Running Head: AN INTERNATIONAL OU TLOOK ON U.S. ELEMENTARY MATHEMATICS An International Outlook on U.S. Elementary Mathematics: Is There Cause for Concern? Megan Patricia Noel University of Florida Thesis completed as partial fulfillment of the requirements for high honors in the College of Education April 2010
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 2 Abstract According to the National Center for Education Statistics, p ublic K 12 education is the backbone of many industrialized nation s education al system s The relative success of the U.S. K 12 education al system as compared to that of other countr ies has significant implications for our economic and technological competitiveness in t he global marketplace (N ational C enter for E ducation S tatistics 2000 ). In the past 60 years there has been a dramatic increase in a ttention to mathemat ics and science proficiency at the federal and state levels. Improving public K 12 science and mathematics education remains one of the most pressing issue s facing policymakers today (National Research Council, 2009). Much of the concern expressed by edu cators and policy makers stems from results of recent comparative studies that show U.S. K 12 students are lagging behind their international classmates, especially in mathematics achievement ( Trends in International Mathematics and Science Study, 2007, 200 3, 1999 ) T his paper examines the importance of elementary mathematics education as it relates to the achievement of U.S. students as compared to that of students in other industrialized countries As part of this examination, I focused on student rela ted, teacher related, curricular, and societal reasons for influencing U.S. elementary mathematics education I then proposed p ossible solutions for improv ing the international standing of the United States in elementary mathematics achievement and identi fied barriers to implementing these solutions.
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 3 The Status of the U.S. in International Comparisons of Academic Achievement in Math International comparisons of student achievement are a common method of e valuating a nation s competitive outlook (N at ional Center for Education Statistics 2000 ). the United States has made efforts to strengthen its K 12 education al system, specifically in the disciplines of science and mathematics in order to compete with global counterparts. For ex ample, during the Cold War the United States focused on education as a key to surpassing the Soviet Union in the space race after the launch of Sputnik in 1957. This educational effort was manifested in the National Defense Education Act of 1958. In 19 83, A Nation at Risk: The Imperative for Educational Reform was released. This historically significant report by President Ronald Reagan 's National Commission on Excellence in E ducation contributed to the sense that Americ an schools are failing. The report cited various studies which point ed to academic underachievement on national and international scales and then suggested 38 recommendations for improvement with regard to co ntent, standards and expectations, time, teaching, leadership and fiscal support ( http://www2.ed.gov/pubs/NatAtRisk/recomm.html ) Project 2061 is another long term initiative by the American Association for th e Advancement of Science (AAAS) designed to help all Americans become literate in science, mathematics, and technology. Founded in 1985, Project 2061 conducts research and develops tools and services such as books, CDs, on line resources, professional development, and public outreach that educators, researchers, parents and education al system This is evident in the 1989 publication, Science for All Americans which defines scientific literacy and lays out some principles for effective learning and teaching. (http://www.project2061.org). The main federal law affecting education from kinde rgarten through high school is t he No Child Left Behind Act, which was passed by Congress and signed into law by P resident Bush in 2002. In an attempt to
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 4 improve the quality of education in the United States and close the achievement gap, No Child Left Behind is built on four principles: stronger accountability for results, more choices for parents, more freedom for states and communities and an emphasis on doing what works based on proven scientific research ( http://www2.ed.gov/nclb/landing.jhtml ) More recently, r eports such as Rising above the Gathering Storm: Energizing and Employing America for a Brighter Econ omic Future released in 2005 by the National Academy of Sciences also urged the United States to make the investments needed to compete, prosp er, and be secure in the global community This report argued that vast improvements were n eeded in the K 12 science and Academy of Sciences 2009). In response to Rising above the Gathering Storm President Bush signed the America Creating Opportunities to Meaningfully Promote Excellence in Technology, Education, and Science Act of 2007 or the America COMPETES Act, which focused on improving thre e areas of importance in education: incr easing research investment, strengthening educational opportunities in science, techno logy, engineering, and mathematics from elementary through graduate school, and developi ng an innovation infrastructure ( www.osa.org). In the 21 st century, t he world has now entered the age of the knowledge economy where education and capital play a criti cal role in driving economic growth (World Education Indicators, 2005). Economically developed c ountries now use international comparisons to ensure that their students are as well educated and technologically advanced as their global competitors and vie w educational achievement as an important indicator of later economic success when the se students workforce s When projecting long term growth in the trade of goods and services in the global economy, policym akers also use international K 12 educational achievement comparisons to evaluate how well different national systems of education are performing.
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 5 International comparisons provide policymakers, educators, and researchers the valuable data needed to obj ectively al systems, assess the relative performance of students in these different systems and identify potential strategies for improving studen t achievement ( Miller, Sen, Malley, and Burns, 2009 ) In th e United States, t he National Center for Education Statistics (NCES) and the Organization for Economic Coo peration and Development (OECD) provide multiple resources and reports that compare international test scores of K 12 students and international stati stics that may be used to help improve U.S. schools and increase student achievement in math, science and reading Although other international comparison study results are available for science, mathemat ics, and reading achievement at various age and gr ade levels, this paper focuses on the Trends in Internation al Mathematics and Science Studies (TIMSS) as the primary source for t he data presented The Trends in International Mathematics and Science Study ( TIMSS ) is a comparison of international studen math and science achie vement carried out every four years since 1995 by th e International Association for the Evaluation of Educational Achievement (IAE) Comparisons in the TIMSS are made at two grade levels. At grade four, comparisons are made betw een students in the 15 countries that participated in the TIMSS in 2003 and 1995 At grade eight, comparisons are made between studen ts in the 32 countries that participated in the 2003 TIMSS and at least one other earlier collection date ( TIMSS 1995, 199 9, or both ) ( National Science ) Because this paper only focuses on elementary mathematics achievement the primary academic data discussed is from the grade four math TIMSS study. Table 1 contains a list of the countries that participated in both the 1995 TIMSS and 2003 TIMSS.
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 6 Table 1. Comparable Countries in the TIMSS 1995 & 2003 Australia Iran, Islamic Republic of Scotland Canada Japan Singapore Cyprus Latvia Slovenia England Netherlands United States Hong Kong, SAR New Zealand Hungary Norway In the book A Splintered Vision William Schmidt a researcher and educator, make s the argument that the Americans need an exemplary K 12 mathematics and science education because competence in these subjects provide s a stron g basis for our continued democracy by helping to create a literate and informed citizenry He further argue s that competence in math and science helps each individual grow, develop, come nearer to reaching his or her individual potential, and feel more a utonomous and empowered in areas that have traditionally been sources of f rustration and anxiety for many learners. Finally, he claim s that math and science literacy provide a sound basis for continuing national prosperity, especially in a n increasingly c ompetitive, information driven, technological, and changing int ernational arena (Schmidt, McKnight, & Raizen 2002). Results from International Reports The Trends in International Mathematics and Science Study (TIMSS) mathematics scale is set from 0 to 1,000 and the target mean is set at 500 Using a consistent wide ranging scale helps make the data comparable between different years the study has been conducted. Data from the 1995 Trends in International Mathematics and Scienc e Study (TIMSS) reported that the average score of United S tates fourth graders was 518 (see Table 2) Although the United States met the 500 score target, it scored below Korea, Japan Australia and Canada who scored 611, 597, 546 and 532 res pectively but scored above England which scored 513. It is important to note that in 1995 Switzerland, France, Sweden, Germany, Spain, and Italy did not have comparable data for this grade level
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 7 Table 2. TIMSS 1995 Mean Scores in Fourth Grade Mathematics Similar results for the percentage of mathematics ques tions answered correctly by elementary students were reported by t he International Assessment of Educational Progress (IAEP 1995 ). As shown in Figure 1, i n this study nine year old students in the United States answered 58 % of questions correctly, which was below four ot her countries with age nine data. Nine year old students in Korea answered 75% of questions correctly, students in Canada answered 60% corr ectly, students in England answered 59% correctly, and students in Spain answered 62% correctly (N ational C enter for E ducation S tatistics 2000 ). Country TIMSS 1995 Mean Scores Fourth Grade Math Singapore 590 Japan 567 Hong Kong SAR 557 Netherlands 549 Czech Republic 541 Austria 531 Hungary 521 United States 518 Latvia 499 Australia 495 Scotland 493 Canada 489 England 484 Norway 476 New Zealand 469 Slovenia 4 62 Iran, Islamic Rep. of 387
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 8 Figure 1. Percentage of Math Question Answered Correctly by Age 9 Students Participating in the Internati onal Assessment of Educational Progress As shown in Table 3, e ight years later, a ccording to the 2003 TIMSS report U.S. fourth grader scores remained steady at 518, which was above the 2003 international average of 495. O f the 24 participating countries in the 2003 study the U nited S tates outscored 1 2 countries and scored below 11 countries. The Organization for Economic Cooperation and Development (OECD) brings together the governments of countries committed to democracy and the market economy from ar ound the world to support sustainable economic growth, boost employment, raise living standards, maintain financial stability, assist other countries' economic development, and contribute to growth in world trade (www.oecd.org). I n 2003 t he U.S. scored in the middle of elementary students in OECD countries that participated in the study, with U.S. fourth graders outscoring Australia, Italy, New Zealand, Norway, and Scotland but being outscored by their peers in Flemish Belgium England, Hungary, Japan, and the Netherlands ( Trends in International Mathematics and Science Study, 2003 )
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 9 Table 3. TIMSS 2003 Mean Scores in Fourth Grade Mathematics Between 1995 and 2003, fourth graders in 6 of the 15 participating countries demonstrated an improvement in math achievement (see Table 4) Unfortunately, t he United Sta tes was not among those countries. In both 2003 and 1995, fourth graders in the United States scored an average of 518 on the mathematics assessment As a result o f this lack of improvement, t he standing of U.S. fourth graders relative to peers in 14 othe r countries was actually lower in 2003 than it was 1995. In 1995, U.S. fourth graders were outperformed by their peers in four countries, while they scored higher than fourth graders in nine countries. In 2003, U.S. fourth graders were Country TIMSS 2003 Mean Score 4 th Grade Math Singapore 594 Hong Kong, SAR 575 Japan 565 Chinese Taipei 56 4 Belgium (Flemish) 551 Netherlands 540 Lithuania 534 Latvia 533 Russian Federation 532 England 531 Hungary 529 United States 518 Canada 511 Cyprus 510 Moldova, Rep. of 504 Italy 503 Australia 499 New Zealand 496 Scotland 490 Slovenia 479 Armenia 456 Norway 451 Iran, Islamic Rep. of 389 Philippines 358
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 10 out performed by fo urth graders in seven countries and th ey scored higher than peers in seven countries (T rends in I nternational M athematics and S cience S tudy 2003) Table 4. Difference between 1995 TIMSS and 2003 TIMSS Mean Fourth Grade Math Scores Country TIMSS 1995 Mea n Score Fourth Grade Math TIMSS 2003 Mean Score Fourth Grade Math 1995 to 2003 Difference Fourth Grade Math Singapore 590 594 4 Hong Kong, SAR 557 575 18 Japan 567 565 3 Netherlands 549 540 9 Latvia 499 533 34 England 484 531 47 Hungary 521 529 7 United States 518 518 0 Canada 489 511 23 Cyprus 475 510 35 Australia 495 499 4 New Zealand 469 496 26 Scotland 493 490 3 Slovenia 462 479 17 Norway 476 451 25 Iran, Islamic Rep. of 387 389 2 As illustrated in Table 5, f our years af ter the discouraging 2003 study results, the average mathematics s core for U.S. fourth graders in the 2007 TIMSS improved to 529, higher than the TIMSS scale average of 500. At grade four, this average U.S. mathematics score was higher than the scores of students in 24 of the 35 other countries participating and lower than the scores of students in 10 of the participating c ountries including Hong Kong, Singapore, Chinese Taipei, Japan, Kazakhstan Russian Federation, England, Latvia, the Netherlands, and L ithuania U.S. fourth graders increased their performance from 1995 to 2007 by 11 points; however during this same 12 year period England, Hong Kong SAR, Slovenia, Latvia, New Zealand, Australia, and the Islamic Republic of Iran had higher gains ( Trends i n International Mathematics and Science Study, 2007 )
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 11 Table 5. TIMSS 2007 Mean Scores in Fourth Grade Math Country TIMSS 2007 Mean Score s Fourth Grade Math Hong Kong SAR 607 Singapore 599 Chinese Taipei 576 Japan 568 Kazakhstan 549 Russian Feder ation 544 England 541 Latvia 537 Netherlands 535 Lithuania 530 United States 529 Germany 525 Denmark 523 Canada 519 Australia 516 Hungary 510 Italy 507 Austria 505 Sweden 503 Slovenia 502 Armenia 500 Slovak Republic 496 Scotland 494 New Z ealand 492 Czech Republic 486 Norway 473 Ukraine 469 Georgia 438 Iran, Islamic Rep. of 402 Algeria 378 Colombia 355 Morocco 341 El Salvador 330 Tunisia 327 Kuwait 316 Qatar 296 Yemen 224
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 12 Possible R easons for these Findings According to the T rends in I nternational M athematics and S cience S tudy (TIMSS) data from 1995, 2003, and 2007, the United States is neither leading nor lagging behind in elementary math achievement However, because the U.S. is one of the wealthiest countries in the world in per capita income and is a major competitor in the global economy it is important to understand why elementary students in the United States are not outscoring their international peers in mathematics Res earchers, educators, and policy makers alike a re interested in i dentifying factors that may account for the persistent gap in U.S. math achievement (N ational C enter for E ducation S tatistics 2000 ) The following sections of this paper discuss student related, teac her related, curriculum related, and societal factors that may be contributing to this gap Student Related Factors Every al system is affected by the size and characteristics of its student population Student diversity exists in al m ost every classroom around the world because of different ethnic, racial, socioeconomic and cultural backgrounds as well as varying levels of ability that students bring with them to their classrooms Although there are many student related factors that could account for the gap in U.S. ele mentary math achievement this paper focuses on th r e e potential contributing factors: the percentage of youth in the total population, socioeconomic status of learners and language proficiency of learners in the G 8 countries, or the eight most industrial izes democratic countries Percentage of Youth in the Total Population Examining the relative percentage of yout h in the total population of a G 8 country is important because a country with a very large youth population will often have a much larger p roportion of its resources devoted to K 12 education. However, if the student population is too large, per pupil allocations may be quite low. G 8 c ountries with a smaller youth population percentage, such as Japan, are usually able to invest more financ ial
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 13 resources per pupil than other G 8 countries who have to spread funding across a much larger student population (N ational C enter for E ducation S tatistics 2000) In raw numbers, in 1995 the United States had the largest youth population (ages 0 19 ) among the G 8 countries at approximately 77 million (see Table 6) Russia followed with a youth population of approximately 42 million followed by Japan at approximately 29 million, Germany at approximately 17 .5 million, France at approximately 16 mill ion, the United Kingdom at approximately 15 million Italy at approximately 12 million, and Canada at approximately 8 million. Based on relative percentages, 5 to 19 year olds represented 28.8% of the total population in the United States in 1995 In th e other G 8 countries, the percentage of youth in the total population ranged from 28.5% in Russia to 21.1% in Italy during this same time period ( www.census.gov ). Table 6. Relationship between Youth in the Total Population and TIMSS 1995 Mean Math Score G 8 Country # of youth (ages 0 19) in total population : 1995 % of youth (ages 0 19) in total population : 1995 TIMSS 1995 Mean Math Score Japan 28,795,429 23.0 567 United States 76,691,814 28.8 518 Canada 8,040,618 27.1 489 Italy 12,085,170 21.1 Not Ava ilable France 15,703,098 26.3 Not Available Germany 17,579,406 21.5 Not Available United Kingdom 14,812,440 25.4 Not Available Russia 42,321,571 28.5 Not Available As shown in Table 7 in 2003 the United States again had the largest youth populatio n aged 0 to 1 9 among G 8 countries at approximately 81 million. Russia again followed with a youth population of approximately 35 million, followed by Japan at approximately 25 million Germany at approximately 16 million, France at approximately 15 milli on, the United Kingdom at approximately 14 million Italy at approximately 11 million, a nd Canada at approximately 8 million 0 1 9 year olds Based on relative percentages, 0 to 1 9 year olds represented 28 % of the total population in the United States in 2003 In the other G 8 countries, the percentage of youth in the total population ranged from 18.9% in Italy to 25.2 % in France (www.census.gov)
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 14 Table 7 Relationship between Youth in the Total Population and TIMSS 2003 Mean Math Score G 8 Country # of youth (ages 0 19) in total population : 2003 % of youth (ages 0 19) in total population: 2003 TIMSS 2003 Mean Math Score Japan 25,178,768 19.8 565 Russia 35,219,119 24.4 532 United Kingdom 14,835,751 24.7 531 United States 81,132,452 28.0 518 Canada 7,864,522 24.7 511 Italy 10,974,314 18.9 503 France 15,685,856 25.2 Not Available Germany 16,980,618 20.6 Not Available Four years later i n 2007 the 82 million 0 to 1 9 year olds represented 27.3 % of the total population in the United States (see Table 8) Russia followed with 31 million 0 to 1 9 year olds representing 22.1% of the total population. In the other G 8 countries, the corresponding p ercentages ranged from 18.6 % in Italy to 24.9 % in France Table 8. Relationship between Youth in the Total Population and TIMSS 2007 Mean Math Score G 8 Country # of youth (ages 0 19) in total population : 2007 % of youth (ages 0 19) in total population: 200 7 TIMSS 2007 Mean Math Score Japan 23,839,919 18.7 568 Russia 31,181,849 22.1 544 United Kingdom 14,455,351 23.8 541 United States 82,304,668 27.3 529 Canada 7,691,601 23.4 519 Italy 10,806,521 18.6 507 France 15,830,174 24.9 Not Available Germany 16,229,438 19.7 525
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 15 According to the se data sets in 1995, 2003, and 2007 the United States cons istently had the largest youth population among the G 8 countries, however it did not have the highest mean math score on the TIMSS in any of these years The percentage of youth in the total population of a country is linked to elementary math achievemen t because this data can be combined with educational expenditure information to determine per pupil funding allocations for K 12 education. T his paper will later ex amine the relationship between educational expenditure and the percentage of youth in the t otal population Socioeconomic Status of Learners A significant amount of research indicates a relationship between student learning outcomes and socioeconomic factors More specifically, there is a substantial body of research documenting the damagin g effects of poverty on K 12 academic achievement. In the United States, r esearch has shown that c hildren living in low income families have lower levels of performance in school, are more likely to be kept back a grade, and have below average graduation rates (National Center for Education Statistics, 2000) Poverty levels correlate language proficiencies Consequently, this lack of opportunities p rogressed often results in more unmotivated students and lower teacher morale ( Kohlhaas, Lin & Chu 2010). These children may require basic prov isions from the school, such as free or reduced meals and may not have access to essential school supplies suc h as paper and pencils at home Math achievement is directly affected by poverty levels. A compelling body of research demonstrates that connectedness and engagement with school is a key determinant of academic achievement and educational attainment The child who is well nourish ed, physically active, and well rested is likely to have advantages regarding cognition compared with the child who experiences deficits in any of these areas. The child who has difficulty seeing, difficulty paying attention, o r is bullied at school will struggle to succeed academically and will feel less connected and engaged with school. In turn, the child who is less connected and engaged with school
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 16 will be less motivated to attend (Basch, 2010) S tudents who live in pover ty are less likely to focus in school concentrate during math than a child who is full. Students who live in poverty also do not have access to tut oring and extra resources. Child poverty statistics represent the additional time and resources that may need to be devoted to basic needs in the education al system s in each country. According to the National Center for Education Statistics (2000) the percentage of children living in poverty among the G 8 countries is not the highest in the United Sta tes at first glance ; however the percentage of children living in poverty is the highest in the U.S. after the impact of taxes and government transfers on income such as welfare and social security are considered Not only are absolute poverty rates of children in the U.S. high but the ability of federal government programs to reduce the proportion of children in pove rty is lower compared to Canada, the U nited Kingdom, and France For example, in the United Kingdom 29.6% of all children live in poverty before go vernmen t programs are considered, but only 9.9% of all children are considered to be living in poverty after government programs are considered. In t he United States 25.9% of all children are classified as living in poverty befo re government programs are considered and 21.5% of children are still classified as living in poverty even after government programs are factored in These outcomes may res ult from less funding being devoted to poverty reduction programs in the U.S. or from U.S. poverty reduction programs not being as effective as those implemented in other countries. Ultimately, math achievement is directly aff ected by socioeconomic status (SES) A seminal research study that empirically examined a nationally representative sample of kindergarten children found substantial of c hildren from the lowest SES group as they begin kindergarten. Higher SES students were also found to have received, on average, more reported instructional time spent on mathematics, higher use of math manipulatives, worksheets, textbooks and chalkboard w ork than their low SES peers. In a document p repared for the U. S.
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 17 Secretary of Education students from low income families were found to be 35% le ss likely than students in high income families to take advanced mathematics courses (Wang, 2009) Langu age Proficiency of Learners I ncreased language diversity among the K 12 student population has created new challenges for school systems in many countries due to the rising number of children in schools who do not speak the official school language For example, in the United States c hildren who speak a language other than English at home and who also experience difficulty speaking English face greater challenges progressing in school and, after they become adults, they experience similar challenges in th e labor market ( Cunningham, 2003 ). Eight percent of U.S. elementary students aged 5 17 years old speak a language other than English at home. According to the National Center for Education Statistics 27% of nine year olds in Italy said that they usually speak a language other than the official school language at home. This was followed by 21% of nine year olds in Switzerland 13% in Spain, 10% in Germany nine percent in Sweden and France (N ational C enter for E ducation S tatistics 2000). The 2006 Ameri can Community Survey (ACS) provides additional language proficiency data for the United States and shows that of the 53 million children aged 5 17 years in the U.S., 11 million children speak a language other than English at home and 3 million children spe ak ki & Shin, 2008). Similarly, t he National Center for Education Statistics Schools and Staffing Survey rep orts that nearly 4 million, or eight percent, of U.S. K 12 students were identified as limited English profici ent in 2003 20 04 ( Leaks & Stonehill, 2008) According to the National Clearinghouse for English Language Acquisition (NCELA), there were more than 5 million English language learners (ELLs) in the United States by 2005, a figure tha t has grown by nearly 61% in the past decade ( Leaks & Stonehill, 2008). At both eighth and fourth grades, students from homes where the language of the test is always or almost always spoken had higher average achievement on the 2003 TIMSS in mathematics than those who spoke it less frequently (Mullis, 2004) Several studies suggest that standardized tests are usually based on an English
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 18 speaking population and are inherently biased against English language learners. In contrast to multiple choice problems, performance items require students not only to read questions but to explain how they solved the problems in writing. Specifically, ELLs may not be successful at solving word problems and may be challenged by the academic language used in such assessments. In addition, the inclusion of extraneous information or distracters negati Therefore, language proficiency directly affects elementary mathematics achievement. Summary of Student Related Factors According to this data, the United States currently h as the largest youth population among the G 8 industrialized countries participating in international comparisons of math achievement The United States also has one of the highest percentage s of children living in poverty after federal government progra ms are considered a nd is faced with a rapidly increasing population of limited English proficient learners in the school system All of these student related factors influence elementary mathematics achievement. Research proves that poverty and language proficiency negatively impact mathematics achievement and the size of the youth population compared Teacher Related Factors According to the National Center for Educat effective educational systems, since they strongly influence the quality of instructi on offered in the classroom (p. 28). When identifying underlying reasons for gaps in international math achi evement, i t is also important to investigate how teachers in the United States compare to teachers in other countries. K 12 teachers in the United States are often seriously underprepared in the di sciplines of mathematics and science especially given the demands of new and changing curricula and an increasingly diverse student body ( Schmidt et al., 2002 ) Three t eacher related factors explored in this paper that partially account for
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 19 the gap in U.S. elementary mathematics achievement include preservice t eacher preparation teacher in service training and professional development and student to teacher ratios Preservice Teacher Preparation According to a National Center for Education Statistics Report (2000) German elementary public school teachers co mplete several more years of study than ele mentary teachers in Italy Spain, France, Sweden and the United S tates Public school e lementary teachers in Germany study 19 years while public school e lementary teachers in Italy study 13 years ; public school elementary teachers in Spain study 15 years and public school elem entary teachers in France Sweden, and the United States study 16 years Because this data indicates that children in different countries are being taught by teachers with varying amount s of preservice education, this variable may impact differences in mathematics achievement across countries After examining the TIMSS 2003 International Report, I can conclude that there are certain requirements for being a mathematics teacher that influ ence student mathematics achievement. For example, Italy, the only G 8 country that does not require teachers to have a university degree or equivalent, has the lowest mean mathematics score on the 2007 TIMSS. Similarly, Italy also is the only G 8 countr y that does not require math teachers to complete a pre practicum and supervised practicum. It is important to note, however, that requirements for certification vary across states in the United States and provinces in Canada. A summary of the current re quirements for elementary school mathematics teacher preparation in the G 8 countries is included in Table 9.
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 20 Table 9. C urrent Requirements for Elementary School Mathematics Teacher Preparation in G 8 Count r ies G 8 Country Pre practicum and Supervis ed Practicum Passing an Examination University Degree or Equivalent Completion of a Probationary Teaching Period Completion of an Induction Program Japan Yes Yes Yes Yes Yes Russia Yes Yes Yes No No United Kingdom Yes Yes Yes Yes Yes United States Yes Yes Yes Yes No France n/a n/a n/a n/a n/a Italy No Yes No Yes No Germany n/a n/a n/a n/a n/a Canada Yes Yes Yes Yes Yes Teacher In Service Professional Development Improving the quality of preparation of new teachers and the ongoing professional dev elopment of those in the current teaching force are key s to educational improvement. Teacher training varies widely between countries. In countries involved in international comparisons including Japan, France, Germany, and the People's Republic of China goals for teacher preparation are set at the national level. In the United S tates however, each state sets standards for teacher preparation ( Cobb, 1999 ) Once teachers enter the workforce, s ome countries like Germany maintain an extensive, structured system of teacher support in the form of a two year mentoring apprenticeship. During these apprenticeships, teachers receive a reduced class schedule, participate in classroom observations and assisted teaching opportunities, and receive continu ing profe ssional development. Similarly, i n Japan, new teachers rec eive intensive mentoring and on
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 21 the job training. In contrast, in the United States, formal teacher mentoring programs are scarce. In general, U.S. preservice teachers comple te 12 weeks of studen t teaching and these teacher apprenticeships vary widely across schools and districts in terms of availability, length, and quality (N ational C enter for E ducation S tatistics 2000). One encouraging trend noted i n the last 11 years in the United States is that teacher education has increasingly become par t of the mission of degree granting colleges and universities; the duration of training has increased; and the importance of clinical practice through lengthy student teaching experiences and/or internships has gained prominence ( Cobb, 1999 ) As summarized in Table 10, a ccording to data from the 2007 TIMSS International Report 60% of U.S. fourth grade students had teachers who participated in profession al development for math content; 50% of U.S. fourth gra de students had teachers who participated in professional development for mathematics p edagogy; 63% of U.S. fourth grade students had teachers who participated in professional develop ment for mathematics curriculum; and 47% of U.S. fourth grade students ha d teachers who participated in professional development for mathematics assessment (Mullis et al., 2008) Although this is not the highest percentage of teachers participating in professional development in mathematics among the G 8 countries the United States remains among the top three G 8 countries with the highest percentage of children taught by teachers who have participated in professional development in mathematics. professional development in mathematics does seem to i nfluence mathematics achievement scores. For example, Italy has the lowest 2007 TIMSS mean score and also has the lowest percentage of fourth grade students with teachers who have participated in professional development in mathematics.
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 22 Table 10. F ourth Grade Percentage of Students by Their Participation Percentage of Fourth Grade Participation in Professional Develop ment in Mathematics in the Past 2 Years G 8 Country Math Content Math Pedagogy/ Instruction Math Curriculum Math Assessment 2007 TIMSS Mean Score Fourth Grade Math Japan 48 55 16 21 568 Russia 66 67 68 55 544 United Kingdom 60 70 65 43 541 United States 60 50 63 47 529 France n/a n/a n/a n/a n/a Italy 22 25 14 14 507 Germany 44 37 38 27 525 Canada 36 39 41 39 519 Student to Teacher Ratios In addition to the amount of time teachers spend in school, a nother teacher related factor that should be considered i s studen t to teacher ratios, which can impac t a and opportunities for individualized instruction In general, educators believe that students who spend more time in instructional classes and in classes with lower student to teac her ratios are exposed to greater learning opportunities than other students (National Center for Education Statistics, 2000). According to the National Center for Education Statistics, in the U.S. most student to teacher ratios were lower in secondary sc hool than in elementary school, which is of concern since younger students usually need extra support and more access to teachers than older students In 2003, the student to teacher ratio at the primary level was lower in the United States than it was in all but one of the other G 8 countries (Table 11) At this time, i n the United States there was one teacher for every 15 primary level students. This ratio does not seem to correlate with academic mathematics achievement because
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 23 Italy, which has the lowest student to teacher ratio of 11 students for one teacher had the lowest mean math score among the G 8 countries on the 2003 TIMSS (Organization for Economic Co operation and Development, 2005) Figure 2. G 8 Countries Compared by the Number of Elementary Students Per One Teacher in 2003 Table 11. Elementary School Student to Teacher Ratios Compared to 2003 TIMSS Mean Math Scores G 8 Country 2003 Elementary School Student to Teacher Ratio 2003 TIMSS Mean Score Fourth Grade Mat h Japan 20 :1 565 Russia 17 :1 532 United Kingdom 21 :1 531 United States 15 :1 518 Canada n/a 511 Italy 11 :1 503 France 19 :1 Not Available Germany 19 :1 Not Available Similarly in 2007, the U.S. student to teacher ratio at the primary leve l was lower than the ratio in all but one of the G 8 countries (Table 12) Italy remained the G 8 country with the lowest student to teacher ratio in
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 24 2007 with 10.5 students for every teacher as well as the G 8 country with the lowest mean math score on t he 2007 TIMSS. Therefore, I can conclude that the student to teacher ratio does not have a profound impact on fourth (Organization for Economic Co operation and Development, 2009) Figure 3. G 8 Countries Compare d by the Number of Elementary Students Per One Teacher in 2007 Table 12 Elementary School Student to Teacher Ratios Compared to 2007 TIMSS Mean Math Scores G 8 Country 2007 Elementary School Student to Teacher Ratio 2007 TIMSS Mean Score Fourth Grade M ath Japan 19:1 568 Russia 17:1 544 United Kingdom 19.4:1 541 United States 14.6:1 529 Canada n/a 525 Italy 10.5:1 507 France 19.7:1 n/a Germany 18.3:1 519
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 25 Summary of Teacher Related Factors The amount of schooling that preservice public elemen tary teachers receive differs from an international perspective; therefore this factor seems to account for the lower U.S. elementary mathematics achievement scores. Likewise, t he quality of preservice teacher education is also different across countries. Unlike countries such as Germany and Japan that require national level teacher certification, teacher preparation programs in t he United States vary widely because certification registration and sta ndards for teacher preparation vary by state. Thus, man y U.S. elementary teachers may not be as qualified as their international counterparts. In service teacher professional development also seems to impact the math achievement of fourth graders. On the contrary, lower student to teacher ratios do not show a correlation with higher math achievement. Curriculum Related Factors Although teacher quality is important, research indicates that the curriculum materials used also have a profound impact on student achievement. In the U.S. mathematics and science te achers are often expected to teach using curricula stem ming from conflicting opinions and lack of clarity about what should be covered T he main curricular resource used in U.S. K 12 schools is commercial textbooks and packages (Schmidt et al., 2002 ) Co nsequently, the instructional strategies used by teachers reflect the attitudes and methods of mandated textbooks and packages These texts provide needed resources but contain limited guidance for novice teachers or teachers who do not have a strong cont ent background in math or science According to Schmidt in A Splintered Vision e provide as their fundamental resources encyclopedic, inclusive textbooks filled with brief coverage of many topics and with a preponderance of low demand tasks for student and local control over assessment tools and standards for evaluating achievement puts additional pressure on American textbo ok publishers
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 26 In A Splintered Vision Schmidt et al. compa red U.S. elementary mathematics textbooks with those of other countries participating in the TIMSS studies and found that U.S. textbooks include many more topics than do those from other countries U.S. mathematics textbooks average 30 to 35 topics per ye ar In comparison, math t extbooks in Japan range from 20 topics to fewer than 10 topics per year and Germany is similar to Japan. Schmidt et al. argue that i t is essentially impossible for U.S. textbooks that are so inclusive to compensate for unfocused national curricul a. Instead, U.S. math textbooks support and extend the lack of focus seen in the national U.S. math curriculum As a result math textbooks in the U.S. are la rge and cover many more topics than their international counterparts but thes e texts cover topics much more shallowly (Schmidt et al., 2002 ). Structure of the Mathematics Curriculum In addition to the issues related to the quantity of time students spend in school, the issue of the q uality of intended instructional time can also be explored by examining the number of topics that U.S. elementary mathematics teachers are supposed to cover. T he U.S. composite shows an intention to cover far more elementary mathematics topics than the majority of other countries involved in the TIMSS including Germany and Japan (see Table 13) For example, in grade four, the United States includes 25 topics, while Japan intended curriculum includes approximately 20 topics and Germany number of topics at this grade is a pproxi mately 17 (Schmidt et al., 2002 ). According to the 2007 TIMSS International Mathematics Report, the United States mathematics curriculum intends on covering far more TIMSS topics than any other G 8 country excluding Italy. The data presented also contr ibutes to the hypothesis that the United States covers more topics with less depth, and consequently, mathematics achievement suffers. Similarly, Italy has the lowest 2007 TIMSS mean mathematics score and intends on covering the most amount of TIMSS math topics among G 8 countries in the curriculum (Mullis, 2008).
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 27 Table 13. Summary of TIMSS Mathematics Topics in the Intended Curriculum in 2007 G 8 Country Number of Intended TIMSS math topics to be taught up to and including fourth grade 2007 TIMSS Mean Math Score Japan 24 568 Russia 10 544 United Kingdom 25 541 United States 34 529 Canada 28 525 Italy 35 507 France n/a n/a Germany 23 519 In A Splintered Vision Schmidt et al. argue that t in the U.S. math curriculum is achieved at the expense In other words, t eachers are required to cover many topics but with limited instructional time allocated for each topic. Therefore, mathematics teachers in the United States cover more topics in less depth than do teachers in oth er countries, and as a result, students have less of an understanding of the topics covered. Summary of Curriculum Related Factors Textbooks contribute to the unfocused curriculum that unqualified teachers teach to students in the United States. In A S plintered Vision Schmidt et al. described U.S. science and mathematics textbooks as That is, U.S. textbooks include many more topics text books, and the few most emphasized topic s account for less content th an is the case internationally. Societal Factors In addition to student related, teacher related, and curricular factors the manner in which countries structure their education al system s also influences educational experienc e s and therefore may account for some of the differences in mathematics achievement across nations (Schmidt et al., 2002 ) Societal factors mentioned in this
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 28 paper that may account for the gap in U.S. math achievement include the amount of time students s pend in school and educational expenditures Amount of Time Students Spend in School In addition to curricula, public attention in the United States has increasingly focused on the number of hours children spend in school, and many groups have been conce rned that both the school day and academic year are too short (National Center for Education Statistics, 2000). This recent concern is evident in President proposal to extend the length school days in addition to extending the school year. T hese concerns are also reflected in an increase of extended school day programs, initiatives for full year schooling, and national research efforts such as the National Education Commission on Time and Learning (www.afterschoolalliance.org) It is impor tant to note that the quantity of intended instructional time does not necessarily indicate that instruction is of higher quality. For example, elementary students in Italy attend school for longer days and longer school years than any other G 8 country; however Italy has the lowest 2007 TIMSS mean math scores (see Table 14) Similarly, Japan has the highest 2007 TIMSS mean math scores but has the shortest school year and shortest length of school days among the G 8 coun tries ( www.inca.org.uk ). Table 14 Summary of Length of School Year/Day among G 8 Countries Compared with 2007 TIMSS Mean Fourth Grade Math Score G 8 Country Length of School Year (in days) Length of School Day (in hours) 2007 TIMSS Mean 4 th Grade Math Scores Japan 175 4 568 Russi a n/a n/a 544 United Kingdom 190 5.5 541 United States 180 5 7 529 Canada 180 200 6.5 525 Italy 200 8 507 France 180 6 n/a Germany 188 208 6.5 519
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 29 Educational Expenditures Another societal factor that may contribute to tional gap in mathematics achievement is educational expenditures. Clearly, industrialized n ations want to ensure that they invest enough resources in their educational systems to create a workforce that is as well educated and technologically sophisticat ed as those of their global competitors (National Center for Education Statistics, 2000) The f investment in education is education expenditure as a percentage of gross domestic product (GDP ) According to the National Center fo r Education Statistics, 2000). In 2003, the United States spent 4.1 percent of its gross domestic product on primary and secondary education. Of the other G 8 countries, the United Kingdom and France spent a higher percent age of their GDP on pr i mary and secondary education. As summarized in Table 15, t he U.K spent 4.6 percent of its total gross domestic product on primary and secondary education and France spent 4.2 percent of its total GDP on education Italy spent 3.6 percent of its total g ross domestic product on primary and secondary education, Germany spent 3.3 percent, and Jap an spent 3.0 percent (Miller et al., 2007) In 2005, the United States decreased its percent of allocation of gross domestic product on education to 3.8 percent al located to education. In 2005, France was the only G 8 country with a higher percentage of its GDP than the U.S. at 4 percent. Germany and Italy both spent 3.2 percent of the ir the gross domestic product was 2.9 percent during this same time period (Miller et al., 2009). Another major economic indicator used in international comparisons is education expenditures per student. According to the National Center for Education Statis Statistics, 2000). In 2003, the U.S. expenditure per student was the highest of the G 8 countries at $8,900 for
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 30 both primary and secondary education (see Table 15) Italy followed at $7,700 per pupil then France at $7,200 per pupil. Japan and the United Kingdom both spent $6,800 per student was at $6 ,500 (Miller et al., 2007). In 2005, the United States once again had the highest annual education expenditure per student at $9,800, while France was $7,500, Italy and Japan both spent $7,300, and Germany and the United Kingdom both spent $6,900 per st udent (Miller et al., 2009). Table 15. 2003 Annual Education Expenditure as a Percentage of GDP and Per Student Compared with 2003 TIMSS Mean Fourth Grade Math Score G 8 Country Annual Education Expenditure as a Percentage of GDP: 2003 Annual Educa tion Expenditure Per Student: 2003 2003 TIMSS Mean Score Fourth Grade Mathematics Japan 3.0 $6,800 565 Russia n/a n/a 532 United Kingdom 4.6 $6,800 531 United States 4.1 $8,900 518 Canada n/a n/a 511 Italy 3.6 $7,700 503 France 4.2 $7,200 Not Availa ble Germany 3.3 $6,500 Not Available According to the data from the comparative indicators, it seems that educational expenditure does not play an extremely significant role in determining mathematics achievement. For example, Japan spends the least a mount of annual educational expenditure per student but has the highest TIMSS scores among the G 8 countries. highest mathematics achievement necessarily as important as the way in which the money is spent. Although student related and teacher related factors partially account for the difference in U.S. math achiev ement, curriculum related and societal factors seem to have the greatest impact on the success of a al system. The structure of the U.S. education al system seems to be one of the biggest issues. Because t he United States has the larges t youth population and spends the most in annual education expenditure
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 31 per student among the G 8 countries, one can conclude that the qual ity of the education in the United States may be below average to account for the lower TIMSS scores The U.S. do es n ot have the highest student to tea cher ratios students in the United States do not spent as much time in school each year and the math curriculum pushes teachers to cover far more topics than any other country in the same amount of time How can we expe ct our students to succeed on international standardized mathematics achievement tests if we do not give them the tools necessary to do so ? Possible Solutions Currently, t he United States has a mathematics curriculum without a clear focus, ca utious and inclusive textbooks, and teaching that echoes this uncertainty of goals and means. How has this happened? How have we become so disorganized in our views about what we must accomplish and how we m ust accomplish it? (Schmidt et al., 2002 ). We as a nation are not happy with where we are in terms of education, so we must stop questioning the past and look to the future. In A Splintered Vision Student Rela ted Solutions The United States has the largest youth population and the highest percentage of children in poverty accounting for government programs, yet does not spend the highest percentage of its gross domestic product on primary and secondary educati on out of the G 8 countries. The United States does, however, spend the most in annual education expenditure per pupil, but per pupil expenditure may not be a factor indicating quality of instruction. The student population in the United States is also f illed with students of different cultures and students who speak different languages. Students need to be supported in order to succeed. Children who live in poverty must have their basic needs met before they can begin to learn, and English language lea rners need sufficient support in their native language. Therefore, the federal government must take on a larger financial responsibility for education. Government programs to reduce
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 32 the percentage of children in poverty need to either be revised or given more financial support. Once students are supported through government programs and English as a second language (ESL) programs in schools they will be set up for success. Teacher Related Solutions Although the blame should not solely be placed on teac hers, they do play a significant role in student mathematics achievement. Teachers in the United States should have high quality preservice training and in service professional development in math content, pedagogy and instruction, curriculum, and assessm ent in the form of classes, internships, field experiences to prepare the m for careers in education. T he nation should also set minimum standards for teacher education rather than allowing states to have sole control. Once in the classroom, teachers shou ld still be expected to attend professional development workshops to be better trained in the art of teaching mathematics, acquire the skills needed to be effective mathematics teachers, and continually be refreshed in mathematics content. Teachers should also have access to appropri ate instructional resources such as textbooks and curriculum guides that support a focused mathematics curriculum and challenge students to engage in higher order thinking. Reduction of student to teacher ratios in the United States must also take place so that students are more likely to receive a quality education with more individualized attention. Curriculum Related Solutions Policies that result in large scale structural changes in the mathematics curriculum are much m ore lik ely to produce dramatic changes in student achievement than merely providing suggestions for curricular improvements or seeking even more hours of work from teachers. The United States must find an intellectually coherent vision to guide changes in U.S. mathematics and science education policies. T rying to provide curricular experiences with too many content topics seems destined not to produce the desired results (Schmidt et al., 2002 ). Therefore, the U.S. must reform the national mathematics cur riculum in an
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 33 organized, systematic way This curriculum should contain an appropriate number of mathematics topics that can be covered more thoroughly by teachers Societal Solutions Although funding for education is a constant concern for teachers and administrators, the United States should more concentrate on the allocation of funds rather than the amount of expenditure per pupil. Educational expenditure is usually spent on transportation for students, maintaining the physical buildings, and sala ries. Once all of these are factored out, there is little money left for educational resources and technology. Therefore, the United States should either allocate a higher percentage of the GDP to annual educational expenditure, or each state should reor ganize the budgets for education. Barriers to implementing solutions Although there is significant evidence in favor of change, it is hard to see any indication of change taking place because of a plethora of barriers to implementing the solutions for imp roving U.S. education and increasing the international standing of U.S. elementary students in mathematics One of these barriers is deciding which vision for a coherent science and mathematics curriculum is most beneficial for students in the United Stat es The first step to change is to condense the mathematics curriculum so that teachers can devote more time and instruction to each mathematics topic However, t here are many differing opinions and ideas about this issue that one must first decide who m akes the ultimate decision of which topics to include in the curriculum The second barr ier to implementing a solution for our broad mathematics curriculum is time. Reform efforts in science and mathematics education offer such powerful visions, but thes e visions take time to reach local classrooms and do so only after state and local interpretation and adaptation (Schmidt et al., 2002). This problem must be fixed immediately in order for the children of the United States to be successful; however the pr ocess of change can be slow and daunting.
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 34 The third, perhaps most major, barrier to implementing solutions is funding Money revolves around the entire process of fixing the U.S. education al system It costs money to create more government programs tha t get children out of poverty, and it costs schools money to create more support for limited English proficient (LEP) students. It also costs money to pay for teachers to receive professional development training, reduce the studen t to teacher ratio, and create new textbooks that support a more new, condensed curriculum. Therefore, creating a coherent mathematics education program implementing change in a timely matter, and having the financial support necessary, among other factors, are all barriers tha t impede policymakers, educators, and researchers from making a change for the better. Conclusion It is evident that the United States has educational problem s far beyond average international test scores in science and mathematics The United States ha s a broad elementary mathematics curriculum supported by textbooks with too many topics T his very large U.S. youth population with the highest percentage of children in poverty and rising number of English language learners is also expected to excel on i nternational mathematics achievement tests over their international peers The TIMSS data is evidence that t he United States needs to make a change. Our educational system is not doing the best it can for the children, the future of our country. If th e U.S. has government programs that have the least impact on children in poverty and the U.S. is one of the countries with the most children in poverty, there is something wrong. The U.S. also has the largest youth population but does not spend the most o n educational expenditures as a percentage of its gross domestic product. These results are evidence that the federal government needs to take on more financial responsibility for education. If students are expected to grow up and become citizens who com pete in a global marketplace, we must prepare them for success. We must support students through government and school programs, we must support
AN INTERNATIONAL OUTLOOK ON U.S. ELEMENTARY MATHEMATICS 35 teachers with teacher training professional development and appropriate resources and we must have one organ ized, systematic path of mathematics education that everyone in the field of education follows.
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