Abstract
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.
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Notes
- 1.
Required and elective courses stemmed from the A+ programs as identified by the TEDS-M MCK score. Using the TEDS-M PCK score to identify the top 10 % of programs yielded only slightly different results. The PCK top 10 percent of programs come from the same four countries, Poland (1), the Russian Federation (14), Taiwan (19), and the U.S. (5) with only slightly different programs within those countries. This may be explained, at least in part, by the .93 correlation between the two scores at the program level. This correlation is only .75 at the individual future teacher level (see Robinson 1950 for a discussion of the relationship between individual correlations and group correlations). The vast majority (31) of the 39 A+ MCK programs were also in the PCK top 10 percent. Eight programs appeared only in the MCK top 10 (4 from the Russian Federation and 4 from the U.S.); eight others (three from the Russian Federation, two from Taiwan, and three from the U.S.) appeared only in the PCK top 10. Requirements according to the PCK top 10 were the same as the MCK top 10 with the addition of one university mathematics topic (analytic geometry). Because the results differed so little between the MCK A+ and the PCK A+ programs, no further analyses based on PCK are reported.
- 2.
For both organizational and operational reasons, public and private sample data collection was conducted in two consecutive years. The public colleges/universities sample adhered to the TEDS-M timeline and was the only sample included in official TEDS-M reports. The following year the study was conducted with the sample of private colleges/universities according to all TEDS-M sampling and study procedures. For further details, see Appendix A of Breaking the Cycle: An International Comparison of U.S. Mathematics Teacher Preparation (The Center for Research in Mathematics and Science Education 2010).
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Schmidt, W., Cogan, L. (2014). Greater Expectations in Lower Secondary Mathematics Teacher Preparation: An Examination of Future Teachers’ Opportunity to Learn Profiles. In: Blömeke, S., Hsieh, FJ., Kaiser, G., Schmidt, W. (eds) International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6437-8_18
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