International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn

This volume reports on the Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M). The study sampled students in their final year of teacher education to teach mathematics in primary or lower secondary school. There were 14,000 future primary teachers and 8,000 future lower secondary teachers from 16 different countries sampled.

The future teachers took paper and pencil tests, mostly multiple-choice, to ascertain their mathematics content knowledge (MCK) and their mathematics pedagogical content knowledge (MPCK). It also surveyed the students on beliefs about teaching and mathematics, as well as, courses taken and topics studied.

MCK and MPCK are concepts that have been discussed since Shulman introduced them in 1958 in “Paradigms and research programs in the study of teaching: a contemporary perspective” (in M. C. Wittock, ed., Handbook of research on teaching, 3rd ed., pp. 3–36). Nevertheless, the concepts are still somewhat fuzzy. The questions used to score the students serve as definitions. For those readers who are interested, the released items for primary level can be found at http://www.ugr.es/~tedsm/resources/Informes/Result_Viejo/PrimariaItemsLiberados.pdf and at the secondary level at http://www.ugr.es/~tedsm/resources/Informes/Result_Viejo/SecundariaLiberados.pdf.

So, what do we learn from the study? As the lead editor pointed out: “TEDS-M showed that studies in the field of higher education are challenging and difficult to do.” (p. 44) In short, more questions are raised by the study than are answered.

For example, student teachers from Taiwan and Singapore significantly outperformed those students from other countries in both MCK and MPCK. But we know high school students in those two countries outperform students in other countries on standardized paper and pencil mathematics tests. One can ask: Do high school students do better because they have better trained teachers or do the student teachers do better because they were trained better in high school? More generally, one can ask: Do student teachers that perform better on such tests become more competent teachers?

In addition, to explain the high scores in some countries one paper pointed out that in Singapore all student teachers must pass O-level mathematics, regardless of the subject they plan to teach. In general, the top performing countries recruit top performing students into teaching. Being accepted into a teacher-training program is very competitive in most high-scoring countries. One reason for the heated competition in Singapore is that student teachers receive full pay during their two years of teacher training.

At this time, education researchers are just beginning to learn how to conduct international comparison studies of teacher preparation. Therefore, there is no help in this volume for math faculty members who seek information to guide the restructuring of programs for future teachers. In a paper by Yeping Li, some proposed next steps for this study are laid out: looking at teacher practices in teacher education programs and the training of teacher educators; longitudinal studies of teacher preparation; and comparison of other policies in effect in different systems in different countries, such as recruitment.

One can hope that when and if such follow up studies and others are conducted; there will be helpful advice for mathematicians who work with future teachers. It is hard to believe, though, that there will be any simple answers.

Diane Resek is Professor Emerita in mathematics at San Francisco State University. Her PhD from University of California, Berkeley was in the area of algebraic logic. Most of her professional work has been in mathematics education, especially in curriculum development. Her email is resek@sfsu.edu.