Abstract
This article analyzes the experiences of prospective secondary mathematics teachers during a teaching methods course, offered prior to their student teaching, but involving actual teaching and reflexive analysis of this teaching. The study focuses on the pedagogical difficulties that arose during their teaching, in which prospective teachers lacked pedagogical content knowledge and skills. It also analyzes the experience of the course itself, which was aimed at scaffolding the work of prospective teachers on developing their pedagogical content knowledge and skills.
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References
Anghileri, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9, 33–52.
Ball, D., & Bass, H. (2004). Knowing mathematics for teaching. In R. Strässer, G. Brandell, B. Grevholm, & O. Helenius (Eds.), Educating for the future. Proceedings of an international symposium on mathematics teacher education (pp. 159–178). Sweden: Swedish Academy of Science.
Ball, D., & Cohen, D. (1999). Developing practice, developing practitioners: Towards a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). San Francisco: Jossey-Bass.
Ball, D., Hill, H., & Bass, H. (2005). Knowing mathematics for teaching. Who knows mathematics well enough to teach third grade and how can we decide? American Educator, 29(3), 14–22, 43–46.
Ball, D., Lubenski, S., & Mewborn, D. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teacher education (pp. 433–455). Washington, DC: AERA.
Ball, D., & McDiarmid, G. (1990). The subject matter preparation of teachers. In W. R. Houston (Ed.), Handbook of research on teacher education (pp. 437–449). New York: Macmillan.
Ball, D. L., Thames, M. H., Bass, H., Sleep, L., Lewis, J., & Phelps, G. (2009). A practice-based theory of mathematical knowledge for teaching. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd conference of the international group for the psychology of mathematics education (Vol. 1, pp. 95–98). Thessaloniki: PME.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–404.
Brown, C., & Clark, L. (Eds.). (2006). Learning from NAEP: Professional development materials for teachers of mathematics. Reston, VA: NCTM.
Carpenter, T. P., & Fennema, E. (1991). Research and cognitively guided instruction. In E. Fennema, T. P. Carpenter, & J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 1–16). Albany: State University of New York Press.
Cooney, T., & Wiegel, H. (2003). Examining the mathematics in mathematics teacher education. In A. Bishop, M. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (pp. 795–822). Dordrecht: Kluwer.
Crespo, S. (2003). Learning to pose mathematical problems: exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270.
Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 34(2), 94–116.
Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29, 1–20.
Feinman-Nemser, S., & Remillard, J. (1996). Perspectives on learning to teach. In F. Murray (Ed.), The teacher educator’s handbook: Building a knowledge base for the preparation of teachers (pp. 63–91). San Francisco, CA: Jossey Bass.
Glaser, B., & Strauss, A. (1967). The discovery of grounded theory. Strategies for qualitative research. Chicago: Aldine Publishing Company.
Graeber, A. (1999). Forms of knowing mathematics: What preservice teachers should learn. Educational Studies in Mathematics, 38, 189–208.
Kahan, J., Cooper, D., & Bethea, K. (2003). The role of mathematics teachers’ content knowledge in their teaching: A framework for research applied to a study of student teachers. Journal of Mathematics Teacher Education, 6, 223–252.
Laborde, C., & Perrin-Glorian, M.-J. (2005). Introduction. Teaching situations as object of research: Empirical studies within theoretical perspectives. Educational Studies in Mathematics, 59, 1–12.
Lampert, M., & Ball, D. L. (1999). Aligning teacher education with contemporary K-12 reform visions. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 33–53). San Francisco: Jossey-Bass.
Lester, F. (1994). Musings about mathematical problem solving research: 1970–1994. Journal for Research in Mathematics Education, 25(6), 660–675.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: Lawrence Erlbaum Associates.
Merseth, K. (2003). Windows on teaching math: Cases of middle and secondary classrooms. New York: Teachers College Press.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Peterson, B. (2005). Student teaching in Japan: The lesson. Journal of Mathematics Teacher Education, 8, 61–74.
Polya, G. (1954). Mathematics and plausible reasoning; Vol. 1. Introduction and analogy in mathematics; Vol. 2. Patterns of plausible inference. Princeton, NJ: Princeton University Press.
Polya, G. (2004). How to solve it. Princeton, NJ: Princeton University Press.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: The Free Press.
Stigler, J. W., & Stevenson, H. (1992). The learning gap: Why our schools are failing and what we can learn from Japanese and Chinese education. New York, NY: Summit Books.
Vacc, N., & Bright, G. (1999). Elementary preservice teachers’ changing beliefs and instructional use of children’s mathematical thinking. Journal for Research in Mathematics Education, 30(1), 89–111.
Vygotsky, L. (1986). Thought and language. Cambridge, MA: MIT Press.
Watson, A., & Mason, J. (2005). Mathematics as a constructive activity. Learners generating examples. Mahwah, NJ: Lawrence Erlbaum Associates.
Wilson, P., Cooney, T., & Stinson, D. (2005). What constitutes good mathematics teaching and how it develops: Nine high school teachers’ perspectives. Journal of Mathematics Teacher Education, 8, 83–111.
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Karp, A. Analyzing and attempting to overcome prospective teachers’ difficulties during problem-solving instruction. J Math Teacher Educ 13, 121–139 (2010). https://doi.org/10.1007/s10857-009-9127-y
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DOI: https://doi.org/10.1007/s10857-009-9127-y