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PAGE 1 1 TEACHER TRAINING AND STUDENT PERFORMANCE ON THE END OF COURSE EXAM IN ALGEBRA 1 By CATHY GRIFFIN HARGIS A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMEN TS FOR THE DEGREE OF DOCTOR OF EDUCATION UNIVERSITY OF FLORIDA 2012 PAGE 2 2 2012 Cathy Griffin Hargis PAGE 3 3 To my family, without your support none of this would have been possible. PAGE 4 4 ACKNOWLEDGMENTS This endeavor would not have been possible w ithout the support of my family, colleagues, and friends. To my husband, Herb, this past year has been extremely trying for you and even though you struggle to remember what I am doing, thank you for always being supportive of my educational goals. To my s on, Matt, I wish you were still here to celebrate my accomplishment with me. I miss you. To my daughter Rebekah, thank you for changing your life to help me care for your father and allowing me to een my emotional support someone I could depend on to help me keep things going smoothly at home, and at Imajyn, you have been my inspiration to complete this challeng e and I hope it gives you the incentive to reach for the st ars in your educational quest. To Vision and Mattayah, ce while I was trying to work. You guys mean the world to me and just remember I will alwa ys be there for you. I would this even when I was ready to give up. Thanks for listening to my complaints, concerns, and for being there when I ne eded you. I love you, Mom. To my father, I wish you could To my colleagues and friends, Life presented many obstacles and challenges for me to overcome to m ake this a there a will there is a way Dr. Behar Horenstein, my doctoral committee chair and advisor, has provided me with guidance, patience, and encouragement throughout the process. I probably would PAGE 5 5 not h ave finished this project without her faith in my abilities her understanding, and continued support. Thank you for believing in me. Dr. Garvan, your assistance in the statistical portion of my study was a sa ving grace and I thank you for being patient with me. And to Dr. Crockett and Dr. Oliver, thank you for your direction and participation on my committee. I would also like to thank my professors in the cohort who took time out of their busy lives to travel to Naples for our classes. Your continued support has provided the motivation to keep going. motivators to each other to complete this journey. I especially would like to thank Michele, Danielle, Theresa, Susan, and Jocelyn thank you for being there as a good listener when things got rough, as a mentor to go to because one of us always had the victory for all of us. We were a team! Lastly, thanks to the school district, principals, and teachers that were permitted to participate in my study. Without you none of this would have been possible. I do vey and return your informed consent document. PAGE 6 6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 ABSTRACT ................................ ................................ ................................ ..................... 9 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 11 Statement of the Problem ................................ ................................ ....................... 17 Research Questions ................................ ................................ ............................... 18 Statement of Hypothesis ................................ ................................ ......................... 18 Significance of Study ................................ ................................ .............................. 19 Limitations ................................ ................................ ................................ ............... 19 Definitions ................................ ................................ ................................ ............... 21 2 REVIEW OF THE LITERATURE ................................ ................................ ............ 22 Impact of Teacher Training Programs on Teacher Effectiveness ........................... 22 Teacher Training and Student Achievement in Mathematics ................................ .. 30 Mathematician versus Mathematics Education Major ................................ ............. 36 End of Course Exams and Student Achievement ................................ ................... 38 History of En d of Course Exams ................................ ................................ ...... 38 Algebra 1 EOC ................................ ................................ ................................ 41 Gender and Student Achievement in Mathematics ................................ ................. 42 Ethnicity/Race and Student Achievement in Mathematics ................................ ...... 47 Socioeconomic Status and Student Achievement in Mathematics ......................... 51 Summary ................................ ................................ ................................ ................ 55 3 METHODOLOGY ................................ ................................ ................................ ... 60 Research Design ................................ ................................ ................................ .... 60 Pa rticipants ................................ ................................ ................................ ............. 60 Data Collection ................................ ................................ ................................ ....... 60 Description of Teacher Data ................................ ................................ ............. 62 Description of Student Data ................................ ................................ .............. 63 Statistical Analysis ................................ ................................ ................................ .. 63 Limitations ................................ ................................ ................................ ............... 64 4 RESULTS AND ANALYSIS ................................ ................................ .................... 67 Additional Research Findings ................................ ................................ ................. 78 Summary ................................ ................................ ................................ ................ 79 PAGE 7 7 5 DISCUSSION ................................ ................................ ................................ ......... 86 Summary of Results ................................ ................................ ................................ 86 Discussion ................................ ................................ ................................ .............. 87 I mplications ................................ ................................ ................................ ............. 91 Recommendations for Future Research ................................ ................................ 92 Summary ................................ ................................ ................................ ................ 93 APPENDIX A ADMINISTRATIVE RULE 6A 4.0262 ................................ ................................ ...... 95 B TEACHER BACKGROUND SURVEY ................................ ................................ .... 96 C INFORMED CONSENT OFFICIAL DOCUMENT ................................ ................... 99 LIST OF REFERENCES ................................ ................................ ............................. 100 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 110 PAGE 8 8 LIST OF TABLES Table page 2 1. Algebra 1 standards ................................ ................................ ........................... 57 3 1. Demographics of teacher participants ................................ ................................ 65 4 1. Mathe matics courses taken by teachers ................................ ............................ 81 4 2. Educational methods courses taken by teachers ................................ ............... 82 4 3. Training methods and number of ma thematics and education coursework ........ 83 4 4. Teacher gender and number of mathematics and education coursework .......... 84 4 5. Teacher rac e/ethnicity and number of mathematics and education coursework ................................ ................................ ................................ ......... 85 PAGE 9 9 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the De gree of Doctor of Education TEACHER TRAINING AND STUDENT PERFORMANCE ON THE END OF COURSE EXAM IN ALGEBRA 1 By Cathy Griffin Hargis May 2012 Chair: Linda Behar Horenstein Major: Educational Leadership Research studies have yielded inconclusive results about t he relationship between teacher training pro grams and student achievement. With the implementation of end of course exams as a graduation requirement in the state of Florida ; continual need to fill teaching positions, rising student enrollment, and legislated class size limits; the level of student performance may become dependent on the type of teacher training. The purpose of this study was to determine if there was a relationship between teacher training and student performance on the end of cours e exam in Algebra 1. Algebra 1 end of course exam scores were collected from 7 90 students among 15 Algebra 1 teachers in one southwest Florida school district. Student gender, race/ethnicity, and socioeconomic status data were also collected to determine i f these variables influenced student performance. Teacher variables were gender, race/ethnicity college major, degree, teacher training program, certification, and years teaching mathematics and Algebra. Student data was stratified based on teacher traini ng method: traditional program; alternative certificat ion, and subject area testing. F requency distribution, descriptive statistics, hierarchical linear modeling, Wilcoxon PAGE 10 10 signed rank test, Wilcoxon Two Sample test, and Kruskal Willis test s were conducted. There was no significant difference found on studen t Algebra 1 EOC performance and type of training program of the teacher; or when comparing gender and race/ethnicity to mean test scores. There was a significant difference when comparing students on s o cioeconomic status. Lower socioeconomic status of student resulted in on average lower mean test score s When comparing student performance based on major in mathematics or education mathematics major, there was no significant difference in the s mean test score as well as no significant difference due to student gender, race/ethnicity, or socioeconomic status The number of mathematics and educational methods courses taken by teacher s showed no significant difference in mean scores. Howev er, there was an increase in the number of mathematics courses females take compared to males. No difference was noted with teacher ethnicity. The se exploratory findings replicate some of the previous studies on student achievement and teacher training pro grams which showed inconclusive findings. PAGE 11 11 CHAPTER 1 INTRODUCTION Teacher training programs have been a controversial topic for many years. However, b ecause the need for teachers outnumbers the number of graduates from traditional teacher education progr ams, states have looked to alternative programs to provide teachers at a faster rate. As a result, researchers have raised concerns about the relationship between alternative ly certified teachers and their relationship to student achievement (Darling Hammo nd, 1999; Flores, Desjean Perotta, & Steinmetz, 2004; Glazerman, Mayer, & Decker, 2006; Suell & Piotrowski, 2006). Studies also indicate that factors other than teacher quality or their training are linked to student achievement including student gender, r ace/ethnicity, and socioeconomic status. Findings from such studies suggest that student demographics should be considered when determining what type of teaching training program would be effective in reaching the needs of all students. In 2007, the Nation every American child has equal access to a high quality, world class educational Meanwhile, r esea rchers have stressed the idea that a certified teacher in the subject area that they are teaching should be provided to every child With the shortage of certified teachers available, alternative programs have proliferated to ensure that teacher vacancies are filled. The National Center for Education Information (NCEI) reported as of 2008, 48 states and the District of Columbia provided at least one alternative option for certifying elementary and secondary teachers. School districts in Florida are required to offer a competency based alternative certification PAGE 12 12 program, either th rough a web based program developed by the state or one developed by the district and approved by the state (NCAI, 2010). According to the National Center for Alternative Certificatio n (NCAI), approximately 500,000 teachers have entered the teaching profession through alternative programs since 1985 (as reported in NCEI, 2010). Darling Hammond (1990) was one of the first researchers to point out inconsistencies in the definition of an alternative certification and that not all programs are equal in structure or requirements. The question whether or not alternative programs are equivalent to the traditional program and if they can provide students with a qualified teacher still lingers What makes a qualified teacher? The answer to this question varies and this is where the controversy begins. A ccording to t he No Child Left Behind Act of 2001 a highly qualified teacher meet s three requirements: (1) holds higher degr ee from an accredited or approved institution; (2) has a valid state certificate; and (3) has demonstrated subject matter competency for each core academic subject assigned. Some researchers report teacher s (Darling Hammond, 2002, Zientek, 2007). Others suggest alternative programs do not adequately prepare them to teach competently (Darling Hammond, 1990; Wise & Darling Hammond, 1992). Ballou and Podursky (2000) suggested there are multitudinous regulation s and requirements preventing those that want to teach an opportunity to enter the teaching profession. Teachers are also required to have a broad knowledge of curriculum and standards; knowledge of discipline and classroom management techniques; identify and meet the needs of diverse learners; have good communication skills with students, parents, and colleagues; effectively use technology PAGE 13 13 as a teaching tool; and promote a classroom atmosphere of enthusiasm and motivation. Researchers have pointed out that these are some of the characteristics where alternatively certified teachers have difficulties (Darling Hammond, 1996; Darling Hammond, Chung, & Frelow, 2002; Darling Hammond, Holtzman, Gatlin, & Heilig, 2005). Goldhaber and Brewer (2000) compared the imp act of alternative and traditional emergency certification in mathematics do no worse than students who have teachers specific training (a mathematics degree or certification) outperform those without subject Hammond, Berry, and Thoreson (2001) at the researchers did not (p. 31). In his report, the Secretary of Education Rod Paige (2 is little evidence that education school course work leads to improved student claiming that the y were not being scientifically linked to teacher ef fectiveness. In their rebuttal, Darling Hammond and Youngs (2002) indicat ed that Paige did not support many of his statements with scientifically based research. In their review of various studies on student achievement; Wilson, Floden, and Ferrini Mundy ( 2002) found a positive relationship between teacher education and teacher effectiveness. PAGE 14 14 In the 1998 2000 Third International and Mathematics and Science Study Video Study (TIM S S Video Study) researchers assessed teachers and their teaching methods in se ven countries to identify teacher characteristics and their impact on teacher quality and student achievement. When comparing the results, they found that student performance in the United States was lower than in the other countries studied and that many factors contributed to this The National Center for Education Statistics (2003) summarized the findings as: c ompared to the teaching styles of teachers in other countries with higher student achievement, teachers in the United States were inferior in the coherence across mathematical problems and within their presentations, the topics covered and the procedural complexity of the mathematical problems, and classroom practices regarding individual student work and homework in cl (p. 4) Heibert et al (2003) propose d that in order to improve systems of teaching in the United States, we must first establish specific learning goals and align teaching standards to these goals. The y asserted that the United States spends too much time focusing on what to implement rather than how to implement when trying to make improvements. Moyer Packenham, Bolyard, Kitsantas, and Oh (2008) examined teacher qualities Partn ership (NSF MSP) Program toward identifying exemplary mathematics and science teachers They report ed or lack thereof, of K 12 Findings c oncerning what m akes an effective teacher and whether or not it matters if the teacher PAGE 15 15 has received training through the traditional program or by an alternative certification program are inconclusive T he debate about whether or not mathematics teachers should be mathema ticians or should be required to take a minimum number of mathematics courses in their education program of study continues According to the 2008 Science, Technology, research o n teacher quality conducted over the last 20 years revealed that, among those who teach math and science, having a major in the subject taught has a suggested that simply requiring teachers to take more mathematics courses was not the answer to the problem of inadequate preparation of teachers. They proposed that mathematicians and educators work together to develop a curriculum t o help 399). Again, what makes a highly qualified teacher of mathematics remains inconclusive. Gender, race/ethnicity, and socioeconomic status also affect student performance especially in mathematics. Though gaps in stu dent achievement in mathematics between males and females are relatively small, beginning in grade eight or nine, they their participation in higher level mathematics courses (Nagy, Trautwein, Baumert, Koller, & Garrett, 2006). Research has suggested this may be due to a lower mathematics self concept for females (Crombie, Sinclair, Silverthorn, Bryne, DuBois, & Trinneer, 2005; Simpkins, Davis Kean, & Eccles, 2005; Tsui 2007; You, 2010). Females have always been judged to males in mathematical ability and this PAGE 16 16 message continues to be conveyed (Geist & King, 2008). Males tend to take higher level mathematics courses even though females tend to receive highe r grades (Reigle Crumb, 2006). However, on the 2006 mathematics section of the Scholastic Aptitude Test (SAT), males outperformed females by a mean difference of 34 points (Tsui, d women also scored lower than their male counterparts. Research has shown that African American and Latino students enroll in lower level mathematics courses and do not usually progress to the more advanced courses regardless of their level of ach ievement (Reigle Crumb, 2006). She attributed this at when African American students perceive they will receive lower returns to their educational investments or will receive un equal (p. 117) they reject the ducational goals This could explain why African American and Latino male stu dents begin at the same educational level as their White male peers but do not reach the same level of mathematical coursework. Noguera (2008) maintained that in order to close the racial achievement gap educators es of inequity typically lie outside of schools in disparities in income and wealth, in inequity in parent education and access to health Most of the research reported mathemati cs achievement using aggregated socioeconomic status (SES) of the school rather than individual students thus, it is hard When PAGE 17 17 low SES students are enrolled in high SES schoo ls they tend to feel socially isolated Research suggests that this sense of isolation prevents them from meeting higher achievement in mathematics. This is especially true when the high SES school has a low race/ethn ic population (Crosnoe, 2009). All of t hese factors may become more salient in studies of student mathematics achievement with the passage of Florida Senate Bill 4. Beginning with students entering ninth grade in the 2011 school year, this bill will impact graduation requirements. For the first time in the history of the state, all students enrolled in Algebra 1 will be required to take an end of course (EOC) exam. At th e time of this study, the E O C exam will only count for 30% of their final grade for ninth graders. However, in the future, stud ents will be required to pass the exam to receive high school credit in Algebra 1. End of course exams in mathematics will replace the Florida Comprehensive Assessment Test (FCAT) mathematics test. Statement of the Problem With the implementation of the en d of course exam in Algebra 1, teacher training may be a more important factor in student success than previously suggested Given the number of teacher vacancies, the type of teacher training may influence the level of student performance In future years student achievement in mathematics will affect subsequent enrollment in mathematic courses and graduation status. Research has shown that teacher quality is an important factor in student achievement (Darling Hammond, 2000; Darling Hammond, et al. 2005; Dee & Cohodes, 2008; Goldhaber & Brewer, 2000). The purpose of this study was to determine if there was a relationship between teacher training and student performance on the end of course exam (EOC) in Algebra 1. PAGE 18 18 Research Questions 1. Is there a relationsh ip between teachers who completed a traditional preparation program and those who received alternative certification on student performance on the end of course exam in Algebra 1? After adjusting for student gender, race/ethnicity, and socioeconomic status is there a relationship between teacher preparation method and student performance on the end of course exam in Algebra 1? 2. Is there a relationship between teachers who majored in mathematics and those who were education majors with an emphasis in mathemat ics on student performance on the end of course exam in Algebra 1? After adjusting for student gender, race/ethnicity, and socioeconomic status is there a relationship between teacher s who majored in mathematics and those who were education majors with an emphasis in mathematics on student performance on the end of course exam in Algebra 1? 3. Is there a relationship between the number of mathematics courses taken by the teacher and preparation type, teacher gender, and teacher race/ethnicity? 4. Is there a relat ionship between the number of educational methods courses taken by the teacher and preparation type, teacher gender, and teacher race/ethnicity? Statement of Hypothesis 1. There will be no significant difference in the relationship between teachers who comple ted a traditional preparation program and those who received alternative certification on student performance on the end of course exam in Algebra 1. There will be no significant difference in the relationship between teacher preparation method and student performance on the end of course exam in Algebra 1 after adjusting for student gender, race/ethnicity, and socioeconomic status. 2. There will be no significant difference in the relationship between teachers who majored in mathematics and those who were edu cation majors with an emphasis in mathematics by student performance on the end of course exam in Algebra 1. There will be no significant difference in the relationship between teachers who majored in mathematics and those who were education majors with an emphasis in mathematics on student performance on the end of course exam in Algebra 1 after adjusting for student gender, race/ethnicity, and socioeconomic status. 3. There will be no significant difference in the relationship between the number of mathemati cs courses taken by the teacher and preparation type, teacher gender, and teacher race/ethnicity. 4. There will be no significant difference in the relationship between the number of education al methods courses taken by the teacher and preparation type, teach er gender, and teacher race/ethnicity. PAGE 19 19 Significance of Study The purpose of the study was to determine the relationship between teacher training and student performance on the end of course exam in Algebra 1. The findings of this study will contribute to t he research on teacher training and student achievement in mathematics. Up to this point, research findings in this area have been inconsistent. The results may foster the identification of criteria that educational leaders can use in hiring qualified math ematics teachers. These findings may also be useful in the state of Florida as well as other states that are moving to end of course exams instead of minimum competency based graduation tests. Results of this study may also provide information to the direc tors of teacher preparation programs (both traditional and alternative) concerning where curricular deficiencies exist. The findings may also lead to the development of criteria that can be used to establish alternative programs so that both programs are o f similar caliber. Limitations before taking the EOC exam. Students enrolled in Algebra 1(regular and honors level) were level two or above on previous year Florida Comprehensive Ass essment Test (FCAT) mathematics score, but the FCAT does not measure algebraic skills alone. This is a pre were treated like cohort groups as they were attached to each teacher participant. Thus there was n o random sampling or random assignment in this study. When comparing the content area score of the EOC, it is important to remember that there are three forms of the test. Equating was used to ensure that the T scores on the different test forms have the s ame meaning and are comparable, but a given PAGE 20 20 content area score should only be compared for a specific test form between schools. This study compar ed the T scores for all forms between all teachers and did not investigate if one version of the test produced higher scores than another. Another limitation is that the different sections of the test were not studied to provide information on how the students performed on each section. Doing this may have provided additional informatio n regarding areas where stud ents need further instruction. Such information might have pointed out to mathematics teacher training programs areas where extra instruction is needed for students. Teachers in Florida come from all over the United States. Many of them have completed thei r degrees from a variety of traditional and alternative teacher education programs. A study conducted by Humphrey and Wechsler (2005) confirmed th e many variations in the alternative certification route even within a given state and questioned the usefulne ss of comparing different programs. This study did not analyze each program to determine differences and the ir impact on student performance. However, a new category subject area testing was studied as a result of teacher survey responses. This category falls under alternative certification but warrants independent analysis. responses. However this study did not measure social desirability bias, a behavior that may occur when par ticipants are responding to self report measures. Since the study was conducted in one Southwest Florida district, the results may not be transferable to other school districts in Florida or other states. PAGE 21 21 Definitions A LTERNATIVE C ERTIFICATION designed to p repare individuals that have not pursued conventional or traditional routes to teacher certification through college or university training; programs vary from state to state. E ND OF C OURSE E XAMS comprehensive tests taken during the second semester that co ver s the objectives of the curriculum. P EDAGOGICAL C ONTENT an understanding of how particular topics, problems, k nowledge or issues are organized, presented, and adapted to the diverse interests and abilities of learners, that are presented for instruction (Shulman, 1987) Q UALITY T EACHER individuals who: from an accredited college or university; valid state certificate; subject matter competency for each core academic subject assigned and ; has a broad knowledge of curricu lum and standards; knowledge of discipline and classroom management techniques; able to identify and meet the needs of diverse learners; has good communication skills with students, parents, and colleagues; and promotes a classroom atmosphere of enthusiasm and motivation. S UBJECT A REA T EST designed to assess subject matter knowledge and skills and is used to obtain subject area certification. T RADITIONAL / CONVENTIONAL teacher training process utilizing an accredited P ROGRAMS program through a college or uni versity requiring course work and student teaching. PAGE 22 22 CHAPTER 2 REVIEW OF THE LITERA TURE A review of the literature provide s a framework study ing the relationship between teacher training and student performance on the end of course (EOC) exam in Algebra 1. Chapter 2 includes an overview of the re search relevant to this study: (a) impact of teacher training programs (both traditional and alternative) on teacher effectiveness, (b) teacher training and its effect on student achievement in mathematics, (c) end of course exams and student achievement, (d) gender and student achievement in mathematics, (e) ethnicity/race and student achievement in mathematics, and (f) socioeconomic status and student achievement in mathematics. Impact of Teacher Training Programs on Teacher Effectiveness For many decades traditional and alternative teacher training programs have been controversial. With the continual need to fill vacant teaching positions due to retirement and attrition, rising student enrollments, and legislated c lass size limits; schools, universities, and district administrators are looking for expedient ways to certify new teachers who can meet workforce demands in mathematics and science. Studies have been conducted to determine which method of teacher preparat ion produces the most effective teacher the alternative approach (AC) or the traditional/conventional approach (TC). However the findings are inconclusive (Cohen Vogel & Smith, 2007; Darling Hammond, 2000; Dee & Cohodes, 2008; Glazerman, Mayer, & Decker, 2006 ; Kane, Rockoff, & Staiger, 2006; Nunnery, Ka plan, Owings, & Pribesh, 2009). but no consensus on how to train good teachers or ensure that they have mastered PAGE 23 23 essential skills examination of essential skills and content knowledge that would obviously vary by grade level and acade accredited teacher education program and student teaching in schools. He disagrees effectively teaching. Cohen Vogel and Smith (2007) analyzed data obtained from the 1999 2000 administration of the Schools and Staffing Survey (SASS) of elementary and secondary teachers. They tested four core assumptions that have been used in arguments for expanding alternativ e certification programs (AC): from fields outside education; AC attracts top quality, well trained teachers; AC disproportionately trains teache rs to teach in hard to staff schools; and AC alleviates out of t proportion of first year AC and TC teachers with education degrees who entered teaching either directly from colle ge or university programs, from another job in education (e.g., teaching in a private school), or from non education related p 741 742). By comparing AC and TC teachers academic qualifications; whether or not they were placed in hard to s taff schools; and whether or not they taught at least one course outside their major or minor field of study, they found four core assumptions were false. Many of the teachers entering an alternative program already had a degree in education but were not c ertified to teach and used the AC PAGE 24 24 program as a means to obtain certification; the recruits did not come with better qualifications or attend selective undergraduate institutions; were not more likely to teach in hard to staff schools; and AC programs were not an effective way to solve the problem of out of field teaching problem. Harrell (2009) conducted a study to determine if the results of teacher examinations accurately measure teacher quality. Using the results from the Texas Examinations of Educator S tandards (TExES), the researcher examined traditional indicators of teacher content knowledge for candidates seeking certification in grades 8 through 12 life science or grades 8 through 12 mathematics. The indicators were: upper level content area coursew ork, upper level content area grade point average and the time elapsed between the TExES content examination and the completion of the last upper level course in the content area. Using descriptive data (mean, mode, and standard deviation), he found that f orty percent of the 8 12 mathematics candidates failed the state content examination although an analysis of their transcript indicated strong content preparation, high grade point averages and recent coursework completed. Linear regression analysis reve aled that upper level content area coursework, grade point average and the time elapsed between the initial attempt on the TExES were statistically significant to the TExES content examination score; F (3, 81) = 3.076; p = .032. Harrell re commend ed that po licy makers re examine how high stakes teacher testing relates to teacher content knowledge associated with the degree programs offered by colleges and universities and whether the current method of high stakes testing exacerbate s the teacher shortage prob lems in high need fields such as science and mathematics (p. 65). PAGE 25 25 Goldhaber (2007) studied t he relationship between teacher testing and teacher effectiveness By examining learning gains from a data set in North Carolina, he found a positive relationship b etween some licensure tests and student achievement. H owever, he cautioned that the results of the tests allow ed individuals to teach who were not highly effective in improving student achievement and den ied those who could become effective teachers becaus e of their failure on these tests (p. 767). He acknowledged that teacher tests are not the same across the country and what may be identified as meeting the criteria in one state may not be the same in another state. He found that there is little informati on available on whether or not school districts use the testing results in their selection process. Kane, et al (2006) measured teacher effectiveness by looking at student performance and differences in teacher certification within the same schools. They (p. 43). Strong, Gargani, and Hacifazlioglu (2011) used three types of experiments to determine if evaluators knew how to accurately evaluate te achers for effectiveness. In t he first experiment tested evaluators were asked to correctly categorize teachers as highly effective versus low effective using student achievement as a basis for their effectiveness. The y watched video excerpts of classroom lessons and were asked to place t eachers in the high or low effectiveness groups and to explain their rational for the placement. In t he second experiment an analy sis of the criteria evaluators used when making their evaluations was undertaken This experi ment was conducted in another state with a larger selection of evaluators The third experiment used highly trained evaluators, an established observational measure, and the PAGE 26 26 evaluators observed a full length video (rather than excerpts) of presentations of classroom lessons. The evaluators used research questions based on agreement (did the individual evaluators agree with each other on categorizing the teachers), criteria (what did the evaluators use as criteria for teacher effectiveness when allowed to ch oose their own methods), confidence (how confident were the evaluators that they made accurate assessments), accuracy (how well the evaluators categorized the teachers correctly), replication (did they get the same results each time), and discrimination (d id any items on the observation protocol effectively discriminate between high and low performing teachers). The researchers concluded that the ere absolutely inaccurate, leading us to question whether educators can identify effective teachers when they see suggested developing an observational measure that c ould predict teacher effectiveness. Tournaki Lyublinskaya, and Carolan (2009) conducted a study to determine if the certification pathway influenced teacher efficacy and effectiveness. Teacher candidate studies followed three different routes: conventional method that allow ed teachers to be employed as the teacher of record in the classroom while completing their m degree; ent rance into a teaching requirements ; and completi on of ts. All three groups were placed in high schools in the same school district. The participants took surveys designed to measure teacher efficacy and teacher effectiveness in their last semester of studies. Two prearranged classroom observations PAGE 27 27 were conduc ted during the spring semester of the school year. O bservers complete d was no significant difference in efficacy and effectiveness between the participants in the three pathways to certification. Flores, Desjean Perrotta, and Steinmetz (2004) found that teacher efficacy was affected by type of certification. When compared to alternative certification teachers, teachers who completed traditional programs reported having gr eater confidence in their teaching ability Without time to observe other teachers, experience mentoring or practice their skills before becoming the teacher of record, alternatively certified teachers were less likely to try new instructional methods as compared to the traditional teachers whom were given this opportunity. Scribner and Akiba (2010) found that alternatively certified teachers whom had a deeper content knowledge and prior experience in related fields to the subject they were teaching did no t make them better teachers. This was reinforced when Boyd, Goldhaber, Lankford, and Wyckoff (2007) studied the research available on the effect of teachers to have more s ubject area knowledge in math could enable them to teach more effectively, and improve student assessments in math One study compared Florida teachers certified by the traditional approach and an alternative program established by the University of West Florida (UWF). This program First year teachers in a northwest Florida school district (both traditionally certified, the UWF program, and other alternative progra ms) were evaluated using a Likert scale PAGE 28 28 that alternatively certified teachers expressed similar levels of competencies as traditionally certified teachers. The UWF alternat ively certified teachers stressed the use of mentors and in service support functions as important components, whereas the traditionally certified teachers acknowledged that their internships provided the support they needed to increase their proficiency ( Suell & Piotrowski, 2006). A similar study conducted by Wayman, Foster, Mantle Bromley, and Wilson (2003) concluded that teachers trained through alternative certification routes expressed similar levels of competencies as traditional certified teachers. T he use of self reporting mechanisms and a lack of empirical data were limitations of both studies. Piccolo (2008) reviewed the research on how mathematics content should be effectively presented to students. She concluded mathematics teaching comprises these three components: general pedagogy, content Teachers must be able to effectively plan lessons and motivate students (general pedagogy), hav both content and pedagogy into a form of knowledge that comprises representations of analogies, illustrations, examples, explanations, and demonstrations so that the content a term phrased and defined by Lee Shulman i n 198 7 ) (p p 46 47). Capraro, Capraro, Parker, Kulm, and Raulerson (2005) as cited in Piccolo (2008) believe pedagogical content knowledge is PAGE 29 29 learned during teacher preparation programs and initial teaching experiences. Ball, Thames, and Phelps (2008) co ncurred that pedagogical content knowledge was important and concluded that more research is needed to understand how to improve the content preparation of teachers. Using results from the National Educational Longitudinal Study of 1988 (NELS:88) as their source for determining the relationship between subject specific teacher certification and academic degrees and teacher quality, Dee and Cohodes (2008) make him or her ine Kerr and Berliner (2002) believe that teachers need extensive training in order to develop a deeper knowledge of subject matter and the ability to teach this subject matter to a diverse student population. Wenglinsky (2 002) asserted th at a link between teacher quality and student achievement is dependent on the classroom practices of the teacher. He concluded that research asserts, tea chers ma d e about classroom practices can greatly Some researchers argue that the differences lie in the interpretation of the research results. Darling Hammond (2000) disagreed w ith Ballou and Podgursky (2000) (NCTAF) Ballou and Podursky asserted that teacher education makes no difference in teacher performance and student learning and students would be better off without state regulations on how much training teachers must receive before entering the classroom (p. 6). However, Darling Hammond suggested that a lack of preparation leads to high PAGE 30 30 teacher attrition rates and lower levels of learning (p. 53 ). Darling Hammond cited Ferguson (1991) findings that to defend her position She use d this example im 31). Ballou and Podursky disregarded these findings. Selko and Fero (2005) reviewed the criteria used to define alternative certification programs They found that there was no common definition As a result of their work on creating a new alternative pathway to teaching they urged educators to look closely at alternative programs and to distinguish high quality alternative paths to certification programs that hold candidate s responsible (p. 34). Since alternative certification programs are here to stay, it is important for state and national standards be established to meet the needs of stud ents entering into these programs. Study results suggest that whether or not the type of teacher training program has had a positive or negative effect on teacher effectiveness is inconclusive. Teacher Training and Student Achievement in Mathematics Darlin g Hammond, et al (2005) examined the relationship between student degree levels using a data set from Houston, Texas. Students enrolled in a traditional teacher education program that led to certification were compared to individuals participating in the Teach for America (TFA) program and other alter native certification programs. Using regression analysis of 4th and 5th grade student achievement gains in reading and mathem atics over a period of six years, traditionally certified teachers PAGE 31 31 produced significantly stronger student achievement gains than the participants who were alternatively certified through TFA. A study conducted in Florida measuring the effects on student a chievement of an alternative program Troops to Teachers (TTT) produced opposite results. An analysis of status and student mathematics scores after controlling for course taug ht, grade level, et al 2009). The TTT teachers showed a significant positive effect on student achievement in mathematics when compared to all other teachers teaching the same subject at the same grad e level in the same schools ( d = +0.05) (p. 262). While comparing TTT teachers to other teachers within the same school, same grade level, and years of experience they found ent in 262). Students with TTT teachers 262). The difference betwee n the TFA and TTT programs lies in how the teachers are university and are placed in an all expense paid five week intensive training program which includes coursework a nd student teaching prior to being placed in the classroom. higher degree from an accredited college or university and a separated or retired military service requirement The potential recruits are eligible for financial aid assistance and are required to find an alternative program or traditional program in the PAGE 32 32 state they wish to be employed. They must also sign a three year commitment to teach at a public school within a high need district. It is possible the TTT teachers went through a traditionally certified teacher curriculum which may account for the positive effect they had on student achievement. Glazerman, et al (2006) also found that alternatively certified teac hers impacted mathematics achievement. Using TFA teachers for their data source they found a positive impact on mathematics achievement when compared to certified teachers. They reported a difference equivalent to 15 percent of a standard deviation, equiva lent to on e month of instruction (p. 84). Laczko Kerr and Berliner (2002 ) compared certified teachers who had completed a minimum of 45 hours of coursework in education with uncertified teachers from Teach for America, provisional teachers, emergency teach degrees with little or no education coursework. Using the Stanford Nine (SAT 9) to analyze student achievement in grades 3 8; they concluded that students who had certified teachers scored higher than the uncertified tea chers. Using NELS:88 as their primary source of data, Goldhaber and Brewer (2000) and science and teacher certification. They found the following relationships: 1. Students o f teachers with mathematics degrees and/or certification in mathematics achieved better than students of teachers without subject matter preparation. 2. Student test scores in mathematics were higher when the teacher of record held professional or full sta te certifica scores when taught by a teacher who was certified out of field or held private school certification, PAGE 33 33 3. Students degrees in mathematics outperformed the students taught by teachers who were not credentialed in the same field. 4. Students taught by an uncertified science teacher or a teacher who held a private school certification showed lower scores. 5. Measurement of student achievement growth revealed no signifi cant differences between mathematics or science student test scores for teachers with emergency certification and those traditionally certified (p. 145 ). Using the same data source, Dee and Cohodes (2008) also concluded that teachers who were subject certi fied demonstrated gains in mathematics achievement. Darling Hammond (1999) examined how teacher qualifications and other state policies such as teacher recruitment and professional development affect student ost consistent significant predictor of student achievement in reading and mathematics in each year tested is the proportion of well qualified teachers in a state: those with full certification and a major in the field they teach ( r between .61 and .80, p < 29). She reported that states with rigorous teaching standards for teachers and rarely hire unqualified teachers have the highest student achievement gains (p. 18). Moyer Packenham, et al (2008) examined the different types of instruments use d to identify mathematics and science teacher quality characteristics in 48 nationally funded mathematics and science education awards. The six characteristics were teacher behaviors, practices, and beliefs; subject knowledge; pedagogical knowledge; experi ence; certification status; and general ability. The study revealed that the following beliefs (85.4%); (b) subject knowledge (81.3%); and (c) pedagogical knowledge PAGE 34 34 (7 7.1%). (p. 584). These teacher characteristics are most likely to be associated with student achievement. Clo t felter, Ladd, and Vigdor (2010) studied teacher credentials and their effect on student achievement in North Carolina. Teachers are certified thro ugh the certification route is a lateral entry program requiring individuals to have at least a ch they are assigned to teach. The teachers are required to enroll in a teacher education program to complete the required class work and must complete at least six semester hours of coursework each year. A lateral entry license is issued for two years, an d may be renewed for a third year (p. 670). A regular license includes both initial (completion of state wide approved teacher education program, 10 weeks of student teaching, and passing scores on applicable Praxis II tests), and continuing license (after three years of four cohorts of tenth grade students in school years 2000 through 2003. The final sample included only students that could be matched with teacher s on at leas t three EOC tests. license averaged 0.06 standard deviations lower than those taught by teachers with a However, they found that when lateral entry teach er s continue teaching they are no less effective than teachers with a regular license. The authors attribute this to the ir training and also selection Since many lateral entry teachers leave the profession this suggests that perhaps those that remain are more effective than those that leave. The PAGE 35 35 study also revealed that students taught by teachers certified in math increased their achievement on average by about 0.11 standard deviations (p. 671). In a 2008 final report of the National Mathematics Advisory Panel, educational policy observers reported concerns about the difficulties students have with mathematics achievement beginning in late middle school where for most students, algebra coursework begins. They support ed of recommendations: 1. T eachers must know in detail the mathematical content they are responsible for teaching and its connections to other important mathematics, both prior to and beyond the level they are assigned to teach. However, because most studies have relied on proxies for mathematical knowledge (e.g., course work as part of a certification program), existing research does not provide definitive evidence fo r the specific mathematical knowledge and skill that are needed for teaching. 2. More precise measures should be developed to uncover in detail the the mathematical and pedagogical knowledge needed for teaching. 3. The mathematics preparation of elementary and middle school teachers in the classroom. T his includes pre service tea cher education, early career support, and professional development programs. A critical component of this recommendation is that teachers be given ample opportunities to learn mathematics for teaching. That is, teachers must know in detail and from a more advanced perspective the mathematical content they are responsible for teaching and the connections of that content to other important mathematics, both prior to and beyond the level they are assigned to teach ( pp 37 38) The panel suggested that studen ts need better prepar ation in the basic principles of arithmetic in order to be successful in Algebra. PAGE 36 36 Again, the findings regarding the impact of traditional/conventional programs versus alternatively certified programs on student achievement in mathemati cs remain inconclusive Mathematician versus Mathematics Education Major Another factor that determin es the effect on student achievement is whether the teacher received a degree in mathematics or is an education major with an emphasis in mathematics. Prou mathematics the better his teaching. He feels strong ly mathematical knowledge does not imply strong teaching knowledge Goulding, Rowland, and Barber (2002) as cited in Bass (2005) studied the relationship between mathematics, mathematicians, and ic ts b etween mathematicians and wrote that while education uses mathematical knowledge this can be viewed as ap plied mathematics. He asserts that for mathematicians to contribute to education they must understand what is useful and usable to the mathematics educator. Bass point ed out that the changes that have come about in mathematics education are the result of e ducators not mathematicians. Mathematicians have criticized t he National Council of Teachers of Mathematics new national standards for mathematics education Wagner, Speer, and Rossa (2007) followed a mathematician through the delivery of an undergraduate course on differential equations and found that mathematicians may need assistance in curriculum delivery because the y lack exposure to teacher PAGE 37 37 education programs. Even though they possess the curricular content knowledge of the subject matter they have no t acquired the instructional practices to present this knowledge to their students. Wagner, et al (2007) yet not obtained merely through t They stated that the traditional forms of teacher preparation including general courses in mathematics and courses in pedagogy were in sufficient for preparing quality mathematics teachers. They sugge sted that more research was needed to determine precisely what other forms of knowledge would benefit the preparation of mathematicians for the classroom and insure mathematics education majors have adequate subject content knowledge. Ferrini Mundy and Fin dell (2010) debated the following two perspectives that have influenced the design of programs for the preparation of secondar y school mathematics teachers 1. Prospective high school teachers should study essentially whatever mathematics majors study be cause this will best equip them with a coherent picture of the discipline of mathematics and the directions in which it is heading, which should influence the school curriculum. 2. Prospective high school teachers should study mathematics education metho ds of teaching mathematics, pedagogical knowledge in mathematics, the 9 12 mathematics curriculum, etc. (p. 31). The authors f ound two problems with requiring the same mathematical preparation for mathematics teaching as for mathematics majors. First, th e mathematical demands of teaching are completely different than conducting mathematical research. Teachers with 33). Second, by separating content from pe dagogy, perspective teachers PAGE 38 38 may fail to acquire pedagogical content knowledge. Education courses in pedagogy help prospective teachers actively engage their students in learning, mak ing the subject matter meaningful, build ing on what the students know, an d relat ing this information to other academic areas. Mathematics majors do not receive this instruction. There was no consensus on whether or not a mathematician makes a more qualified teacher because of their content knowledge or whether an education majo r is more qualified As many researchers indicate, more collaboration between mathematics departments and education departments are needed to develop more qualified mathematics teachers in both mathematics subject content and pedagogy (Bass, 1997, 2005; Fe rrini Mundy & Findell, 2010; Nebres, Cheng, Osterwalder, & Wu, 2006 ; Wu, 2011) End of Course Exams and Student Achievement End of course exams are used in many countries to measure student succ ess and teacher effectiveness. According to the Center on Educ ation Policy (2008) many states History of End of Course Exams One of the first researchers to study the effects of curriculum based external exit examinations (CBEEE) on achievement was Bishop (1997). It had been hypothesized ould improve teaching and learning of 2). A CBEEE has the following traits: 1. Produces signals of student accomplishment that have real consequences for the student; 2. defines achievement relative to an external standard, not relative to other students in the classroom or the school; PAGE 39 39 3. is organized by discip line and keyed to the content of specific course sequences; 4. signals multiple levels of achievement in the subject; and 5. covers almost all secondary school students (p. 3). He found er weight to academic achievement when they make admission and hiring decisions; so T he author explained that when CBEEEs are used the incentives available to students, parents, teachers and administrators are improved. Students are not pressured to outperform their colleagues (rank in class), teachers do not feel they are required to give higher grades than students deserve, and administrators can use results of CBEEEs to challenge teac hers to raise standards in their classroom. When looking at Canadian schools, Bishop, Moriarty, and Mane (1997) learned deviation better prepared in mathematics and 15 pe rcent of a standard deviation better 5). Using data from the National Association of Education Progress (NAEP), Bishop (2005) concluded that the introduction of Universal CBEEEs in New York and North Carolina during the 1990s was associated with large increases in math achievement on NAEP 27). He noticed the CBEEEs to substantially increase academic achievement withou t decreasing school 1. They signal the full range of student ach ievement to universities and to employers, so all students get increased rewards better jobs and access to prefe rred university programs if they study harder. PAGE 40 40 2. Doing poorly on a European Universal CBEEE means you graduate with a record of modest accomplishment. 3. End of course exams pressure individual teachers to improve their teaching. 4. The component exams of the Universal CBEEEs are more challenging and higher in quality than the minimum competency test (MCT) and standards based exams (SBE) that dominate student accountability in the U.S. (p. 28). Bishop, Mane, and Bishop (2001) examined the differences bet ween minimum competency exams and curriculum based external exit exams and their relationship to student achievement and learning conditions. They concluded that students are made more aware of their achievement level and have the incentive to do better on CBEEEs. Because the exams usually contain more difficult material, teachers spend more time on cognitively demanding skills and strategies and it encourage s t hem to set higher standards in the classroom. To determine the success of curriculum based extern al Mathematics and Science Study (STEMS) and the International Assessment of curriculum based exit exam systems are ahead of students from other countries at a comparable level of economic development including the United States by 0.67 2 Bishop (1997) also concluded that curri culum based end of course exams had an impact on school policies and instructional practices. Higher minimum standards were set for becoming a teacher, higher teacher salaries (30 34 percent higher for secondary teachers) were noted, and more teachers ma jored in the subject they are assigned to teach. PAGE 41 41 Algebra 1 EOC With the implementation of Senate Bill 4, Florida has moved to end of course exams to measure student achievement. Students entering high school in school year 2011 were required to take an end of course exam in Algebra 1. assessment measures achievement of students enrolled in Algebra 1, or equivalent course, by assessing student progress on the benchmarks of the Next Generati on Sunshine State Standards (NGSSS) ( see Table 2 1) that are assigned to Algebra 1 course desc The exam is given in one 160 minute session with a 10 minute break after the first 80 minutes. Students that did not finish in the allotted time were allowed to continue testing; however testing must be concluded within one school day. The Algebra 1 EOC assessment was administered via a computer based testing platform. There were three forms of the test each form containing questions common to all three forms, questions unique to each form, and field test questions. Each form included 35 40 multiple choice (four answer choices given) and 25 30 fill in responses (solve a problem and record a numerical answer). Each form contained 5 reporting categories with different numbers of questions within a test form; however across all test f orms. The reporting categories were: Functions, Linear Equations and Inequalities (55%), Polynomials (20%), and Rationals, Radicals, Quadratics, and Discrete Mathematics (25%). Students received a T score using a scale of 20 80. On the T score scale, 5 0 was the statewide average and all interpretations were norm PAGE 42 42 referenced interpretations. Each school district was responsible for assigning a letter grade to the scale score and using this grade as 30% of the final grade for the course. Gender and Student Achievement in Mathematics For many years males have been identified as being superior to females in mathematical ability on standardized tests (Beller & Gafni, 1996; Campbell & Beaudry, 1998; Kimball, 1989). Recent studies indicate that these findings ar e no longer valid (Geist & King, 2008; Georgiou, Stavrinides, & Ka lavana, 2007; Tsui, 2007). A dditional studies indicate that any gender gaps that continue may be related to affective and sociological factors (Ai, 2002; Kimball, 1989; Nagy, et al 2006). J acobs, Lanza, Osgood, Eccles, and Wigfield (2002) studied perceptions of self competence and task values in children across grades 1 through 12 in mathematics, language arts, and sports domains. Using Hierarchical Linear Modeling (HLM) they determined that of their math competence, and significant gender effects for slope and acceleration socialization in the home and society by parents, peers, media and role models they see around them. Boys start out with higher perceptions of their math competence in mathematics at first grade, but their competence beliefs decline at a faster rate than f differential rates of decline, boys and girls had similar beliefs about p. 517 518). Task values for males and females rate math more when they felt competent in the subject. PAGE 43 43 While past research has indicated that males reach higher mathematical levels than females, current research revealed that females are reaching the same level in mathematical ability. Georgiou, et al (2007) found no significant differences between eighth grade boys and girls in math achievement. Using data obtained from self report scales of Attitudes Towards Mathematics Sca le, Maths Achievement Attribution Scale, a math achievement test (TIMSS) and the Affective Reactions Scale, the authors concluded the following: 1. The mean scores of boys and girls in mathematics achievement were not significantly different (boys mean sco re = 4.07, SD score = 3.82, SD = 1.8, t = .78, p > .05); 2. High achieving boys had significantly higher mean scores in ability attributions than all other groups ( X = 3.42). However, high achieving girls did not have significantly hi gher mean score in effort attributions than high achieving boys; 3. High achieving boys and girls do not differ significantly in their attitudes towards mathematics (i.e. they both find it to be an attractive subject). This was not true for low achieving b oys and girls; 4. Students who do well in mathematics find the topic challenging, while those who do not do well find it threatening; 5. High achievement could predict a positive attitude towards mathematics, but such an attitude could not predict good ach ievement (p p 336 338). From data collected internationally, Else Quest, Hyde, and Linn (2010) also concluded that males and females differ very little in mathematics achievement. They also found that the more positive attitude s toward mathematics held b y males may influence their enrollment in more advanced courses and navigation towards careers with an emphasis in mathematics suggest ing that affective and sociological factors play a huge role in gender gaps that may exist. PAGE 44 44 (2010) conducted a qualitative, comparative study of females who were identified as gifted and had scored in the 95th percentile on the quantitative section of the SAT. Their goal was to determine whether academic experiences (teacher interactions, curricu la, and test taking strategies) or home strategies (parental teaching and expectations) were instrumental in their mathematics achievement. Prior test results showed that males continually score higher than females on the SAT math (M). According to College sco ring at or above 700 on the SAT M were female, compared to 63.5% who were The study involved t wenty three females from different rural and suburban high schools in Northwestern United States. There were interviewed in four categories: school/math related questions; future plans; learning behaviors; and personal questions. Additional information was collected such as report cards, teacher comments, and standardized test scores. The results indicated that more than half attributed their success to their abilities which challenge s previous research that indicated female success in mathematics was due to luck or hard work. These students also felt that mathematics was useful in their lives, were persiste nt when faced with difficult concepts, that parental influence played as an important reinforce ment and that acknowledgement from their teachers for their success reinforced th eir mathematical self concept. They did not feel their teachers treated them di fferently from their male classmates and the enthusiasm the teachers had for the subject helped challenge them to achieve. PAGE 45 45 Ai (2002) also found that the effect of girls attitude toward mathematics on math ement and parent ward mathematics. Nagy, et al (2006) identified 10th grade students attending academically oriented schools in Germany. They compared their test scores, self concepts of ability for math and biology, and interest in the subject (intrinsic value) at the en d of 10th grade and then again in the middle of 12th grade. They fo und that self concepts ( d =.52, p < .01) and higher math intrinsic value ( d = .21, p < .05) than females, whereas females reported higher biology self concepts ( d = .15, p < .05) and higher biology intrinsic value ( d = .51, p < .01) despite being outperformed by the more advanced mathematics courses than females and vice ver sa for biology. Van de gaer, Pustjens, Van Damme, and De Munter (2008) reinforced this conclusion in a study that determined the relationship between mathematics participation and mathematics achievement in high school. They administered mathematics achiev ement tests to Flemish students in equivalent US grades of 7, 8, 10, and 12 to determine if the number of classroom hours spent in mathematics equated to student achievement. They reported a reciprocal relationship between mathematics participation and mat hematics achievement in grades 10 and 12. The Flemish system does not allow for flexibility in academic courses based on the academic plan a student PAGE 46 46 has chosen after eighth grade. They found that females tend to spend more classroom time in mathematics tha n their male counterparts in grades seven and eight resulting in only a slight variation in achievement. A s they progress through school females tend to spend less classroom time in mathematics resulting in lower achievement scores. Borrowing from research by Eccles and Wigfield (2002), the authors suggested that mathematical self influence the participation rate. concept development in the secondary years was conducted in three distinct cultural settings: Australia (Sydney), the United States (Michigan), and Germany by Nagy, Watt, Eccles, Trautwein, Ludtke, and Baumert (2010). Studying students in grades 7 through 12; they concluded the following: 1. A general decline in mathematics self concept was evident in all three countries; 2. gender differences in mathematics self concept were found in all settings; 3. males score higher than females at the beginning of grade 7 in all contexts, but the magnitude of these gender differences varied; 4. there was no evidence for gender differences in s elf concept change (p p 499 500). Marks (2008) reviewed the research from 31 countries and found that the gender gaps in mathematics have continued to decrease in recent years. He found no relationship in achievement gaps due to affective and sociological factors as reported by Ai (2002); Else Quest, et al (2010); Nagy, et al (2006) Beilock, Gunderson, Ramirez, and Levine (2010) found that many fe male teachers have anxiety toward mathematics and this may provide negative consequences for PAGE 47 47 the m The ir anxiety endorses stereotyping that boys are better at mathematics and girls are better at reading (p. 1860). Clo t felter, et al (2010) studied the effe cts of teacher gender on student ach ievement. They found that when both teacher and student were female as compared to a male teacher and female student there was a negative effect of 0.105. However, female teachers were equally effective in teaching both male and female students. Male teachers are as effective teaching male students as female teachers are teaching female students. Additional studies show mixed results. U sing NELS :88 data Dee (2006) found that same gender teachers/students had a positive effect on student achievement. Contradicting this finding was Krieg (2005) who concluded that regardless of gender, students taught by female teachers perform better than those taught by males. However, other studies conclude that teacher gender has no eff ect on student achievement (Dreissen, 2007). Ethnicity/Race and Student Achievement in Mathematics Research has shown that Blacks (37.7 percent) and Hispanics (33 percent) take lower level mathematics courses more often than Whites (26 percent) (Finn, Gerb er, & Wang, 2002). Given this information begets the question what effect did this have on level of achievement in the courses they do take? In a study using national data from Adolescent Health and Academic Achievement (AHAA), Reigle Crumb (2006) studied high school math ematics patterns of minorities and Whites in relation to their gender. He found that when African Americans and Latino males take Algebra 1 during ninth grade (usually they begin high school in a lower mathematics class then their W hite pe ers), it does not improve their chances of PAGE 48 48 reaching higher level or more advanced mathematics courses although this was not true for females. The findings showed that academic performance was not predictive of whether or not they would be successful later. Klopfenstein (2004) studied the racial differences in Advanced Placement (AP) course participation rates in Texas. Using predicted probability of enrolling in at least one AP course she found that minorities enroll at lower rates than comparable Whites an d recent migrant Hispanic students were least likely to enroll even when they were actively considering ap plying to a four year college. B lack males are predicted to B lack females fare slightly better but still participate at between 60 and 70 percent of the white female. On average, Hispanic females are even less likely to take an AP course than Black females, while 121). When Blac k and Hispanic students were given White traits (attitude and behavior) the participation Black students. When high income was included as a coefficient, the participat ion gap closes by approximately 90 percent or more for Hispanic students and by 98 percent for B The implications of these findings indicated that income was an important factor in whether or not minorities participate in AP courses which may be due to lack of resources such as parental support, limited academic role models at home, and knowledge about possible educational advantages that are available to them Asian American students have continually performed well in mathematical a chievement. Zusho, Pintrich, and Cortina (2005) studied the relationship between PAGE 49 49 achievement motives, achievement goals, and motivational outcomes on a math test given to Asian Americans and Anglo American college students. Using a 5 point Likert scale on all measures except the mathematics achievement t est, the following was observed. There were no significant differences between the Anglo and Asian samples on need for achievement, goal orientations mastery goal orientation (focus on learning and underst anding), performance approach orientation (tendency to focus on their performance after taking the mathematics test), interest (personal interest as well as enjoyments of ta sk). There were significant differences on fear of failure alpha for the Anglo sample of .78 and an alpha for the Asian sample of .83 ( p < .001 significant difference) ; performance avoidance goal orientation (defined as student focus on not looking dumb or stupid relative to other students) alphas, .86 Anglos and .85 Asians ( p < .01 significant difference); mathematics achievement ( p < .05 significant difference); anxiety (nervousness and tenseness before, during, and after the mathematics test) alphas .76 Anglo and .80 Asian ( p < .05). The researchers concluded that even though Asian Americans have a heightened fear of failure they do not let this interfere with their subsequent motivation or performance in mathematics. They felt that additional resea Research has also been conducted on how teacher race impacts student achievement. Dee (2004) asked if teacher s were more effective with students who PAGE 50 50 performance and their assignment to teachers of their own race (this was not the intent students from 79 schools for four years (grades K 3), student achievement was measured each spring using the Stanford Achievement Tests in ma th and reading. Because of the limited number of Hispanic, Asian, and Native American participants they were taken out of the data. Two thirds of the students remaining were White with 94 percent of them having White teachers and for the remaining Black st udents only 45 percent had Black teachers. There was a wide distribution variation in the different schools: city schools 97 percent of the students and 50 percent of the teachers were Black; urban/rural schools 93 percent of the students and 97 percen t of the teachers were White; and suburban schools contained 38 percent Black students and 26 percent of the teachers were Black. The results indicated: Black students that have a Black teacher for a year showed a 3 5 percentile point increase in math sc ores; and Black students with Black teachers had a 3 6 percentile point increase in reading scores. White students (male and female) with a White teacher scored 4 5 percentile points higher in math, however only male students had scores 2 6 percentil e points higher when learning from a White teacher. Females showed no significant difference. The researcher cautions that these results may not be attributed to race but to differences in teacher quality that could not be directly observed, such as for Bl ack students in predominately Black schools there is a tendency to attract and retain high quality Black teachers but lower quality White teachers, and for White students the opposite could be a factor (predominately White schools attracts more qualified W hite teachers and less qualified Black teachers). Dee proposed that schools recruit teachers based on the level PAGE 51 51 of disadvantaged students in the school and that schools that have predominately more of one race than another are unable to recruit highly qual ified teachers of the other race. U sing socioeconomic status and whether the school was segregated with a higher number of one race or another, Dee found that among White students, being assigned a White teacher had similar effects regardless of school typ e, however the opposite was true for Black students. The advantages of having a Black teacher in a school that had a high level of disadvantaged and racial segregation were consistent with the belief that lower quality White teachers were assigned to the s chool. Finally a comparison was made within the classroom and the results indicated that students still performed better when taught by teachers from their own race. Dee cautions using this data as an avenue to segregate students and teachers for the purpo se of increasing student achievement due to the adverse social consequences this could create. Socioeconomic Status and Student Achievement in Mathematics Much of the research concerning socioeconomic status (SES) has concentrated on how the SES characteri stics of the school population affect student achievement (Chiu, 2010; Crosnoe, 2009; Yang, 2003). Using mathematics test scores and questionnaires obtained from the Organization for Economic Cooperation and Development Program for International Student As sessment (OECD) to assess 15 year old students from 41 countries, Chiu (2010) looked at how country, family and school characteristics were linked to student achievement. Previous research revealed that when students come from a two parent home, they will typically have higher SES, more communication with parents, and more educational resources available to them compared to student s that come from divorced or separated parents who face more challenges in caring for them. There is usually a difference in the type of school they PAGE 52 52 attend. Higher SES students tend to have better educational resources available to them based on the location of the school. Richer countries also provide a better educational environment for their students that can place them at an ad vantage compared to those living in poorer nations. Using stratified sampling of the original participants and fitting the data with a graded response Rasch model, measurement error was reduced. The results indicated 1657). Students in richer or more equal countries had higher mathematics scores, with country gross domestic product per ca pita showing the largest country link to mathematics achievement. Students with higher SES, who were native born, speaking the national language at home, living with two parents, without residual grandparents or with fewer siblings (especially older ones) scored higher in mathematics than other students. Students with more advantageous schoolmates (higher SES) or more school resources (class time, educational material, and mathematics teachers with university degrees) had higher mathematics scores (p. 1666) (2003) Crosnoe (2009) studied the effect of socioeconomic desegregation and the effect ariant of social comparison theories, contends that students evaluate themselves relative to may find themselves at a disadvantage from a curriculum and social perspective since as the SES level of their school rises they are being compared to students that are better PAGE 53 53 prepared for high school, have had access to better educational resources, and the high SES parents are usually more educated. All of these factors could predict future educational attainments. He found that low income students in higher SES schools could have demonstrated higher achievement gains if not for the unintended side effec ts such as feeling socially isolated. Low income minority students also faced psychosocial disadvantages when placed in high SES schools with low minority populations. When measuring school SES in terms of family income rather than parent education, minori ty low income students are again at a curricular and psychosocial disadvantage. students are typically better prepared for high school, enjoy greater standing with school personn in Crosnoe, 2009, p. 711). Crosnoe indicated that as the number of high SES students rises in a school there is more competition for the low income students for coursework and grade s. These students can become labeled as academically and socially inferior to their peers even though this finding would be unlikely in lower SES schools. Crosnoe (2009) proposed basing desegregation on parent education and not income. Using multilevel ana lysis, Opdenakker and Van Damme (2001) studied Belgium (Flemish) secondary education to determine the relationship between school composition (e.g. mean school ability level, mean school SES, school ability heterogeneity) and characteristics of school proc ess and their effect on mathematics sensitive to school composition than low ability students, and that high ability students PAGE 54 54 from low SES families are most sensitive to th a later study by Opdenakker, Van Damme, Fraine, Landeghem, and Onghena (2002) they noted this level of sensitivity was probably due to poorer family resources. They m high SES families it is important to find like minded people and enough opportunity to learn; perhaps more is at stake for high The Secondary Education Institutional Exam is an important exam taken by s tudents in Turkey and is used to determine which sele ctive schools they can attend. level had a po sitive impact on achievement. Children of highly educated mothers the family Another study conducted by Jacobs and Harvey (2005) analyzed the differences between parents of high and low achieving students in Australia. They concluded that the educational a chievements obtained by the parents led to more expectations of the school to be effective at educating their children. Using multiple regression analyses the strongest pr ediction of high achievement. If education was not a high priority for the parent, than the students were not pushed by their parents to reach high academic achievement. PAGE 55 55 Using the Walberg productivity model as a basis for their study, Koutsoulis and Campbe ll (2001) studied the influence of the home environment on male and female school motivation and achievement. The model had the components of aptitude, instruction, and environment and determined how they contribute to student achievement. The study was co nduc ted in high schools in Cyprus. T hey found that the parents encouraged their children to attend college, did not put additional pressure on them to achieve, and provid ed more psychological support. The opposite was found for low SES families where additional pressure and less psychological support was found which impacted student academic self concept in mathematics and science affecting achievement. The relationship between income level and mathematics achievement has been documented by Chiu (2010); Opdenakker, et al (200 2 ); and Yang (2003). While the findings reported suggest that particular ethnic/racial and socio ec onomic groups outscore others, it is important to keep in mind that such findings do not apply to every i ndividual within these groups. Moreover, the majority of the studies report quantitative results and do not explore the contextual, socio historical, o r cultural factors that might have influenced the reported findings. Summary The purpose of the study was to determine the relationship between teacher training and student performance on end of course exam in Algebra 1. The results of previous studies reg arding whether traditional or alternative certification programs produce more effective and qualified teachers have been inconclusive (Darling Hammond, 2005; Dee & Cohodes, 2008; Monk, 1994). Other factors influence student PAGE 56 56 achievement in mathematics such as gender, race/ethnicity, and socioeconomic status. ; however this is not the focus of this study. End of course exams (EOC) are beginning to replace competency based testin g programs such as the FCAT mathematics test. As a result, teachers need to be knowledgeable in their subject area, able to convey this knowledge to their students, and capable of teaching a diverse population Certification in mathematics is required for all teachers in the state of Florida in order for them to be qualified to teach all levels of mathematics in grades 6 through 12. They can become certified by passing subject area exams or by meeting certain course qualifications. (See Appendix A) PAGE 57 57 Table 2 1 A lgebra 1 s tandards Standard Objective LA.910.1.6.1: The student will use new vocabulary that is introduced and taught directly; LA.910.1.6.2: The student will listen to, read, and discuss familiar and conceptually challenging text; LA.910.1.6 .5: The student will relate new vocabulary to familiar words; LA.910.3.1.3: The student will prewrite by using organizational strategies and tools (e.g., technology, s preadsheet, outline, chart, table, graph, Venn Diagram, web, story map, plot pyramid) to develop a personal organizational style. MA.912.A.1.8: Use the zero product prop erty of real numbers in a variety of contexts to identify solutions to equations. MA.912.A.10.1: Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guessing and checking, solving a simpler problem, writing an equation, working backwards, and creating a table. MA.912.A.10.2: Decide whether a solution is reasonable in the context of the original situation. MA.912.A.10.3: Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities, rational or radical expressions, or logarithmic or exponential functions). MA.912.A.2.3: Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. MA.912.A.2.4: Determine the domain and range of a re lation. MA.912.A.2.13: Solve real world problems involving relations and functions. MA.912.A.3.1: Solve linear equations in one variable that include simplifying algebraic expressions. MA.912.A.3.2: Identify and apply the distributive, associative, an d commutative properties of real numbers and the properties of equality. MA.912.A.3.3: Solve literal equations for a specified variable. MA.912.A.3.4: Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. MA.912.A.3.5: Symbolically represent and solve multi step and real world applications that involve linear equations and inequalities. PAGE 58 58 Table 2 1. Continued Standard Objective MA.912.A.3.7: Rewrite equations of a line into slope intercept form a nd standard form. MA.912.A.3.8: Graph a line given any of the following info rmation: a table of values, the x and y intercepts, two points, the slope and a point, the equation of the line in slope intercept form, standard form, or point slope form. MA.912.A.3.9: Determine the slope, x intercept, and y intercept of a line given its graph, its equation, or two points on the line. MA.912.A.3.10: Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line. MA.912.A.3.11: Write an equation of a line that models a data set, and use the equation or the graph to make predictions. Describe the slope of the line in terms o f the data, recognizing that the slope is the rate of change. MA.912.A.3.12: Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. MA.912.A.3.13: Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology. MA.912.A.3.14: Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, an d elimination methods. MA.912.A.3.15: Solve real world problems involving systems of linear equations and inequalities in two and three variables. MA.912.A.4.1: Simplify monomials and monomial expressions using the laws of integral exponents. MA.912.A. 4.2: Add, subtract, and multiply polynomials. MA.912.A.4.3: Factor polynomial expressions. MA.912.A.4.4: Divide polynomials by monomials and polynomials with various techniques, including synthetic division. MA.912.A.5.1: Simplify algebraic ratios. MA.912.A.5.4: Solve algebraic proportions. MA.912.A.6.1: Simplify radical expressio ns. MA.912.A.6.2: Add, subtract, multiply, and divide radical expressions (square roots and higher). MA.912.A.7.1: Graph quadratic equations with and without graphing technology. PAGE 59 59 Table 2 1. Continued Standard Objective MA.912.A.7.2: Solve quadrati c equations over the real numbers by factoring and by using the quadratic formula. MA.912.A.7.8: Use quadratic equations to solve real world problems. MA.912.A.7.10: Use graphing technology to find approximate solutions of quadratic equations. MA.912.D .7.1: Perform set operations such as union and intersection, complement, and cross product. MA.912.D.7.2: Use Venn diagrams to explore relationships and patterns and to make arguments about relationships between sets. MA.912.G.1.4: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines. (FLD OE, 20 12 ) PAGE 60 60 CHAPTER 3 METHODOLOGY An overview of the quantitative method used in this study will be presented in Chapter 3 and is divided into the following subsections: (a) research design ; (b) participants; (c) data collection ; and (d) statistical analysi s. Research Design After receiving permission from the University of Florida Institutional Review Board and the school district where the study took place, principals and teachers of Algebra 1 in the 2011 school year were contacted to request their partici pation in this survey design study Participants The study was conducted in one Southwest Florida school district comprised of 11 middle schools and nine high schools. All teachers with a teaching assignment that included Algebra 1 or Algebra 1 honors and their eighth or ninth grade students enrolled in these courses were potential participants. Approximately 40 teachers and 2500 students were potential participants in this study. Due to lack of participation by middle school teachers, they were not include d in the study. All but one high school had at least one teacher responding and taking part in the study. Fifteen teachers and 7 90 students were the actual participants in the study. Data Collection Teachers were given a questionnaire adapted from the 2009 NAEP Mathematics Teacher Background Questionnaire and asked to self report: (a) gender; (b) race/ethnicity; (c) college major; (d) highest degree obtained; (e) method of teacher certification for mathematics; (f) undergraduate or graduate mathematics cour ses taken; PAGE 61 61 (g) education methods courses taken ; (h) years of experience teaching mathematics; and (i) years of experience teaching A lgebra 1. (See Appendix B) Participants were given the choice of completing the survey online through surveymonkey.com or by downloading the survey which was attached to their request for participation email and returning the completed survey to the researcher. Each teacher was also required to sign the informed consent form ( see Appendi x C) and return to the researcher. Teacher certification information was verified through the Florida Department of Education Teacher Certification website. Teacher data was coded by the school (M01 M11) for middle and (H01 H09) for high school. Each t eacher was also assigned a number (MT01 MT19 or HT01 d known only to the researcher. Teac her data was coded as follows: gender: 0 = male, 1 = female; race/ethnicity: 1 = Whi te, 2 = Black, 3 = Hispanic, 4 = Asian, 5 = American Indian or Alaskan Native, 6 = other; college major: 1 = mathematics, 2 = mathematics education, 3 = education, 4 = other mathematics related field, 5 = other majors; highest degree obtained: 1 = B.S. or B.A., 2 = M.A., M.S., or M. Ed, 3 = Ed.S, 4 = Ph.D or Ed.D; mathematics courses taken: 0 = did not take, 1 = did take; education courses taken: 0 = did not take, 1 = did take; teacher training program or method used for certification in mathematics: 1 = tr aditional program, 2 = Troops to Teachers, 3 = Teach for America; 4 = other accelerated program, 5 = Florida subject area test only, 6 = other; and type of Florida certificate: 1 = professional, 2 = temporary, 3 = emergency. PAGE 62 62 Student data was collected and coded based on middle or high school status (M001 M100 or H001 H2400) and remained anonymous except to the researcher. Other independent variables of the students included: (a) gender ; (b) race/ethnicity ; and (c) socioeconomic status. This information was collected from existing data available from the district data warehouse program. Student data was coded by the following: gender: 0 = Male, 1 = Female; r ace/ e thnicity: 1 = White, 2 = Black, 3 = Hispanic, 4 = Asian, 5 = Other; and SES by free/reduced lu nch status: 1 = does not qualify, 2 = free, and 3 = reduced. Algebra 1 e nd of course exam test scores (dependent variable) were collected from the 2011 data provided by the Florida State Department of Education and retrieved from the district data warehous e program. The FLDOE reported the scores as a T score. Students without test scores were removed from the study. Description of Teacher Data Fifteen teachers participated in the study, 11 (73.3%) were White and four teachers (26.67%) were Hispanic, 11 (73. 3%) were male teachers and four (26.67%). were female. Three teachers (20.00%) majored in mathematics, three teachers (20.00%).majored in education with an emphasis in mathematics, and nine teachers (60.00%) majored in other areas including biology, aerona utical science, aerospace engineering, business, accounting and finance, and liberal arts. Two teachers (13.33%) held a doctoral degree, one teacher (6.67%) had a specialist degree, four teachers Subject certification in mathematics included: one teacher (6.67%) with 5 12 math, three teachers (20.00%) with 5 9 math, nine teachers (60.00%) with 6 12 math, one teacher (6.67%) with 9 12 math, and one teacher (6.67%) with 5 9 math and 6 12 PAGE 63 63 math. Eight teachers (53.33%) with alternative certification were certified by subject area testing, two teachers (13.33%) certified by alternative programs, and five teachers (33.33%) were traditionally trained. The mean for years t eaching mathematics was 10.20 with a standard deviation ( SD ) of 9.50. Experience ranged from one year to 37 years. The mean for years teaching Algebra was 5.47 with a SD of 5. 1 9 while the range was one to 20 years (See Table 3 1 for Demographics of t eacher p articipants). Description of Student Data Data from 429 males (54.3%) and 361 (45.7%) females were analyzed. The race/ethnicity of the sample was: White (n = 295) or 37.34%, Black (n = 84) or 10.63%, Hispanic (n = 374) or 47.34%, and other (n = 37) or 4. 68%. SES was determined by lunch status. The number of students that did not qualify for free/reduced lunch was 317 (40.2%), while 413 (52.3%) qualified for free lunch, and 59 (7.48%) qualified for reduced lunch. Statistical Analysis Using the type of trai ning program as the control variable, teacher characteristics teacher variables of gender, major type number of years teaching Algebra 1, subject certification, number of educ ation courses, and number of mathematics courses were compared to student variables of gender, race/ethnicity, and SES to determine what effect they have on student performance on the EOC in Algebra 1. Frequency distributions were used to describe teacher and student data Mean and standard deviation ( SD ) were used to compare teacher and student data in relationship to test scores. Spearman Correlation Coefficients were used to analyze PAGE 64 64 teacher variables of years teaching Algebra 1 to number of math courses taken and num ber of education courses taken to analyze the strength of their associations such as if one variable increases, does the other variable increase or decrease? Wilcoxon scores for teacher variables on number of mathematics courses taken and numb er of education courses taken were compared with teacher training methods, race/ethnicity, and gender H ierarchical Linear Modeling (H LM ) is a procedure that analyzes group correlations and was used in this study to determine the relationship between teach er training and student gender, race/ethnicity, and SES. Limitations There was limited participation by schools and teachers. The results of the study may not accurately reflect the true effect of teacher training on student achievement. There was also an imbalance in the number of traditionally certified teachers compared to the alternatively certified. Many of the alternatively certified teachers obtained their certification to teach mathematics by taking the subject area exam offered by the Florida Depar tment of Education. PAGE 65 65 Table 3 1. Demographics of t eacher p articipants Participant n umber Ethnicity Gender College m ajor Highest d egree Training p rogram Florida c ertificate t ype Subject/ g rade l evels c ertification Years teaching m ath Years teac hing Algebra 1 HT06 White Male Business Master s Subject area testing Temporary 6 12 M ath 2 1 HT09 White Male Accounting f inance Specialist Subject area testing Professional 6 12 M ath 6 6 HT10 White Female Liberal a rts Bachelor' s Subject area testing Professional 6 12 M ath 5 9 M ath 7 5 HT13 White Female Mathematics Bachelor's Subject area testing Professional 6 12 M ath 12 5 HT07 Hispanic Male Education Doctorate Subject area testing Professional 5 9 M ath 10 1 H T16 White Male Education Master s Subject area testing Professional 5 9 M ath 1 1 HT17 White Male Aeronautical s cience Master s Subject area testing Professional 5 9 M ath 5 3 HT18 White Male Aerospace engineering Bachelor's Subject area testing Tempor ary 9 12 Math 1 1 HT02 White Male Biology Bachelor's Alternative Professional 5 12 Math 8 3 HT03 Hispanic Male Education Bachelor's Traditional Professional 6 12 Math 11 10 HT01 Hispanic Male Applied math Doctorate Alternative (E ducator Preparation Institute Edison State College) Professional 6 12 Math 37 7 HT04 White Female Education Traditional Professional 6 12 Math 24 20 PAGE 66 66 Table 3 1 Cont inued Participant n umber E thnicity G ender College m ajor Highest d e gree Teacher t raining p rogram Florida c ertificate t ype Subject/ g rade l evels c ertification Years t eaching m ath Years teaching Algebra 1 HT05 White Female Mathematics e ducation Bachelor's Traditional Professional 6 12 M ath 14 12 HT11 White Male M athematics e ducation Bachelor's Traditional Professional 6 12 Math 11 4 HT12 Hispanic Male Mathematics e ducation Bachelor's Traditional Professional 6 12 Math 4 3 PAGE 67 67 CHAPTER 4 RESULTS AND ANALYSIS The purpose of Chapter 4 is to present the findings r elated to each of the research questions. Research Question 1: Is there a relationship between teachers who completed a traditional preparation program and those who received alternative certification on student performance on the end of course exam in Alg ebra 1? Descriptive statistics were used to compare teacher training methods with Algebra 1 T scores of the students in each category. The mean T score for students of teachers who completed a traditional training program was 45.7 1 SD = 10.05, minimum T score = 20, and maximum T score = 78. Students of alternatively trained teachers had a T score mean = 40.65, SD = 7.99, minimum T score of 27 and a maximum T score of 56. Subject area testing teachers had student mean T score = 43.9 1 SD = 10.98, minimum T score of 20, and maximum T score of 67 The results support the hypothesis for research question one of no significant difference in the relationship between teachers who completed a traditional preparation program and those who received alternative certi fication on student performance on the end of course exam in Algebra 1 After adjusting for student gender, race/ethnicity, and socioeconomic status is there a relationship between teacher preparation method and student performance on the end of course exa m in Algebra 1? The GLIMMIX Procedure is a hierarchical modeling procedure used when data have hierarchical or clustered structures such as students nested within schools. In this study it was used to determine the relationship between teacher training, s tudent performance on the Algebra 1 EOC, and the effect on student variables of gender, race/ethnicity, and socioeconomic status. Hierarchical linear modeling (HLM) used covariance parameter estimation, Type III Tests of Fixed Effects to determine the PAGE 68 68 sign ificance of teacher training and student performance on the Algebra 1 EOC on each of the variables. Student gender produced F value = 0.19, and Pr > F = 0.6 7 a statistically non significant finding meaning that there was no significant difference between t eacher preparation method and student performance on the end of course exam in Algebra 1 after adjusting for gender. Student race/ethnicity produced F value = 1.48, and Pr > F = 0.24 and was also not statistically significant meaning that there was no sign ificant difference between teacher preparation method and student performance on the end of course exam in Algebra 1 after adjusting for race/ethnicity However, student socioeconomic status produced F value = 3.91, and Pr > F = 0.0 4 which was statisticall y significant demonstrating there was a significant difference due to socioeconomic status When comparing all variables, SES superseded all other variables ( F value = 3.76, Pr > F = 0.04) thus it was impossible to see the effects of teacher major type ( F value = 0.08, Pr > F = 0.7 9 ), type of teacher training ( F value = 0.14, Pr > F = 0.7 2 ), years teaching mathematics ( F value = 2.05, Pr > F = 0. 20 ), and years teaching Algebra ( F value = 0.77, Pr > F = 0.4 1 ) on student performance results. To determine if t he concept (a social context where individuals judge their abilities by comparing themselves to others in their group and is influenced by was a facto r in the differences in student test scores, descriptive statistics were collected at a low SES school and a high SES school. The results were as follows : S tudents on free/reduced lunch ( n = 50) at a high SES school had a mean test score = 45.34, SD = 9.0 2 compared to the students that did not qualify for free/reduced lunch ( n =116) with a mean test score = 50.2 9 SD = 7.76. All students were taught by teachers with subject PAGE 69 69 area testing. The SES level of the school did not seem to impact test scores. An an aly sis of a low SES school showed the following results S tudents on free/reduced lunch ( n = 136) had a mean test score = 44.43, SD = 9.57 and student s that did not qualify for free/reduced lunch ( n = 7 ) had a mean test score of 40.14, SD = 13.52. These stude nts had a traditionally certified teacher. Again, there seem s to be no impact The results indicated that the effect of the type of teacher training program on student performance on the Algebra 1 EOC is only stat istically significant when compared to the student socioeconomic status. Research Question 2: Is there a relationship between teachers who majored in mathematics and those who were education majors with an emphasis in mathematics on student performance o n the end of course exam in Algebra 1? Descriptive statistics were used to compare Algebra 1 EOC test scores of students with teachers who majored in mathematics and with teachers who majored in education with an emphasis in mathematics. Three teachers we re identified in each category. The mean T score for the 226 students of the teachers with mathematics major was 46.6 8 SD of 10.1 4 and with a minimum T score of 20.0 and maximum T score of 78.0. The mean T score for the 144 students of education majors w ith an emphasis in mathematics was 44.1 6 SD of 9.79, and with a minimum T score of 20.0 and a maximum T score of 64.0. There was no statistic significance in student performance on the end of course exam when compared to mathematics majors and education m ajors with an emphasis in mathematics. The findings showed there was no significant difference between and student performance on the end of course exam in Algebra 1. PAGE 70 70 There were 420 students of teachers ( n = 9) without either a teacher with a mathematics major or education major with an emphasis in mathematics with a mean test score of 43.7 3 SD = 10.86, and a minimum T score of 20.0 and a maximum T score of 67.0. Again, no statistical significance was noted demonstrating that there was no significant difference in the relationship between teachers who majored in mathematics and those who were education majors with an emphasis in mathematics by student performance on the end of course exam in Algebra 1. After adjusting for stude nt gender, race/ethnicity, and socioeconomic status is there a relationship between teacher preparation method and student performance on the end of course exam in Algebra 1? Student gender and performance on the Algebra 1 EOC produced the following resul ts: males ( n = 429) mean T score of 44.3 8 SD = 10.33, minimum T score of 20.0 and a maximum T score of 67.0; females ( n = 361): mean T score of 44.9 7 SD = 10.78, minimum T score of 20.0 and maximum T score of 78.0. There was n o significant difference in performance due to gender. Race/ethnicity and performance on the Algebra 1 EOC results were: White ( n = 295) mean T score of 47.4 2 SD = 9.5 2 minimum T score of 20.0 and maximum T score of 67.0; Black ( n = 84) mean test of 41.58, SD = 11.0 6 minimum T sco re of 20.0 and maximum T score of 64.0; Hispanic ( n = 374) mean T score of 43.2 4 SD = 10.7 5 minimum T score of 20.0 and maximum T score of 78.0; and other ( n = 37 includes all individuals not classified as White, Black, Hispanic, or Asian) mean T score of 43.81, SD = 10.4 4 minimum T score of 20.0 and maximum T score of 58.0. No significant difference in performance was noted for race/ethnicity. Socioeconomic status (SES) was determined by participation in free/reduced lunch program. Students that did n ot qualify ( n = 317) had a mean T score PAGE 71 71 of 47.1 8 SD = 10.10, and a minimum T score of 20.0 and a maximum T score of 67.0. Students on free lunch ( n = 413) had a mean T score of 42.67, SD = 10.2 3 minimum T score of 20.0 and a maximum T score of 64.0. Stud ents on reduced lunch (n = 59) had a mean T score of 45.07, SD = 12.10, minimum T score of 20.0 and a maximum T score of 78.0. There was no significant difference in student performance for SES when comparing with teacher major. The findings showed that th ere was no significant differences between teacher training program and student performance on the Algebra 1 EOC when comparing teacher training (m athematics major or education major with an emphasis in mathematics ) by gender, race/ethnicity, and socioecon omic status and there was no significant difference between teachers who majored in mathematics and those who were education majors with an emphasis in mathematics on student performance on the end of course exam in Algebra 1 after adjusting for gender, ra ce/ethnicity, and socioeconomic status Research Question 3: Is there a relationship between the number of mathematics courses taken by the teacher and preparation type, teacher gender, and race/ ethnicity? The state of Florida uses a Statewide Course Nu mbering System (SCNS) to allow smooth articulation between universities and colleges. T o better facilitate a way to obtain an accurate list of mathematics courses a teacher may have taken in their undergraduate or graduate study, a list of mathematics cour ses from the University of Florida course catalog for mathematics majors and education majors with an emphasis in mathematics were provided to each teacher. A link to the university course descriptions was provided for teachers to examine the content of th e course for clarification. The original intent of the study was to look for a relationship between the PAGE 72 72 content of mathematics courses taken and teacher variables. However, it became evident there was no pattern to the types of courses taken by the teacher s. (See Table 4 1 for teacher training programs and mathematics courses taken.) Therefore, it was the number of mathematics courses taken by the teachers in the different preparation types used in the analysis Using descriptive statistics traditionally tr ained teachers were compared with alternatively certified teachers, and those teachers whom received certification by subjec t area testing in mathematics. Traditionally trained teachers ( n = 5) had a mean score for mathematics courses taken of 13.40, SD = 3.5 1 and a range of nine courses to 18 courses. Alternatively trained teachers ( n = 2) had a mean score for mathematics courses taken of 9.00, SD = 2.8 3 and a range of seven courses to 11 courses. Teachers taking the mathematics subject area test ( n = 8) had a mean score for mathematics courses taken of 7.75, SD = 4.9 5 and a range one course to 15 courses. The NPAR1WAY procedure was used for an analysis of variables of teacher training and number of mathematics courses. Wilcoxon scores (rank sums) provid ed the expected sum of scores under the null hypothesis i f no differences among programs and number of mathematics courses were found. T raditionally trained teachers ( n = 5) had a sum of scores of 56.50, with an expected value under the null hypothesis (Ho ) of 40.0, SD = 8.1 1 and a mean score of 11.30. Teachers trained by alternative methods ( n = 2) had a sum of scores of 14.50, with an expected value under the Ho of 16.0, SD of 5.8 5 and mean score of 7.25. The subject area testing teachers ( n = 8) had a sum of scores of 49.00, with an expected value under the Ho of 64.0, SD of 8.57, and mean score of 6.1 3 PAGE 73 73 The Kruskal Wallis Test (a non parametric version of ANOVA) was used to test the null hypothesis since there was no difference between variables. R esul ts of the Chi square = 4.2 5 degrees of freedom ( df ) = 2, and Pr > Chi Square = 0.1 2 showed no significance between number of mathematics courses taken and type of teacher training. The findings s howed that there was no significant difference between the n umber of mathematics courses taken by the teacher and preparati on type (See Table 4 3 for results). Teacher gender and number of mathematics courses were also compared using descriptive statistics, Wilcoxon Scores Test, Wilcoxon Two Sample Test, and Kruska l Willis Test. The mean score for males ( n = 11) was 8.45, SD = 4.61, minimum number of mathematics courses = 1.0 and a maximum number of mathematics courses = 15.0. Females ( n = 4) had a mean score of 13.50, SD = 3. 70 minimum number of mathematics course s =10.0 and a maximum number of mathematics courses of 18.0. Wilcoxon scores (rank sums) for males had a sum of scores = 74.0, an expected value under the null hypothesis (Ho) = 88.0, SD under Ho =7.60, and a mean score of 6.7 3 Females results were: sum o f scores = 46.0, an expected value under the Ho = 32.0, SD under the Ho = 7.60, and a mean score = 11.50. Wilcoxon Two Sample Test is a test of the null hypothesis to determine that there is no difference between two variables. In this analysis, the variab les are the number of mathematics courses taken and teacher gender. The Wilcoxon statistic equals 46.0 which was greater than 32.0, the expected value under the null hypothesis. As a result the NPAR1WAY procedure produces right sided p values. The t approx imation yielded one sided Pr > Z = 0.0 5 which was statistically significant. The two sided t PAGE 74 74 09 which was also statistically significant at a trend level The normal approximation (Z = 1.7 8 ) yielded a one sided Pr > Z of 0.0 4 which was statistically significant. The two 0. 08 which was also statistically significant at a trend level The t and normal approximation showed that there was a significant difference between the number of mathematics courses taken by the teacher and teacher gender. The Kruskal Wallis test yie lded a chi square of 3.3 9 df = 1, and Pr > chi square = 0.0 7 which was also statistically significant at a trend level rejecting the null hypothesis of no significant difference between the number of mathematics courses taken by the teacher and teacher g ender (See Table 4 4 for results) Teacher race/ethnicity and the relationship to number of mathematics courses taken were analyzed using the same methods described above. Descriptive statistics were: the mean score for Whites ( n = 11) of 8.9 1 SD = 5.22, minimum number of mathematics courses = one and maximum number of mathematics courses = 18.0. Hispanics ( n = 4) had a mean score of 12.25, SD = 2.75, minimum number of mathematics courses of 9.0 and maximum number of mathematics courses of 15.0. No other r ace/ethnic groups were identified. Wilcoxon scores (rank sums) for Whites had a sum of scores = 78.50, an expected value under the null hypothesis (Ho) = 88.0, SD under Ho =7.60, and a mean score of 7.1 4 Hispanic results were: sum of scores = 41.50, an ex pected value under the Ho = 32.0, SD under the Ho = 7.60, and mean score = 10.3 8 Wilcoxon Two Sample Test measured the number of mathematics courses taken with the race/ethnicity. The Wilcoxon statistic equaled 41.5 which was greater than 32.0, PAGE 75 75 the expect ed value under the null hypothesis. As a result the NPAR1WAY procedure produced right sided p values. The t approximation produced one sided Pr > Z = 0.1 3 and two 6 which were not significant. The normal approximation (Z = 1.18) yielded a one sided Pr > Z = 0.1 2 and two sided Pr > 0.2 4 which were not significant. The t and normal approximation showed that there was no significant differe nce in the relationship between the number of mathematics courses taken by the teacher and teacher race/ethnicity The Kruskal Wallis test yields a chi square of 1.56, df = 1, and Pr > chi square = 0.02 which was not significant, supporting the hypothesis on the relationship between the number of mathematics courses taken and teacher race/ethnicity (See Table 4 5 for results) The findings for research question three varied. The re was no significant difference between the number of mathematics courses taken by the teacher and preparation type and race/ethnicity of the teacher. However, the re was a significant difference in the number of mathematics courses taken by the teacher and teacher gender Research Question 4: Is there a relationship between the numbe r of educational methods courses taken by the teacher and preparation type, teacher gender, and race/ethnicity? The same statistical procedures used in research question three were also us ed for research question four. Teachers were given a list of educat ional methods courses and a link to the University of Florida course descriptions for clarification of the content of the courses. As with the mathematics courses, there was no set pattern of course taking by the different teacher groups so instead of exam ining the content of the PAGE 76 76 educational methods courses tak en by the teachers (See Table 4 2 for number of educational methods courses taken by teacher groups), the number of educational methods courses were analyzed. Descriptive statistics compared the tradi tionally trained teachers, alternative certification teachers, and teachers certified with the mathematics subject area exam on the number of educational methods courses that were taken in undergraduate or graduate study. The following results were reveale d: traditionally trained teachers ( n = 5), had a mean score of 11.40, SD = 6.2 3 and a minimum of four and maximum of 20.00 for the number of educational methods courses taken; alternatively certified teachers ( n = 2), mean score of 7.50, SD = 0.7 1 and a minimum of seven to a maximum of eight for the number of educational methods courses taken; and teachers taking the mathematics subject area exam ( n = 8), mean score of 5.6 3, SD = 4.37, and a minimum of zero to a maximum of 13.00 for the number of educatio nal methods courses taken. The Wilcoxon test was also performed for the variables of teacher training and number of educational methods courses. Traditionally trained teachers ( n = 5) had a sum of scores of 54.0, an expected value under the null hypothesis (Ho) of 40.0, SD = 8.12, and a mean score of 10.80. Teachers trained by alternative methods ( n = 2) had a sum of scores of 16.0, an expected value under the Ho of 16.0, SD = 5.8 6 and mean score of 8.00. Teachers using subject area testing ( n = 8) had a s um of scores of 50.00, an expected value under the Ho of 64.0, SD = 8.59, and mean score of 6.25. The Kruskal Wallis test was also performed with the following results: Chi Square of 3.2 2 degrees of freedom = 2, and Pr > Chi Square = 0. 20 which revealed n o PAGE 77 77 statistical significance between the number of educational methods courses taken an d the type of teacher training (See Table 4 3 for results) Teacher gender and race/ethnicity were also compared to the number of educational methods courses taken by the teachers. The Wilcoxon Scores (rank sums) for variable (number of educational methods courses) classified by variable (teacher gender) results were males ( n = 11): sum of scores = 84.0, an expected value under the Ho = 88.0, SD under the Ho = 7.6 2 and a m ean score of 7.6 4 ; females ( n = 4): sum of scores = 36.0, expected value under Ho = 32.0, SD under Ho = 7.6 2 and a mean score of 9.00. The Wilcoxon Two Sample test used the variables of the number of educational methods courses taken and teacher gender. T he Wilcoxon statistic equals 36.00 which was greater than 32.0, the expected value under the null hypothesis. As a result the NPAR1WAY procedure produces right sided p values. The t approximation yielded one sided Pr > Z = 0.3 3 and a two significant. The normal approximation (Z = 0.4 6 ) yielded a one sided Pr > Z of 0.32 which was not statistically significant. The two sided normal approximation yielded Pr > 5 which was also not statistically significant. The Kruskal Wallis Test yielded a chi square of 0.2 8 df = 1, and Pr > chi square of 0. 60 which reveals no statistically significance between teacher gender and the number of educational methods courses taken (See Table 4 4 for results) Teacher race/ethnicity and the relationship to number of educational methods courses taken were also analyzed using the same methods described above. The descriptive statistics were: the mean score for Whites ( n = 11) of 7.36, SD = 5.64, PAGE 78 78 minimum number of educational methods courses of zero and a maximum number of mathematics courses of 20. Hispanics ( n = 4) had a mean score of 9.00, SD = 4.69, minimum number of educational methods courses of four and a maximum number o f mathematics course s of 15.0. No other race/ethnic groups were identified in the study. Wilcoxon scores (rank sums) for Whites had a sum of scores = 83.0, an expected value under the null hypothesis (Ho) = 88.0, SD under Ho =7.6 2 and a mean score of 7.5 5 Hispanic results w ere: sum of scores = 37.0, an expected value under the Ho = 32.0, SD under Ho = 7 .6 2 and a mean score = 9.25. The Wilcoxon Two Sample Test compared the number of educational methods courses taken with teacher race/ethnicity. The Wilcoxon statistic equals 37.0 which was greater than 32.0, the expected value under the null hypothesis. As a result the NPAR1WAY procedure produced right sided p values. The t approximation produced one sided Pr > Z = 0.28 a nd two significant. The normal approximation (Z = 0.59) yielded a one sided Pr > Z = 0.2 8 and two The Kruskal Wallis test yields a chi square of 0.43, df = 1, and Pr > chi square = 0.51 which was not statistically significant (See Table 4 5 for results) Additional Research Findings The CORR procedure was used to determine the relationship between three variables: number of years teaching Algeb ra, number of mathematics courses taken, and number of educational methods courses taken. The mean, standard deviation median, minimum and maximum were analyzed for each variable for the 15 teachers involved in the study. For years teaching Algebra: mean = 5.4 7 SD = 5.19, median = 4.00, minimum = 1.00, and maximum = 20.00; number of mathematics courses: mean = PAGE 79 79 9.80, SD = 4.84, median = 10.00, minimum = 1.00, and maximum = 18.00; number of educational methods courses: mean = 7.80, SD = 5.29, median = 8.00, minimum = 0, and maximu m = 20.00. n = 0) were used to determine the relationship between two of the variables. Comparing years teaching Algebra to the number of mathematics courses yields rho = 0.64, and p = 0.01 was statistically significant. Y ears teaching Al gebra to the number of educational methods courses yields rho = 0.3 8 and p = 0.16 and was not statistically significant. Comparing number of mathematics courses to the number of educational methods courses yields rho = 0.34 and p = 0.21 was not statistica lly significant. Summary The purpose of C hapter 4 was to describe the quantitative results of the data analysis of this study. The findings revealed: 1. No significant differences were found on student performance on the Algebra 1 EOC and the type of training of their teacher. Comparison of student variables of gender and race/ethnicity revealed no significant differences in Algebra 1 test scores. However, student variable of socioeconomic status was statistically significant. Results revealed that the lower t he economic status of the student (free lunch), the lower the mean score of the Algebra 1 EOC. 2. No significant differences were found between student performance on the Algebra 1 EOC and teachers that majored in mathematics, education with an emphasis in ma thematics, or the variety of other majors the teachers demonstrated. No significant difference was found when comparing teacher variable of mathematics major or education major with an emphasis in mathematics on student variables of gender, race/ethni city, and socioeconomic status. 3. There was no significant difference in the number of mathematics courses taken and type of teacher training. There was also no significant difference in race/ethnicity of the teacher and the number of mathematics courses taken. H owever, there was a significant difference in the number of mathematics courses taken and teacher gender. Female teachers mean scores for number of mathematics courses taken was significantly higher than the mean scores for PAGE 80 80 males. There was also a signific ant difference in the number of mathematics courses taken and number of years teaching Algebra. 4. There was no significant difference in the number of educational methods courses taken by teachers and type of teacher training program, teacher gender, or race /ethnicity of teacher. There also was no significant difference in the number of years teaching Algebra to the number of educational methods courses taken by the teacher. 5. There was no significant difference in the number of mathematics courses taken to the number of educational methods courses. PAGE 81 81 Table 4 1. Mathematics courses taken by teachers Course number Course title Number of teachers taking course Traditional Alternative Subject a rea t esting (n = 5) (n = 2) ( n = 8) MGF1106 Mathematics for libe ral arts majors 0 0 2 MAC1105 College algebra 3 2 2 MAC1114 Trigonometry 1 2 3 MAC1140 Precalculus 0 0 3 MAC1147 Precalculus: algebra and trigonometry 1 1 0 MAC2311 Analytic geometry and calculus 1 5 1 6 MAC2312 Calculus 2 5 2 3 MAC2313 Calculus 3 5 1 3 MHF3404 History of mathematics 4 0 2 MHF3202 Sets and logic 3 0 1 MTG3212 Geometry 2 2 2 MAP2302 Differential equations 5 1 3 MAP4102 Probability theory 3 0 3 MAD3107 Discrete mathematics 5 0 3 MAD4203 Combinatorics 2 0 0 MAD4401 Numerical ana lysis 3 1 2 MAS4105 Linear algebra 4 2 3 MAS4301 Abstract algebra 4 0 3 MAS4203 Number theory 3 0 1 MAA4226 Real analysis 1 0 2 MAA4227 Complex analysis 1 0 3 STA4321 Mathematical statistics 1 4 2 7 STA4322 Mathematical statistics 2 3 1 5 PAGE 82 82 Table 4 2. Educational methods courses taken by teachers Course number Course title Number of teachers taking course Traditional Alternative Subject area testing (n = 5) (n = 2) ( n = 8) EDF1001 Introduction to the teaching profession 3 2 3 EDF2085 Int roduction to diversity for educators 4 2 3 EDF3110 Human growth and development 5 1 3 EDF3210 Educational psychology 4 2 4 EDF3214 Learning and cognition in education 3 1 3 EDF4430 Measurement and evaluation in education 3 1 3 SDS3430 Family and comm unity involvement in education 1 0 0 SDS4410 Interpersonal communication skills 1 0 2 EDG3377 Mathematics and science 3 0 2 EDG4203 Elementary and secondary curriculum 1 0 2 EDG4204 Curriculum and instruction for secondary learners 5 1 4 EDM4403 Middl e school education 0 0 1 ESE4340C Effective teaching and classroom management in secondary education 2 1 4 MAE2364 Explorations teaching secondary mathematics and science 2 0 0 MAE4331 Secondary school mathematics methods and assessment 3 1 1 MAE4941 P racticum in teaching secondary mathematics and science 1 0 0 MAE4947 Secondary mathematics practicum 2 0 0 MAE5327 Middle school mathematics methods 1 0 1 MAE5395 Multicultural math methods 1 0 0 MAE6313 Problem solving in school mathematics 1 0 1 TS L4324 ESOL strategies for content area teachers 4 2 3 EEX4394 Differentiated instruction 2 0 2 EEX3257 Core teaching strategies 2 0 1 EEX3616 Core classroom management strategies 2 1 2 PAGE 83 83 T able 4 3. Training methods and number of mathematics and educ ation coursework Teacher training Number of observations Variable number of courses Mean Standard deviation Traditional 5 Math (a) education (b) 13.4 11.4 3.5 6.2 Alternative 2 Math (a) education (b) 9.0 7.5 2.8 0.7 Subject a rea t esting 8 Math (a) education (b) 7.8 5.6 4.9 4.4 (a) p value for this test equals 0. 12. (b) p value for this test equals 0.20. PAGE 84 84 Table 4 4. Teacher gender and number of mathematics and education coursewo rk Teacher gender Number of observations Variable number of courses Mean Standard deviation Ma l e 11 Math (a) education (b) 8. 5 7. 1 4.6 4.6 Female 4 Math (a) education (b) 13.5 9. 8 3.7 7. 2 (a) p value for this test equals 0. 09. (b) p value for this test equals 0.65. PAGE 85 85 Table 4 5. Teacher race/ethnicity and number of mathematics and education coursework Teacher Race Number of observations Variable number of courses Mean Standard deviati on White 11 Math (a) education (b) 8.9 7.4 5.2 5.6 Hispanic 4 Math (a) education (b) 12.3 9.0 2.8 4.7 (a) p value for this test equals 0.3. (b) p value for this test equals 0.6. PAGE 86 86 CHAPTER 5 DISCUSSION The purpose of this study was to determine if there was a relationship between teacher training programs and student performance on the Algeb ra 1 EOC exam. The findings of this study are presented in Chapter 5 The implications of these findi ngs on the future of teacher training programs and recommendations are discussed Summary of Results T eacher training methods of traditional/conventional program, alternative certification, and subject area testing were compared to student test scores. No statistically significant differences were found when comparing teacher training programs to student performance on the Algebra I EOC. However, when student socioeconomic status (SES) was compared to teacher training programs, students with low SES (free o r reduced lunch status) test scores were statistically lower compared to the students who provided their own lunch There was no statistically significant difference in student performance of teachers with a degree in mathematics compared to those with a d egree in education with an emphasis in mathematics or other majors reported by the teachers in the study. Student variables of gender, race/ethnicity, or socioeconomic status showed no statistically significant difference to teacher major areas of study. A n analysis of the number of mathematics courses and the number of educational methods courses taken by the teachers showed no significant difference when compared t o the teacher training method. Teacher variables of gender and race/ethnicity wer e studied a nd showed mixed results. Female teachers mean score for number of mathematics courses was significantly higher than for males. There was no PAGE 87 87 statistically significant difference when comparing teacher gender to number of educational methods courses taken. R ace/ethnicity of teachers showed no statistically significant difference in either the number of mathematics courses taken or educational methods courses taken. Comparing number of years teaching Algebra showed a significant difference in the number of mat hematics courses taken. The longer a teacher taught Algebra, the more mathematics courses taken. However, o verall, teacher training programs do have some effect on student performance. This effect was found in the socioeconomic status of the student where the qualifications of teachers do make a difference. Discussion Previous studies that looked at teacher training and student achievement were inconclusive (Cohen, et al 2007; Darling Hammond, 2000; Tournaki, et al 2009; Wayman, et al 2003). This study d emonstrated that there was no significant difference on student performance based on test results on the Algebra 1 EOC by the type of training program a teacher completed. This may be the first study to look at the impact of teacher training on student per formance on e nd of course exams in Florida. As the state moves to the implementation of these exams as a graduation requirement instead of FCAT Math, more studies will be need ed. This becomes more relevant as teacher pay and continued employment are becomi ng partly based on student performance on EOC exams and FCAT 2.0 Reading in Florida (F lorida Statute 1012.34). This study required teachers to self report their teacher training program Notably, there was no way to analyze each program to determine if the y were equivalent in program requirements. Researchers have noted that this is one the major concerns with alternative programs. All programs are not equal in requirements and vigor and as such, PAGE 88 88 it is impossible to lump them all into the same category with out depleting the strength of some and overinflating the weaknesses of others (Darling Hammond, et al 2005; Humphrey & Wechsler, 2005 ; Selko & Fero, 2005). One interesting finding in this study was that many of the teachers ( n = 8) became certified to tea ch mathematics by taking the subject area exam which demonstrated competency in subject content knowledge. A review of the educational methods courses taken by these teachers indicat es that they may have followed some type of traditional program but in an other discipline. As a result, this was treated as another category and provided an additional look at how teachers become certified to teach mathematics. Researchers have observed ocioeconomic status impacts their achievement (Crosnoe, 200 9; Koutsoulis & Campbell, 2001; Opdenakker & Van Damme, 2001). Many studies have shown that SES can be a determining factor in whether or not that student is successful. Factors such as limited access to educational experiences, less parental inv olvement among those who are working multiple jobs to maintain the household, and having less qualified teachers in the classroom as a result of school location may contribute to lower levels of student achievement. Crosnoe (2009) studied the effects of lo w income students that are placed in a high SES school and found that they were also at a disadvantage Interestingly, they did not progress as well as the high SES students even though they have had access to better educational resources. However, simply placing low SES students in a high SES school does not eradicate other psychosocial effects that they may face. Also, students may gain a sense of affinity and thus might remain an outsider in their school. PAGE 89 89 This study revealed that socioeconomic status had an impact on student performance. Low SES (free/reduced lunch) students scored lower than those students that did not qualify for free/reduced lunch. Students taught by teachers with subject area testing or alternative certification had lower mean test sc ores than the students of (a social context where individuals judge their abilities by comparing themselves to others in their group and is influenced by if was a factor in determining how low SES students performed when placed in a high SES school. Traditionally, low SES schools will have the least qualified teachers; however the school with the highest number of low SES students in the district studied had traditionally trained teachers in the classroom. This provided an advantage to these students based on the results of the study. Another concern related to student achieve ment is teachers content knowledge of mathematics which teachers should be required to possess. Previous studies have shown mixed results regarding whether a teacher needs to be a mathematics major or an education major with an emphasis in mathematics. Th e argument seems to be that mathematics majors do not have strong pedagogical content knowledge, therefore do not know how to instruct students and that education majors do not have sufficient subject content knowledge to adequately teach mathematics (Ferr ini Mundy & Findell, 2010; Proulx, 2008; Wagner, Speer, & Rossa, 2007). The results of this study indicated that there was no statistical difference in whether a teacher was a mathematics major or education major with an emphasis in mathematics. PAGE 90 90 The array of mathematics courses taken by teachers within the different training programs indicated that there was no obvious pattern or set of required courses. Wh ile comparing the different programs it became evident that both the traditionally trained teachers an d the subject area testing teachers took the most courses. The fact that the subject area testing teachers took as many or more than the alternative certified teachers indicates that mathematics was a subject area that they were required to take in their m ajor area of study or an interest they pursued. Another interesting findings concerning mathematics coursework was the significance of the number of courses taken by female teachers. This negates previous research that indicated females were spending less time in mathematics classrooms due to lower self concept of their ability to be successful (Nagy, et al 2006 ; Van de gaer, et al 2008). These findings suggest females may be more confident in their mathematical abilities and are pursuing careers that inv olve mathematical knowledge When comparing the number of educational methods coursework completed by teachers in the different training programs, it also became apparent that alternatively certified teachers did not take as many courses, however it did no t prove to be significant. However these findings raise the question of how important pedagogy really is and whether or not methods courses are needed to make an effective teacher as originally proposed by Shulman (1987). Teacher race/ethnicity was not a s ignificant factor in either the number of mathematics courses or educational methods courses. Research has shown that students may perform better when their teacher is of their race/ethnicity, but it also shows that many times in schools where one race/eth nic group is more dominant than PAGE 91 91 others, that minority students suffer because they do not have the role models of their race/ethnic group available. In these same schools, there is the tendency to attract more qualified teachers of the dominant race/ethnic group and less qualified teachers of the lesser race (Dee, 2004). Implications The findings contribute to previous research that continues to demonstrate varied results regarding whether or not the type of teacher training program has an effect on student achievement. Perhaps, alternative programs in general have improved because of the demand for teachers or because the No Child Left Behind Act of 2001 has mandated revamping alternative programs to ensure that there are highly qualified teachers i n every classroom. The findings also point that a dministrators need to be cognizant of their student population and ensure that educational needs. Further studies will be need ed whether mathematicians or education majors shou ld be placed in the classroom or whether additional collaboration between mathematics departments and education departments of colleges is needed to determine the best way to prepare mathematics teachers. As Florida moves to implementing EOC exams and requ iring a passing grade of level 3 ( equivalent to a letter grade of C ) to meet graduation requirements, teachers will be held increasingly more accountable for the success L earning does not stop when a teacher becomes certified. Thus, wise d istr ict and school administrators will find ways to provide ongoing staff development that is geared toward the individual needs of the teacher and/or school PAGE 92 92 University teaching requirements does not ensure that all individuals will become effective teacher s This process takes practice, mentorship by an effective teacher, recogniz ing and meet using technology to enhance instruction, and communicat ing effectively with students, parents, colleagues, and administrators. These ski lls are essential to those who wish to become teachers. Unfortunately, not all teacher training programs provide this. Recommendations for Future Research Researchers continue to study and debate about the most effective way to provide quality teachers in changing school environment s In the haste to fill positions, administrators may be overlooking the traits necessary to enhance student performance. Future research should look at the following areas: 1. Replicate this study in other states and compare those results to the findings in this study. 2. Locate alternative certification and teacher preparation programs with standardized mathematic s requirements and compare students of those teachers to determine which program results in better student achievement. 3. Ana lyze the impact EOC exams have on graduation rates longitudinally and determine how EOC exams impact graduation rates. 4. Analyze the scores on each standard of the end of course exams and use the finding to suggest that whether remediation of standards can b est be met by current teachers or whether instruction geared toward those standards will need to be provided by colleges and universities with expanded subject content during teacher preparation. 5. Future studies should explore how alternatively and traditio nally trained teachers results. 6. Replicate the study and collect teacher data earlier in the school year, and/or obtain letter of support for study from someone in the district offic e. 7. Assess teacher skill level relative to skills they are teaching. PAGE 93 93 8. Determine what pedagogy is necessary in the teaching of mathematics and provide ongoing professional development in the use of instructional strategies (ie, breaking instruction down into smaller parts and then bringing it together as a whole, providing culturally responsive approached, and use of repetition or practice of skills Summary The purpose of this study was to determine the relationship between teacher training programs and stude nt performance on the end of course exam in Algebra 1. Chapter 5 provided a review of the findings, discussion of the findings and implications of these results, and recommendations for future research. When considering the results, it is important to poin t out that the sample size was limited due to the voluntary nature of the participants. However, the findings d emonstrated that there was no significant relationship between the type of teacher training program and student performance on the Algebra 1 EOC. The findings showed that low SES (free/reduced lunch) students scored lower than those students that did not qualify for free/reduced lunch. Students taught by teachers with subject area testing or alternative certification had lower mean test scores than the students of traditionally trained teachers As the state of Florida moves to implement end of course exams to meet graduation requirements in the academic areas of mathematics, science and social studies, it is hers are present in all classrooms. However, given rising student enrollment, teacher attrition, state mandated class size requirements, and teacher retirement there is a concomitant need to fill teacher vacancies rapidly. As a result, some individuals are entering alternative teacher t raining programs to attain certification and fill these positions. PAGE 94 94 For many years, researchers have disagreed as to whether or not alternative programs produce teachers of the same caliber as the traditionally trained program (Cohen Vogel & Smith, 2007; Darling Hammond, 2000; Dee & Cohodes, 2008; Glazerman, et al. 2006, Kane, et al. 2006; Nunnery, et al. 2009). Studies have shown that student achievement is related to the teacher effectiveness in how subject matter is presente d students (Moyer Packenham, et al. 2008, Wilson, et al. 2002). While this was not the focus of this study, the present results indicated that there was no statistical difference in whether a teacher was a mathematics major or education major with an empha sis in mathematics. PAGE 95 95 APPENDIX A ADMINISTRATIVE RULE 6A 4.0262 Specialization Requirements for Certification in Mathematics (Grades 6 12) Academic Class. (1) Plan One. A bachelor's or higher degree with an undergraduate or graduate major in mathematics, o r (2) Plan Two. A bachelor's or higher degree with thirty (30) semester hours in mathematics to include the areas specified below: (a) Six (6) semester hours in calculus, (b) Credit in geometry, (c) Credit in probability or statistics, and (d) Credit in abstract or linear algebra, (3) Plan Three. A bachelor's or higher degree with specialization requirements completed for physics and twenty one (21) semester hours in mathematics to include the areas specified below: (a) Six (6) semester hours in calc ulus, (b) Credit in geometry, (c) Credit in probability or statistics, and (d) Credit in abstract or linear algebra. Specific Authority 1001.02, 1012.55, 1012.56 FS. Law Implemented 1001.02, 1012.54, 1012.55, 1012.56 FS. History New 7 1 90, Amended 7 1 7 00. (FLDOE, 2011) PAGE 96 96 APPENDIX B T EACHER BACKGROUND SURVEY General Directions: The survey will take approximately fifteen minutes to complete. All responses will be kept confidential. The information obtained will be used for research purposes in determinin g the relationship between teacher training and student achievement on the end of course exam in Algebra 1. Your participation may benefit development opportunities for t eachers. Please fill in the blanks or circle only one answer for each question except where noted. Personal Information 1. Name: _________________________________________________________ 2. Current School: __________________________________________________ 3. Grade level of students in your class: _________________________________ 4. Which of the following best describes you? a. White b. Black or African American c. Hispanic d. Asian e. American Indian or Alaskan Native f. Other _____________________ 5. What is your gender? a. Male b. Fe male Educational Background 6. In your undergraduate or graduate coursework, which of the following was your major? a. Mathematics b. Mathematics education c. Education d. Other mathematics related field: List here___________________________ e. Other majors: List here __ _______________________________________ 7. What is the highest degree obtained? a. B.S. or B. A. b. M.A., M.S., or M. Ed. c. Ed. S d. Ph. D or Ed. D PAGE 97 97 8. Place a check in the blank for each mathematics course you have taken in your undergraduate or graduate s tudies. Course names and numbers are from the state university system in Florida. Course descriptions may be accessed at http://www.registrar.ufl.edu/catalog/prog rams/courses/math.html Note: Exact course names/number may differ from state to state. Check all that are similar to the courses you have taken. ____ Mathematics for Liberal Arts Majors 1 (MGF 1106) ____ College Algebra (MA C 1105) ____ Trigonometry (MAC 1114) ____ Precalculus (MAC 1140) ____ Precalculus: Algebra and Trigonometry (MAC 1147) ____ Analytic Geometry and Calculus 1 (MAC 2311) ____ Calculus 2 (MAC 2312 or 2512 or 3473) __ __ Calculus 3 (MAC 2313 or 3574) ____ History of Mathematics (MHF 3404) ____ Sets and Logic (MHF 3202) ____ Geometry (MTG 3212) ____ Differential Equations (MAP 2302) ____ Probability Theory (MAP 4102) ____ Discret e Mathematics (MAD 3107) ____ Combinatorics (MAD 4203) ____ Numerical Analysis (MAD 4401) ____ Linear Algebra (MAS 4105) ____ Abstract Algebra (MAS 4301) ____ Number Theory (MAS 4203) ____ Real Analysis (MAA 4226) ____ Complex Analysis (MAA 4227) ____ Mathematical Statistics 1(STA 4321) ____ Mathematical Statistics 2 (STA 4322) List other courses taken: ____________________________________________ _________________________ ________________________________________ 9. Place a check in the blank for each education course you have taken in your undergraduate or graduate studies. Course names and numbers are from the state university system in Florida. Course d escriptions may be accessed at http://www.registrar.ufl.edu/catalog/programs/courses/edstl.html Note: Exact course names/number may differ from state to state. Ch eck all that are similar to the courses you have taken. ____ Introduction to the Teaching Profession (EDF 1005) ____ Introduction to Diversity for Educators (EDF 2085) ____ Human Growth and Development (EDF 3110) ____ Educational Psychology (EDF 3210) ____ Learning and Cognition in Education (EDF 3214) ____ Measurement and Evaluation in Education (EDF 4430) ____ Family and Community Involvement in Education (SDS 3430) ____ Interpersonal Communica tion Skills (SDS 4410) PAGE 98 98 ____ Mathematics and Science (EDG 3377) ____ Elementary and Secondary Curriculum (EDG 4203) ____ Curriculum and Instruction for Secondary Learners (EDG 4204) ____ Middle School Education (EDM 4403) ____ Effective Teaching and Classroom Management in Secondary Education (ESE 4340C) ____ Explorations Teaching Secondary Mathematics and Science (MAE 2364) ____ Secondary School Mathematics Methods and Assessment (MAE 4331/5332) ____ Practicum in Teaching Secondary Mathematics and Science (MAE 4941) ____ Secondary Mathematics Practicum (MAE 4947) ____ Middle School Mathematics Methods (MAE 5327) ____ Multicultural Math Methods (MAE 5395) ___ Problem Solving in School Mathematics (MAE 6313) ____ ESOL Strategies for Content Area Teachers (TSL 4324) ____ Differentiated Instruction (EEX 4394) ____ Core Teaching Strategies (EEX 3257) ____ Core Classroom Management Strat egies (EEX 3616) List other courses taken: ___________________________________________ _______________________________________________________________ 10. Which teacher training program or method did you use for certification in mathematics? a. Traditional method (college degree program with educational methods coursework) b. Troops to Teachers c. Teach for America d. Other accelerated program: List program __________________________ e. Florida subject area test only f. Other _______ _____________________________ 11. What kind of Florida Certificate do you currently hold? a. Professional b. Temporary 12. List the subject/grade levels on your Florida Certificate: __________________________________________________________ ______ ________________________________________________________________ ________________________________________________________________ Teaching Experience 13. How many years (including this year) have you taught mathematics? ________ 14. How many years (including this year) have you taught algebra 1? __________ (adapted from NAEP Mathematics Teacher Background Questionnaire, 2009) PAGE 99 99 APPENDIX C INFORMED CONSENT OFFICIAL DOCUMENT PAGE 100 100 LIST OF REFERENCES Ai, X. (2002). Gender di fferences in growth in mathematics achievement: Three level longitudinal and multilevel analyses of individual, home, and school influences. Mathematical Thinking and Learning, 4 (1), 1 22. doi: 10.1207/S15327833MTL0401_1 Alexander, K. L., Entwisle, D. R., & Olson, L. S. (2007). Lasting consequences of the learning gap. American Sociological Review, 72 (2), 167 187. doi:.1177/000312240707200202 Ball, D. L., Thames, M. H., & Phelps G. (2008). Content knowledge for teaching: What makes it special? Journal of T eacher Education, 59 (5), 389 407. doi: 10.1177/0022487108324554 Ballou, D. & Podgursky, M. (2000). Reforming teacher preparation and licensing: What is the evidence? 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American Educational Research Journal, 44 (4), 959 1001. doi: 10.3102 /002831207308223 Zusho, A., Pintrich, P. R., & Cortina K. S. (2005). Motives, goals, and adaptive patterns of performance in Asian Americans and Anglo American students. Learning and Individual Differences, 15 141 158. doi: 10.1015/j.lindif.2004.11.00 PAGE 110 110 BIOGRAPHICAL SKETCH Cathy Griffin Hargis was born in Henderson, KY in 1954. She went to Webster County High School in Dixon, KY. After graduating from high school in 1972, she attended Henderson Community College in Henderson, KY. Mrs. Hargis married and w attend school or day care she returned to school at Indiana State University Evansville (which later became the University of Southern Indiana), and graduated in 198 3 with a Bachelor of Science in science teaching: primary emphasis in biology; supporting area in general science; and a minor in physical education. While attending the Indiana State University Evansville, she received the academic award in Physical Education fo r two consecutive years After relocating to Naples, FL in 1984 she began her educational career in Collier County as a high school biology, physical science, and health teacher selor education from the University of South Florida Ft. Myers campus. After teaching for 14 years, Mrs. Hargis became a school counselor at Barron Collier High. Mrs. Hargis has had the opportunity to open two new high schools (Gulf Coast High as a schoo l counselor and Palmetto Ridge High as the Director of Guidance). She currently serves as a school counselor at Beacon High School, an alternative school for students not meeting academic success in the traditional school setting. In 2009, she graduated fr om University of Florida with a Specialist degree in educational leadership. In 2010, Mrs. Hargis was selected by the Florida School Counselor Association as the High School Counselor of the Y ear for the state of Florida. 