Leland S. Cogan

Who takes what math and in which track? Using TIMSS to characterize U.S. students' eighth-grade mathematics learning opportunities

This article examines the range of eighth-grade mathematics learning opportunities in the United States, drawing on data gathered for the Third International Mathematics and Science Study (TIMSS). Sources of variation in the provision of learning opportunities are identified, and patterns in eighth-grade mathematics course offerings are compared across schools. Comparison of students’ learning opportunities includes consideration of the specific course in which they were enrolled, the type of textbook employed for the course, and the proportion of time teachers devoted to teaching specific topics. Analyses revealed a mismatch between the mathematics course title and the textbook employed in the course for nearly 30% of U.S. eighth-grade students. Course-textbook combinations demonstrated significant relationships with the time teachers devoted to specific topics and the international topic difficulty score. Some differences in mathematics learning opportunities were found on the basis of a school’s location (urban, rural, suburban), size, and percentage of minority enrollment. We contend that the significant relationships found were not consistent enough to provide a satisfactory explanation for the observed variation and that individual student differences, which often provide an implicit rationale for tracking, also represent an inadequate explanation for the observed diversity in curricular opportunities. We conclude that recognizing the multiple definitions for students’ classroom mathematics learning experiences is an important step in reform and policy discussions.

The Role of Opportunity to Learn in Teacher Preparation: An International Context.

This article examines the teacher preparation program learning opportunities afforded future lower secondary mathematics teachers and future elementary teachers who may teach mathematics. Data from U.S. participation in the recent international Teacher Education and Development Study in Mathematics are explored against international profiles to address a critical issue oft cited in the teacher education literature: Given the finite time available, what sort of balance is provided for course work across the areas of mathematics content, mathematics pedagogy, and general pedagogy? Results demonstrated major differences for lower secondary preparation programs in both the types of topics or courses covered and the relative emphasis across the three areas in those countries statistically outperforming the United States in comparison to U.S. programs. Similar but less striking differences were noted among elementary programs. These results should provide important empirical evidence relevant to the ongoing policy dialog concerning identifying the specific content of a quality teacher preparation program.

Preparing Future Math Teachers

Poor precollege math abilities, and too little emphasis on college-level math, can reduce the number of highly capable math teachers. The U.S. Presidents Council of Advisors on Science and Technology recommends that the federal government provide support over the next decade to recruit and train at least 100,000 new science, technology, engineering, and mathematics (STEM) teachers of middle school (ages 11 to 13) and high school. Their strong academic backgrounds should include both “deep content knowledge in STEM subjects and mastery of the pedagogical skills required to teach these subjects well” (1).

Content Coverage Differences across Districts/States: A Persisting Challenge for U.S. Education Policy.

This article utilizes the 1999 TIMSS-R data from U.S. states and districts to explore the consequences of variation in opportunities to learn specific mathematics content. Analyses explore the relationship between classroom mathematics content coverage and student achievement as measured by the TIMSS-R international mathematics scaled score. District/state-level socioeconomic status indicators demonstrated significant relationships with the dependent variable, mathematics achievement, and the classroom-level measure of content coverage. A three-level hierarchical linear model demonstrated a significant effect of classroom content coverage on achievement while controlling for student background at the student level and SES at all three levels documenting significant differences in mathematics learning opportunities as a function of the U.S. education system structure.

The Role of Subject-Matter Content in Teacher Preparation: An International Perspective for Mathematics.

Abstract International comparative studies in education provide a fresh perspective on K-12 education policy by enabling countries to learn from each other’s approaches. The recently conducted Teacher Education and Development Study—Mathematics provides a worldwide lens by which to examine the role of subject-matter in the preparation of US teachers of mathematics for primary and lower secondary students. More specifically, a previous study looking at the international top-performing teacher preparation programmes identified a common set of learning experiences (topics/content) related to mathematics. This empirically derived international benchmark is used in this paper to examine the quality of the mathematics preparation of future US teachers in various university and college programmes.

The Concept of Opportunity to Learn (OTL) in International Comparisons of Education

Items addressing the Opportunity to Learn (OTL) construct, the idea that the time a student spends in learning something is related to what that student learns, was included in the mathematics portion of PISA 2012 for the first time. Several questions on the student survey were designed to measure students’ opportunity to learn important concepts and skills associated with the assessed mathematical literacy. This chapter traces the development of this type of information in international comparisons of education and discusses four types of items that have been developed for this purpose. It also discusses the unique challenge of measuring this concept in PISA as it focuses on literacy, the knowledge students have acquired over their schooling to date, rather than on the content knowledge students have gained from schooling during a particular year or at a particular grade level. The specific OTL items and their purpose are identified from the Student Questionnaire section of Appendix A in the PISA 2012 Assessment and Analytic Framework.

Emphasis and Balance among the Components of Teacher Preparation: The Case of Lower-Secondary Mathematics Teacher Education

This article examines the teacher preparation program learning opportunities afforded future lower secondary mathematics teachers and future elementary teachers who may teach mathematics. Data from U.S. participation in the recent international Teacher Education and Development Study in Mathematics are explored against international profiles to address a critical issue often cited in the teacher education literature: Given the finite time available, what sort of balance is provided for course work across the areas of mathematics content, mathematics pedagogy, and general pedagogy? Results demonstrated major differences for lower secondary preparation programs in both the types of topics or courses covered and the relative emphasis across the three areas in those countries statistically outperforming the United States in comparison to U.S. programs. Similar but less striking differences were noted among elementary programs. These results should provide important empirical evidence relevant to the ongoing policy dialog concerning identifying the specific content of a quality teacher preparation program.

Supporting classroom instruction The Textbook Navigator/Journal

Researchers at the Center for the Study of Curriculum at Michigan State University have developed a tool to help teachers implement the Common Core State Standards in mathematics by letting standards, not textbooks, guide their instruction. Using the web-based Textbook Navigator/Journal, teachers can pick a standard and ask which portions of the textbook cover it, or they can use the Navigator to identify which Common Core standards are embodied in a particular lesson in the textbook. The Navigator lets teachers control their mathematics instruction, liberating them from rigidly following textbooks and allowing them to focus on teaching the content their students are expected to learn. The Navigator is based on the results of careful analyses of 34 textbook series and 185 individual mathematics textbooks.

Greater Expectations in Lower Secondary Mathematics Teacher Preparation: An Examination of Future Teachers’ Opportunity to Learn Profiles

The Teacher Education and Development Study in Mathematics (TEDS-M) tested students in their final year of teacher preparation on their knowledge of mathematics undergirding secondary school mathematics (MCK). Several articles have explored the relationship between students exposure to specific opportunities to learn (OTL) in their programs to their knowledge as demonstrated on the TEDS-M assessment. Here we sought to identify the courses that virtually all future teachers took in the top-achieving (A+) TEDS-M programs. Despite the fact that the top-achieving programs came from four countries on three continents, a set of nine courses that nearly every future teacher in these programs had taken was readily evident. Requirements had a strong emphasis on calculus with a majority of the nine courses, six, being university mathematics courses. This set of courses differed dramatically in number and focus from the set of empirically identified required courses among the international bottom 25 percent of programs or the set identified among the top-achieving programs in the U.S. The relatively large number of A+ requirements and electives demonstrated a greater consistent vision for teacher preparation than the few standards identified among the international bottom 25 percent of programs. This observation led to the hypothesis that excellence, at least as its measured by the TEDS-M MCK, may have very few paths leading to it but conversely many ways to arrive at much less impressive performance.

The Role of Content Knowledge in Mathematics Teacher Preparation: A Study of Traditional and Alternative Teacher Preparation in Texas

Employing data from a stratified random survey of newly certified teachers in Texas, we compare the mathematical content preparation of traditional teacher program graduates with graduates of alternative programs. We find that graduates of traditional programs have statistically significantly higher content preparation even when taking precollege preparation into account. These findings were consistent across different types of alternative programs. Alternatively certified teachers reported higher college entrance exam scores in mathematics, but this was statistically significant only for Grades 4 to 8. After merging survey results with NCES (National Center for Education Statistics) data about the schools at which teachers were employed, we found similar demographic characteristics between the two types of teachers—alternatively certified teachers were not more likely to teach in disadvantaged schools. Finally, while the content preparation of teachers was consistent across types of schools, teachers in disadvantaged schools tended to have lower SAT and ACT scores for both alternatively and traditionally prepared teachers.