LIST OF REFERENCES ................................ ................................ ............................. 194 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 207 PAGE 8 8 LIST OF TABLES Table page 2 1 The Seven Elements: Components of a Math Enhanced Lesson. ..................... 86 3 1 Cross referenced NCTM Sub standards for Grades 9 12 ................................ 101 4 1 Mathematics Ability means ................................ ................................ ............... 116 4 2 Personal Mathematics Efficacy ................................ ................................ ......... 116 4 3 Mean differences in data collection points for Personal Mathematics Efficacy 116 4 4 Mathematics Teaching Effi cacy ................................ ................................ ........ 116 4 5 Mean differences in data collection points for Mathematics Teaching Efficacy 116 4 6 Personal Teaching Efficacy ................................ ................................ .............. 117 4 7 Mean differences in data collection points for Personal Teaching Efficacy ...... 117 4 8 Correlations between continuous variables ................................ ...................... 118 4 9 Correlations between continuous and dichotomous variables .......................... 119 4 10 Independent samples t test for continuous antecedent variables ..................... 120 4 11 Chi square for categorical antecedent variables ................................ ............... 120 4 12 ANCOVA summary ................................ ................................ ........................... 120 4 13 Adjusted posttest Mathematics Ability means ................................ ................... 120 4 14 MANOVA Personal Mathematics Efficacy ................................ ........................ 120 4 15 MANOVA Mathematics Teaching Efficacy ................................ ....................... 121 4 16 MANOVA Personal Teaching Efficacy ................................ .............................. 121 A 1 Example Seven Elements of a Math enhanced Lesson ................................ ... 160 A 2 Cross referenced NCTM Sub standards for Grades 9 12 and Example Topics ................................ ................................ ................................ ............... 164 PAGE 9 9 LIST OF FIGURES Figure page 2 1 Triadic reciprocal ity model ................................ ................................ ................. 88 2 2 Triadic reciproc ality model of variables under investigation. Adapted from Social Foundation of Th ought and Action ................................ .......................... 88 2 3 The National Resear ch Center for Career and Technical Education: Seven Elements of a Math Enhanced Lesson m odel ................................ ................... 89 2 4 Sample building trades math enhanced lesson: Using the Pythagorean the orem ................................ ................................ ................................ ............. 89 3 1 Research design mathematics ability. ................................ .............................. 102 3 2 Research design effica cy measures. ................................ ................................ 102 4 1 .............. 122 4 2 ............ 122 4 3 .... 123 4 4 ... 123 4 5 Distribution of the control week two of the teaching methods course ................................ ........................ 124 4 6 s Personal Mathematics Efficacy scores week 12 of the teaching methods course/after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson ................. 125 4 7 week 15 of the teaching methods course ................................ ......................... 126 4 8 scores week two of the teaching methods course ................................ ............ 127 4 9 scores week 12 of the teaching methods course/after the preservice teachers in th e treatment group delivered their first mathematics enhanced lesson ....... 128 4 10 athematics Efficacy scores week 15 of the teaching methods course ................................ .............. 129 4 11 Personal Mathematics Efficacy ................................ ................................ ......... 129 PAGE 10 10 4 12 week two of the teaching methods course ................................ ........................ 130 4 13 week 12 of the teaching methods course/after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson ................. 131 4 14 eaching Efficacy scores week 15 of the teaching methods course ................................ ......................... 132 4 15 aching Efficacy scores week two of the teaching methods course ................................ ............ 132 4 16 Teaching Efficacy scores week 12 of the teaching methods course/after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson ....... 133 4 17 scores week 15 of the teaching methods course ................................ .............. 134 4 18 Mathematics Teaching Efficacy ................................ ................................ ........ 134 4 19 nal Teaching Efficacy scores week two of the teaching methods course ................................ ................................ 135 4 20 Teaching Efficacy scores week 12 of the teaching methods course/after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson ................. 136 4 21 15 of the teaching methods course ................................ ................................ ... 137 4 22 week two of the teaching methods course ................................ ........................ 137 4 23 week 12 of the teaching methods course/after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson ................. 138 4 24 week 15 of the teaching methods course ................................ ......................... 139 4 25 Personal Teaching Efficacy ................................ ................................ .............. 139 PAGE 11 11 LIST OF ABBREVIATIO NS ANCOVA Analysis of Covariance AYP Adequately Yearly Progress CTE Career and Technical Education MANOVA Multivariate Analysis of Variance MTE Mathematics Teaching Efficacy MTIS Mathematics Teaching and Integration S trategies NCLB No Child Left Behind NCTM N ational C ouncil of T eachers of M athematics PME Personal Mathematics Efficacy PTE Personal Teaching Efficacy STEM Science, Technology, Engineering, and Mathematics PAGE 12 12 Abstract of Dissertation Presented to the Graduate School of the University of Flo rida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EFFECT S OF MATH EMATICS INTEGRATION ON MATHEMATIC AL ABILITY AND EFFICACY OF PRESERVICE TEACHE RS By Christopher T. Stripling May 2012 Chair: T. Grady Roberts Major: Agricultural Education and Communication T he purpose of this study was to determine the effects of mathematics teaching and integration strategies ( MTIS) on preservice agricultural ability, personal mathematics efficacy, mathematics teaching efficacy, and personal teaching efficacy in a teaching methods course T he independent variable of interest was the MTIS treatment Dependent variables include d mathemati cs teaching efficacy, personal mathematics efficacy, personal teaching efficacy, and mathematics ability of the preservice teachers. The research was quasi experimental and utilized a nonequivalent control group design. The sample consisted of preservice teachers enrolled in AEC 4200 Teaching Methods in Agricultural Education during the Fall 2011 semester at the University of Florida ( n = 19). Data collected were mathematics ability (as measured by the Mathematics Ability Test ), mathematics teaching effi cacy, personal mathematics efficacy, and personal teaching efficacy (as measured by the Mathematics Enhancement Teaching Efficacy Instrument ) ANCOVA was used to determine if significant differences existed in mathematics ability based upon the MTIS trea tment. T he analysis revealed a significant difference in PAGE 13 13 the mathematics ability of preservice agricultural teachers based upon the MTIS treatment while controlling pretest mathematics ability scores. Thus, the MTIS treatment had a positive effect on th e mathematics ability scores of the preservice teachers MANOVAs were used to determine if significant differences existed in mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy based upon the MTIS treatment. T he analys e s did not reveal a significant difference in the mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy of preservice agricultural teachers based upon the MTIS treatment Th erefore, the MTIS treatment did not have an effect on the mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy of the preservice teachers Participants had low to moderate mathematics ability were moderately efficac ious in mathematics teaching efficacy, and efficacious in personal mathemati cs efficacy and personal teaching efficacy. This study found that a teaching methods course that utilizes the MTIS treatment can improve mathematics ability, but the treatment had no effect on the mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy of the preservice teachers. Based on these findings, recommendations for a gricultur al teacher educators and researchers were given. PAGE 14 14 CHAPTER 1 INTRODUCTION Why are 6 1 % of fourth grade American students 6 6 % of eighth grade American students (National Center f or Educational Statistics, 2009b ), and 74% of twelfth grade American students not proficient in mathematics (National Center for Educational Statistics, 2011 )? Additionally, why do 35% of college freshmen at two year public institutions and 16% at four year public insti tutions participate in remedial mathematics courses (National Center for Educational Statistics, 2004)? These statistics are troubling and a shortage of students educated in the STEM disciplines ( science, technology, engineering, and mathematics ) will ha ve major economic and national security implications ( PTC MIT Consortium 2006). With that in mind, educators are part of but the solution may not just fall on mathematics educa tors. Agricultural education and more specifically preservice agricultural teachers may be an integral part of the solution. Prescott, Rinard, Cockerill and Baker (1996) stated that academic and vocational subjects should be integrated to maximize lea rning opportunities. To that end, a gricultural education is a ripe academic area with numerous opportunities for contextualization of core academic subjects (Stripling, Ricketts, Roberts, & Harlin, 2008). Chapter 1 will provide a historical conte xt to the continuing national quest to solve educational deficiencies among American students and focus on the educational initiatives to date designed to correct persistent student deficiency in mathematics More purposely, Chapter 1 will describe the ro le of Career and Technical Education in PAGE 15 15 improving the mathematics content knowledge of secondary students and outline a research response Educational Reform in the United States The pursuit of solutions to correct the enduring problems in public schools became nationally prominent with the help of a publication known as, A Nation at Risk: The Imperative for Educational Reform by the 1983 National Commission on Excellence in Educat ion (National Research Council, 1988). According to A Nation at Risk : The Imperative for Educational Reform United States educational achievements had been matched and were being surpassed by other countries (National Commission of Excellence in Educatio n, 1983). This claim was also supported by several other reports that declared that education in the United States was deteriorating (Vinovskis, 2009). As a result reform of core academic subjects, including mathematics, became a major priority in the 1 980s (Phipps, Osborne, Dyer, & Ball, 2008) Educational Reform in the 1980s T he year 1983 was a year of national concern that led to educational reform efforts by federal and state governments, schools, and colleges (U.S. Department of Education, 198 4). A Nation at Risk : The Imperative for Educational Reform called for increasing graduation rates, higher academic standards, more instructional time, improved teacher education programs, and greater accountability for elected officials (Vinovskis, 2009) The report also found that remedial mathematics courses at four year public colleges had increased by 72% from 1975 to 1980, which represented 25% of all mathematics courses offered at those four year public colleges (National Commission of Excellence i n Education, 1983). PAGE 16 16 The generally accepted theme of the 1980s educational reform movement was subjects and cognitive skills should be reemphasized (National Research Council 1988 p. 60 ). As a result, teacher education programs place d more emphasis on core academic subject s and field based experiences (U. S. Department of Education, 1984). According to Vinovskis (2009), the Southern Regional Education Board was a key leade r in advocating for data to compare the educational progress of the states. The report, The Need for Quality suggested the need for improving teaching and learning at all levels of education. In 1988 the South ern Region al Education Board released Goals for Education: Challenge 2000 which described the following 12 educational goals: 1. All children will be ready for the first grade (p. 10) 2. Student achievement for elementary and secondary students will be at national levels or higher (p. 11) 3. The school dropout rate will be reduced by one half (p. 13) 4. 90 percent of adults will have a high school diploma or equivalency (p. 14) 5. 4 of every 5 students entering college will be ready to begin college level work (p. 15) 6. Significant gains will be achieved in the mathematics, science, and communications competencies of vocational education students (p. 16) 7. The percent age of adults who have attended college or earned two year, four year, and graduate degrees will be at the national average s or higher (p. 18) 8. The quality and effectiveness of all college s and universities will be regularly assessed, with particular emphasis on the performance of undergraduate students (p. 19) 9. All institutions that prepare teachers will have effective teacher education programs that place primary emphasis on the knowledge and performance of graduates (p. 20) PAGE 17 17 10. All states and localities will have schools with improved performance and productivity demonstrated by results (p. 22) 11. Salari es for teachers and faculty will be competitive in the marketplace, will reach important benchmarks, and will be linked to performance measures and standards (p 23) 12. States will maintain or increase the proportion of state tax dollars for school s and colle ges while emphasizing funding aimed at raising quality and productivity (p. 25) In 1989, several g overnors led an initiative that developed national educational goals and predicted that by the year 2000 graduating high school students would be achieving high levels of academic success ( National Commission on Teaching and 1996). History has revealed their prediction did not come to fruition. Educational Reform in the 1990s In 1988, a campaigning future president, George H. W. Bush, declared he wanted to be the education president and lead a revitalization of quality in American schools (Walker, 1988). In 1990, President Bush unveiled the following six national goals : 1. By the year 2000, all children in America will start school ready to learn 2. By the year 2000, we will increase the percentage of students graduating from high school to at least 90 per cent 3. By the year 2000, American students will leave grades four, eight, and t welve having demonstrated competency over challenging subject matter, including English, mathematics, science, history, and geography 4. By the year 2000, U.S. students will be first in the world in science and mathematics achievement 5. By the year 2000, ever y adult American will be literate and possess the knowledge and skills necessary to compete in a global economy and exercise the rights and responsibility of citizenship 6. By the year 2000, every school in America will be free of drugs and violence and offe r a disciplined envi ronment conducive to learning ( Swanson 1991 pp. 2 4 ) PAGE 18 18 However reports in the early 199 0s indicated that the United State s was still losing ground to other countries and was ranked near the bottom on international test s in mathematics and science ( National Commission on Teaching and 1996) In 1990, 88% of fourth grade American students and 87% of eighth grade American students were not proficient in mathematics (National Center for Educational Statistics, 2009 a ) In 1991, U.S. 13 year olds ranked 13th out of 14 countries on the International Assessment of Educational Progress ( National Commission on Teaching and As a result of continued educational deficiencies among U.S. students, President Clinton signed Goal 2000: Educate America Act into law on March 31, 1994 The purpose of the act was to improve learning and teaching by providing a national framework for education reform; to promote the research, consensus building, and syste mic changes needed to ensure equitable educational opportunities and high levels of educational achievement for all students; to provide a framework for reauthorization of all Federal education programs; [and] to promote the development and adoption of a v oluntary national system of skill standards and certifications ( P. L. 103 227, 1994 para. 1 ) Goals 2000 : Educate America Act declared the following eight national goals: 1. By the year 2000, all children in America will start school ready to learn 2. By the year 2000, the high school graduation rate will increase to at least 90 percent 3. By the year 2000, all students will leave grades 4, 8, and 12 having demonstrated competency over challenging subject matter including English, mathemat ics, science, foreign languages, civics and government, economics, arts, history, and geography, and every school in America will ensure that all students learn to use their minds well, so they may be prepared for responsible citizenship, further learning, and productive employment in our Nation's modern economy PAGE 19 19 4. By the year 2000, the Nation's teaching force will have access to programs for the continued improvement of their professional skills and the opportunity to acquire the knowledge and skills needed to instruct and prepare all American students for the next century. 5. By the year 2000, United States students will be first in the world in mathematics and science achievement 6. By the year 2000, every adult American will be literate and will possess the kno wledge and skills necessary to compete in a global economy and exercise the rights and responsibilities of citizenship 7. By the year 2000, every school in the United States will be free of drugs, violence, and the unauthorized presence of firearms and alc ohol and will offer a disciplined environment conducive to learning 8. By the year 2000, every school will promote partnerships that will increase parental involvement and participation in promoting the social, emotional, and academic growth of children (P. L. 103 227 1994 section 102 ) Concerns over the education of American youth rose to the forefront of American politics in the mid 1990s A Gallup poll reported the American public believed educational quality of public schools was the most important issue of the 1996 presidential election (USA Today 1996 ). The Gallup poll also revealed the American public believed good teachers were vital to improving the academic success and 1996 ). The American public had valid reasons to be concerned. I n 1995, U.S. fourth graders were ranked 7 th among 16 countries and U.S. eighth graders were ranked 13th among 20 countries on international test s in mathematics ( National Center for Educational Statistics 2009 a ) Also in 1995, the Third International Mathematics and Science Study (TIMSS) indicated that a U.S. student in the final year of a secondary school scored below the average student in 14 other countries and above the average student in two other co untries 2000 a p. 28 ) Further more on the assessments in physics and advanced PAGE 20 20 mathematics, the United States was among the lowest scoring countries (National Center for Educational Statistics, 2000a, p. 18) T he National Center for Educational Statistics (2000b) reported that in 1996 only 7% of 17 year olds students in the United States could solve mathematics problems requiring several steps and 8 0 % of fourth grade American students and 77 % of eighth grade American students were not proficient in mathematics (National Center for Educational Statistics, 2009 a ). As a result of continued poor academic performance in the 1990s, t he National Commission on Teaching and (1996) proposed the follow ing three premises were needed for educational reform: 1. What teachers know and can do is the most important influence on what students learn. 2. Recruiting, preparing, and retaining good teachers is the central strategy for improving our schools. 3. School refor m cannot succeed unless it focuses on creating the conditions in which teachers can teach, and teach well (p. 11) The commission also reported a need for teacher preparation and professional development to be reinvented and o rganize d around standards fo r students and teachers National Commission on Teaching and 1996, p. 11) and for teacher education programs to defragment the practice of teaching subject matter in isolation of teaching methodology On March 26, 1996, President Clint the business leaders, and educators convened for the National Education Summit and committed to achieving students. The governors pledged to develop internationally competitive academic standards and assessments in each state within the next two years and to reallocate funds to provide the professional development, PAGE 21 21 infrastructure, and new technologies needed to meet these goals ( The National Commissio n on Teaching and 1996, p.3) Also in 1996 The National Commission on Teaching and (1996) posited that when students do not succeed in school, they are less likely to be employed and be contributing members of society as compared to students 20 years ago. The commission also posited that the failure of American education would have history the success of the nation depended on its abil ity to teach. Furthermore, the commission purported that e very teacher must know how to teach students in ways that help them reach high levels of intellectual and social competence ew courses, tests, and achers cannot use them productively ( National Commission on Teaching and 1996, p p. 3 5). As described above, c ompetencies of teachers were held in high regard by the participants of the commission and their report provided the following about the proficiency of teaching: E xpert teachers use knowledge about children and their learning to fashion a wide variety of learning o pportunities that make subject matter come alive for young people who learn in very different ways. They know how to support continuing development and motivation to achieve while creating incremental steps that help students progress toward more complicated ideas and performances. They know how to diagnose sources of problems and how to identify strengths on which to build. These skills make the difference between teaching that creates learning and teaching that just marks t ime Needless to say, this kind of teaching requires high levels of knowledge and skill. To be effective, teachers must know their subject matter so thoroughly that they can present it in a challenging, clear, and compelling way. They must also know how t heir students learn and how to make ideas accessible so that they can construct Research confirms that teacher knowledge of subject matter, student learning, and teaching methods are all important elements of teacher effect iveness. Furthermore, studies show PAGE 22 22 that teacher expertise is the most important factor in student achievement. ( 1996, p.6) T eaching is more than delivering information, testing, and grading ( National Com mission on Teaching and 1996). Q ualified teachers of mathematics need a deeper understanding of the ir subject matter, a better understanding of how students learn, the expertise to create learning experiences, and an understanding of how to motivate learners ( National Commission on Teaching and 1996) Thus, a national goal was proposed by the commission that in 2006 all American students would have qualified teaching National Commission on Teaching and Future 1996, p. 10 ) Reform in the 1990s established national goals called attention to the need for competent teachers, and spurred the creation of content an d performance standards. As a result, progress was made in establishing content and performance standards for K 12 education According to data released by the U.S. Department of Education b efore the Goals 2000: Educate America Act only 19 states had co ntent standards and none had performance standards (Vinovskis, 2009) In 1997, 42 states had content standards and 8 states had performance standards, but by the end of 2000, all states had content standards and 28 states had performance standards. Educational Reform in the 2000s to the Present As mentioned earlier an initiative by g overnors did not deliver on their prediction that graduating high school students would be achieving high levels of academic success by the year 2000 and the national goals of President Bush and President Clinton did not come to fruition PAGE 23 23 In 2000, 7 7 % of fourth and 75% eighth grade American students were not proficient in mathematics (National Center for Educational Statistics, 2009 a ). As a result, most postsecondary institutions offer ed at least one remedial mathematics course ( Parr, Edwards, & Leising 2006). In 2003, the National Center for Educational Statistics determined that 71% of all Title IV, degree granting, two and four year in stitutions that admit freshmen were offering at least one remedial mathematics course. Even though two year public schools were the most likely institutions to provide remedial courses (98% reported that they did so), public four year universities were clo se behind with 80% reporting that they offered at least one such course ( Parr, Edwards, & Leising, 2006 p. 81 ) I n 2007, the mathematics woes of American students continued to persist. On an international test in mathematics, U.S. fourth graders were r anked 11 th among 36 countries and U.S. eighth graders were ranked 9th among 40 countries ( National Center for Educational Statistics 2009 a ) The 2009 a published report by the National Center for Educational Statistics (2009b) reported that 6 1 % of fourth grade students and 6 6 % of eighth grade students were not proficient in the National Assessment of Educational Progress mathematics. a report by the National Commission on Mathematics and Scie nce Teaching for the 21 st Century (2000) emphasized the need for qualified mathematics and science teachers and called for an ongoing system to improve the quality of mathematics and science teaching in grades K Th is report was similar to oth er calls for reform issued in the 1980s and 1990s. The National Commission on Mathematics and Science Teaching for the 21 st Century also claimed that the nation and its people are depende nt on the American education system, its effectiveness, and more spe cifically the mathematics and science education of PAGE 24 24 American students. The following denotes the stance of the National Commission on Mathematics and Science Teaching for the 21 st century (2000) : M athematics and science will also supply the core forms of knowledge that the next generation of innovators, producers, and workers in every country will need if they are to solve the unforeseen problems and dream the dreams that will define ( p. 4) The report by the National Commission on Mat hematics and Science Teaching for the 21 st Century proposed four reasons signifying the need for competencies in mathematics and science among American students: 1. T he rapid pace of change in both the increasingly interdependent global economy and in the Ame rican workplace demands widespread mathematics and science related knowledge and abilities 2. O ur citizens need both mathematics and science for their everyday decision making 3. M athematics and science are intere sts 4. T he deeper, intrinsic value of mathematical and scientific knowledge shapes and defines our common life, history, and culture. (p. 7) also proposed two major messages: improve their performance in mathemat improving mathematics and science achievement is better mathematics and science National Commission on Mathematics and Science Teaching for the 21 st Century, 2000, p. 7). On January 8, 2002, President George W. Bush signed into law the Elementary and Secondary Education Act of 2001, known as the No Child Left Behind Act. Major initiatives of the legislation were to improve the academ ic success of American students prepare and recruit highly qualified teachers and establish national accountability for American schools (U. S. Department of Education, 2002). No Child PAGE 25 25 Left Behind established periodic assessments in mathematics and reading and demanded highly qualified teachers. More specifical ly, No Child Left Behind sought to U. S. Department of Education, 2002, p. 69) of mathematics teachers. Thus, t his legisla tion supported the calls for better teaching of the 1980s and 1990s (National Commission on Mathematics and Science Teaching for the 21 st Century, 2000 ; National Commission on Teaching and National Research Council, 1983 ) and the na tional goal providing all American students with qualified teachers. I n an effort to "turn our schools around" (para. 1), the National Governors Association Center for Best P ractices and the Council of Chief State School Officers (2010) released their Common Core State Standards for K 12 education (Association of Public and Land Grand Universities, 2010). According to the National Governors Association and the Council of Chie f State School Officers (2010) t he Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and r elevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the globa l economy. ( Mission statement, para 1 ) increasingly high level of demand that our teachers have a more sophisticated and deeper understanding of mathematics ( Michigan State University Center for Research in Mathematics and Science Education 2010 p. 19 ) PAGE 26 26 In 2007, the National Governors Association called for K 12 teachers that were qualified in the STEM (science, technology, engineering, and mathematics) disciplines rvices, and processes that can be sold in the Association (2007) also called for accountability among STEM teacher preparation programs and suggested the following accou ntability measures: 1. Greater impact of teacher preparation program graduates on public school student achievement 2. Higher teacher program graduate scores on exit and/or licensure exams 3. Higher teacher satisfaction with their preparation programs 4. Higher principal satisfaction with recent hires f rom preparation programs (p. 12) The National Governors Association (2007) also posited that systems often lack clear, well articulated expectations for individual institutions, including how they are to relate to one another and to industry, communities, and K 12 obligated to provide more remedial math and English courses, which signifies a lack of college read iness among high school graduates. A report by Michigan State University Center for Research in Mathematics and Science Education (2010) reported that preservice teachers in the United States receive weak preparation in mathematics and are ill prepa red to teach a demanding mathemat ics curriculum that is severely needed to compete internationally. The Michigan State University Center professed that teacher education programs must educate preservice teachers not only in formal mathematics but also in the practical teaching of mathematics. The C enter also described the mathematics deficiency PAGE 27 27 among teachers as moving from a g athering s torm to a p erfect s torm because of the adoption of more challenging and rigorous mathematics standards in which teachers do not possess the necessary competencies to teach. Michigan State University Center for Research in Mathematics and Science Education 2010, p. 15) that U. S. pr e performance performance. For that reason, a charge was given to break the vicious cycle in which we find ourselves where the weak K 12 mathematics curriculum taught by teachers with an inadequate mathematics background produces high school graduates who are similarly weak. Some of them then become future teachers who are not given a strong preparation in mathematics and then they teach and the cycle continues. ( Michigan State University Center f or Research in Mathematics and Science Education 2010 p. 3 ) According to National Research Council (2009), few academic institutions provide explicit training in critical thinking and analysis, and few classroom experiences challenge students in this regard. Moreover, mathematical analysis is often not incorporated into the classes beyond a very basic level, and students have few opportunities to engage in quantitative reasoning. For example, students are rarely presented with real data or asked to s uggest a strategy when the data do not point to a data and simplify scenarios. Even laboratory and field experiences may involve some means of data cleaning so that students will be ab le to draw activities more difficult, but it is vital that students have the opportunity to engage with real world systems and to be forced to evaluate disparate data; they should be a sked to make decisions on the basis of these data and to explain and defend their choices (p p 41 42) T oday the states have become partners with federal governments in developing and implementing NCLB [No Child Left Behind], and states are allowed to set their own student academic content and performance standards as well as define what p 1 2). According to Vinovskis PAGE 28 28 (2009), financial support for K 12 education has increased significantly due to various educational reform efforts for Educational Reform: Career and Technical Education In 1996 the National Association of Secondary School Principals called for an integrated curriculum and suggested that teaching content in isolation distorts knowledge. The National Association of Secondary School Principals also stated that curricul a should al low students to apply their knowledge to real life scenarios or authentic experiences, thus aiding students in linking their educational experiences to future use. Similarly, the National Research Council (1988) stated that for agricultural education to c ontinue to produce highly qualified graduates there must be an emphasis on traditional academic skills through an integrated curriculum. Mathematics educators have also seen the need for an integrated curriculum and have called for contextualized learning activities (Shinn et al., 2003). Swartz (2003) professed, t here is a great deal of qualitative and anecdotal evidence from school classrooms that infusion [ or contextualized] lessons both improve student thinking and e nhance content learning. Teachers report that student interest in their learning improves, their understanding of the content they are learning deepens, many students do better on content area tests, and many students begin using the thinking strategies i ntroduced in these lessons When using infusion [or contextualization] as an approach to teaching thinking and enhancing learning, the learning students engender will prepare them to enter an increasingly complex and technological world with skills that t hey will need to use information meaningfully, to make sound judgments, and to develop confidence in themselves as thoughtful people. (p p 247 249) PAGE 29 29 Bailey (1998) suggested that broad based occupational areas such as agriculture can provide a meaningful con text for mathematics. Taylor and Mulhall (1997) stated that agriculture could act as a unifying theme of curricula and provide real world meaning. Shinn et al. (2003) proclaimed that econdary agricultural education, through the use of relevant curriculu m delivered from a student centered perspective by skillful teachers, has high potential for engaging students in active, hands on/minds on learning p. 23 ). Shinn et al. also called for the ag ricultural education profession to embrace the role of improving mathematics achievement of secondary students. secondary agricultural education to become more than vocational agr iculture to prepare students for careers that require competencies in science and mathematics and to help students to effectively use new technologies The National Research Council also service education program s must be revised and expanded to develop more competent teachers p p. 6 7) of agriculture to make the fundamental shift described above. mathematics education researchers ( Parnell, 1995; Romberg & Kaput, 1999) the current direction of math education is toward a more practical or meaningful and connected form of teaching and learning al., 2003 p.14 ). In 2003, Shinn et al. purported that c ontextual relationships have the potential to strengthen lin kages among the learning environments of school, home, and community and add meaning to mathematics for students A report published by the National Council for Agricultural Education in 2003, outlined 12 promising practices PAGE 30 30 that teachers should i mplement in an attempt to increase student achievement in is dependent on the interaction of contextually rich curriculum and inquiry based instructional strategies suppo rted by effective teacher preparation and professional 2003, p. 29). According to Myers and Thompson (2009), p rofessional development is paramount to moving the profession forward in integrating academics into agric ultural education programs. Instruction in integrating math, science, and reading at the preservice and inservice levels are professional growth functions that should be embraced at the national, regional, state, university, and local levels. (p. 83) In 2006, Stone et al. posited that c areer and t echnical e ducation provides a context for using an integrated curriculum to teach mathematics and facilitates the transferability of skills. R esearch has shown that teaching mathematics concepts found within career and technical education coursework improv e d standardized measures of mathematics ( Stone et al 2006, p. 69 ) CTE [Career and Technical Educa tion] educators are not trained to teach math, however, explicit math content, such as algebraic formulas, rarely makes it onto the blackboard ( Stone et al 2006, p. 4) To that regard, Stone et al. (2006) emphasized the following five core principles t hat will be discussed further in Chapter 2 for enhancing mathematics in Career and Technical Education: 1. Develop and sustain a community of practice among the teachers. 2. Begin with the CTE curriculum and not the math curriculum. 3. Understand that math is an essential workplace skill. 4. Maximize the math in the CTE curriculum. PAGE 31 31 5. Recognize that CTE teachers are teachers of math in CTE, and not math teachers (p. 69) Stone et al. also called for the Math in CTE model which contributed to the increase in mathematics performance on standardized measures reported above to be utilized by teacher education programs as a means of teaching future educators how to teach contextualized mathematics T he federal Carl D. Perk ins Career and Technical Education Improvement Act of 2006 required career and technical courses to contain academic content provides states with unprecedented latitude and funding that may be used to align CT [career technical] studies with broader h igh school reform (Bottoms & Young 200 8 p. ii ). According to a report published in 2008 by the Southern Region al Education Board, education chiefs, CTE [Career and Technical Education] leaders and other decision makers from 12 states explore [d] more deeply the significant contributions career/technical education can make to high school reform. The conference marked a decisive first step in crafting a new vision for high school success one that calls on states and school systems to break free o f long held beliefs about the sharp division between academic and career/technical education and weld the strongest elements of both i nto a powerful engine of reform. (Bottoms & Young, 2008, p. ii) The Educational leaders mentioned above issued the followi ng challenges for state educators and policy makers: Challenge 1: Align new and existing career/technical curricula with essential college and career readiness standards. Challenge 2: Create a flexible system of optional career pathways in high schools to better prepare all students for college and careers. developing career/technical and academic programs that: (1) link high school to postsecondary studies and work, (2) ble nd academic and technical studies, and (3) connect students to a goal. Challenge 4: Assess the contributions career/technical education can make to improving academic and technical achievement. PAGE 32 32 Challenge 5: Prepare and enable career/technical teachers to t each essential academic skills through application in authentic activities, projects and problems. (Bottoms & Young, 2008, p. iii) For too long, states have overlooked the contributions that high quality CTE can make in solving the persistent problem of high school underachievement Young, 2008, p. iii) Research shows that good CTE programs can reduce high school dropout rates and increase the earning power of high school graduates. More students stay in school when they can concentrate on career and technical studies. Students who struggle to learn specific academic skills in a traditional classroom environment are often better served through the project based learning and problem solving strategies that are hallmarks of T courses. (Bottoms & Young, 2008 p. i ) In view of that Parnell (1996) stated, n o longer can the debate over the importance of vocational or academic programs be allowed to degenerate into an either/or argument. The basis for good teaching is combining an information rich subject matter content with an e xperience rich context of application. (p. 1) Statement of the Problem Mathematic deficiencies of elementary, secondary and postsecondary students continue to persist almost thirty years after the published report, A Nation at Risk : The Imperative for Educational Reform (National Commission of Excellence in Education, 1983) T h e lack of mathematic s proficiency among U. S. students is well document ed ( Michigan State University Center for Research in Mathematics and Science Education 2010; National Center for Educational Statistics, 2000 a, 2000b 2004, 2009 a, 2009b 2010 2011 ; National Commission of Excellence in Education 1983 ; U.S. Department of Education 2002 ) and large scale reform efforts have failed to significantly improve K 12 education (Vinovskis, 2009) Furthermore, many preservice teachers who will be charged with improving the mathematical ability of American students are not proficient PAGE 33 33 in mathematics; this has created a troubling cycle in which teachers that are not proficient in mathematics are producing students with mathematical defic iencies, who then become the next generation of mathematic s deficient teachers (Michigan State University Center for Research in Mathematics and Science Education, 2010). As a result there have been numerous calls for all subject areas to contribute to the learning of academic content, but preservice agricultural teachers are ill prepared to make a meaningful contribution (Stripling & Roberts, in press ) Therefore, t he fundamental problem this study addressed is the lack of m athematics proficiency among preservice agricultural education teachers. Purpose of the Study T he purpose of this study was to determine the effects of mathematics teaching and integration strategies (MTIS) on preservice agricultural ability, personal mathematics efficacy, mathematics teaching efficacy, and personal teaching efficacy in a teaching methods course Statement of Objectives The following objectives framed this study: 1. De termine the effect s of mat hematics teaching and integration strategies in the teaching methods course on mathematics ability 2. De termine the effect s of mathematics teaching and integration strategies in the teaching methods course on personal mathematics efficacy 3. De termine the effect s of mathematics teaching and integration strategies in the teaching methods course on mathematics teaching efficacy 4. De termine the effect s of mathematics teaching and integration strategies in the teaching methods course on personal teaching efficac y PAGE 34 34 Statement of Hypotheses The research questions were framed as null hypotheses for statistical analysis and the significance level of .05 was determined a priori. H 01 There is no significant difference in the mathematics ability of preservice agri cultural education teachers based upon the mathematics teaching and integration strategies treatment H 02 There is no significant difference in the personal mathematics efficacy of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment H 03 There is no significant difference in the mathematics teaching efficacy of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment. H 04 Th ere is no significant difference in the personal teaching efficacy of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment. Significance of the Study This study seeks to add to the limited know ledge of preservice agricultural personal mathematics efficacy, mathematics teaching efficacy, and personal teaching efficacy. In addition, t his study provides information on the effectiveness of math teaching and integration in preservice teacher education programs and this information will be significant to agricultural teacher educators. T he results of this study could provide valuable insight into improving the mathematics teaching of future secondary agricultural educators, thus improving the mathematics content knowledge of secondary students ( Hill, Rowan, & Ball, 2005; National Commission on Mathematics and Science Teaching for the 21 st Century, 2000; ure, 1996; Sikula Buttery & Guyton 1 996 ) This information will be significant to secondary students because PAGE 35 35 s tudents have a competitive advantage when they are able to draw upon meaningful ( Shi nn et al., 2003, p.6) Information on effective ways to improve mathematics content knowledge of secondary students will also be meaningful and significant for national, regional, state, university, and local educational leaders seeking to improve mathemat ics proficiency and prepare American students for careers in the STEM (science, technology, engineering, and mathematics) disciplines projections show a 22% increase in job opening by 2014 (Terrell, 2004). This information will also aid secondary school s in meeting Adequately Yearly Progress (AYP)/benchmarks established by the No Child Left Behind Act. Improved content knowledge of American students will assist the United States in maintain ing food safety and security, sustainable natural resources (Shi nn et al 2003) and avert major economic and national security disasters (PTC MIT Consortium, 2006 ). This research will answer the call of the National Research Agenda for Agricultural Education and Communication by adding literature to the following priority areas : Priority 3: Sufficient scientific and p rofessional w orkforce t hat a ddresses the c hallenges of the 21st c entury Priority 4: M eaningful, e ngaged l earning in a ll e nvironments Priority 5: Programs of d emonstratable e fficiency and e ffectiveness ( Doerfert 20 11 pp. 9 10 ) Based on the aforementioned research priority areas and the information presented above literature regarding improved mathematics proficiency among America n students would be significant to postsecondary agricultural educator s, preservice teachers, secondary students, industry leaders, national economic and security leaders and national, regional, state, university, and local educational leaders. PAGE 36 36 Definition of Terms The following terms have been operationally defined for the objectives of this study: 1. M ath enhanced lesson is an agricultural lesson that incorporates Stone, Alfeld, enhanced lesson. 2. Mathematics ability is defined by the students scores on the 26 items that are contained on the Mathematics Ability Test which is a researcher developed instrument 3. Mathematics teaching efficacy belief about their capabilities to teach mathematics. In this study, mathematics teaching effic acy was defined as the Mathematics Enhancement Teaching Efficacy Instrument by Jansen (2007). 4. Personal mathematics efficacy is self belief about their capabilities to solve mathematics problems. In t his study, personal mathematics efficacy was defined as the Mathematics Enhancement Teaching Efficacy Instrument by Jansen ( 2007) 5. Personal teaching efficacy is self belief about their capabilities to teach. In this study, personal teaching efficacy was defined as the score on 12 items contained in the Mathematics Enhancement Teaching Efficacy Instrument by Jansen ( 2007) 6. Preservice agricultural teachers are agricultural education majors in their final year of a teacher preparation program. 7. Teaching methods course on the selection and use of teaching strategies, methods/approaches, and techniques; eva luating learning; and managing learning environments for 1) 8. Mathematics teaching and integration strategies is the incorporation of the following three elements into a teach ing methods course: (a) a lecture on the seven components of a math enhanced lesson, (b) random assignment of the N ational C ouncil of T eachers of M athematics sub standards among the preservice teachers, and (c) requiring two of the micro teaching lessons t o be math enhanced PAGE 37 37 Limitations of the Study The results of this study are subject to the following limitations: A random sample of preservice teachers was not selected due to the fact that the preservice teachers self registered for a teaching methods lab section that best fit their schedule of classes, thus the preservice teachers were not randomly assigned to their teaching methods lab sections T herefore, the findings of this study should not be generalized beyond the sample unless data confirms the sample is representative of other p opulations of preservice agricultural education teachers Assumptions of the Study The following assumptions were made for the purposes of this study: 1. Participants involved in the study perfor m ed to the best of their ability. 2. Participants involved in the study responded truthfully. 3. Mathematics ability, personal mathematics efficacy, mathematics teaching efficacy, and personal teaching efficacy were measured accurately. Chapter 1 Summary Chapter 1 provided a historical context to the continuing national quest to solve educational deficiencies among American students and focused on the educational initiatives to date designed to correct persistent student deficiency in mathematics. More pu rposely, C hapter 1 described the role of c areer and t echnical e ducation in improving the mathematics content knowledge of secondary students and outline d a research response. The reform efforts of the 1980s focused on demanding more from teacher s, students and administrators and called for a reemphasis on basic subjects and cognitive skills (National Research Council, 1988). This was a result of long standing PAGE 38 38 academic underachievem e nt by American students (National Research Council, 1988) and a loss of ed ucational standing in the world (National Commission of Excellence in Education, 1983). The 1990s were a time of public concern over education and a Gallup poll reported that education was the most important issue in the 1996 Presidential election (USA Today 1996 ). Teachers were also believed to be one of the most vital aspects of National Commission on Mathematics and Science Teaching for the 21st Century, 2000; National Commission on Teaching and 1996; USA Today, 1996). The 1990s were also a time when the United States was still losing ground to other countries educationally (The National Commission on Teaching and Reform in the 1990s established nation al goals, called attention to the need for competent teachers, and spurred the creation of content and performance standards. Educational f indings similar to the 1980s and 19 90s have been reported in the 21st century Reports from the National Center fo r E ducation S tatistics (2000 a, 2000b 2004, 2009 a, 2009b 2010 ) still reveal ed that deficiencies in mathematics continue to persist among American students. In 2002, the No Child Left Behind Act was signed into law and called for highly qualified teachers and the establishment of national accountability for American schools (U. S. Department of Education, 2002). The National Governors Association (2007) called for K 12 teachers that were qualified in the STEM (science, technology, engineering, and mathema tics) disciplines and the National Commission on Mathematics and Science Teaching for the 21st Century (2000) purported the need for qualified mathematics and science teachers. The PAGE 39 39 National Commission on Mathematics and Science Teaching for the 21st Cen tury (2000) also purported that the nation and its people have been dependent on the American education system, its effectiveness, and more specifically the mathematics and science education of American students. Chapter 1 reported that c areer and technical education was found to possess great potential for improving the mathematics proficiency among American students though the use of an integrated curriculum (Bailey, 1998; Bottoms & Young, 2008; Shinn et al., 2003; Stone et al., 2006) p.14). In 2003, Shinn et al. professed ontextual relationships have the potential to strengthen linkages among the learning environments of school, home, and community and add meaning to mathematics for students In 2006, Stone et al. emphasiz ed that career and technical education provides a context for teaching mathematics, and found that teaching mathematics concepts occurring naturally within career and technical education coursework improv ed f mathematics p. 69) As a result, Stone et al. also called for the Math in CTE model which contributed to the increase in mathematics performance on standardized measures reported above to be utilized by teacher education programs. Shinn et al. (2003 ) proclaimed that econdary agricultural education, through the use of relevant curriculum delivered from a student centered perspective by skillful PAGE 40 40 teachers, has high potential for engaging students in active, hands on/minds on learning environments rich al. also called for the agricultural education profession to embrace the role of improving mathematics achievement of secondary students. The objectives of this study were framed b ased on t he af orementioned information. T he purpose of this study was to determine the effects of MTIS on preservice agricultural mathematics teaching efficacy, and personal teaching efficacy in a teachi ng methods course The results of this study could provide valuable insight into improving the mathematics teaching of future secondary agricultural educators, thus improving mathematics content knowledge of secondary students ( Hill, Rowan, & Ball, 2005; National Commission on Mathematics and Science Teaching for the 21 st Century, Sikula Buttery & Guyton 1 996 ). Based on the above mentioned statement, this information would be significant to post secondary agricultural educators, preservice teachers, secondary students, industry leaders, national economic and security leaders, and national, regional, state, university, and local educational l eaders. Chapter 1 also operationalized terms important to this study and recognized the limitations and assumptions of the study Chapter 2 theoretical framework and reviews literature pertinent to the study. PAGE 41 41 CHA PTER 2 REVIEW OF LITERATURE Chapter 1 provided a historical context to the mathematics deficiency among American students that has continually persisted for over 30 years and that mathematics deficiency provided the basis for this study. T he purpose of th is study was outlined, which was to describe the effect of a mathematics integration treatment in a personal mathematics efficacy, mathematics teaching efficacy, and personal teaching efficacy. Chapter 1 also provided the objectives that framed this study, along with the hypotheses. Key terms were defined and assumptions and limitations were stated. Chapter 2 introduces constructivism and describes the theoretical f ramework and the conceptual model utilized to guide this study. Additionally, Chapter 2 will present prominent literature related to the various co mponents of the conceptual model utilized in this study. Constructivism Constructivism is the grand theo ry encompassing this study. According to Doolittle and Camp (1999) constructivism is the construction of meaning from a theoretical position but as a continuum that is usually divided into three categories: cognitive constructivism, social constructivism, and radical constructivism. Cognitive Doolittle & C amp, 1999 p. 7). Social constructivism Doolittle & PAGE 42 42 Camp, 1999 p. 9). Radical constructivism suggests that knowledge is subjective and is constructed internally by the learner (Doo little & Camp, 1999) The primary focus of constructivism is cognitive development and deep understanding that process by active learners interacting with their surround physical and soc (Fosnot, 2005, p. 34). Constructivists believe learning is development ; a state of imbalance facilitates learning, reflection drives learning, and social interactions provoke further thinking (Fosnot, 2005). The following are essential factors of constructivist pedagogy: Learning should take place in authentic and real understoo Students should be assessed formatively, serving to inform future learning r and encourage multiple perspectives and representations of content. (Doolittle & Camp, 1999, p p .9 13) Fosnot (1996) and Schunk (2004) concurred that constructivism has a theoretical foundation entrenched in Sociocultural Theory (Vygotsky, 1978) and th e Theory of Cognitive Development (Piaget, 1972). According to Brooks and Brooks ( 1993 ) and Fosnot c onstructivism is a theory about knowledge, thinking, and learning not a theory about teaching Constructivism in the context of teaching promotes students to think, create, and be engaged in the learning process p.45 ) More specific to mathematics, many contemporary theorists contend that constructivism represents a viable model for explaining how mathematics is learned (Cobb, 1994; Lampert, 1990; Resnick, 1989). Like many other forms of knowledge, mathematical knowledge is not passively absorbed from the environment PAGE 43 43 but rather is constructed by individuals as a consequence of their interactions. (Schunk, 2000, p. 284) Theoretica l Framework s ocial c ognitive t heory served as the theoretical framework for this study. Social c ognitive theory seeks to explain the cognitive development al changes experienced by people during a lifetime and provides a foundation for social learning (Bandura, 1989). Theory asserts that c ognitive development includes multifaceted sequences over time and that most cognitive skills are socially cultivated (Bandura, 198 6 ) The theory also asserts that c ognitive change or learning requires certain prior capabilities (Bandura, 1986, p. 487). The symbolizing capability allows people to adapt and change their environment; the forethought capability allows people to anticipate behavioral consequences and m otivate themselves based on expected results ; the vicarious capability allows for observational learning; the self regulatory capability allows people to regulate their behavior by examining internal standards and their responses to their prior actions ; th e self reflective capability allows people to examine their thought processes and to analyze their personal experiences ( Bandura, 1986 ) Thus, people have the ability to shape direct and vicarious experiences into many forms within biological limits ( Band ura, 1986 retained in neural codes, rather than being provided ready made by inborn Bandura, 1986, p. 22). Furthermore, human thought and conduct are influenced by th e interaction of experiential and physiological factors (Bandura, 1986). PAGE 44 44 35). Triadic Reciprocality Bandura ( 1977, 1978, 1982 1986 1989, 1997 ) describe d behavior using the framework of triadic reciprocality or reciprocal interactions among behavior, environmental influences and personal factors. In the social cognitive view people are neither driven by inner forces nor automatically shaped and controlled by external stimuli. Rather, human functioning is explained in terms of a model of triadic reciprocality [see F igure 2 1 on page 88 ] in which behavior, cognit ive and other personal factors, and environmental events all operate as interacting determinants of each other. ( Bandura, 1986, p. 18) The interacting determinants of the triadic reciprocality model influence each other bidirectionally (Bandura, 1986). H owever, according to Bandura (1997), the reciprocal interactions are not of equal strength and o ne determinant may demonstrate dominance o ver the others; although, in most situations, the determinants are vastly interdependent. Furthermore time is neede d for casual factors to exercise their influence, and that time makes it possible for one to study or understand the reciprocal causations (Bandura, 1997). The reciprocal causation of personal factors and behavior can be characterized as the interaction (Bandura, 1986, p. 25) and i s and emotions (Bandura, 1989). Additi onally, p ersonal factors include the biological properties of a person (Bandura, 1989). For instance, t he physical structure of the brain affects PAGE 45 45 behavior and the reciprocal interaction is the effect of behavioral experiences on the structure of the brain (Bandura, 1989). The reciprocal causation of environment al influences and personal factors can be described as the interaction between the environment a and emotions (Bandura, 1989). houghts, beliefs, and emotions are shaped social status and physical characteristics (e.g., age, size, race, and gend er) alters their social environment (Bandura, 1989). The reciprocal causation of behavior and environmental influences can be characterized as behavior modifying environmental conditions and those conditions affecting behavior (Bandura, 1989). The envir onment is not conceptualized as a fixed entity but is shaped by personal and behavioral influences (Bandura, 1989). According to Bandura (1989) most facets of the environment do not exert influence unless the environment is activated by a n appropriate beh avior environmental causation For this study the behavior or teaching contextualized mathematics the environment or the teacher education program and the teaching methods course and personal factors or demographic varia bles mathematics teaching efficacy, personal teaching efficacy, personal mathematics efficacy, and mathematics ability influence each other biodirectionally ( F igure 2 2 p. 88 ). Behavior : Teaching Contextualized M athematics The variable that will be discussed in this section is the act of teaching contextualized mathematics In the aforementioned theoretical and conceptual frameworks, teaching contextualized mathematics is a behavior. When examined PAGE 46 46 through the theoretical l ens of social cognitive theory (Bandura, 1986) teaching mathematics found naturally in agriculture or contextualized mathematics is influenced bidirectionally by environmental and personal determinants within triadic reciprocal causation (Bandura, 1977, 19 78, 1982 1986 1997). The behavior of teaching agriculture has also been influenced by the call to integrate academic subjects with in career and technical education As stated previously combining an information rich sub ject matter content with an experience rich context of Expectations and ideals endorsed by current reform efforts in mathematics education (e.g., NCTM, 2000) challenge prospective teachers in their thinking about mathem atics teaching and learning. Teachers are asked to teach in ways that promote an integrated, connected view of mathematics, rather than a procedural, rule based view. (Benken & Brown, 2008 p. 1 ) As a result, emphasis has been placed on teaching academi c subjects in context. Contextualized learning advocates that neither general education nor vocational education can be taught in isolation but must be integrated to maximize the benefit for the learner (Prescott, Rinard, Cockerill, & Baker, 1996). A gric ultural education is a ripe academic area with numerous opportunities for contextualization (Stripling, Ricketts, Roberts, & Harlin, 2008) The mathematics integration literature specific to agricultural education is limited. However, several studies have been conducted to test the effectiveness of the Math in CTE model (Stone et al. 2006) which is discussed in greater detail later in Chapter 2 on various product variables (Dunkin & Biddle, 1974). In a study of 38 secondary agricultural classes, Pa rr, Edwards, and Leising (2006) sought to determine if students that participated PAGE 47 47 in a contextualized, mathematics enhanced high school agricultural power and technology curriculum and a ligned instructional approach would develop a deeper and more sustain ed u nderstanding of selected mathematical concepts than students who participated in the traditional curriculum, thus resulting in less need for postsecondary mathematics remediation (p. 84) Results indicated that the math enhanced agricultural power and technology remediation on the postsecondary mathematics placement test. Students who took part in the math enh anced curriculum were less likely to need postsecondary remediation. The practical significance of the finding was reported to be a large effect d of .83. In a similar study published in 2008, Parr, Edwards, and Leising investigated if students in a math enhanced agricultural power and technology course would differ significantly from students in a traditional agricultural power and technology course in their technical skill acquisition. The findings revealed no significant difference, thus the math enhanced agriculture power and technology curriculum did not lessen technical skills. In a third study investigating the effects of a math enhanced agricultural power and technology curriculum Parr, Edwards, and Leising (2009) did not find a signif icant difference in the mathematics ability of the secondary students. Parr et al. (2009) hypothesized that this of incomplete implementation of the treatment as reported by some experimental teachers coupled with an interve ntion time frame of only one semester (p. 1). The Young, Edwards, and Leising (2008, 2009) inquiries were very similar to the studies of Parr, Edwards, and Leising (2006, 2008, 2009). Young et al. (2008) sought to determine if mathematics enhanced agri cultural power and technology curriculum PAGE 48 48 would significantly increase the mathematical ability of the participants compared to a traditional mathematics agricultural power and technology curriculum. The study consisted of 32 Oklahoma high school classes, but the results did not show a significant statistical difference in mathematics ability between the experimental and control groups. However, the authors reported that the results revealed practical significance and that the effect size was small (Young et al., 2008). In 2009, Young et al. published a second study that mirrored Parr et al. (2008). However, this investigation was a one year analysis verses a semester long analysis. The results also mirrored the results of Parr et al. (2008) in which tec hnical competence was not diminished by the mathematics enhanced curriculum. Furthermore, r elated to the behavior of teaching contextualized mathematics is science integration ( Phipps, Osborne, Dyer, & Ball, 2008 ). According to Phipps Osborne, Dyer, and Ball (2008), the call for science to be integrated into secondary agricultural education has contributed to the development of agriscience programs and coursework Research on effective agriscience teaching includes strategies for teaching mathematica l competencies (Phipps et al., 2008). Moreover research has shown that mathematics teaching is associated with increases in science achievement (Phipps et al., 2008). However, in a synthesis of agricultural teacher education programs, Myers and Dyer (20 04) discovered a gap in the literature on how agricultural teacher education programs should prepare preservice teachers to meet the academic demands of agriscience teaching The integration of mathematics c ontent has also been extended to other career and technical education programs ( Stone et al., 2006) To that end, Stone et al. (2006) PAGE 49 49 enhancing mathematics instruction in five high school career and technical education ( CTE) p rograms (agriculture, auto technology, business/marketing, health, and information technology) Each program area was considered a replication of the experimental study. The study was conducted for one academic school year and the combine d number of participants from each program area/sample consisted of 236 career and technical teachers, 104 math teachers, and 3,950 students from 12 states. The career and technical educators had a mathematics teacher partner that provided support in d eve loping math enhanced lessons and suggested instructional methodologies. Survey data collected from the participants of the study indicated that the pedagogic framework ( Stone et al., 2006, p. 40). Stone et al. found that the math enhanced curriculum did not reduce the technical skill or occupational content knowledge. Three mathematics assessments (TerraNova, ACCPULACER, and WorkKeys) were given to determine if the Math in CTE model improved the mathematics ability of the secondary students. The TerraNova scores of the experimental group showed a positive increase in scores by slightly more than 4% and the experimental effect was report ed to be a moderate or medium effect according to Cohen. The experiment al condition accounted for 13% of the variance in the classes. The ACCPULACER scores for the experimental group were also found to be higher than the control by almost 3% and the experimental condition accounted for 10% of the variance in the classes. T he effect size was determined to also be a moderate or medium effect. The third test, WorkKeys, did not reveal a significant difference in the experimental and control group scores. The researchers stated that the pretest scores were higher on the WorkKe ys PAGE 50 50 test than the TerraNova and ACCPULA CER. The researchers hypothesized that an effect may not have been detected because the WorkKeys test contained lower level math questions. Qualitative data indicated that the Math in CTE model was a positive experi ence for the teachers and students. The teachers considered the model to be effective and perceived it as a true model of integration. Many teachers felt that the Math in CTE model improved their overall teaching competencies. Interestingly, many of t he [CTE and math] teacher teams reported passing through a period in which they had to overcome tensions and anxiety in working together, especially on the part of the CTE teachers who often expressed a lack of confidence in mathematics. One math teacher d escribed his CTE absolute fear as he stepped into that realm he was not familiar with. However, these fears emerged, as he further explained, We have three math teachers on the staff, and he (the CTE teacher) has now become a sort of d ( Stone et al., 2006, p. 56) The math teachers expressed that the partnerships had a reciprocal effect and increased their teaching repertoire and t h e CTE teachers became more confident in their ability to teach the math found within their program area. The teachers noted that developing the math enhanced lessons and the concept maps were vital parts of the Math in CTE model. The te achers also noted that the students were getting it ( Stone et al., 2006, p. 74) and were seeing the connections between the ir CTE class and their math class T able 2 1 (p p 86 87) and F igures 2 3 and 2 4 (p. 89) illustrate and explain the seven elements of a math enhanced lesson that w ere developed, utilized, and were found to be effective at increasing the mathematical ability of the secondary students in the Stone et al. (2006) study. PAGE 51 51 Personal Factors This se ction will discuss demographic variables, self efficacy/teaching efficacy and mathematics ability, which are considered personal factors. Each personal factor has a reciprocal causative relationship with the behavior of teaching contextualized mathematics and the physical and social environment s of the teacher education program and the teaching methods course. agency operates within Demographic variables Few studies report the effects of demographic variables such as gender and age on the behavior of teaching. Most studies only describe the sample in terms of demographic vari ables. I n a study by Miller and Gliem (1996), the mathematical problem solving ability of preservice agricultural teachers was found to have a negligible relationship with gender. Halat (2008) found a statistically significant difference in gender of pr eservice secondary The van Hieles described five levels of reasoning in geometry. These levels, hierarchical and continuous, are level I (Visualization), level II (Analysis), level III (Order ing), level IV (Deduction), and level V (Rigor) which indicated intermediate acquisition of van Hiele level III, and females had a mean score of 2.07 which indicated no acquisition of the van Hiele level III. However, Halat in thinking levels the difference was not statistically significant. Thus, significance was fo und related to gender in secondary preservice teachers but not elementary preservice PAGE 52 52 teachers. On the other hand, Edgar, Roberts, and Murphy (2009) determined in a study consisting of 82 preservice agricultural education teachers that gender did not have a significant effect on the teaching efficacy of preservice teachers. In addition, Edgar et al., found that age and academic standing did not have a significant effect on the teaching efficacy of preservice agricultural teachers. In a study with secondar y agricultural teachers, Miller and Gliem (1994) reported that age did significantly affect mathematical problem solving ability. Roberts, Mowen, Edgar, Harlin, and Briers (2007) collected data from 68 preservice agricultural teachers and reported tha t personality type s of preservice agricultural teachers were negligibly related to teaching efficacy. Contradicting those results, Roberts, Harlin, and Briers (2007) found that the personality type extroversion was substantially related to overall teach ing efficacy preservice agricultural teachers. In respect to research on ethnicity Edgar et al. (2009) found that ethnicity did not have a significant effect on the teaching efficacy of preservice agricultural teachers. Fu rthermore, Gordon (2002) interviewed over 200 teachers of color and stated that a color tend not to be encouraged to enter the teaching force by their own families and co suggested that teacher education programs should provide realistic experience with teachi city PAGE 53 53 Self efficacy exists between personal facto rs, environmental factors, and behavior. According to Bandura (1997), s elf efficacy is a personal factor that determinants. By influencing the choice of activities and the motivational le vel, beliefs of personal efficacy make an important contribution to the acquisition of knowledge structures on which skills are founded. An assured sense of efficacy supports the type of efficient analytic thinking needed to ferret out predictive knowledg e form causally ambiguous environments in which many factors combine to produce efforts. Belief s of personal efficacy also regulate motivation by shaping aspirations and execution. The self assurance with which people approach and manage difficult tasks determines whether they make good or poor use of their capabilities. Insidious self doubts can easily overrule the best of skills. ( p.35) Pajares (2002) declared that many thoughts affect human behavior, and self efficacy is a central component of social cognitive theory Perceived self efficacy is one s personal judgment of his/her capability to perform a task or behavior (Bandura, 1997). Self efficacy is influenced by m astery experiences, vicarious experiences, social influences, and physiological or emotional states (Bandura, 1997). Thus, previous personal successes, watching others succeed, being told that he/she can succeed, and positive biological feedback can all in crease a efficacy. (Roberts, 2003, p. 30) A s belief in their ability to manage learning and their proficiency of academic related tasks governs their ambitions, motivation for learning, and academic achievements (Bandura, 1993). A more specific type of self efficacy is known as teacher or teaching efficacy (Stripling et al., 2008) Teacher efficacy is the self belief generate preferred outcomes in student s (Soodak & Podell, 1996 ). According to PAGE 54 54 Tschannen Mora n, Woolfolk Hoy, and Hoy (1998), t eacher efficacy is a self belief in his or her a bility to plan, develop, and perform learning related task in a particular context Guskey and Passaro (1994) defined teacher efficacy as a teacher belief in his or her ability to have an effect on student learning for all types of student Teachers with high teaching efficacy exert more effort in planning and organization (Allinder, 1994) and persevere th r ough challenges and undesired results (Godd ard, Hoy, & Woolfolk Hoy, 2004). According to Tschannen Moran et al. (1998), teacher efficacy is cyclical in nature with either a positive or negative effect. Greater efficacy leads to greater effort and persistence, which leads to better performance, which in turn leads to greater efficacy. The reverse is also true. Lower efficacy leads to less effort and giving up easily, which leads to poor teaching outcomes, which then produce decreased efficacy. Thus, a teaching performance that was accomplished w ith a level of effort completed, becomes the past and a source of future efficacy beliefs. ( Tschannen Moran et al., 1998 p. 2 34 ) Once teaching efficacy beliefs stabilize they are diffi cult to change (Bandura, 1997; Tschannen Moran et al. 1998) Bandura (1993 promote learning affect the types of learning environments they create and the level of academic progress thei Goddard, Hoy, and Woolfolk Hoy (2000) found that collective efficacy was positively related to differences between schools in student mathematics and reading achievement Similar to teacher efficacy, c ollective efficacy is a social systems belief in its ability to socially execute a task or perform a behavior ( Bandura 1997 ) In the context of a school, collective efficacy is the summative belief of the faculty and staff to organize and implement necessary action s to positi vely affect student s (Goddard, 2001) According to Bandura (1997), if faculty of PAGE 55 55 a school have a strong sense of collective efficacy the school will succeed academically, and when the faculty have a weak sense of collective efficacy the school will not ma ke progress academically The study of teacher or teaching efficacy has also been extended to preservice teachers. Several studies have been conducted recently investigating the teaching efficacy of preservice agricultural education teachers. Knobloch (2001) investigated the personal and general teaching efficacy of prospective agricultural, extension, and agribusiness educators enrolled in an agricultural education foundations course. The spring quarter group consisted of 43 preservice teache rs. Knobloch found that the personal and general teaching efficacy of the 43 preservice teachers increased but not significantly after peer teaching. The autumn quarter group consisted of 44 preservice teachers. The personal and general teaching efficac y of the 44 participants did increase, but not significantly after an early field experience of 10 days or 80 hours. Knobloch also reported that after a peer teaching the autumn group once again increased in personal and general teaching efficacy, and gen eral teaching efficacy was not significantly different after the peer teaching. However, Knobloch did report a significant increase in personal teaching efficacy after peer teaching. Knobloch (2001) significantly increased perso nal teaching efficacy after students had completed the early field experience Thus, observing teaching in a natural setting may aid future educators in becoming more efficacious (Knobloch, 2001). Knobloch (2006) compared students from two agr icultural education programs: t the end of the PAGE 56 56 student teaching internship, student teachers at both universities who perceived their teacher education program positively were more effica cious at the end of their student teaching internship ( r 2 = .17 & .50, large effect sizes) Student teachers at the UI had five important relationships with teaching self efficacy at the end of student teaching: trust in clients ( r 2 = .26); collective efficacy ( r 2 = .44); academic emphasis ( r 2 = .56); cooperating teacher competence ( r 2 = .19); and perception of student teaching experience ( r 2 = .72) (Knobloch, 2006, p.42) w ith a medium effect size ( r 2 = .20) experience. Knobloch also reported that students at each institution were similarly efficacious, and their teacher efficacy did not change fro m the beginning to the end of the student teaching experience. Furthering the research of Knobloch (2001, 2006), Roberts, Harlin, and Ricketts (2006) examined the teaching efficacy of 33 preservice agricultural education teachers from Texas A&M Universit y at different points during the student teaching experience. Data were collected on the first day of the four week student teaching block, the last day of the four week student teaching block, middle of the 11 week student teaching experience, and after the 11 week student teaching experience. The instrument utilized during the study was the of Efficacy Scale ( Tschannen Moran & Woolfolk Hoy, 2001) 9 point rating scale, framed around the question, How Much Can You Do? (1 = Nothing, 3 = Very Little, 5 = Some Influence, 7 = Quite a Bit, and 9 = A Great Deal) Roberts et al. (2006) found that the teaching efficacy student engagement scores increased overall from the first day o f the four week student teaching block ( M = 7.06, SD = .98) to the end of the student teaching experience ( M = 7.24, SD = 1.05). PAGE 57 57 However, Roberts et al. found that teaching efficacy student engagement scores were the highest after the student teaching blo ck ( M = 7.31, SD = .96) and the lowest during the middle of the 11 week student teaching experience ( M = 6.67, SD = 1.06). The mean student engagement scores were statistically different ( F (3, 90) = 9.08, p = .00) [,and] t he effect size for the observed p 2 = .23) (Cohen, 1988) (Roberts et al., 2006, p. 88) Similar results were reported for the teaching efficacy instructional strategies scores. Teaching efficacy in instructional strategies increased overall from the first day of the four week student teaching block ( M = 7.21, SD = .91) to the end of the stu dent teaching experience ( M = 7.52, SD = 1.06). Teaching efficacy instructional strategies scores were near their highest point after the student teaching block ( M = 7.46, SD = .98) and the lowest during the middle of the 11 week student teaching experien ce ( M = 7.01, SD instructional strategies scores also differed statistically ( F (3, 90) = 4.56, p = .01) observed effect size was small p 2 = .13). The teaching efficacy classroom management scores we re also similar to the instructional strategies and the student engagement scores. However, the overall increase was not as great compared to the two previous constructs: the first day of the four week student teaching block ( M = 7.37, SD = .88) to the e nd of the student teaching experience ( M = 7.40, SD = 1.09). Once again however, the highest scores were reported after the four week student teaching block ( M = 7.46, SD = .96) and the lowest scores were reported during the middle of the 11 week student teaching experience ( M = 7.05, SD = 1.13). In contrast to the student engagement and instructional strategies scores results indicated that classroom PAGE 58 58 management scores did not differ significantly ( F (3, 90) = 2.53, p = .06) 2006, p. 88) Robert s teaching efficacy scores were statistically lower during the middle of the eleven week experience for student engagement, instructional strategies, and overall teachin g efficacy Classroom management scores were lower during the middle of the 11 week experience but were not statistically significant. Roberts et al. also reported the overall teaching efficacy scores: first day of the four week block ( M = 7.21 SD = .85), last day of the four week block ( M = 7.41, SD = .94), middle of the 11 week student teaching experience ( M = 6.91, SD = 1.04), and end of the 11 week student teaching experience ( M = 7.39, SD = 1.03). The overall teaching efficacy scores incr eased overall from the initial data collection point to the last data collection point. The highest scores were reported after the four week block and the lowest scores at the middle of the 11 he overall teaching effic acy scores revealed a statistical difference ( F (3, 90) = 5.78, p = .00), which represented a small p 2 = .16) As described above, a general trend emerged from the data for all three constructs and overall teaching efficacy. The scores during the four week block, then decreased by the mid point of the student teaching experience, and finally increase again by the conclusion of the experience (Roberts et al., 2006, p 89). Harlin, Roberts, Briers, Mowen, and Edgar (2007) replicated the study conducted by Roberts et al (2006) with a sample consisting of 99 preservice agricultural education teachers from the following four institutions: Tarleton State University, Texas A&M PAGE 59 59 University, Texas Tech University, and Oklahoma State University. The following scores were reported: student engagement first day of the four week block ( M = 6.91, SD = .80), l ast day of the four week block ( M = 7.09, SD = .81), middle of the 11 week student teaching experience ( M = 6.74, SD = .94), and end of the 11 week student teaching experience ( M = 7.42, SD = .79); instructional strategies first day of the four week block ( M = 6.95, SD = .91), last day of the four week block ( M = 7.31, SD = .82), middle of the 11 week student teaching experience ( M = 7.17, SD = .88), and end of the 11 week student teaching experience ( M = 7.64, SD = .81); classroom management first day of the four week block ( M = 7.23, SD = .98), last day of the four week block ( M = 7.35, SD = .81), middle of the 11 week student teaching experience ( M =7.07, SD = 1.01), and end of the 11 week student teaching experience ( M = 7.59, SD = .82); overall teac hing efficacy first day of the four week block ( M = 7.03, SD = .80), last day of the four week block ( M = 7.25, SD = .76), middle of the 11 week student teaching experience ( M = 6.99, SD = .84), and end of the 11 week student teaching experience ( M = 7.55 SD = .74). Results indicated statistical significance was found over time for all teaching efficacy scores, but the effect sizes were negligible. Pairwise comparison confirmed that efficacy scores were significantly lower for student engagement, instru ctional strategies, and overall teaching efficacy during the middle of the 11 week student teaching experience. Classroom management efficacy scores were lower but not significantly different. Consistent with Roberts et al (2006), the data of Harlin et al. Scores in all three constructs and overall teaching efficacy increased during the four week block, then decreased by the mid point PAGE 60 60 of the student teaching experience, and finally increased again at the c onclusion of the student teaching experience Roberts, Mowen, Edgar, Harlin, and Briers (2007) sought to determine if a relationship existed between teaching efficacy and personality type of 68 student teachers or preservice teachers at Texas A& M University. Consistent with Roberts et al. (2006) and Harlin et al. (2007), teaching efficacy scores in student engagement and classroom management were found to be the lowest during the middle of the 11 week student teaching experience, and the scores in all three constructs and the overall teaching efficacy of the student teachers increased overall from the first data collection point at the beginning of the four week student teaching block to the final data collection point after the 11 week student t eaching experience. The same theme general theme teaching efficacy levels increased during the four week block decreased to their lowest levels in the middle of the 11 week field exp erience, and then increased to their highest levels at the end of the 11 week field experience On the personality type assessment ( Myers Briggs Type Indicator ), Roberts et al. (2007) reported 67.6% of the student teachers were extroversion versus 32.4% introversion, 66.2% sensing versus 33.8% intuition, 64.7% feeling versus 35.3% thinking, and 45.6% perceiving versus 54.4% judging. Only two correlations between personality type scores and teaching efficacy scores were fou nd to be statistically significant. Sensing (S) had a negligible negative relationship with efficacy in instructional strategies at the end of the 11 week field experience (r = PAGE 61 61 c lassroom management in the middle of the 11 week field experience (r = .26). (Roberts, 2007, p. 98) (Roberts et al., 2007). Stripling, Ricke tts, Roberts, and Harlin (2008) extended the research of Roberts et al. (2006), Harlin et al. (2007) and Roberts et al. (2007) to include examining the impact of the teaching methods course on teaching efficacy. Data were collected for two years at the Un iversity of Georgia and Texas A&M University, and the sample consisted of 102 preservice agricultural education teachers. The overall teaching efficacy mean before the teaching methods course was 6.65 ( SD = .11), after the methods course/before student te aching mean was 7.15 ( SD = .11), and the after student teaching mean was 7.29 ( SD = .16). Likewise, the instructional strategies, student engagement, and classroom management scores increased at each data collection point. The following scores were repor ted: student engagement prior to the methods course ( M = 6.56, SD = 1.03), after the methods course/before student teaching ( M = 7.02, SD = .94), and after student teaching ( M = 7.11, SD = 1.03); instructional strategies prior to the methods course ( M = 6.61, SD = 1.11), after the methods course/before student teaching ( M = 7.25, SD = .94), and after student teaching ( M = 7.43, SD = .96); after student teaching prior to the methods course ( M = 6.76, SD = 1.18), after the methods course/before student teaching ( M = 7.17, SD = 1.05), and after student teaching ( M = 7.34, SD = 1.04). Significant difference existed for mean student engagement scores over time ( F (2,191) = 5.84, p = .00). The effect size for the difference was a medium effect size ( 2 = .0 9). Significant differences were also found in the mean instructional strategies scores over time ( F (2,191) = 12.16 p = .00). The effect size for this difference was a large effect size ( 2 = .18). Differences were also present in the mean classroom mana gement PAGE 62 62 construct scores over time ( F (2,191) = 4.86, p = .01). The effect size for the difference was a medium effect size ( 2 = .09). (Stripling et al., 2008, p. 125) Post hoc analysis revealed a significant difference at the .05 level for student engage from before the methods course ( M = 6.65, SD = 1.03) to after the methods course/before student teaching ( M = 7.02, SD = .94) Stripling et al., 2008, p. 126) Stripling et al. also reported a significant difference ( p < .05) between the instructional strategies score from before the methods course ( M = 6.61, SD = 1.11) and after the methods course/before student teaching ( M = 7.25, SD = .94 ) The classroom management scores did not reveal a significant difference except for the aforement ioned classroom management overall teaching efficacy score. Roberts, Harlin, and Briers (2008) studied the effect that placing two student teachers at the same internship site had on teaching efficacy. The study was a quasi experimental study, and data were collected for two years or over four semesters during the student teaching semesters at Texas A&M University The sample consisted of 150 preservice teachers, but complete data were only collected from 138 students. Of the 150 student teachers 88 or 58.7% were placed in pairs. The data revealed that s tudent teachers placed alone ( M = 7.21, SD = .82) began the field experience slightly less efficacious than those placed in pairs ( M = 7.42, SD = .78). By the middle of the field experience, both grou ps exhibited less teaching efficacy, with those placed in pairs ( M = 6.91, SD = .88) slightly lower than those placed alone ( M = 7.03, SD = .91). By the end of the experience, both groups rebounded; those placed alone ( M = 7.45, SD = .81) were slightly higher tha n those placed in pairs ( M = 7.34, SD = .94). Student teachers placed alone exhibited their highest levels of efficacy at the end of the experience, while those placed in pairs were most efficacious at the beginning of the field experience. (Robe rts et al., 2008, p. 20) A statistically significant difference in teaching efficacy was not found between being placed alone or in a pair ( F ( 1,130 ) = .01, p = .93). PAGE 63 63 Edgar, Roberts implementing structured communication between cooperating teachers and student teachers would have on The sample consisted of 82 preservice teachers that were student teaching. The overall tre nd in teaching efficacy scores was consistent with Roberts et al. (2006), Harlin et al. (2007), and Roberts et al. ( 2007 ) in which teaching efficacy scores decreased at the middle of the student teaching experience, but then increased above the initial me asurement of efficacy. Results did not reveal a significant change in teaching efficacy because of the structured communication protocol. The researchers hypothesized that during the structured communication protocol the student teachers may have felt th at their teaching was criticized, and this may have contributed to a the slight lowering of teaching efficacy as compared to the control group. Research has also linked preservice teacher efficacy to attitudes toward children and control (Woolfolk & Hoy 1990) ndergraduates with a low sense of teacher efficacy tended to have an orientation toward control, taking a pessimistic view of extrinsic rewards, and punishments to make students study Tschannen Moran et al. 1998 p. 235) Student teachers often underestimate the complexity of the teaching task and their ability to manage many agendas simultaneously. Interns may either interact too much as peers with their students and find th eir classes out of control or they may grow overly harsh and end up not liking their teacher self They become disappointed with the gap between the standards they have set for themselves and their own performance. Student teachers sometimes engage in self protective strategies, lowering their standards in order to reduce the gap between the requirements of excellent teaching and their self perceptions of teaching competence. ( Woolfolk Hoy, 2000, p. 6 ) PAGE 64 64 According to Tschannen Moran et al. (1998), teach er education programs should allow preservice teachers 236) H owever teacher education programs should work on develop ing one skill set at a time. Student teaching allows the preservice t eacher to develop personal efficacy beliefs and a sink or swim approach could negatively affect teacher efficacy and the development of teaching competencies ( Tschannen Moran et al 1998). Kagan (1992) noted i f a [teacher education] program is to promo te growth among novices, it must require them to make their pre existing personal beliefs explicit; it must challenge the adequacy of those beliefs; and it must give novices extended opportunities to examine, elaborate, and integrate new information into their existing belief system. In short, pre service teachers need opportunities to make knowledge their own (p. 77) Mathematics ability /content knowledge According to Putnam and Borko (2000), t must have rich and flexible knowledge of the subjects they teach. They must understand the central facts and concepts of the discipline, how these ideas are connected, and the processes used to establish new knowledge and determine the validity of claims ( p.6) However, m any studies have contributed to the mou nting evidence that preservice teachers in general, lack an understanding of the mathematics content that they are charged to teach ( Adams, 1998; Ball & Wilson 1990 ; Bryan, 1999; Frykholm, 2000 ; Fuller, 1996; Goulding, Rowland, & Barber, 200 2 ; Matthews & Seaman, 2007; Miller & Gliem, 1996; Michigan State University Center for Research in Mathematics and Science Education, 2010 ; Stacey, Helme, Steinle, Baturo, Irwin, & Bana, 200 1 ; Stoddart, Connell, Stofflett, & Peck 1993 ; Stripling & Roberts, 2012a, 2012b in press ; Wilburne & Long, 2010 ) PAGE 65 65 A comprehensive literature search revealed only a few studies th at investigated the mathematics ability of agricultural education teachers or preservice teachers. Stripling and Roberts (2012b) sought to determine the mathematics ability of senior preservice teachers at the University of Florida during the Fall 2010 semester. Stripling and Roberts reported that the preservice teachers averaged 35.6% on a 26 item agricultural mathematics instrument and concluded that the preservice teachers were not proficient in agricultural mathematics concepts. Additionally, Stripling and Roberts investigated the associations between the types of mathematics courses completed in instrument. Results revealed moderate correlations between mathematics ability and basic high school mathematics ( r = .43), advanced high school m athematics ( r = .47), basic college mathematics ( r = .46), and advanced college mathematics ( r = .40). In addition, Stripling and Roberts reported a low correlation between mathematics ability and intermediate college mathematics ( r = .10) and a negligib le correlation between mathematics ability and intermediate high school mathematics ( r = .03). Therefore, Stripling and Roberts concluded that the aforesaid associations suggest that advanced mathematics coursework resulted in higher scores on the mathemat ics assessment. Similarly, Stripling and Roberts ( in press ) investigated the mathematics ability of nine teacher education programs, which resulted in a sample of 98 preserv ice teachers. Based on their sampling criteria Stripling and Roberts reported that the population mean was estimated with 95% confidence to be in the range of 28.5% to 48.5%. As a result, Stripling and Roberts concluded that preservice agricultural educa tion teachers are not PAGE 66 66 proficient in mathematics. Similar to Stripling and Roberts (2012b) Stripling and Roberts ( in press ) reported a substantial correlation between mathematics ability and advanced high school mathematics ( r = .50) l ow correlations between mathematics ability and basic high school mathematics ( r = .24), advanced high school mathematics ( r = .25), basic college mathematics ( r = .23), and intermediate college mathematics ( r = .14), and a negligible correlation between mathematics ab ility and intermediate high school mathematics ( r = .06). Additionally, Stripling and Roberts ( in press ) observed a low correlation between mathematics ability and receiving a grade of an A ( r = .22) or a grade of a B ( r = .11) in highest mathematics cour se completed in college and n egligible correlations between mathematics ability and receiving a C ( r = .09), a D ( r = .04), or an F ( r = .01) in highest mathematics course completed in college. Furthermore, Stripling and Roberts found that p reservice te achers that completed an advanced mathematics course scored 19.48 percentage points higher than those that did not complete an advanced mathematics course and those that re ceived an A in their highest college mathematics course scored 6.40 percentage point s higher than those that did not receive an A. Moreover, 39% of the variance in mathematics ability was explained with the following five variables: advanced college mathematics, university 7, university 1, grade of an A in highest college mathematics, an d university 8. According to Stripling and Roberts, the universities were included in the regression model because significant differences were found in the mathematics ability scores between universities. Miller and Gliem (1994) sough t to explain the variance in the mathematical ability of agricultural teachers. A mathematical problem solving test was developed by the PAGE 67 67 researchers to test mathematical ability. Scores on the mathematical problem solving test ranged from 26.67% to 100%. The mean score on the test was 66.47% ( SD = 2.96). The relationships between mathematical problem solving ability and the following variables were not significant: age and highest level of college mathematics coursework completed. However, the relation ships between mathematical problem solving ability and years of teaching experience, final college grade point average, ACT math score and attitude toward including mathematics concepts in the curriculum and instruction of secondary agriculture programs we re significant. Miller and Gliem concluded that the teachers in the study were not proficient in solving agriculturally related mathematical problems. Furthermore, the researchers also stated that the highest level of mathematics need to solve the proble ms on the instrument was algebra. A similar study was conducted by Miller and Gliem (1996), but the participants in the study consisted of 49 preservice agricultural education teachers from The Ohio State University. The study used the same instrument as Miller and Gliem (1994), and the range of scores was 0% to 87.8%. Miller and Gliem reported that 87.8% of the preservice teachers scored lower than 60%, and the mean score was 37.13% ( SD = 2.92). Grade point average, level of mathematics courses taken, and gender were found to have negligible relationships with mathematical problem solving ability. A moderate relationship was found between mathematics ability and number of mathematics courses completed. A substantial positive relationship was found bet ween mathematics ability and ACT math score. Miller and Gliem also reported that preservice teachers with higher scores had completed advanced mathematics courses, completed a fewer number of mathematics courses, and possessed higher ACT math scores. The PAGE 68 68 Persinger and Gliem (1987) investigated the mathematical ability of seconda ry agricultural teachers and their students. The sample consisted of 54 teachers and 656 students. The agricultural teachers mean score on the 20 question mathematics ability test was 12.35 ( SD = 4.36) problems solved correctly, or 61.75%. The researche rs reported that 28% of the teachers solved 50% or less of the problems correctly. Students of the mathematics deficient teachers were also shown to not be competent in mathematics. The average score for the secondary students was 5.6 ( SD = 4.54) out of 20 or 28%. Persinger and Gliem also reported that 82% of the students scored lower of their students. A plethora of re search has been conducted on the mathematics ability/content knowledge of preservice elementary teachers. Hill, Rowan, and Ball (2005) reported that knowledge was significantly related to student (p. 371). Matthews and S eaman (2007) in a study involving 48 preservice elementary teach ers with conceptual understanding of algorithms used to solve whole number computation problems (p. 8). In a study of 366 pr eservice teachers, Pomerantsev and Korosteleva (2003) reported that preservice teachers lack a conceptual understanding of mathematical symbols, have knowledge of the structure of an algebraic expression ess a poor grasp of algebraic rules. A study that consisted of 93 preservice elementary teachers reported the PAGE 69 69 participants possessed deficiencies in understanding the real number system (Adams, 1990). Simon (1993) found that 41 preservice elementary teac hers were deficient in their conceptual understanding and procedural understanding of division Fuller (1996) data suggested that preservice elementary teachers have mainly a procedural knowledge of mathematics, and preservice teachers believe good teac hers show and tell students how to do work The Fuller findings are supported by Ball and Willson (1990), Borko et al. (1992), and Onslow, Beynon, & Geddis (1992). Putt (1995) reported that 52% of the 704 elementary and middle school preservice teachers in the researcher s sample were unable to order numbers containing decimals from smallest to largest. In a similar study, Stacey et al. (2001) investigated the knowledge of 553 preservice elementary school teachers and determined that 20% of the preservic e teachers did not possess an expert knowledge of decimal numeration. Stacey et al (2001) Stoddart, Connell, Stofflett, and Peck ( 1993 ) stated that an entry level assessment showed that the sample of teacher candidates or elementary preservice teachers ( n = 83) are deficient in the mathematics content they are required to teach (54% were mathematically inadequate) Stoddard et al (1993) also reported that a majority of the participants could solve simple computation problems, but only 50% of the participants able to provide accurate conceptual Stoddart et al., 1993, p. 235). PAGE 70 70 Similarly, Bryan (1999) reported a lack of mathematics conceptual d epth among secondary preservice mathematics teachers. The study conducted by Bryan u tilized interviews to explore the conceptual understandings of mathematical ideas. The researcher reported that 37% of the time participants could not offer an explanati on for a mathematical idea. If an explanation was given, the explanation was flawed 37% of the time, and the participants were only able to offer a conceptual sound explanation 22% of time. Consequently, m any of the participants indicated that mathematic s content to be learned had only been presented as something to be memorized. knowledge of functions was not sufficient. Wilburne and Long (2010) investigated the mathematics abi lity of 70 secondary preservice teachers as measured by items developed from the 11 th The mean proportion of correct responses for number and operations, geometry and measurement, algebra, and data analysis and probability strands were .86, .84, .79, and .78 respectively Wilburne & Long, 2010, p. 5) The preservice teachers scored considerably lower on the pre calculus items with a mean proportion of correct responses of .37, thus indicating a need for increase d competency in pre calculus concepts before student teaching. Ball and Wilson (1990) compared the mathematics ability and pedagogical content knowledge gained from alternative routes versus traditional teacher education p rograms underlying mathematical meanings of the procedures and ideas Ball & Wilson, 1990, p. 5) of mathematics problems. PAGE 71 71 either gro Ball & Wilson, 1990, p. 5). Ball and Wilson also reported that less than 50% of either group could develop representations of division of fractions and both groups lacked an understanding o f mathematical proofs No significant differences were found in the mathematic ability of alternatively prepared or traditionally prepared preservice teachers entering or exiting their programs. Latterell (2008) described the mathematics knowledge of 10 secondary mathematics preservice teachers using both qualitative and quantitative data and conceptualized the study as a snapshot of a typical preservice secondary mathematics teacher. From the data the following f our themes emerged : The pre service sec ondary mathematics teacher enjoys and has knowledge of secondary mathematics; does not enjoy nor have a deep understanding of undergraduate mathematics; is drawn to teaching and not overly drawn to mathematics; and has a medium level of commitment to the N ational Council of Teachers of Mathematics [standards] ( Latterell, 2008, p. 1) Results from Latterell indicating that preservice teacher are competent in secondary mathematics (all participants scored 90% or above on an instrument based on secondary mathe matics) are contradictory to the findings of many of the studies mentioned above. Environment In this section, two variables will be discussed the teacher education program and the teaching methods course. Both variables have reciprocal causative relationships with the beh avior of teaching contextualized mathematics and the various personal factors under investigation in this study. PAGE 72 72 Teacher education program In the context of social cognitive theory and triadic reciprocality, t he teacher education program is the underl y ing environment for preservice teachers to develop into effective educators The goal of preservice teacher education is to make the most effective use of the time available to prepare future edu cators for the task awaiting them More specifically, t eacher education programs should create opportunities for prospective teachers to develop productive beliefs and attitudes toward teaching and learning mathematics alambous, Panaoura, & Philippou, 2009, p. 161) Ensor (2001) found that beginning teachers drew upon their professional argot a way of talking about teaching and learning mathematics Berry (2005) stated that research proven instructional strategies in mathematics and literacy make a difference in student achievement as teacher educators incorporate the strategies into the teacher education program. However, Wilson, Floden, and Ferrin i Munday (2001) purport ed that the research base in teacher education is thin. As a result, Berry (2005) called for teacher education programs to collect data on the effectiveness of the teachers the ir programs produce. According to Berry (2005), approximately 50% of students in a teacher education program will graduate as teacher candidates, and only 70% of the graduates will enter the teaching profession. Furthermore, p reservice teachers sometimes finish their academic program with trivial chang es in their content knowledge, teaching and learning beliefs ( Kagan, 1992; Seaman, Szydlik, Szydlik, & Beam, 2006 ) O ne cause is that teacher education programs do not connect pedagogy and academic content throughout the teacher education program ( Ishler Edens, & Berry, 1996) PAGE 73 73 Swortzel (1999) professed that there is also a lack of empirical research on teacher education in agriculture Swortzel study described the landscape of agricultural teacher education programs in the United States Accord ing to Swortzel (199 9 ) t he average preservice agricultural education program has 41 teaching majors educated by 1.7 full time equivalent faculty members 37). Swortzel also reported that 59% of the agricultural teacher education programs were locat ed in college s of agriculture 2 3 % were in colleges of education, and 18% were in colleges of business or technology. According to Swortzel, m ost teacher education programs (86%) are on the semester system, offer a four year degree program (81%), and are accredited by a regional or national association (96%). Swortzel also discovered that t he median minimum grade point average for admissions to an agricultural teacher education program was 2.50 and t he mean number of semester credit hours for four year degree certification programs was 130.5 with a range of 120 148. In addition, Swortzel reported agricultural teacher education programs require a median of 12 weeks of student teaching, and 93% also require d e arly field based experiences before student teaching (average of 60.2 clock hours) Swortzel also reported that 71% of agricultural teacher education programs require multicultural educatio n coursework, 75% require exceptional children coursework and 88% require coursework in computers/instructional technologies. McLean and Camp (2000) qualitatively investigated 10 teacher education programs that were nominated as quality programs by peer s in the profession. McLean and Camp (2000) found considerable variations in course offerings with 18 total courses s PAGE 74 74 30). Methods of teaching agriculture was the most comm on followed closely by program planning in agricultural education, and student teaching. The least offered courses were agricultural youth organizations, curriculum assessment and development, ethics in agricultural education and extensio n, and FFA advis ement. McLean and Camp also identified 118 topic s taught in the course s and suggested that the se topic s could be divided into five curricular areas or courses: experiential components, foundations, program and curriculum planning, teaching methods, and te aching technology. Myers and Dyer (2004) emphasized the importance of field experience in agricultural education programs and stated that students in their decision to pursue a career in agricultural education Har lin, Edwards, and Briers (2002) investigated preservice teachers perceived elements of importance before and after a student teaching experience. According to Harlin et al. student teachers perceived a cooperating teacher who is willing to be a mentor, a cooperating teacher who communicates clear expectations to the student teacher and discipline policies that are in place and enforced as the most important elements before a student teaching experience Harlin et al. reported after the student teachin g experience the perceived elements of importance were a well rounded program emphasizing instruction, SAEs, and youth leadership activities and a cooperating teacher who is willing to be a mentor As a result, the cooperating teacher and the student teac hing site affect preservice teachers perception s of the agricultural teaching profession (Harlin et al., 2002), and what is more the teaching methods utilized by the cooperating teacher influence the teaching practices of the preservice teacher ( Garton & Cano, PAGE 75 75 1994; McKee, 1991 ) Additionally Myers and Dyer (2004) purported that the teacher and the student teacher, the relationship between the cooperating teacher and the university supervisor also appears to be very important Myers and Dyer (2004) also reported that the best predictor of teaching performance was found to be agricultural education coursework grade point average (p 46) from a teacher preparation program Shinn (1997) reported that the number of classes taken in teaching a n d learning was the most influential factor in selecting effective teaching strategies and this support ed Myers and teaching and learning should be the primary foc us of agricultural teacher education programs Barrick (1993) also support ed the claim above by professing that teaching and learning are the central mission of the profession. According to Myers and Dyer the literature on preservice agricultural teacher education revealed the following nine deficiencies: 1. Evaluation of coursework and experiences needed throughout the teacher preparation program to best prepare future teachers of agriculture. 2. An investigation of why more female and ethnic minorities are not entering the agricultural education professorate. In addition to identifying obstacles, solutions to these problems also need to be investigated. 3. A trend analysis of teacher education faculty numbers and identification of duties beyond traditional teacher education. 4. The importance of agricultural education student organizations in the preparation of future teachers of agriculture and in the recruitment and retention of students into teacher preparation programs. 5. An analysis of alternative certificat ion practices for secondary teachers of agriculture. 6. Characteristics of successful cooperating teachers. PAGE 76 76 7. Characteristics of successful preservice teachers. 8. Identification of predictors of success for student teachers 9. Evaluation of the teacher education pr ogram model to determine if the current model is still the best fit for teacher education programs to fulfill growing and diverse roles and responsibilities. (p. 49) Myers and Dyer (2004) number of institutions with agricultural ed ucation programs are not actively producing certified agricultural education instructors 45). In 1995, only 79 of 93 agricultural education programs produced a qualified agricultural teacher graduate (Camp, 1998). This may be attributed to the teach er educator role has evolved from preparing preservice teachers and providing professional development for secondary teachers to other duties such as developing and delivering postsec ondary faculty development, student recruitment, and teaching college wide coursework. In regard to teacher education coursework requirements, t he American Association for Agricultural Education (2001) called for general education requirements that develop theoretical and practical understanding and suggested that general education comprise one third of the agricultural education program hours. I n addition, the standards stated that mathematics coursework is an expectation within general education, but no specific recommendations for coursework were given. However, according to Conant ( as cited in Swortzel, 1995 past an introductory level can prospective teachers gain a coherent picture of the subject so the National Council for Accreditation of Teacher Education (1994) standards, Swortzel (1995) recommended that the agricultural preservice teacher curriculum require two PAGE 77 77 only literature found that specifically identified or suggested mathematics r equirements for agricultural teacher education programs. Teaching methods course The teaching methods course is theoretically expressed as part of the physical and social environment from a social cognitive prospective, which as stated earlier, is bidire ctionally affected by the determinants of the triadic recepricality model (Bandura, 1986, 1997) The teaching methods course is an instructional methodology course that focuses on the selection and use of appropriate teaching strategies and techniques in formal educational settings (Roberts, 2009). Furthermore, in the context of this study, the preservice teachers will teach contextualized mathematics lessons to each other during the teaching methods course. The behavior of micro teaching is theoreticall y a component of the social environment. As stated previously, in social cognitive theory, the environment is not conceptualized as a fixed entity but is shaped by personal and behavioral influences (Bandura, 1989). Thus, micro teaching influences the en vironment of the teaching methods course. To that end, Bandura (1986) stated that not only do people learn from their actions, they can also learn by vicarious experiences or by observational learning. Observational learning allows a person to develop ge neralizations that can be used to influence future behavior without having to learn by experimentation or trial and error (Bandura, 1986). According to Bandura, most human behaviors are learned by observing others. Moreover observational learning increa ses The literature specific to an agricultural education teaching methods course is limited. However, as described in the self efficacy section, several studies have been PAGE 78 78 conducted to de termine the effects of a methods course on teaching efficacy in agricultural education. McClean and Camp (2000) recommended that preservice agricultural teacher education programs include lessons and experiences related to teaching methods for agricultural education. To that end, Ball and Knobloch (2005) examined the pedagogical knowledge acquired in agricultural education teaching methods courses. A ce nsus study was conducted to identify the (a) required reading resources, (b) nature and type of assignments, and (c) teaching methods p. 49). A survey was administered to collect the data, and 47 of 64 teacher educator s responded for a 73% response rate. However, only 43 responses were usable based on the a priori criteria of the course being exclusive to agricultural education. As a result, 43 teaching methods course syllabi were obtained for analysis. The researchers found that a total of 72 readings were required by 42 teachers. Four teacher educators (9.30% ) required four reading resources. Three teacher educators (7.0%) required three reading resources. Fourteen teacher educators (32.6%) required two reading resources. Twenty one educators (48.8%) required one reading resource. One teacher educator (2.3%) did not require a reading resource. (Ball & Knobloch, 2005, p. 51) Methods of Teaching Agriculture was required by 25.7% of teacher educators. Ball and Knobloch (2005) reported that this made the Newcom b et al. book the most frequently required text. As a result, Ball and Knobloch recommended that teacher educators consider text s outside of the profession, since one resource that was originally published in 1986 is widely used. Furthermore, one teacher good, comprehensive, up to date textbook is not currently available for this course Ball & Knobloch, 2005, p. 53). PAGE 79 79 The most frequent assignments found within the teaching methods course syllabi were lesson plans and micro teaching, which were required by 90% of teacher educators. The mean number of required lesson plans was 4.19 and the mean number of micro teachings was 3.89 per course. Exams and participation/attendance were the second most frequ ent assignments, required by 67.5% of the teacher educators. Quizzes were required by 47.5% of teacher educators, and unit plans, papers, essays, philosophy statements, and critiques were required by 40%. The following is a list of other assignments that were reported in the teaching methods syllabi of the teacher educators: homework (35%), field experiences (17.5%), portfolio (17.5%), technology (12.5%), bulletin boards (12.5%), course notebooks/internship handbooks (10%), management plans (10%), objecti ves, questions/cognitive levels (7.5%), modules (7.5%), interest approaches (7.5%), FFA activities/guidebook (5%), and games (2.5%). Ball and Knobloch (2005) also found that 22 different teaching methods were taught among the teaching methods courses. T eacher educators spent 20.8% (Range: 2.2 to 55.7%) of their course time on teaching methods. More than one third ( N = 15) of the courses spent less than 15% on teaching methods. The problem solving approach to teaching was taught by 23 teacher educators and 11.6% of course time was spent teaching this method. One third ( N = 13) of the teacher educators listed teaching methods, in general, as a topic in their syllabi. Nine of the top ten most commonly espoused methods were identical to methods cited in Ne wcomb et al (Ball & Knobloch, 2005, p. 52) The researchers concluded that little time is actually spent on teaching methods, erhaps one teaching methods course simply does not permit enough time to absorb, practice, and reflect upon the vast amount of pedagogical knowledge that an agriculture teacher must obtain PAGE 80 80 A study by Cano and Garton (1994a) sought to determine the personality type of preservice agricultural education teachers enrolled i n an agricultural teaching methods course and determined that all personality types were represented as measured by the Myers Briggs Type Indicator As a result, Cano and Garton (1994a) suggested that ith all of the learning relationships between preservice agricultural teachers ( n = 82) learning styles as determined by the Group Embedded Figures Test performance during a micro teaching of a teaching methods course, and the final course grade of the teaching methods course. Results indicated that 41% of the participants were field dependent and 59% were field ( r = 20) was found 8), and the results suggested that the more field independent a preservice teacher is the higher their score might be in a micro teaching that uses the problem solving preferred learning style and final course score w as low and positive (r = .21) Garton, 1994b, p. 8), indicating that field independent preservice teachers are more likely to have a higher final course average. As a result, Cano and Garton (1994b) purported that preservice teachers of agriculture need to have an understanding of how learning styles affect Several studies have been conducted investigating various aspects of a mathematics methods course. Burton, Daane, and PAGE 81 81 content knowledge for teaching mathematics differences between elementary pre (p. 1). The experimental met hods course incorporated 20 minutes of mathematics content into each class session. The difference in scores was found to be significant in favor of the experimental group as measured by the Content Knowledge for Teaching Mathematics Measure (Hill, Schil ling, & Ball, 2004) The addition of 20 minutes of mathematics content instruction accounted for 18% of the variance in content knowledge for teaching mathematics scores Dogan Dunlap, Dunlap, Izquierdo, and Kosheleva (2007) tested An Integrated Collabo rative, Field Based Approach to Teaching and Learning Mathematics (ICFB). ICFB is a pedagogical approach in which learners enrolled in a teacher education program simultaneously take mathematics teaching methods and mathematics content course s. The instr uctors of the courses collaborate and share common assignments and requirements. A one group pretest posttest design was utilized for the survey research A majority of the participants were of Hispanic ethnicity and were preservice elementary teachers. Typical responses in the pre Dogan Dunlap et al., 2007, p. 8). The pre survey also indicated that 26% believed an understanding of mathematical concepts would help in solving real life problems and another 15% Dogan Dunlap et al., 2 007, p p 8 9). The post survey found that fewer students indicated that mathematics was difficult and 58% believed mathematics was helpful in solving real life problems compared to 26% on the pre survey. The PAGE 82 82 researchers concluded that the ICFB approach Dogan Dunlap et al., 2007, p. 12). Rule and Harrell (2006) analyzed mathematical attitudes through the use of symbolic drawings before and after a mathematics teaching me thods course with 52 Rule & Harrell, 2006, p. 241). The posttest images were 72.1% posi tive and with 70.5% positive associat ed images. Rule & Harrell, 2006, p. 241) as a result of the teaching methods course. Pretest images and interpretations focused on grades time and peer/teacher pressure struggle, and lack of success in mathematics In contrast, p osttest images and interpretations revealed (a) greater understanding of mathematical concepts through use of concrete materials; (b) greater engagement in mathe matics through interesting activities and discourse with peers; (c) a sense of accomplishment from teaching practicum lessons taught to elementary students ( Rule & Harrell, 2006, p. 255) The researchers recommended that the symbolic drawings be utilized in a teaching methods course because the drawings help to shift mathematics anxiety to a more positive state. Kinach (2002) sought to develop the mathematics pedagogical content knowledge of secondary preservice teachers through a series of three tasks during a teaching methods course. Kinach (2002) developed the teaching experiment to make about instructional explanations explicit for specific school mathematics topics Kinach collected data qualitatively. In Task 1 p articipants of the study were asked to explain integer addition and subtraction, but only 1 of 21 PAGE 83 83 participants gave an accurate explanation. The preservice teachers possessed procedural knowledge of integer addition and subtraction at this stage o f the experiment beliefs by asking them to explain integer subtraction on the number line. During Task 2 participants discovered they lacked the conceptual knowledge to explain intege r subtraction on the number line and started to sense a need to develop knowledge about why rules work to complement their procedural understanding to effectively teach i nteger understandings with the use of algebra tiles Algebra tiles environment for explaining integer computation ( Kinach, 2002, p. 63). Qualitative data suggested that by the end of the teaching experiment the preservice teachers adv Kinach, 2002, p. 63). The data also revealed that hen pressed to teach for understanding, a nd not just information or skills, teacher candidates began to see the conceptual intricacies of so called simple topics like adding and subtracting integers Kinach, 2002, p. 63). As a result of the favorable findings, the researcher proposed a general cognitive strategy to be used in a mathematics methods course for the development of pedagogi cal content knowledge. The cognitive strategy utilizes the following five elements to guide cognitive development for pedagogical content knowledge: identify, assess, challenge, transform, and sustain. In a study involving one preserv ice mathematics teacher, Wilson (1994) examine d the evolving knowledge and beliefs of a preservice secondary mathematics teacher as she participated in a mathematics education course [teaching methods] that PAGE 84 84 emphasized mathematical and pedagogical connecti ons and applications of the function concept Data were collected by interviews, observations, collecting assignments and test, and a written instrument. Wilson found that the participant did not like theoretical mathematics that did not result in procedural or concrete answers. The preservice teacher and procedures in an organized fashion, explaining exactly which procedures students W ilson, 1994, p. 354). Before the methods course the preservice teacher believed functions to be a collection of concrete procedures B y the end of the course understanding of functions were at acceptable levels. Wilson also recommended that m odels for mathematics teacher education should seriously consider the idea of integrating mathematics content and pedagogy, with a significant component of that integrat ion consisting of activities that encourage teachers to reflect on their own views of mathematics and mathematics teaching while actively exploring important mathematical concepts and processes that they will be required to teach. Such an approach will all ow teachers to make important connections in their own mathematical understanding and improve the chances that such an integrated approach will be reflected in their future teaching. ( Wilson, 1994, p. 369) Chapter 2 Summary Chapter 2 provided a review of the literature related to the problem of this study C (1986) social cognitive theory and the model of triadic reciprocality provided the theoretical and concept ual frameworks. Relevant research related to the three classes of determinants of the triadic reciprocality model were summarized and teaching contextualized mathematics was conceptualized as a behavioral determinant. The behavior of teaching contextuali zed mathematics by preservice teachers is influenced by academic integration, demographic variables, self efficacy, mathematics PAGE 85 85 ability, and teacher education program variables. Stone et al. (2006) has provided a research proven method for teaching mathem atics in career and technical education classrooms. Several studies in agricultural education have also shown the Stone et al. model to be effective at teaching mathematical concepts in secondary classrooms. Research on demographic variables revealed a n egligible effect on the behavior of teaching Self efficacy and more specifically teacher efficacy research revealed that teaching efficacy is affected by various components of the triadic reciprocality model and r esearch related to the mathematical abil ity of preservice agricultural education teachers show ed mounting evidence of mathematical deficiencies. Finally, t he teacher education program was conceptualized as the physical and social environment for developing teaching competencies, and teaching methods course s that incorporated academic content were shown to be effective at increasing mathematical ability. Chapter 3 will provide the methodology that outlined this study. PAGE 86 86 Ta ble 2 1. The Seven Elements: Components of a Math Enhanced Lesson. Element s/Steps Teacher Directions 1. Introduce the CTE lesson. Explain the CTE lesson. Identify, discuss, point out, or pull out the math embedded in the CTE lesson. 2. Assess relates to the CTE lesson. As you assess, introduce math vocabulary through the math example embedded in the CTE. Employ a variety of methods and techniques for assessing awareness of all students, e.g., questioning, worksheets, group learning activities, etc. 3. Work through the math example embedded in the CTE lesson. Work through the steps/processes of the embedded math example. Bridge the CTE and math language. The transition from CTE to math vocabulary should be gradual throughout the lesson, being sure never to abandon completely either set of vocabulary once it is introduced. 4. Work through related, contextual math in CTE examples. Using the same math concept embedded in the CTE lesson: Work through similar problems/examples in the same occupational context. Use examples with varying levels of difficulty; order examples from basic to advanced. Continue to bridge CTE and math vocabulary. Check for understanding. PAGE 87 87 Table 2 1. Continued Element s/Steps Teacher Directions 5. Work through traditional math examples. Using the same math concept as in the embedded and related, contextual example s: Work through traditional math examples as they may appear on tests. Move from basic to advanced examples. Continue to bridge CTE and math vocabulary. Check for understanding. 6. Students demonstrate their understanding. Provide students opportunities for demonstrating their understanding of the math concepts embedded in the CTE lesson. Conclude the math examples back to the CTE content; conclude the lesson on the topic of CTE. 7. Formal assessment. Incorporate math questions into formal assessments at the end of the CTE unit/course. Note Building Academic Skills in Context: Testing the Value of Enhanced Math Learning in CTE (Stone et al., 2006, 12). PAGE 88 88 Figure 2 1. Triadic reciprocality model (Bandura, 1986, p. 24) Figure 2 2. Triadic reciprocality model of variables under investigation. Adapted from Social Foundation of Thought and Acti on (Bandura, 1986) Behavior Personal Factors Environment Behavior = Teaching Contextualized Mathematics Personal Factors = Demographic Variables, Math Teaching Efficacy, Personal Teaching Efficacy, Personal Math Efficacy, and Math Ability Environment = Teacher Education Program and Teaching Methods Course PAGE 89 89 Figure 2 3. The National Research Center for Career and Technical Education: Seven Elements of a Math Enhanced Lesson model (Stone et al., 2006 p. 13 ) Figure 2 4. Sample building trades math enhanced lesson: Using the Pythag orean theorem (Stone et al., 2006 p. 13 ) PAGE 90 90 CHAPTER 3 METHODOLOGY Chapter 1 provided a historical context to the mathematics deficiency among American students that has continually persisted for over 30 years and that mathematics deficiency provided the basis for this study. T he purpose of this study was outlined, along with specific objectives a nd hypotheses Key terms were defined and assumptions and limitations were stated. Chapter 2 described the theoretical framework and the conceptual model utilized to guide this study. Additionally, Chapter 2 presented prominent literature related to the various components of the conceptual model utilized in this study. In Chapter 3 the meth ods used to address the research objectives are d iscussed. Specifically, Chapter 3 reports the research design, procedures, population and sample, instrumentation data collection, and data analysis. For this study, t he independent variable of interest w as the mathematics teaching and integration strategies (MTIS) treatment Dependent variables include d mathematics teaching efficacy, personal mathematics efficacy, personal teaching efficacy, and mathematics ability of the preservice agricultural educatio n teachers. The following s tudent characteristics were included as antecedent variables : gender, grade point average, number and type of mathematics course s completed in high school and college grade received in last mathematics course completed and age of the preservice agricultural teachers Finally, to account for differences in prior knowledge pretest mathematics ability scores were considered as a covariate PAGE 91 91 Research Design This research was quasi experimental and utilized a nonequivalent control group design ( Campbell & Stanley, 1963) This design was utilized because random assignment of subjects was not possible due to the fact that the subjects under investigation self register ed for a section of a teaching methods course ( AEC 4200 Teaching Methods in Agricultural Education ) that best fit their schedule of classes To that end, t he agricultural education teaching methods course is organized into lectures and labs. The lectures are utilized to deliver content information related to teaching methods, strategies, and approaches. The labs are utilized to allow the preservice teachers to deliver micro teachings to their peers and the micro teachings are based on the content discussed in the lectures. T he MTIS treatment utilized in thi s study was assigned to the teaching methods lab sections randomly. The treatment group was administered the MTIS and the control group received the same instruction except for the MTIS. The composition of the teaching methods course and the treatment a re d iscussed further in the procedures section. The Mathematics Ability Test (Stripling & Roberts, 2012b ) was used to compare mathematics knowledge before and after the MTIS treatment The research design was illustrated by Campbell and Stanley (1963) and is shown in Figure 3 1 on page 102 T he M athematics Enhancement Teaching E fficacy I nstrument (Jansen, 2007) was used to compare efficacy measures before, during and after the MTIS treatment. A s a result, a (1963) nonequivalent control group design was implemented for this study and is shown in Figure 3 2 on page 102 According to Campbell and Stanley (1963), selection interaction effects and possibly regression are thr eats to the internal validity of the nonequivalent control group PAGE 92 92 design. Selection i nteraction effects are when other threats to interval validity interact with the selection of groups in multiple group quasi experimental designs and are mistaken for the effect of the treatment (Campbell & Stanley, 1963) In this study, selection interaction effects were partially controlled by using the pretest mathematic s ability scores as a covariate; however, this does not completely eliminate the risk of possible s election interaction effects. Thus, selection interaction effects are a limitation of this study. Statistical regression is the selection of participants based upon extreme scores (Campbell & Stanley, 1963). This was not an issue in this study. Partici pants were no t selected based on extreme scores Furthermore, the following possible t h reats to internal validity are controlled by the nonequivalent control group design: history, maturation, testing, instrumentation, selection, and mortality (Campbell & Stanley, 1963) Procedures The tre atment of this study was devised by the researcher and was incorporated into the teaching methods course during the final year of a teacher education program at the University of Florida The MTIS treatment consisted of three parts. First, the researcher prepared and delivered a lecture (Appendix A) to the treatment group of preservice teachers, which explained and demonstrated how to use the National nts of a math enhanced lesson model ( Stone, Alfeld, Pearson, Lewis, & Jensen, 2006 ) to teach contextualized mathematics concepts. The lecture was reviewed by an expert on the seven components of a math enhanced lesson to ensure validity. Second, e ach pre service agricultural education teacher in the treatment group was randomly assigned two of the 13 N ational C ouncil of T eachers of M athematics (NCTM) sub standards PAGE 93 93 (Carpenter & Gorg, 2000) that have been cross referenced to the National Agriculture, Food and Natural Resources Career Cluster Content S tandards Third, t he preservice teachers in the treatment group were required to teach the two NCTM sub standards to their peers in the treatment group using the seven components of a math enhanced lesson ( Sto ne et al. 2006) Therefore, e ach preservice teacher in the treatment group participated in the math enhanced lesson lecture, integrated mathematics into two o f the eight normally required micro teachings of the teaching methods course and observed their peers teaching up to 1 2 math enhanced lesson s while roleplaying as a secondary student. In summary, beyond what was previously required in the teaching methods course the treatment added the following three elements: (a) a lecture on the s even components of a math enhanced lesson, (b) random assignment of the NCTM sub standards among the preservice teachers, and (c) requiring two of the micro teaching lessons to be math enhanced. Population and Sample The target population for this study was Florida preservice agricultural education teachers. The accessible population for this study was present undergraduate and graduate students in their final year of the agricultural teacher edu cation program at the University of Florida For this stu dy, the accessible population was a convenience sample which was conceptualized as a slice in time (Oliver & Hinkle, 1981) Gall, Borg, and Gall (1996) stated that convenience sampling is appropriate as long as the researcher provides a detailed descripti on of the sample used and the reasons for selection. To that end, the sample (2012b) study that discovered that Florida preservice teachers were not proficient in the cross referenced NCTM sub standards PAGE 94 94 The sample consisted of 19 preservice agricultural education teachers, 16 females and 3 males. The average age of the sample was 21.5 years old ( SD = 1 12 ) with a range of 20 to 25 All of the participants described their ethnicity as white and were se niors in an undergraduate agricultural education program. T heir self reported mean college grade point average was 3 44 ( SD = 0 28 ) on a 4 point scale. The number of college level mathematics courses completed by the participants ranged from 1 to 5 with a mean of 3 02 ( SD = 1 09 ) and two of the participants reported that they had not completed a math ematics course since high school To that end the time since the previous semester in college to their senior year in high school or about four years prior Lastly, 31 6 % received an A, 21 1 % a B+, 26 3 % a B and 21 4 % a C in their highest level of mathematics successfully complete d in college and the highest most common ly completed course in co llege was introductory statistics Instrument ation T wo instruments were used during this study for data collection the Mathematics Ability Test (Stripling & Roberts, 2012b ) and the Mathematics Enhancement Teaching Efficacy Instrument (Jansen, 200 7). The Mathematics Ability Test is a researcher developed instrument that was developed based on the 13 NCTM sub standards (Carpenter & Gorg, 2000) that are cross referenced with the National A griculture, F ood and N atural Resources Career Cluster Content S tandards (National Council for Agricultural Education, 2009) The Mathematics Ability Test consists of 26 open ended mathematical word problems or two items for each cross referenced NCTM sub standard and the sum of the 26 items measures one construct mathematics ability During item development, the research er met with a secondary mathematics expert to PAGE 95 95 would meet the requirements of the 13 NCTM sub standards. The secondary mathematics expert determined that the 13 NCTM sub standards, and therefore, all seven items were included on the Mathematics Ability Test The remaining 19 items were developed based on NCTM ex amples problems (Carpenter & Gorg, 2000) The 13 cross referenced NCTM sub standards and the corresponding content or process area are provided in Table 3 1 on page 101 The instrument was pilot tested during the Fall 2010 semester at the University of Florida The pilot test consisted of 25 preservice agricultural education teachers and yielded a of .8 0 for the mathematics ability construct Face and content validity of the instrument was established by a panel of experts consisting of agricultural education and mathematics faculty from three universities and two secondary mathematics experts A demographic section was added to the Mathematics Ability Test and the participants self reported gender, age, ethnicity, grade point average, number of math courses taken, highest level of mathematics taken, and grade received in last mathematics course completed. Additionally the researcher and a mathematics exper t individually score d the Mathematics Ability Test and items were scored incorrect, partially correct (students set the problem up correctly but made a calculation error), or correct. T he scorer s used a rubric that was developed by two secondary mathematics experts to score each item. Inter PAGE 96 96 and the analysis yielded a of .95. Furthermore, a copy of the inst rument is provided in App endix B The Mathematics Enhancement Teaching Efficacy Instrument (Jansen, 2007) was developed and validated during a doctoral dissertation at Oregon State University and is divided into the following three constructs: mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy ( see Appendix C ) The instrument utilizes a different rating scale for each construct personal mathematics efficacy (1 = not at all confident to 4 = v ery confident ), mathematics teaching effi cacy (1 = s trongly disagree to 5 = s trongly agree ), and personal teaching efficacy (1 = n othing to 9 = a great deal of influence ) (Jansen, 2007). Jansen reported that face and content validity was established by a panel of experts that included represe nta tives from Oregon, Utah, and Washington E xploratory and confirmatory factor analyses were used to verify the construct and discriminate validity of the instrument Jansen pilot tested the instrument with Utah secondary agricultural teachers and reported that the for the mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy constructs to be .9 2 .8 9 and .9 1 respectively. J ansen also conducted a larger study with a target population of all Oregon and Washington secondary agricultural teachers. The larger study consisted of 230 participants and Jansen reported the alpha coefficients for the mathematics teaching efficacy, personal mathematics efficacy, and perso nal teaching efficacy constructs to be .88, .8 4 and .9 1 respectively. Scores for each construct were calculated by averaging the corresponding items after reverse coding items 2, 4, 5, 7, 9, 10, 11, and 13. Lastly, for this study, t he post hoc reliabilities for the mathematics PAGE 97 97 teaching efficacy, personal mathematics efficacy, and personal teaching efficacy constructs were .93, .80, and 89 respectively. Data Collection The data collection period of this study was during the F all 2011 academic semester Data were collected from preservice agricultural teachers during the ir final year of an agricultural teacher education program at the University of Florida The agricultural education preservice teachers volunteer ed to parti cipate and take the Mathematics Ability Test and the Mathematics Enhancement Teaching Efficacy Instrument (Jansen, 2007) by signing an informed consent, which was approved by the Institutional Review Board at the University of Florida ( Appendix D ) Partic ipants were informed that the researcher would protect their privacy rights by ensuring anonymity and appropriate storage of data. In addition, s ince students received and completed the instruments during their agricultural education courses, they were informed that participation in the study would not have an impact on their course grades. A script (Appendix E ) was also developed and read to standardize administration, minimize error variance, and experimenter effects. The Mathematics Ability Test took the participants approximately 60 minutes to complete and was administered twice : ( a ) week two of the Fall 2011 semester ; and ( b ) week 16 or the last week of the Fall 2011 semester The Mathematics Enhancement Teaching Efficacy Instrument (Jansen, 2007) took the participants approximately 8 minutes to complete and was administered three times : ( a ) week two of the Fall 2011 semester ; ( b ) week 12 of the Fall 2011 semester/ after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson ; and ( c ) week 15 of the Fall 2011 semester PAGE 98 98 Analysis of Data Data were analyzed using SPSS version 1 7 for Windows TM Frequencies, means, and standard deviations were calculated to summarize demographics, mathematics teaching efficacy, personal mathematics efficacy, personal teaching efficacy, and mathematics ability of the preservice agricultural education teachers MANOVAs were used to determine if significant differences existed in mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy based upon the MTIS treatment. ANCOVA was also used to determine if a significant difference existed in mathematics ability based upon the MTIS treatment. P artial eta squared was used to calculate effect size, and Huck (2008) descriptors were utilized to describe the effect ( .01 is a small effect size .06 is a medium effect size and .14 is a large effect size) According to Huck (2008) the use of inferential statistics is appropriate for this type of research. Huck stated that inferential statistics can be used with a current sample to make inferences to an abstract population population that is comprised of p resent and future members. Huck (2008) also purported that abstract populations exist s of current accessible populations Furthermore, Huck stated that abstract populations can be conceptu alized from convenience samples that are described in detail. Consistent with Huck Gall, Gall, and Borg (2003) justified the use of inferential statistics with a convenience sample. Gall et al. (2003) data collected from a convenience sample if the sample is carefully conceptualized to Demographic data from the previous year of graduating preservice agricultural education teachers at the University of Florid a PAGE 99 99 supported that the convenience sample was representative of the target population. In addition, qualitative data from the teacher educators at the University of Florida confirmed that the convenience sample was representative of the target population Despite the researcher s efforts to reduce deviations from the aforementioned methodology a few differences should be noted in the actual implementation. First, 2 of the 13 preservice teachers in the experimental group only developed and taught one math enhanced lesson. Secondly, 2 of the 13 preservice teachers in the experimental group misplaced their second assigned N ational C ouncil of T eachers of M athematics sub standard and as a result, were randomly assigned another sub standard to replace the standard that was lost by the preservice teachers Thirdly, a few preservice teachers were absent on the scheduled data collection days. Two preservice teachers were absent on the initial administration of the Mathematics Enhancement Teaching Efficacy I nstrument (Jansen, 2007) Therefore, they completed the instrument two days after the other participants. For the third administration of the Mathematics Enhancement Teaching Efficacy Instrument one preservice teacher was absent and completed the effica cy measure one day after the other participants. One preservice teacher was also absent on the second administration of the Mathematics Ability Test This preservice teacher completed the mathematics ability instrument one day after the other participants The researcher was unable to compare the data collected during and after the schedule d data collection s because the data was collected anonymously. H owever, after visually inspecting scatterplots of the data, the research determined that there were n o outliers present and therefore, the deviations in data collection did not affect the results of the study PAGE 100 100 Also, t he second administration of the Mathematics Ability Test was inadvertently given on the same day as a final for a number of the participants. This may explain why some of the preservice teachers anecdotally put forth less effort and showed less work on the open ended mathematical word problems on the second ad ministration. Lastly, one preservice teacher was absent for one of the math enhanced micro teaching labs. Chapter 3 Summary In Chapter 3 the methods used to address the research objectives wer e d iscussed. Specifically, Chapter 3 reported the research design, procedures, population and sample, instrumentation data collection, and data analysis. T he independent variable in this study was the MTIS treatment Dependent variables were mathematics teaching efficacy, personal mathematics effic acy, personal teaching efficacy, and mathematics ability of the preservice teachers. Student characteristics were included as antecedent variables. The research design of this study was identified as a nonequivalent control group design (Campbell & Stanley, 1963) and threats to validity were discussed The target population of this study was Florida preservice agricultural education teachers, and the accessible population was acknowledged. T he accessible population was also categorized as a conve nience sample and justification for the method was given. The instruments used in the study were identified and the validity and reliability for each instrument was discussed. The data collection methods were outlined, and the methods used to analyze the data were reported. Chapter 4 will present the findings of this study based on the research objectives PAGE 101 101 Table 3 1. Cross referenced NCTM Sub standards for Grades 9 12 Content/Process Area NCTM Sub standards Number & Operations 1A. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. 1B. Understand meanings of operations and how they relate to one another. 1C. Compute fluently and make reasonable estimates. Algebra 2C. Use mathematical models to represent and understand quantitative relationships. 2D. Analyze change in various contexts. Geometry 3A. Analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships. Measurement 4A. Understand measurable attributes of objects and the units, systems, and processes of measurement. 4B. Apply appropriate techniques, tools, and formulas to determine measurements. Data Analysis & Probability 5A. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. 5B. Select and use appropriate statistical methods to analyze data. 5C. Develop and evaluate inferences and predictions that are based on data. Problem Solving 6B. Solve problems that arise in mathematics in other contexts. 6C. Apply and adapt a variety of appropriate strategies to solve problems. Note Principle and Standards for School Mathematics ( Carpenter & Gorg, 2000 ) PAGE 102 102 Figure 3 1 Research design mathematics ability. Figure 3 2 Research design efficacy measures. PAGE 103 103 CHAPTER 4 RESULTS Chapter 1 provided a historical context to the mathematics deficiency among American students that has continually persisted for over 30 years and that mathematics deficiency provided the basis for this study. T he purpose of this study was outlined, along with specific objectives and hypotheses. Key terms were defined and assumptions and limitations were stated. Chapter 2 described the theoretical framework and the conceptual model utilized to guide this study. Addition ally, Chapter 2 presented prominent literature related to the various components of the conceptual model utilized in this study. Chapter 3 discussed the methods used to address the research objectives and reported the research design, procedures, popul ation and sample, instrumentation, data collection, and data analysis. The independent variable in this study was the mathematics teaching and integration strategies (MTIS) treatment. Dependent variables include d mathematics teaching efficacy, personal mathematics efficacy, personal teaching efficacy, and mathematics ability of the preservice agricultural education teachers. The following student characteristics were treated as antecedent variables : gender, grade point average, number and type of mathem atics courses completed in high school and college, grade received in last mathematics course completed, and age of the preservice agricultural teachers. Also to account for differences in prior mathematics knowledge pretest mathematics ability scores were used as a covariate The research design was quasi experimental and utilized a nonequivalent control group design (Campbell & Stanley, 1963) Data collected were mathematics ability (as measured by PAGE 104 104 the Mathematics Ability Test ), mathematics te aching efficacy, personal mathematics efficacy, and personal teaching efficacy (as measured by the Mathematics Enhancement Teaching Efficacy Instrument ) Data were analyzed using frequencies, m eans, standard deviations, an ANCOVA and MANOVAs Chapter 4 presents the findings obtained by this study. The results address the objectives and hypotheses in determining the influence of the MTIS treatment on the mathematics ability, mathematics teaching efficacy personal mathematics efficacy, and personal teaching efficacy The sample consisted of preservice teachers enrolled in AEC 4200 Teaching Methods in Agricultural Education during the Fall 2011 semester ( n = 19). As outlined in Chapter 3 mathematics ability data were collected (a ) week two of the Fall 2011 semester; and (b ) week 16 / the last week of the Fall 2011 semester M athematics teaching efficacy personal mathematics efficacy, and personal teaching efficacy data were collected (a ) w eek two of the Fall 2011 semester ; (b ) week 12 of the Fall 2011 semester/ after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson ; and (c ) week 15 of the Fall 2011 semester The response rate for each collecti on was 100%. Prior to the study, the researcher developed Mathematics Ability Test was pilot tested during the Fall 2010 semester at the University of Florida to assess reliability. The pilot test consisted of 25 preservice agricultural education teachers and yielded a of .8 0 for the mathematics ability construct The Mathematics Enhancement Teaching Efficacy Instrument was develo ped and validated during a doctoral dissertation at Oregon State University and is divided into the following PAGE 105 105 three constructs: mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy. Jansen (2007) pilot tested the i nstrument and reported that for the mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy constructs to be .92, .89, and .91, respectively. For this study, the post hoc reliabilitie s for the mathematics teaching efficacy, personal mathematics efficacy, and personal teaching efficacy constructs were .93, .80, and .89, respectively. Descriptive Statistics of Variables in this Study Mathematics Ability As depicted in Table 4 1 on page 116 ability score s week two of the teaching methods course averaged 45 51 % ( SD = 9.32 ) and the pretest scores ranged from 30.77 % to 57.69 %. At the end of th e teaching methods course or week 16 the control scores averaged 45.19 % ( SD = 11 26 ) and the posttest scores ranged from 30.77 % to 59.62 %. week two to week 16 of the teaching methods course. A distri pretest mathematics ability scores may be found in Figure 4 1 on page 122 and their posttest scores in Figure 4 2 on page 122 increased from week two to week 16 o f the teaching methods course (Table 4 1 p. 116 ) The pretest scores avera ged 38.31 % ( SD = 11.03 ) and the pretest scores ranged from 23. 08 % to 59.62 %. At the end of th e teaching methods course or week 16 the mathematics ability scores averaged 45.71 % ( SD = 11 69 ) and the posttest scores ranged from 36.54 % to 69.23 %. The PAGE 106 106 increase d 7.40 % from week two to week 16 of the teaching methods course. A distribution of the experiment in Figure 4 3 on page 123 and their posttest scores in Figure 4 4 on page 123 P ersonal Mathematics E fficacy week two to week 15 of the teaching methods course ( Table 4 2 p. 116; Figure 4 1 1 p. 129 ). T he scores week two of the teaching methods course averaged 3.52 ( SD = 0.43 ) A fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson ( week 12 of the teaching methods course) personal mathematics efficacy scores averaged 3.67 ( SD = 0.49 ) Week 15 of the teaching methods course, the control hematics efficacy scores averaged 3.67 ( SD = 0.67 ). A distribution 5, 4 6, and 4 7 on pages 124, 125, and 126, respectively The scores increased at each data collection point (Table 4 2 p. 116; Figure 4 11 p. 129 ). The week two teaching methods course average was 3.39 ( SD = 0.49 ) A fter delivering their first mathematics enhanc ed lesson or week 15 the personal mathematics efficacy scores averaged 3.46 ( SD = 0.37 ) Week 15 of the teaching methods course the ( SD = 0.44 ). A distribution found in Figures 4 8, 4 9, and 4 10 on pages 127, 128, and 129 respectively. In addition t he mean differences in personal mathematics efficacy scores from week two to week 15 of th e teaching methods course (data collection points 1 and 3), PAGE 107 107 from week two to week 12 of the teaching methods course / after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson (data collection points 1 and 2), and from week 12 to week 15 of the teaching methods course (data collection points 2 and 3) are presented in Table 4 3 on page 116. were as fol lows: (a) data collection points three minus one was 0.15 ( SD = 0.09); (b) data collection points two minus one was 0.15 ( SD = 0 .20); and (c) data collection points three minus two was 0.00 ( SD = 0.21). Mean differences in the experimental l mathematics efficacy scores were as follows: (a) data collection points three minus one was 0.11 ( SD = 0.28); (b) data collection points two minus one was 0.07 ( SD = .31); and (c) data collection points three minus two was 0.04 ( SD = 0.25). M athema tics Teaching E fficacy As depicted in Table 4 4 (p. 116) and Figure 4 18 (p. 134) t he mathematics teaching efficacy scores increased from week two to week 15 of the teaching methods course. The week two teaching methods course average was 3.40 ( SD = 0.47 ) A fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson (week 12 of the teaching methods course) the control mathematics teaching efficacy scores averaged 3.37 ( SD = 0.67 ) Week 1 5 of the teaching methods course averaged 3.50 ( SD = 0.56 ). efficacy scores may be found in Figures 4 12, 4 13, and 4 14 on pages 130, 131 and 132, respectively. The scores decreased from week two to week 15 of the te aching methods course (Table 4 4 p. 116; Figure 4 18 p. PAGE 108 108 134 ). The scores week two of the teaching methods course averaged 3.69 ( SD = 0.61 ) A fter delivering their first mathematics enhanced lesson (week 12 of the teaching methods course) the mathematics teaching efficacy scores averaged 3.41 ( SD = 0 .97 ) Week 15 of the teaching methods course teaching efficacy scores averaged 3.50 ( SD = 0.98 ). A distribution of the experimental 15, 4 16, and 4 17 on pages 132, 133, and 134, respectively. The mean differences in mathematics teaching efficacy scores from week two to week 15 of the teaching methods course (data collection points 1 and 3), from week two of the teaching methods course to week 12 of the teaching methods course / after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson (data collection points 1 and 2), and from week 12 to week 15 of the teaching methods course (data collection points 2 and 3) are presented in Table 4 5 on page 116 as follows: (a) data collection points three minus one was 0.10 ( SD = 0 .50); (b) data collection points two minus one was 0.03 ( SD = 0.63); and (c) data collection points three minus two was 0.13 ( SD mathematics teaching efficacy scores were as follows: (a) data collect ion points three minus one was 0.1 9 ( SD = 0. 60 ); (b) data collection points two minus one was 0. 28 ( SD = 0 49 ); and (c) data collection points three minus two was 0.0 9 ( SD = 0. 41 ). PAGE 109 109 P ersonal Teaching E fficacy As depicted in Table 4 6 (p. 117) and Fi gure 4 25 (p. 139) t he personal teaching efficacy scores week two of the teaching methods course averaged 7.32 ( SD = 0.62 ) A fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson (week 12) personal teaching efficacy scores averaged 7.00 ( SD = 0.73 ) Week 15 of the teaching methods course ( SD = 0.42 ). A personal tea ching efficacy scores may be found in Figures 4 19, 4 20, and 4 21 on pages 135, 136, and 137, respectively. The scores decreased at each data collection point (Table 4 6 p. 117; Figure 4 25 p. 139 ). The personal teaching efficacy scores week two of the teaching methods course averaged 7.67 ( SD = 0.61 ) A fter delivering their first mathematics enhanced lesson ( week 12 ) the personal teaching efficacy scores av eraged 7.57 ( SD = 0.72 ) Week 15 of the teaching methods course efficacy scores averaged 7.46 ( SD = 1.04 ). personal teaching efficacy scores may be found in Figures 4 22, 4 23, and 4 24 on pages 137, 138, and 139, respectively. The mean differences in personal teaching efficacy scores from week two to week 15 of the teaching methods course (data collection points 1 and 3), from week two to week 12 of the teaching m ethods course / after the preservice teachers in the treatment group delivered their first mathematics enhanced lesson (data collection points 1 and 2), and from week 12 to week 15 of t he teaching methods course (data collection points 2 and 3) are presented in Table 4 7 on page 117 PAGE 110 110 personal teaching efficacy scores were as follows: (a) data collection points three minus one was 0. 29 ( SD = 0. 38 ); (b) data collection points two minus one was 0. 32 ( SD = 0. 48 ); and (c) data collection points three minus two was 0.0 3 ( SD = 0. 55 personal teaching efficacy scores were as follows: (a) data collection po ints three minus one was 0. 2 1 ( SD = 0. 82 ); (b) data collection points two minus one was 0. 10 ( SD = 52 ); and (c) data collection points three minus two was 0. 11 ( SD = 0. 52 ). Relationships Between Variables As part of the description of the variabl es in this study, all variables were examined for correlations. For the purpose of discussion, the terminology proposed by Davis (1971) was used to indicate the magnitude of the correlations. Correlations from .01 to .09 are negligible, .10 to .29 are lo w, .30 to .49 are moderate, .50 to .69 are substantial, .70 to .99 are very strong and a correlation of 1.00 is perfect. Pearson correlations were used for continuous data (Table 4 8 p. 118 ) and point biserial correlations were used for dichotomous data (Table 4 9 p. 119 ) With that in mind, group was coded as control (0) or experimental (1), gender was coded as male (0) or female (1), grade received in most recent college mathematics course was coded as not the grade received (0) or grade received (1) completing a mathematics courses in high school for college credit was coded as not completed (0) or completed (1), and the types of mathematics course s were coded as not completed (0) or completed (1) The types of mathematics courses completed in high school and college by the preservice agricultural teachers were categorized into basic, intermediate, and advanced mathematics by a mathematics expert. The mathematics expert categorized algebra, algebra II, and college algebra as basic mathematics, PAGE 111 111 trigonometry, pre calculus, and statistics as intermediate mathematics, and calculus as advanced mathematics. Furthermore, for readability abbreviations for mathematics teaching efficacy (MTE), personal mathematics efficacy (PME), and personal teaching efficacy (PTE) were used when reporting the results of the correlations. As would be expected, very strong or substantial correlations were discovered wit hin the MTE, PME, PTE, and mathematics ability measures M oderate and substantial associations were found between all the MTE and PME measures but not between PTE and the other efficacy measures MTE 3 was s ubstantial ly associated with the n umber of mathematics courses completed in college ( r = .52 ) and a grade of a C in most recent college mathematics course ( r = .69 ) MTE 3 was moderately associated with completing an advanced mathematics course in high scho ol ( r = .38 ) and a grade of a B in most recent college mathematics course ( r = .48 ) PME 3 was substantial ly associated with completing a basic mathematics course in high school ( r = .52 ) and completing an advanced mathematics course in high school ( r = .57 ) PME 3 was moderately associated with PTE 1 ( r = .34 ) PTE 3 ( r = .30 ) pretest math ability ( r = .47 ) posttest math ability ( r = .40 ) the number of mathematics courses completed in college ( r = .33 ) completing a basic mathematics course in college ( r = .32 ) completing an advanced mathematics course in college ( r = .39 ) and a grade of a C in most recent college mathematics course ( r = .35 ) PTE 3 was moderately associated with age ( r = .38 ) GPA ( r = .36 ) and completing an advanced mathematics course in high school ( r = .37 ) Lastly, p osttest mathematics ability was moderately associated with completing an advanced PAGE 112 112 mathematics course in high school ( r = .33 ) completing a basic mathematics course in college ( r = .30 ) and with completing a mathemati cs courses in high school for college credit ( r = .45 ) Antecedent Variables The following student characteristics were included in this study as antecedent variables : gender, grade point average, number and type of mathematics courses completed in high school and college, grade received in last mathematics course completed, and age of the preservice agricultural teachers. Each of the aforementioned variables was examined to determine if difference s were present between the control and experimental groups. Chi squares were used to determine if significant differences existed between the groups for categorical data, and independent samples t test were used to determine if significant differences exi sted between the groups for continuous data. No statistically significant differences were found between the control and experimental groups in regard to the antecedent variables (Tables 4 10 and 4 11 p. 120 ) Hypothesis Tests Dependent variables in this study include d mathematics teaching efficacy, personal mathematics efficacy, personal teaching efficacy, and mathematics ability of the preservice agricultural education teachers. All of the aforementioned variables were interval data. The independent v ariable in this study was the MTIS treatment, and it is categorical in nature. In addition, the covariate used in the analysis of hypothesis one was the mathematics ability pretest scores, and this data was interval. To determine if significant differen ces existed in the mathematics teaching efficacy, personal mathematics efficacy, personal teaching efficacy, and mathematics PAGE 113 113 ability scores of preservice teacher based upon the MTIS treatment, hypotheses were formulated to frame this study. The decisions to reject or fail to reject the null hypotheses were based upon the ANCOVA and MANOVA procedures used in this study and a priori significance level of .05. Hypothes i s Related to Mathematics Ability H 01 There is no significant difference in the mathematics ability of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment This hypoth esis was tested using an ANCOVA, and the analysis revealed a s ignificant difference in the mathematics ability of preservice agricultural education teachers based upon the MTIS treatment while controlling pretest mathematics ability scores F (1, 16) = 5.36, p < .05 ( Table 4 12 p. 120 ) justed posttest mean score ( M = 40.25, SE = 2.72) was significantly lower than the M = 47.99, SE = 1.81 ; Table 4 13 p. 120 ). The practical significance of the difference was assessed using a partial eta squared, and the effect size was .2 5, which is a large effect according to Huck (2008). Based on the statistically significant difference in adjusted posttest mean and the large effect size the null hypothesis was rejected. Hypothes i s Re lated to Personal Mathematics Efficacy H 02 There is no significant difference in the personal mathematics efficacy of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment This hypothesis w as tested using a MANOVA The mean differences between the personal mathematics efficacy data collection points were the dependent variables. PAGE 114 114 With that in mind, t he analysis did not reveal a significant difference in the personal mathematics efficacy of preservice agricultural education teachers based upon the MTIS treatment T = .02, F ( 2 1 6 ) = 0 .15 p > .05 (Table 4 1 4 p. 120 ) Therefore, the researcher failed to reject the null hypothesis. Hypothes i s Related to Mathematics Teaching Efficacy H 03 There is no significant difference in the mathematics teaching efficacy of preservice agricultural education teachers before and after mathematics teaching and integration strategies This hypothesis was tested using a M ANOVA The mean differences between the mathematics teaching efficacy data collection points were the dependent variables, and the analysis did not reveal a significant difference in the mathematics teaching efficacy of preservice agricultural education teache rs based upon the MTIS treatment T = .06, F ( 2 1 6 ) = 0 .50 p > .05 (Table 4 1 5 p. 121 ) Therefore, the researcher failed to reject the null hypothesis. Hypothes i s Related to Personal Teaching Efficacy H 04 There is no significant difference in the per sonal teaching efficacy of preservice agricultural education teachers before and after mathematics teaching and integration strategies This hypothesis was tested using a M ANOVA. The mean differences between the personal mathematics efficacy data collection points were the dependent variables, and the analysis did not reveal a significant difference in the personal teaching efficacy of preservice agricultural education teac hers based upon the MTIS treatment T = .06, F ( 2 1 6 ) = 0 .49 p > .05 (Table 4 1 6 p. 121 ) Therefore, the researcher failed to reject the null hypothesis. PAGE 115 115 Chapter 4 Summary Chapter 4 presented the findings of this study. The findings were structured based on the objectives and hypothesis that guided this research. The descriptive statistics that were presented were based on the following objectives: ( a ) d etermine the effects of MTIS in the teaching methods course on mathematics ability ; ( b ) d etermine the effects of MTIS in the teaching methods course on personal mathematics efficacy ; ( c ) d etermine the effects of MTIS in the teaching methods course on mathematics teaching efficacy ; an d ( d ) d etermine the effects of MTIS in the teaching methods course on personal teaching efficacy. The null hypothesis tested in this study were: ( a ) t here is no significant difference in the mathematics ability of preservice agricultural education teacher s based upon the MTIS treatment ; ( b ) there is no significant difference in the personal mathematics efficacy of preservice agricultural education teachers based upon the MTIS treatment ; ( c ) there is no significant difference in the mathematics teaching eff icacy of preservice agricultural education teachers based upon the MTIS treatment ; and ( d ) there is no significant difference in the personal teaching efficacy of preservice agricultural education teachers based the MTIS treatment The findings presented in Chapter 4 will be discussed in greater detail in Chapter 5 To that end, Chapter 5 will provide conclusions, recommendations, and implications regarding the findings of this study. PAGE 116 116 Table 4 1 Mathema tics Ability means Pretest Posttest Difference posttest pretest M SD M SD M SD Control group 45.51 9.32 45.19 11.26 0.32 5.36 Experimental group 38.31 11.03 45.71 12.69 7.40 6.56 Table 4 2. Personal Mathematics Efficacy Control group Experimental group Time M SD M SD Week two of the teaching methods course 3.52 0.43 3.39 0.49 Week 12 of the teaching methods course/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson 3.67 0.49 3.46 0.37 Week 15 of the teaching methods course 3.67 0.38 3.50 0.44 Note 1 = n ot at all confident to 4 = v ery confident (Jansen, 2007). Table 4 3 Mean differences in data collection points for Personal Mathematics Efficacy M difference 3 1 SD M difference 2 1 SD M difference 3 2 SD Control group 0.15 0.09 0.15 0.20 0.00 0.21 Experimental group 0.11 0.28 0.07 0.31 0.04 0.25 Table 4 4. Mathematics Teaching Efficacy Control group Experimental group Time M SD M SD Week two of the teaching methods course 3.40 0.47 3.69 0.61 Week 12 of the teaching methods course/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson 3.37 0.67 3.41 0.97 Week 15 of the teaching methods course 3.50 0.56 3.50 0.98 Note 1 = s trongly disagree to 5 = s trongly agree (Jansen, 2007). Table 4 5 Mean differences in data collection points for Mathematics Teaching Efficacy M difference 3 1 SD M difference 2 1 SD M difference 3 2 SD Control group 0.10 0.50 0.03 0.63 0.13 0.14 Experimental group 0.19 0.60 0.28 0.49 0.09 0.41 PAGE 117 117 Table 4 6. Personal Teaching Efficacy Control group Experimental group Time M SD M SD Week two of the teaching methods course 7.32 0.62 7.67 0.61 Week 12 of the teaching methods course/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson 7.00 0.73 7.57 0.72 Week 15 of the teaching methods course 7.03 0.42 7.46 1.04 Note 1 = n othing t o 9 = a great deal of influence (Jansen, 2007). Table 4 7 Mean differences in data collection points for Personal Teaching Efficacy M difference 3 1 SD M difference 2 1 SD M difference 3 2 SD Control group 0.29 0.38 0.32 0.48 0.03 0.55 Experimental group 0.21 0.82 0.10 0.52 0.11 0.52 PAGE 118 118 Table 4 8 Correlations between continuous variables 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1. MTE 1 .80 .74 .43 .48 .59 .33 .20 .16 .36 .39 .11 .39 .11 .44 2. MTE 2 .92 .47 .65 .67 .34 .12 .11 .10 .35 .12 .15 .00 .42 3. MTE 3 .50 .65 .66 .26 .13 .11 .25 .19 .12 .16 .15 .52 4. PME 1 .81 .86 .39 .42 .35 .51 .60 .14 .11 .11 .19 5. PME 2 .84 .27 .20 .22 .68 .60 .26 .09 .07 .03 6. PME 3 .34 .29 .30 .47 .40 .18 .10 .25 .33 7. PTE 1 .74 .63 .01 .24 .44 .26 .13 .33 8. PTE 2 .82 .02 .36 .30 .29 .14 .22 9. PTE 3 .04 .24 .38 .36 .18 .12 10. Pretest math ability .81 .48 .36 .16 .38 11. Posttest math ability .26 .17 .22 .25 12. Age .21 .06 .36 13. GPA .28 .19 14. Time of last math course .31 15. Number of college math courses Note. MTE = Mathematics Teaching Efficacy, PME = Personal Mathematics Efficacy, and PTE = Personal Teaching Efficacy. PAGE 119 119 Table 4 9 Correlations between continuous and dichotomous variables Group Gender Basic HS math course Intermediate HS math course Advanced HS math course Basic College math course Intermediate College math course Advanced College math course Grade of an A Grade of an B Grade of an C College math credit in HS 1. MTE 1 .24 .08 .19 .05 .27 .16 .13 .24 .15 .15 .36 .15 2. MTE 2 .02 .02 .23 .06 .32 .24 .15 .31 .09 .38 .57 .43 3. MTE 3 .00 .02 .16 .17 .38 .21 .01 .11 .09 .48 .69 24 4. PME 1 .13 .06 .48 .08 .62 .36 .07 .14 .07 .23 .36 19 5. PME 2 .24 .11 .57 .06 .54 .46 .01 .29 .03 .40 .52 42 6. PME 3 .19 .08 .52 .01 .57 .32 .17 .39 .09 .20 .35 19 7. PTE 1 .27 .44 .52 .18 .35 .12 .05 .02 .32 .26 .04 19 8. PTE 2 .36 .23 .26 .18 .50 .02 .03 .02 .29 .14 .15 .01 9. PTE 3 .23 .27 .26 .07 .37 .02 .13 .13 .22 .13 .09 .16 10. Pretest math ability .32 .12 .19 .02 .18 .22 .06 .20 .09 .21 .36 .53 11. Posttest math ability .02 .02 .23 .07 .33 .30 .01 .19 .06 .17 .14 .45 12. Age .43 .32 .04 .03 .01 .11 .13 .08 .02 .26 .34 .43 13. GPA .32 .10 .14 .06 .08 .26 .17 .04 .57 .28 .31 .02 14. Time of last math course .33 .29 .00 .12 .15 .16 .06 .03 .07 .00 .09 .31 15. Number of college math courses .07 .13 .08 .14 .24 .11 .18 .13 .16 .13 .01 .24 Note Group was coded as control (0) or experimental (1), gender was coded as male (0) or female (1), grade received in most recent college mathematics course was coded as not the grade received (0) or grade received (1) completing a mathematics courses in high school for college credit was coded as not completed (0) or completed (1), and the types of mathematics courses were coded as not completed (0) or completed (1) PAGE 120 120 Tab le 4 10. Independent samples t test for continuous antecedent variables M difference SE difference t p Age 1.01 0.52 1.97 .66 GPA 0.18 0.13 1.39 .18 Time of last math course 0.63 0.44 1.43 .17 Number of college math courses 0.17 0.56 0.30 .77 Table 4 11. Chi square for categorical antecedent variables X 2 p Gender 2.03 .15 Basic HS math course 0.42 .52 Intermediate HS math course 0.69 .41 Advanced HS math course 0.10 .75 Basic College math course 2.29 .13 Intermediate College math course 0.80 .37 Advanced College math course 0.01 .94 Grade of an A 1.38 .24 Grade of an B 0.02 .88 Grade of an C 2.34 .13 College math credit in HS 1.38 .24 Note Gender was coded as male (0) or female (1), types of mathematics courses were coded as not completed (0) or completed (1), grade received in most recent college mathematics course was coded as not the grade received (0) or grade received (1) and completing a mathematics courses in high school for college credit was coded as n ot completed (0) or completed (1) Table 4 12 ANCOVA summary SS df MS F p p 2 Group 221.00 1 221.00 5.36 .03 25 Error 660.21 16 41.26 Table 4 13 Adjusted posttest Mathematics Ability means M SE Control group 40.25 2.72 Experimental group 47.99 1.81 Table 4 14 MANOVA Personal Mathematics Efficacy Hotell Trace df F p Personal Mathematics Efficacy .02 2 0.15 .86 PAGE 121 121 Table 4 15 MANOVA Mathematics Teaching Efficacy Hotell Trace df F p Mathematics Teaching Efficacy .06 2 0.50 .61 Table 4 16 M ANOVA Personal Teaching Efficacy Hotell Trace df F p Personal Teaching Efficacy .06 2 0.49 .62 PAGE 122 122 Figure 4 M athematics A bility scores Figure 4 M athematics A bility scores PAGE 123 123 Figure 4 M athematics A bility scores Figure 4 Ma thematics A bility scores PAGE 124 124 Figure 4 P ersonal M athematics E fficacy scores week two of the teaching methods course PAGE 125 125 Figure 4 P ersonal M athematics E fficacy scores week 12 of the teaching methods course/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson PAGE 126 126 Figure 4 P ersonal M athematics E fficacy scores week 15 of the teaching methods course PAGE 127 127 Fig ure 4 P ersonal M athematics E fficacy scores week two of the teaching methods course PAGE 128 128 Figure 4 P ersonal M athematics E fficacy scores week 12 of the teaching methods co urse/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson PAGE 129 129 Figure 4 P ersonal M athematics E fficacy scores week 15 of the teaching methods course Figure 4 11. Personal M athematics E fficacy 3.52 3.67 3.67 3.39 3.46 3.5 1 1.5 2 2.5 3 3.5 4 Week two of the teaching methods course After the treatment group delivered their first mathematics enhanced lesson or week 12 Week 15 of the teaching methods course Personal Mathematics Efficacy Control group Experimental group PAGE 130 130 Figure 4 Mathematics T eaching E fficacy scores week two of the teaching methods course PAGE 131 131 Figure 4 Mathematics T eaching E fficacy scores week 12 of the teaching methods course/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson PAGE 132 132 Figure 4 Mathematics T eaching E fficacy scores week 15 of the teaching methods course Figure 4 Mathematics T eaching E fficacy scores week two of the teaching methods course PAGE 133 133 Figure 4 Mathematics T eaching E fficacy scor es week 12 of the teaching methods course/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson PAGE 134 134 Figure 4 Mathematics T eaching E fficacy scores week 15 of the teaching methods course Figure 4 18 Mathematics Teaching E fficacy 3.4 3.37 3.5 3.69 3.41 3.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Week two of the teaching methods course After the treatment group delivered their first mathematics enhanced lesson or week 12 Week 15 of the teaching methods course Mathematics Teaching Efficacy Control group Experimental group PAGE 135 135 Figure 4 P ersonal Teaching E fficacy scores week two of the teaching methods course PAGE 136 136 Figure 4 P ersonal Teaching E fficacy scores week 12 of the teaching methods course/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson PAGE 137 137 Figure 4 P ersonal Teaching E fficacy s cores week 15 of the teaching methods course Figure 4 P ersonal Teaching E fficacy scores week two of the teaching methods course PAGE 138 138 Figure 4 P ersonal Teaching E ffic acy scores week 12 of the teaching methods course/a fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson PAGE 139 139 Figure 4 P ersonal Teaching E fficacy scores week 15 of the teaching methods course Figure 4 25. P ersonal Teaching E fficacy 7.32 7 7.03 7.67 7.57 7.46 1 2 3 4 5 6 7 8 9 Week two of the teaching methods course After the treatment group delivered their first mathematics enhanced lesson or week 12 Week 15 of the teaching methods course Personal Teaching Efficacy Control group Experimental group PAGE 140 140 CHAPTER 5 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS T he purpose of this study was to determine the effects of mathematics teaching and integration strategies (MTIS) on preservice ag ricultural ability, personal mathematics efficacy, mathematics teaching efficacy, and personal teaching efficacy in a teaching methods course The independent variable in this study was the MTIS treatment. Dependent variables includ e d mathematics ability, personal mathematics efficacy, mathematics teaching efficacy, and personal teaching efficacy of the preservice agricultural education teachers. T o account for differences in prior mathematics knowledge pretest mathematics ability scores were used as a covariate The following research objectives and hypotheses guided this study. Objectives T his study was framed by four objectives. 1. Determine the effects of mathematics teaching and integration strategies in the teaching methods course on mathematics ability. 2. Determine the effects of mathematics teaching and integration strategies in the teaching methods course on personal mathematics efficacy. 3. Determine the effects of mathematics teaching and integrati on strategies in the teaching methods course on mathematics teaching efficacy. 4. Determine the effects of mathematics teaching and integration strategies in the teaching methods course on personal teaching efficacy. Hypotheses The research questions were fra med as null hypotheses for statistical analysis, and the significance level of .05 was determined a priori H 01 There is no significant difference in the mathematics ability of preservice agricultural education teachers based upon the mathematics teac hing and integration strategies treatment PAGE 141 141 H 02 There is no significant difference in the personal mathematics efficacy of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment H 03 There i s no significant difference in the mathematics teaching efficacy of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment. H 04 There is no significant difference in the personal teaching efficacy of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment. Methodology This research was quasi experimental and utilized a nonequivalent control group design (Campbell & Stanley, 1963) This design was utilized because random assignment of subjects was not possible due to the fact that the subjects under investigation self registered for a teaching methods lab section that best fit their schedule of classes. The t reatment utilized in th is study was assigned to the teaching methods lab sections randomly. The treatment group was administered the MTIS treatment, which added the following three elements to the teaching methods lab : (a) a lecture on the seven components of a math enhanced le sson, (b) random assignment of the NCTM sub standards among the preservice teachers, and (c) requiring two of the micro teaching lessons to be math enhanced. T he control group received the same instruction in the ir teaching methods lab except for the afor ementioned elements that constituted the MTIS treatment. The target population for this study was Florida preservice agricultural education teachers. The accessible population for this study was present undergraduate and graduate students in their fin al year of the agricultural teacher education program at the University of Florida For this study, the accessible population was a convenience sample which was conceptualized as a slice in time (Oliver & Hinkle, 1981). The PAGE 142 142 sample consisted of preservic e teachers enrolled in AEC 4200 Teaching Methods in Agricultural Education during the Fall 2011 semester ( n = 19). The data collection period of this study was during the Fall 2011 academic semester. Data were collected from preservice agricultural teachers during the ir final year of an agricultural teacher education program at the University of Florida Two instruments, t he Mathematics Ability Test Mathematics Enhancement Teaching Efficacy Instrument were utilized. The Mathema tics Ability Test took the participants approximately 60 minutes to complete and was administered twice : (a ) week two of the Fall 2011 semester; and (b ) week 16 or the last week of the Fall 2011 semester The Mathematics Enhancement Teaching Efficacy Inst rument took the participants approximately 8 minutes to complete and was administered three times : (a ) week two of the Fall 2011 semester ; (b ) week 12 of the Fall 2011 semester / after the preservice teachers in the treatment group delivered their first math ematics enhanced lesson ; and (c ) week 15 of the Fall 2011 semester Additionally, the researcher and a mathematics expert individually score d the Mathematics Ability Test and items were scored incorrect, partially correct (students set the problem up correctly but made a calculation error), or correct. T he scorer s used a rubric that was developed by two secondary mathematics experts to score each item. Inter rater relia bility was assessed Data were analyzed using SPSS version 1 7 for Windows TM Frequencies, m eans and standard deviations were calculated to summarize demographics, mathematics teaching efficacy, personal mathematics efficacy, personal teaching efficacy, and mathematics ability of the preservice agricultural education teachers PAGE 143 143 MANOVAs were used to determine if significant differences existed in mathematics teaching efficacy, personal ma thematics efficacy, and personal teaching efficacy based upon the MTIS treatment. ANCOVA was also used to determine if significant differences existed in mathematics ability based upon the MTIS treatment. Summary of Findings The findings of this study wer e structured based on the objectives and hypothesis that guided this research. Descriptive Statistics of Variables in this Study Mathematics ability week two to week 16 of the teaching methods course. The ir average week two of the teaching methods course was 45 51% ( SD = 9.32 ) and their average week 16 of the teaching methods course was 45.19% ( SD = 11 26 ) mathematics ability mean decreased 0.3 2% from week two of the teaching methods course to week 16 of the teaching methods course. In addition, the ranges of scores were very similar. T he pretest scores ranged from 30.77 % to 57.69 % and the posttest scores ranged from 30.77 % to 59.62 %. The e week two of the teaching methods course to week 16 of the teaching methods course. Their pretest average was 38.31% ( SD = 11.03 ) and the ir posttest average was 45.71% ( SD = 11 69 ) This increase in scores can also be seen in the range of scores week two and week 16 of the teaching methods course. The pretest scores ranged from 23. 08 % to 59.62 % and the posttest scores ranged from 36.54 % to 69.23 %. PAGE 144 144 Personal mathematics efficac y Personal mathematics efficacy was measured on a four point scale: 1 = n ot at all confident to 4 = v ery confident (Jansen, 2007). T he mathematics efficacy scores increased from week two to week 15 of the teaching methods course. The week two teaching methods course average was 3.52 ( SD = 0.43 ) A fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson (week 12 of the teaching methods course ) the control personal mathematics efficacy mean increased to 3.67 ( SD = 0.49 ) Week 15 of the teaching methods course mean (3.67, SD = 0.67 ) was identical to the previous data collection point, but was higher than the initial personal mathematics efficacy mean The scores increased at each data collection point. The week two teaching methods course average was 3.39 ( SD = 0.49 ) A fter delivering their first mathemat ics enhanced lesson (week 12 of the teaching methods course ) the personal mathematics efficacy mean increased to 3.46 ( SD = 0.37 ) Week 15 of the teaching methods course the mean in creased to 3 .50 ( SD = 0.44 ) were as follows: (a) data collection points three minus one was 0.15 ( SD = 0.09); (b) data collection points two minus one was 0.15 ( SD = 0.20); and (c) data collection points three minus two was 0.00 ( SD = 0.21). Mean differences in the experimental PAGE 145 145 three minus one was 0.11 ( SD = 0.28); (b) data collection points two minus one was 0.07 ( SD = .31); and (c) data collection points three minus two was 0.04 ( SD = 0.25). Mathematics t eaching e fficacy Mathematics teaching efficacy was measured on a five point scale: 1 = strongly disagree to 5 = s trongly agree (Jansen, 2007). T he teaching efficacy scores week two of the teaching methods course averaged 3.40 ( SD = 0.47 ) A fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson (week 12 of the teac hing methods course ) the control mathematics teaching efficacy mean decreased to 3.37 ( SD = 0.67 ) From the previous data collection point to week 15 of the teaching methods course, the control mean increased to 3.50 ( SD = 0.56 ) which is also higher than the initial mathematics teaching efficacy mean The scores week two of the teaching methods course averaged 3.69 ( SD = 0.61 ) A fter delivering their fir st mathematics enhanced lesson (week 12 of the teaching methods course ) the mathematics teaching efficacy mean decreased to 3.41 ( SD = 0.97 ) Then, week 15 of mathematics teaching efficacy mean was 3.50 ( SD = 0.98 ) Therefore, the week 15 teaching methods course mean was lower than the initial mathematics teaching efficacy mean as follows: (a) data collection points three minus one was 0.10 ( SD = 0.50); (b) data collection points two minus one was 0.03 ( SD = 0.63); and (c) data collection points three minus two was 0.13 ( SD PAGE 146 146 mathematics tea ching efficacy scores were as follows: (a) data collection points three minus one was 0.19 ( SD = 0.60); (b) data collection points two minus one was 0.28 ( SD = 0.49); and (c) data collection points three minus two was 0.09 ( SD = 0.41). Personal tea ching e fficacy Personal teaching efficacy was measured on a nine point scale: 1 = n othing to 9 = a great deal of influence (Jansen, 2007). T he scores week two of the teaching methods course averaged 7.32 ( SD = 0. 62 ) A fter the preservice teachers in the treatment group delivered their first mathematics enhanced lesson (week 12 of the teaching methods course ) personal teaching efficacy scores averaged 7.00 ( SD = 0.73 ) Week 15 of the teaching methods course ( SD = 0.42 ). Thus, personal mathematics efficacy decreased from week two to week 15 of the teaching methods course. The scores decreased at each data collection point. The week two teaching methods course average was 7.67 ( SD = 0.61 ) A fter delivering their first mathematics enhanced lesson (week 12 of the teaching methods c ourse ) the personal teaching efficacy scores averaged 7.57 ( SD = 0.72 ) Week 15 of the teaching methods course personal teaching efficacy scores averaged 7.46 ( SD = 1.04 ). Mean differences in the control g follows: (a) data collection points three minus one was 0.29 ( SD = 0.38); (b) data collection points two minus one was 0.32 ( SD = 0.48); and (c) data collection points three minus two was 0.03 ( SD personal teaching efficacy scores were as follows: (a) data collection points three minus PAGE 147 147 one was 0.21 ( SD = 0.82); (b) data collection points two minus one was 0.10 ( SD = .52); and (c) data collec tion points three minus two was 0.11 ( SD = 0.52). Hypothesis One This hypothesis was that t here is no significant difference in the mathematics ability of preservice agricultural education teachers based upon the MTIS treatment The ANCOVA procedure revealed a significant difference in mathematics ability scores, F (1, 16) = 5.36, p < .05 ( Table 4 5 p. 116 ) mean score ( M = 40.25, SE = 2.72) was significantly lower than the experimental sttest mean ( M = 47.99, SE = 1.81). The practical significance of the difference was assessed using a partial eta squared, and the effect size was .25, which is a large effect Based on the statistically significant difference in adjusted posttest mean a nd the large effect size, the null hypothesis was rejected. Hypothesis Two This hypothesis was that there is no significant difference in the personal mathematics efficacy of preservice agricultural education teachers based upon the MTIS treatment This hypothesis was tested using a MANOVA and the analysis did not reveal a significant difference in personal mathematics efficacy T = .02, F ( 2 1 6 ) = 0.15 p > .05 Therefore, the researcher failed to reject the null hypothesis. Hypothesis Three Thi s hypothesis was that there is no significant difference in the mathematics teaching efficacy of preservice agricultural education teachers before and after MTIS This hypothesis was tested using a M ANOVA, and the analysis did not reveal a significant dif ference in mathematics teaching efficacy T = .06, F ( 2 1 6 ) = 0.50 p > .05 Therefore, the researcher failed to reject the null hypothesis. PAGE 148 148 Hypothesis Four This hypothesis was that there is no significant difference in the personal teaching efficacy o f preservice agricultural education teachers before and after MTIS This hypothesis was tested using a M ANOVA, and the analysis did not reveal a significant difference in personal teaching efficacy T = .06, F ( 2 1 6 ) = 0.49 p > .05 Therefore, the researcher failed to reject the null hypothesis. Conclusions The sample used in this study was not randomly drawn from the population. With this limitation in mind and based on the findings of this study, the following conclusions were drawn: 1. The MTIS treatment had a positive effect on the mathematics ability scores of the participants. 2. The MTIS treatment did not have an effect on the personal mathematics efficacy scores of the participants. 3. The MTIS treatment did not have an effect on the mathematics teaching efficacy scores of the participants. 4. The MTIS treatment did not have an effect on the personal teaching efficacy scores of the participants. Discussion and Implications Hypothesis Related to Mathematics Ability H 01 There is no s ignificant difference in the mathematics ability of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment The null hypothesis was rejected. Conclusion: The MTIS treatment had a positive effec t on the mathematics ability scores of the participants. To that end, the MTIS treatment had a large effect ( p 2 PAGE 149 149 consistent with Stripling and Roberts ( 2012a ) who reported that a math enhanced agricultural teaching methods course significantly increased the mathematics ability scores of preservice agricultural education teachers at the University of Florida. Further, this finding is consistent with Burton, Daa ne, and Gieson (2008) who also found that the incorporation of mathematics into a teaching methods course positively affected mathematics content knowledge of preservice teachers and Berry (2005) who stated that research proven instructional strategies in mathematics and literacy make a difference in student achievement as teacher educators incorporate the strategies into the teacher education program. In addition, the results and micro teaching utilized in this study support Pascarella and Terenzini (200 5) which stated that peer interaction Thus, the findings of this study suggests that micro teaching that utilizes the seven components of a math enhanced lesson (Stone et al., 2006) can be an appropriate means to improve the mathematics ability of preservice agricultural education teachers. T he results of this study also which purports that cognitive skills can be social ly cultivated and that environment and behavior influences personal factors In this study, the results suggests that the environment or the math enhanced teaching methods course and the behaviors of developing math enhanced lessons teaching those lessons to peers and roleplaying as secondary students within the teaching methods course positively influences the personal factor of mathematics ability T his may also support Bandura assert ion that PAGE 150 150 The d escriptive statistics indicated that the treatment had a leveling effect on the mathematics ability of the preservice teachers enrolled in the teaching methods course. Week two of the teaching methods course the experimental group s pretest mathematics ability scores were ability scores By w eek 16 of the teaching methods cour se the experimental and the ost test mathematics ability scores were within a few tenths of a percentage point This may suggest that the MTIS treatment is effective at providing some remediation to preservice teachers with lower mathemat ics ability scores. Hypothesis Related to Personal Mathematics Efficacy H 02 There is no significant difference in the personal mathematics efficacy of preservice agricultural education teachers based upon the mathematics teaching and integration strategies treatment The null hypothesis was retained. Conclusion : The MTIS treatment did not have an effect on the personal mathematics efficacy scores of the participants. This findi ng is consistent with Stripling and Roberts ( 2012a ) Stripling and Roberts reported that preservice teachers enrolled in the fall 2010 agricultural teaching methods course at the University of Florida were confident in their mathematics ability before and after a math enhanced agricultural teaching methods course. suggest that confidence in personal mathematics efficacy should positively influence the behavior of teaching contextualized mathematics. Then aga cognitive theory would also suggest that low mathematics ability should negatively influence Thus, there is a disconnect between personal mathematics efficacy and mathematics ability among the preservice teachers. One explanation may be that even after the MTIS treatment the preservice teachers are PAGE 151 151 ill informed of the level of mathematics present in the secondary agricultu ral education standards. Understanding this disconnect is important because personal mathematics which Darling Hammond and Bransford (2005) would call subject matter kno wledge. According to Darling Hammond and Bransford s ubject matter knowledge is an essential type of knowledge for effective teaching. E ven though there is a disconnect between personal mathematics efficacy and the prese the researcher finds the mathematical confidence encouraging because the MTIS did not negatively affect the personal mathematics efficacy of the preservice teachers. Theoretically and based on previous research the fact that the preservice teachers were confident in their personal mathematics efficacy before and after the MTIS treatment s hould positively impact (a) their motivation (Bandura, 1997), which in the context of this study is motivation for teaching contextualized mathematics ; (b) the effort put forth in designing learning activities (Allinder, 1994) or math enhanced lesson s (c) the challenges encountered in the learning environment (Goddard, Hoy, & Woolfolk Hoy, 2004), which in this study would be related to teaching contextualized mathematics (d) and the acquisition of knowledge (Bandura, 1997) related to mathematics. The MTIS treatment did not improve the personal mathematics efficacy scores of the preservice teache rs; however, the treatment did not negatively affect personal mathematics efficacy. This is encouraging given the fact that the treatment had a positive effect on the mathematics ability scores of the preservice teachers. PAGE 152 152 Hypothesis Related to Mathematics Teaching Efficacy H 03 There is no significant difference in the mathematics teaching efficacy of preservice agricultural education teachers before and after mathematics teaching and integration strategies The null hypothesis was retaine d. Conclusion: The MTIS treatment did not have an effect on the mathematics teaching efficacy scores of the participants. The aforementioned conclusion related to mathematics teaching efficacy is consistent with Stripling and Roberts ( 2012a ) Stripling and Roberts reported that preservice teachers enrolled in the fall 2010 agricultural teaching methods course at the University of Florida were moderately efficacious in mathematics teaching efficacy before and after a math enhanced agricultura l teaching methods course. The MTIS treatment did not improve the mathematics teaching efficacy scores of the preservice teachers, but then again the treatment did not negatively a ffect mathematics teaching efficacy. Th e fact that the preservice teacher s were moderately efficacious is encouraging perceptions of their ability to teach mathematics or pedagogical content knowledge, which according to Darling Hammond and Bransford (2005) is an essential type of knowledge for teaching. This fact is also encouraging because a (1986) social cognitive theory personal factors influence behavior and the environment. Therefore, in the context of this study, mathema tics teaching efficacy should positively impact the teacher education program, the agricultural teaching methods course, and the teaching of contextualized mathematics. On the other hand, the preservice teachers were only moderately efficacious and were n ot fully confident in the ability to teach contextualized mathematics. PAGE 153 153 Hypothesis Related to Personal Teaching Efficacy H 04 There is no significant difference in the personal teaching efficacy of preservice agricultural education teachers before and a fter mathematics teaching and integration strategies The null hypothesis was retained. Conclusion: The MTIS treatment did not have an effect on the personal teaching efficacy scores of the participants. The MTIS treatment did not improve the personal teaching efficacy of the preservice teachers, but conversely the treatment did not negatively affect personal teaching efficacy. This finding is consistent with Stripling and Roberts ( 2012a ) Stripling and Roberts reported that preservice teachers enrolled in the fall 2010 agricultural teaching methods course at the University of Florida perceived themselves has having Quite a Bit of influence in affecting student learning before and after a math enhanced a gricultural teaching methods course. states that personal factors influence behavior and the environment. I n the context of this study, personal teaching efficacy should positively impact the teacher education pr ogram, the agricultural teaching methods course, and the teaching To that end, the researcher is encouraged because the preservice teachers were efficacious and the treatment did not negatively impact personal teaching efficacy whic h is a measure of the preservice or pedagogical knowledge A ccording to Darling Hammond and Bransford (2005) pedagogical knowledge is essential for teaching However the preservice teachers were not fully confident in the ability to teach and guide student learning. PAGE 154 154 Recommendations for Teacher Education Based on the findings of this study, the following recommendations were made for agricultural teacher education : 1. The MTIS treatment should be cons idered for use in an agricultural teaching methods course to increase the mathematics ability of preservice agricultural teachers. 2. Agricultural educators should consider integrating content related to mathematics and mathematics instruction into teacher education courses. Recommendations for Future Research Based upon the findings of this study, the following recommendations for further research were made: 1. Due to the limited scope of this study replication that utilizes preservice teachers fr om other teacher education programs should be conducted to further validate the effectiveness of the MTIS treatment in increasing the mathematics ability of preservice teachers 2. A major component of the treatment of this study was the preparation of math enhanced lessons by the preservice teachers, micro teaching s of math enhanced lessons delivered by the preservice teachers, and the preservice teachers role playing as secondary students during the micro teachings. To that end, i s the value of this c omponent of the treatment in the preservice teachers preparing the lessons, teaching the lessons, participating as students in the lessons, or a combination of t hese activities? Future research should fur ther investigate the effects of preparing math enha nced lessons teaching math enhanced lessons, and participating in micro teachings of math enhanced lessons efficacy, mathematics teaching efficacy, and personal teaching efficacy. 3. Consis tent with prior research, the preservice teachers in this study were not proficient in mathematics but were confident in the ir mathematics ability. Therefore, t here is a mathematics efficacy and mathema tics ability. Future research should inquire into this disconnect. 4. Consistent with prior research, the preservice teachers in thi s study were moderately efficacious in mathematics teaching efficacy Future research should seek to improve mathematics tea ching efficacy. PAGE 155 155 5. Future research should seek to determine if the use of the MTIS treatment in an agricultural teaching methods course impact s the teaching of mathematics in the secondary agricultural classes of the preservice teachers after graduation 6. Fu ture r esearch should seek to determine if mathematics can be effectively and efficiently integrated into other agricultural teacher education courses 7. Future r esearch is warranted to investigate why preservice teachers have such low mathematics ability. 8. Future research should seek to determine the effects of having an expert in contextualized mathematics deliver instruction to preservice teachers on the teaching of contextualized mathematics. Reflections Upon completion of this study, the researcher reflected on the process and the application of this work. Self efficacy is a social construct by nature (Bandura, 1997). In this study, self efficacy of the preservice teachers may have been i nfluenced by the other preservice teachers in the agricultural teaching methods course This may explain why the preservice teachers were efficacious in personal mathematics efficacy and moderately efficacious in mathematics teaching efficacy when their m athematics ability scores suggest ed otherwise. The social nature of self efficacy may have led the preservice teachers to believe that they were as competent in mathematics and the teaching of contextualized mathematics as their peers resulting in the di sconnect between efficacy scores and mathematics ability scores. Potential implications of a false sense of self efficacy are (a) the preservice teachers may not f e el a need to improv e their mathematics ability and their teaching of contextualized mathema tics, (b) the disconnect between ability and efficacy may negatively impact the mathematics achievement of the future secondary students as a result of being ill prepared in mathematics and for the teaching of contextualized mathematic s within the agricultural PAGE 156 156 education curricula and (c) a false sense of self efficacy may negatively influence the social learning environment of the agricultural teaching methods course and the teacher education program. Furthermore, a philosophi cal discussion that should take place with in agricultural teacher education is how to best prepare preservice teachers for me eting the demands of teaching a subject that contributes to the STEM disciplines. How should the profession ensure that beginning agricultural education teachers are prepared to make a meaningful contribution? With the aforementioned question in mind, Myers and Dyer (2004) discovered a gap in the literature on how agricultural teacher education programs should prepare preservice tea chers to meet the academic demands of agriscience teaching A gricultural teacher education programs are limited in the number of credit hours available in a program of study for agricultural teacher preparation. So, i s the incorporation of STEM content such as the teaching of contextualized mathematics and science into agricultural teacher education coursework appropriate or the best way to prepare preservice teachers for teaching STEM related subject matter? If so, what information or content will be removed from current teacher education courses to allow for the incorporation of STEM content? Regardless of the answer to the aforementioned question, t he author believes the incorporation of STEM content is appropriate because of the nature of agricultu re Agriculture is an applied science. For that reason, the author believes that the incorporation of STEM content is essential for developing the pedagogical content knowledge of preservice teachers. Research in teacher education has shown that the sub ject matters specific PAGE 157 157 Hammond, 2006, p. 82). Thus, generic pedagogy alone does not fully prepare preservice agric ultural education teachers for teaching the science of agriculture ; therefore, there is a need for teaching methods to be taught within the context of the subject (Darling Hammond, 2006). As the role of the secondary agricultural teacher has changed from vocational education to career and technical education that emphasize core academics and seeks to creat e informed citizens (Phipps, Osborne, Dyer, and Ball, 2008), agricultural teacher education programs must also change to meet the demands of the changing role of the secondary agricultural education teacher. However, are the current cross referenced N ational C ouncil of T eachers of M athematics ( NCTM ) sub standards appropriate for secondary agricultural education? The author believes the NCTM sub standard s are appropriate for secondary agricultural education. The NCTM sub standards require the teaching of basic and intermediate mathematics such as algebra, geometry, and basic statistics which are embedded with in essential agricultural skills needed for agricultural careers and college preparation. The author believes that l owering the mathematics standards for secondary agricultural education would prevent the profession from answering the numerous calls for agr icultural education to support core academics and the STEM disciplines. Additionally, the author holds the view that mathematics is fundamental to science, and research has shown that mathematics teaching is associated with increases in science achievemen t (Phipps et al., 2008). Thus, lowering the secondary mathematics standards may have a negative effect on science achievement of secondary students. PAGE 158 158 As a result of this study, t he author plans to continue a similar line of inquiry for at least the next five years. This line of inquiry will have an overarching goal of p reparing p reservice agricultural t eachers to t each m athematics found naturally within the a gricultural e ducation c urricula This research will focus on four primary teacher education variables: (a) preservice teachers, (b) teacher educators, (c) cooperating teachers, and (d) curriculum/instruction. The anticipated outcomes/impacts are (a) i mproved mathematics content knowledge of preservice agricultural education teachers, (b) i mprov ed mathematics pedagogical content knowledge of preservice agricultural education teachers, (c) preservice agricultural education teachers that are proficient in teaching contextualized mathematics (d) e fficient and effective math enhanced teacher educati on courses (e) e ffective secondary agricultural education mathematics instruction and (f) secondary agricultural education students that are better prepared for a griculture, f ood, and n atural r esources careers In addition t he author hopes this study will shed light on the issue of preparing preservice agricultural teachers for their evolving role within the larger context of American education. Moreover the author hopes the results of this study will spur the philosophical discussion described above and the products of the discussion will be (a) improved agric ultural teacher education programs, (b) secondary agricultural education students prepared for scientific careers, (c) an agricultural workforce prepared for the challenges of the 21 st century, and (d) an agricultural education profession that contributes to a growing and vibrant democracy. PAGE 159 159 APPENDIX A TREATMENT M ATERIALS Lecture Outline Title: Teaching Mathematics Found Naturally in Agriculture Course: AEC 4200 Teaching Methods in Agricultural Education Essential Questions : 1. How do we teach contextualized mathematics? 2. What are the 7 elements of a math enhanced les son? 3. What are the cross referenced NCTM standards? Discuss the 7 Elements of a Math Enhanced Lesson Discuss the example math enhanced lesson plan Ask for q uestions related to the seven elements and the example lesson plan Discuss micro teachings: Lab 6: Video and Cooperative Learning Math Enhanced Lesson Lab 8: Demonstration and Individualized Instruction Math Enhanced Lesson Discuss cross referenced NCTM Standards Ask for q uestions related to the cross referenced NCTM standards Essential Questions /Re view: 1. How do we teach contextualized mathematics? 2. What are the 7 elements of a math enhanced lesson? 3. What are the cross referenced NCTM standards? PAGE 160 160 Table A 1. Example Seven Elements of a Math enhanced Lesson Daily Plan Instructor: Mr. Stripling Lesson Title: Got Feed? Unit Title: Animal Nutrition Course: Animal Science Estimated Time: 50 minutes Materials, Supplies, Equipment, References, and Other Resources: Cattle feed Calculators Optional: Oats Corn Cottonseed Hull Whole Cottonseed Soybean Wheat Student Performance Standards (SPSs): Sunshine State Standards: 02.02 02.03 02.04 SC.912.P.8.7 SC.912.P.8.8 SC.912.P.8.9 Daily Objectives 1 SWBAT identify feedstuff commonly found in feed rations using no references with 100% accuracy. 2. SWBAT determine the percentages of each ingredient in a feed ration using no references with 100% accuracy. PAGE 161 161 Table A 1. Continued Preflection/Introduction (Interest Approach) Estimated Time: 1. Introduce the CTE Lesson. Lead the student through the following adventure: Close your eyes and imagine you are in a feed store...you are riding a forklift...oh no...you just poked a hole in a bag of cow feed. You notice that the feed has corn in it...okay look harder...what els e do you see...maybe oats, rye,...Now you are thinking that you could make cow feed, but first you realize you need to calculate the percentages of each ingredient. How are you going to do this? Okay open your eyes. as it relates to the CTE lesson. Show me what you know E moment If 50 pounds of feed contains 30 pounds of corn, 10 pounds of oats, and 10 pounds of other ingredients. What percentage of corn is in the feed ration? Take up show me what you know activity Briefly glance at them while students are working on learning activity one to gain Learning Activity 1 Estimated Time: Instructor Directions / Materials Brief Content Outline Show students examples of different feedstuff found within a feed mix. Then allow the students to find as many feed ingredients as possible in a small feed sample. Next have the students tape and label the feed ingredients on a sheet of paper in their agrisc ience notebooks. List of commonly found ingredients: Oats Corn Cottonseed Hull Whole Cottonseed Soybean Wheat PAGE 162 162 Table A 1. Continued Learning Activity 2 Estimated Time: Instructor Directions / Materials Brief Content Outline 3. Work through the math example embedded in the CTE lesson. Demonstrate how to solve feed example from preflection. 4. Work through related, contextual math in CTE examples. 5. Work through traditional math examples. (30 pounds of corn/50 pounds of feed)*100 = 60% If a farmer plants 25 acres of a 30 acre field, what percentage of the field did he plant? (25 acres/30 acres)*100 = 83.34% Write each ratio as a percent. 1. 4/6 2. 2/7 3. 31/100 4. 3/10 5. 1/25 PAGE 163 163 Table A 1. Continued Summary (Reflection) Estimated Time: Ticket out the door: Were you able to successfully calculate and mix one pound of feed today? If you were successful, describe the process/step you took to accomplish the task. If you were not successful, what prevented you from being successful (i.e. calculating percentages, identifying feedstuff)? What must you do to overcome these barriers to success? Learning Activity 3 Estimated Time: Instructor Directions / Materials Brief Content Outline 6. Students demonstrate their understanding. Students will calculate and mix one pound of feed See lab worksheet Mixing Cattle Feed. Evaluation 7. Formal assessment. assessed on a quiz and a unit test. On these assessments, students will identify feedstuff and work related math examples in an agricultural and traditional context. PAGE 164 164 Table A 2. Cross referenced NCTM Sub standards for Grades 9 12 and Example Topics Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Number & Operations 1A. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Development of the number systems: from whole numbers to integers to rational numbers to real and complex numbers Understanding of very large and small numbers Reading a ruler/tape measure Scientific notation o pH o bacteria colonies Any agricultural problem that utilizes at least two different forms of numbers (i.e., whole numbers, fractions, 1B. Understand meanings of operations and how they relate to one another. Judging the effects of multiplication, division, and computing powers and roots Understanding of permutations and combinations Understanding of vectors and matrices Genetics Combinations and/or placement of flowers in a flower bed Combinations and/or placement of open and closed switches on an electrical circuit Determining the length of one side of a triangular r ose garden based on the other two sides and the desired square footage Investments PAGE 165 165 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Any agricultural problem involving square roots such as enclosing an elliptical flower bed 1C. Compute fluently and make reasonable estimates. Fluency in operations with real numbers, vectors, and matrices Deciding if a problem calls for a rough estimate, an approximation, or an exact answer Judging the reasonable ness of numerical computations and their results Mixing fertilizer Farm equipment depreciation Estimating tree heights Determining basal area Using speed, torque and power measurements to improve efficiency in power transmission systems Agricultural mechanics project bids or estimation of materials Any agricultural problem that involves conversions PAGE 166 166 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Algebra 2C. Use mathematical models to represent and understand quantitative relationships. Understanding the suitability of linear, quadratic, exponential, and rational functions on the basis of data Drawing reasonable conclusions about a situation being modele d Drug withdrawal in animals Interest rate problems Growth problems such as bacteria growth Exploring relationships between two variables such as plant growth and temperature Using models to calculate a market weight 2D. Analyze change in various contexts. Approximating and interpreting rates of change from graphical and numerical data Determining land classes Constructing forms for concrete Analyzing bivariate graphs such as corn prices and ethanol production Any agricultural problems that involve slope or rate of change PAGE 167 167 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Geometry 3A. Analyze characteristics and properties of two and three dimensional geometric shapes and develop mathematical arguments about geometric relationships. Analyzing properties and determining attributes of two and three dimensional objects Exploring re lationship such as congruence and similarity among two and three dimensional objects and solve problems using them Establishing the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others Using trigonomet ric relationships to determine lengths and angles measures Framing a barn or building Rerouting an underground pipe to avoid tree roots/cutting and repositioning For example, a horticulturalist needs to raise the path of the pipe 23 inches over a distan ce of 86 inches and then continue on a path parallel to the original pipe. What angles should she cut the pipe? Using a blueprint and the scale to determine the dimensions of a swine feeder for construction in an agricultural mechanics lab Determining the perimeter of two triangular fields using angle angle similarity and proportions PAGE 168 168 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Measurement 4A. Understand measurable attributes of objects and the units, systems, and processes of measurement. Making decisions about units and scales that are appropriate for problem situations involving measurement Comparing the sound intensity or decibel levels in an agricultural mechanics shop Safety testing of agricultural machinery (e.i., determining how long it will take a tractor to stop based on deceleration rate and initial velocity) Using weights and measures to formulate and package food products Explaining principles of motion, including speed, velocity and acceleration Evaluating vehicle performance and then servicing as needed, including horsepower management, ballasting, soil compaction and fuel efficiency PAGE 169 169 Table A 2. Continued Content /Process Area NCTM Sub standards Concepts/Processes Example Topics 4B. Apply appropriate techniques, tools, and formulas to determine measurements. Analyzing precision, accuracy, and approximation error in measurement situations Understanding and using formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders Using unit analysis to check measurement computations Determining the volume of a grain bin Determining the area of a field Calculating the protective wrap needed to wrap round bales of hay Calculating the volume of concrete needed for the floor of your greenhouse Calculating board feet Any problem that involves conversions Data Analysis & Probability 5A. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. Understanding the differences among surveys, observational studies, and experiments and which types of inference can legitimately be d rawn from each Knowing the characteristics of well designed studies, including the role of randomization in surveys and experiments Determining how to sample and the needed sample size for various types of agricultural studies Using a parallel box plot t o analyze the calorie content of different types of hot dogs Analyzing a histogram of tilapia feeding rates and growth PAGE 170 170 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Understanding of the meaning of measurement data, categorical data, and the term variable Understanding histograms, parallel box plots, and scatterplots and using them to display data Computing basic statistics and understanding the distinction between a statistic and a parameter Cond uct a field study of an ecosystem, and record and document observations of species interactions Surveying consumer perceptions of lactose free milk Testing the effects of wind on coleus transpiration Randomly sampling peanut butter for quality control a nd food safety purposes Maintain accounting information needed to prepare an income statement, balance sheet and cash flow analysis for an agribusiness Computing mean, median, mode, range, and frequency in various agricultural context PAGE 171 171 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Monitor inventory to maintain optimal levels and calculate costs of carrying input and output inventory of an agribusiness 5B. Select and use appropriate statistical methods to analyze data. Univariate data: Be able to display the distribution, describe its shape, and select and calculate summary statistics Bivariate data: Be able to display a display a scatterplot, descri be its shape, and understand regression coefficients, regression equations, and correlation coefficients Display and discuss bivariate data where at least one variable is categorical Identify trends in bivariate data and find functions that model the data Construct a histogram of birth weights of cattle Using a parallel box plot to analyze the calorie content of different types of hot dogs Analyzing a histogram of tilapia feeding rates and growth Examine the scatterplot of rainfall and erosion and determine the type of function (e.g., linear, exponential, quadratic) that might be a good model for the data Computing mean, median, mode, range, and frequency in various agricultural context PAGE 172 172 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Examine crop yields and nitrogen application rates and determine the type of function (e.g., linear, exponential, quadratic) that might be a good model for the data 5C. Develop and evaluate inferences and predictions that are based on data. Using a model of a data set to make predictions and recognize and explain the limitations of those predictions Constructing sampling distributions Understanding how sample stati stics reflect the values of population parameters and using sampling distributions as the basis for informal inference Conduct natural resource inventories and population studies to assess resource status Interpret and evaluate financial statements, including income statements, balance sheets and cash flow analyses Conducting breakeven analysis for an agribusiness. Interpret agribusiness performance data PAGE 173 173 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Evaluating published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions Predict the consequences of delayed payment of expenses, prepayment of expenses and delayed receipts on a financial statement Recognize how changes in prices of inputs and/or outputs influence the financial statements of an agribusiness Analyze records (e. g., budgets, net worth, assets, liabilities) to improve efficiency a nd profitability of an agribusiness Manage resources to minimize liabilities and maximize profit PAGE 174 174 Table A 2. Continued Content/Process Area NCTM Sub standards Concepts/Processes Example Topics Problem Solving 6B. Solve problems that arise in mathematics in other contexts. Be able to solve mathematics problems in an agricultural context Fertilizer rates Mixing feed rations Use speed, torque and power measurements to improve efficiency in power transmission systems Any agricultural mathematics problem 6C. Apply and adapt a variety of appropriate strategies to solve problems. Formulate and refine problems Solve problems in multiple ways Making connections among various ways of thinking about the same mathematical content Any agricultural mathematics problem PAGE 175 175 APPENDIX B MATHEMATICS ABILITY TEST Instructions: Please write your answers in the space provided. If you need additional space, please use the blank sheets of paper that are attached to the instrument and include the problem number beside your work. 1. Mr. Robinson is converting 935 acres of his farm to timber. Using a calculator, he calculated the number of pine seedlings he would need to plant the 935 acres to be 5.112 x 10 5 Mr. Robinson does not know how to read scientific notation and needs your help. How many pine seedlings does Mr. Robinson need to plant to convert his 935 acres to timber? 2. Lauren wants to purchase liquid fertilizer for her garden. Which fertilizer is cheaper per liter: 0.82 liters of fertilizer for $4.45, 1.27 liters of fertilizer for $6.55, or 1.7 9 liters of fertilizer for 8.95? 3. A rose garden will be planted as a border around two sides of a triangular shaped lawn. Two of the vertices of the triangle have coordinates ( 2, 4) and (3, 5). The landscape designer needs to locate the third vertex so that the area of the lawn is 25 square feet. Find the value of k if the coordinates of the third vertex are (3, k ). All coordinates are represented in feet. PAGE 176 176 4. The figure below represents the arrangement of five different flowers around a flag pole, and the labeled points represent the placement of each flower. How many arrangements of flowers are possible? 5. Jason has a 200 gallon spray tank and needs a mixing rate of 2.3 pounds of wettable powder per 12 gallons of water for the proper application rate. How many pounds of powder should Jason add to the tank? 6. The recommended floor space per broiler chicken is 0.75 square feet. How long would a 40 foot wide house need to be to accommodate a flock of 20,000 chickens? E A B C D PAGE 177 177 7. Luke raised two goats during his senior year as part of his SAE project. He sold the goats before going to college for $132 each and invested the money in a savings account that has a 6% interest rate that is compounded annually. Assuming that he doe years? 8. A local butcher purchased a 400 pound feeder steer. The butcher anticipates the steer to gain 20% of its body weight per month. If the weight after each mon th can be found by the function w(x)= x(1.20) n where x is the initial weight and n is the number of months from now, what will be the weight of the steer 5 months from now? 9. The graph below represents growth verses time for a colony of bacteria grown for an growth each hour not linear or constant? 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Number of bacteria Time Bacterial Growth PAGE 178 178 10. John Doe put a pit scraper in his hog house. Slats are 14 inches above the floor at one end of the bui lding and 26 inches above the floor at the other end of the building (the end where wastes are emptied by the scraper). What is the slope of the floor in percent if the building is 152 ft. long? 11. In the figure below, segment AB is parallel to seg ment DE and segment DF is perpendicular to segment CE. Also, segment AD is a straight line. A rancher wants to fence the perimeter of the fields shown below. Assuming that all of the measurements are in feet, how many feet of fence will the rancher have to purchase? 26 30 104 D E E C A F 96 B PAGE 179 179 12. A barn roof has a 30 degree rise, and the barn is 40 feet wide. How many feet does the roof rise? (Hint: the tangent of 30 degrees is 0.58) 13. In the table below, an agriscience student is measuring the intensity of common sounds in an agricultural mechanics lab. If the student discovers that a welding machine produces a sound of 70 decibels and a table saw produces a sound of 110 decibels, how many times greater is the sound intensity of the table saw than the welding machine? Decibels 70 80 90 100 110 120 130 140 Sound intensity in newtons per m 2 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 14. If a tractor has an initial speed of 5 mph and a constant acceleration of 1 mph/s 2 how long will it take for the tractor to cross a pond dam that is 164 feet long? The following formulas may be helpful: d(t) = v i t + 1/2at 2 and PAGE 180 180 15. An agribusiness that is located on the border of the United States and Canada is trying to cut fuel cost. On average, the agribusiness purchases 5,000 gallons of fuel per month. The current price of fuel in Canada is Can$1.50 a liter (Can$ stands fo r Canadian dollars). The current exchange rate is Can$1.49 for each US$1.00 (US$ stands for United States dollar). The current price of fuel in the United States is US$2.97 a gallon. In which country is fuel cheaper? If the agribusiness bought fuel fro m the cheaper source, how much money (in United States dollars) would the agribusiness save in one month? 1 gallon = 3.785 liters 16. Sarah just purchased a farm. The figure below is a diagram of a grain bin that is on the farm Sarah purchased. Sarah would like to know the volume of the grain bin. Help Sarah determine the volume of the grain bin. The following are two formulas that may be helpful: V cylinder 2 h and V cone 2 h 10 ft 40 ft 30 ft PAGE 181 181 Use the scenario below to answer questions 17 and 18. Rachel attends Ola High School and is conducting a food science study. Rachel needs to select a random sample of the student body in her high school. She decides to survey students in the agriscie nce classes, because she believes they will have a better understanding of food science. She then places the names of all students enrolled in the agriscience classes into a hat and draws to determine a random sample of high school students in her school. 17. Did Rachel select a random sample of the student body in her high school? Explain your answer. study Rachel conducted? 19. An agriscience student a t Irwin County High School was interested in studying the bivariate relationship of forage yields and nitrogen application rates. The agriscience student decided to conduct a study to gather data on the relationship. According to the data gathered below, what type of function might be a good fit for the data model? 0 500 1000 1500 2000 2500 3000 3500 4000 4500 0 20 40 60 80 100 120 Forage Yield (lbs) Nitrogen (lbs/acre) PAGE 182 182 20. In raising alfalfa, the harvest removes P 2 O 5 and K 2 O from the soil. To ensure top yields for all harvest, it is recommended that the land be top dressed annually with 55 pounds of P 2 O 5 and 180 pounds of K 2 O for every 4.5 tons of yields. How much K 2 O should be used if the expected harvest is 75 tons? 21. You have purchased a hog feeder at a discount for $75. If the discount was 33%, what was the original cost of the feeder rounded to the nearest penny? 22. Suppose that you are using a landscape plan which calls for covering an area of 4,600 square feet with mulch. If you are required to cover the mulched area to a depth of 4 inches, how many cubic yards of mulch will you need? Round your answer to the nearest hundredth of a yard. 23. Assume that you have previously determined the protein requirement for your cow is 15.17%. You wish to feed this cow a ration consisting of 50% roughage and 50% concentrate. Use the following table to determine what percent protein must be in the concentrate mix. Roughage Crude Protein Corn silage 2.67% PAGE 183 183 Use the following scenario and graph to answer questions 24 26. The data below represents feeder steer prices from a livestock market in Oklahoma. An agriscience student at a local high school computed the least squares regression line for the data. 24. If the regression line for the feeder steer was found to be y = 0.1276x + 176.59, predict the price of a feeder steer that is 375 lbs. 25. What information could the agriscience student gain by computing the correlation coefficient for the data points of price and weight? 26. Explain why the y intercept of the regression line does not have meaning in the feeder steer price verses weight context. y = 0.1276x + 176.59 0 20 40 60 80 100 120 140 160 180 0 100 200 300 400 500 600 700 Price (cwt) Weight (lbs) PAGE 184 184 APPENDIX C MATHEMATICS ENHANCEMENT TEACHING EFFICACY INSTRUMENT PAGE 185 185 PAGE 186 186 PAGE 187 187 APPENDIX D IRB APPROVAL AND INFORMED CONSENT PAGE 188 188 PAGE 189 189 APPENDIX E SCRIPT Experimental Group This semester AEC 4200 is taking part in a research project to help future agricultural education teachers teach mathematics that is found naturally in the agricultural education curricula. During this study you will be asked to complete a mathematics con tent knowledge instrument and a mathematics efficacy instrument at various times. In addition, you will be randomly assigned two agricultural mathematics standards to incorporate into labs six and eight. This research is being conducted by the Agricultur al Education and Communication Department. Your participation in this study will in no way influence your course grade and is completely voluntary The instrument is anonymous, but does ask for an identification number to match the instruments that ar e completed by each participant. Data will be recorded as a group of students and not individually. If you have agreed to participated, have signed the informed consent, and have received an instrument you may begin. Thank you, Christopher Stripling Control Group This semester AEC 4200 is taking part in a research project to help future agricultural education teachers teach mathematics that is found naturally in the agricultural education curricula. During this study you will be asked t o complete a mathematics content knowledge instrument and a mathematics efficacy instrument at various times. This research is being conducted by the Agricultural Education and Communication Department. Your participation in this study will in no way inf luence your course grade and is completely voluntary The instrument is anonymous, but does ask for an identification number to match the instruments that are completed by each participant. Data will be recorded as a group of students and not individ ually. If you have agreed to participated, have signed the informed consent, and have received an instrument you may begin. Thank you, Christopher Stripling PAGE 190 190 APPENDIX F DEMOGRAPHIC INSTRUMENT 1. What is your age? _____ years 2. What is your grade point average (GPA)? _________ 3. What is your gender? a. male b. female 4. How would you describe your ethnicity? a. American Indian or Alaska Native b. Asian c. Black or African American d. Native Hawaiian or Other Pacific Islander e. White f. Other 5. What was the highest level of mathematics that you successfully completed in high school ? a. Algebra 1 b. Algebra 2 c. College Algebra d. Geometry e. Trigonometry f. Pre calculus g. Statistics h. Calculus i. other; please provide course name _________________________ 6. What is the highest level of mathematics that you have successfully completed in college ? a. College Algebra b. Geometry c. Trigonometry d. Pre calculus e. Statistics f. Calculus g. other; please provide course name _________________________ 7. What grade did you receiv e for the highest level of mathematics that you have successfully completed in college ? _________________ 8. When did you take your last math course ? _____________ PAGE 191 191 9. How many college level mathematics courses have you completed? __________ 10. What is your class level? a. freshman b. sophomore c. junior d. senior e. graduate student 11. Did you receive college credit for a math course in high school? Yes / No If so, what math course did you receive college credit for ________________________. PAGE 192 192 APPENDIX F EXPERTS Lecture Reviewer Brian A. Parr Associate Professor and Program Coordinator of Agriscience Education Department of Curriculum and Teaching Auburn University 5040 Haley Center Auburn, AL 36849 5212 Panel of Experts for the Mathematics Ability Test Brian A. Parr PhD Associate Professor and Program Coordinator of Agriscience Education Department of Curriculum and Teaching Auburn University 5040 Haley Center Auburn, AL 36849 5212 Lisa Kasmer PhD Assistant Professor Department of Mat hematics Grand Valley State University A 2 138 Mackinac Hall 1 Campus Drive Allendale, MI 49401 9403 Gary E. Briers PhD Professor Department of Agricultural Leadership, Education, and Communications Texas A&M University 2116 Texas A&M University College Station, TX 77843 T. Grady Roberts PhD Associate Professor Department of Agricultural Education and Communication University of Florida P.O. Box 110540 305 Rolfs Hall Gainesville, FL 32611 0540 PAGE 193 193 Candice Cobb, EdS Secondary Mathematics Teacher Irwin County High School 149 Chieftain Circle Ocilla, GA 31774 Elizabeth Portier EdS Mathematics Department Head and Secondary Mathematics Teacher Irwin County High School 149 Chieftain Circle Ocilla, GA 31774 De veloped the Mathematics Ability Test Rubric Candice Cobb, EdS Secondary Mathematics Teacher Irwin County High School 149 Chieftain Circle Ocilla, GA 31774 Elizabeth Portier EdS Mathematics Department Head and Secondary Mathematics Teacher Irwin County High School 149 Chieftain Circle Ocilla, GA 31774 Mathematics Ability Test Scorer Candice Cobb, EdS Secondary Mathematics Teacher Irwin County High School 149 Chieftain Circle Ocilla, GA 31774 A ligned Miller and Gliem s (1996) Instrument Items to the 13 NCTM Sub Standards Candice Cobb, EdS Secon dary Mathematics Teacher Irwin County High School 149 Chieftain Circle Ocilla, GA 31774 PAGE 194 194 LIST OF REFERENCES Adams, T. 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Changes in teacher efficacy during the early years of teaching. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA. Woolfolk, A. about control. Journal of Educational Psychology, 82 (1). 81 91. Young, R. B., Edwards, M. C., & Leising, J. G. (200 8 ). Effects of a math enhanced A year long experimental study in agricultural power and technology. Journal of Southern Agri cultural Education Research 5 8 (1), 4 1 7 Young, R. B., Edwards, M. C., & Leising, J. G. (2009). Does a math enhanced skills? A year long experimental study in agricultural power and technology. Journal of Agricultural Education, 50 (1), 116 126. doi : 10.5032/jae.2009.01116 PAGE 207 207 BIOGRAPHICAL SKETCH Christopher T. Stripling grew up in Irwinville, Georgia which is a small rural town in South Georgia. H aving parents involved in various aspects of agriculture and education fostered his passion for agricultural education. Christopher graduated from Irwin County High School in 2001 where he was the Irwin County High School FFA President and was a member of the tennis team Upon his high school graduation, Christopher attended Abraham Baldwin Agricultural College and received his a ssociate of s cience in b iological and a gricultural e ngineering with honors in 2003. He then transferred to the Universit y of Georgia and received his Bachelor of Science in a gricultural e ducation in 2005. Upon completing his b achelor of s cience, Christopher married Mindi Lee and accepted a teaching position at Ola High School in McDonough, Georgia as an agriscience teac Teacher of the Year for the 2008 2009 school year. While teaching agriscience, a gricultural l eadership in 2006 and developed and delivered agriscien ce professional development for the agricultural teachers in Georgia In 2009, Christopher accepted a graduate teaching and research assistantship at the University of Florida and began work on a P h .D. in the Department of Agricultural Education and Comm unication. As a graduate teaching and research assistant, Christopher taught various courses in agricultural education and conducted research related to contextualized mathematics teaching, college class attendance, behaviors of successful college instruc tors, teaching assistants, and experiential learning. PAGE 208 208 Furthermore, w hile at the University of Florida, Christopher received the 2010 University ences Young Alumni Award 