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, Volume 49, Issue 2, pp 265–278 | Cite as

Impact of the course teaching and learning of mathematics on preservice grades 7 and 8 mathematics teachers in Singapore

  • Berinderjeet Kaur
Original Article
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Abstract

This paper explores the impact of the course “Teaching and Learning of Mathematics (Grades 7 and 8)” for the preparation of pre-service secondary mathematics teachers. It examines how pre-service teachers perceived mathematical problem solving and communicating mathematical knowledge before and after the course. The main objective of the course is to equip them with a working knowledge of basic teaching principles, an understanding of the theories of learning that inform instruction, and a thorough knowledge of the curriculum. The participants of the study are professor X, who teaches the course, and her five pre-service teachers (PTs). The PTs wrote a journal entry after every topic explored during the tutorials, detailing their learning during the course of study. For their journals, specific prompts were provided for them to reflect on their learning and experiences. At the end of the course the PTs were also interviewed. The interview sought PTs perceptions about their communication of mathematical knowledge during the microteaching sessions. The data collected were subjected to qualitative analysis. The findings of the study show that the course deepened PT’s knowledge of mathematical problem solving and also shaped their ideas about how to communicate mathematical knowledge in ways that address the why and how of it.

Keywords

Pedagogy course Pre-service mathematics teachers Grades 7 and 8 Communication of mathematical knowledge Reflective journals Interviews Narratives 
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References

  1. Allen, D. W., & Ryan, K. A. (1969). Microteaching. Massachusetts: Addison-Wesley.Google Scholar
  2. Ball, D. (1988). Unlearning to teach mathematics. For the Learning of Mathematics, 8(1), 40–48.Google Scholar
  3. Brown, C. & Borko, H. (1992). Becoming a mathematics teacher. In D. A. Grows (Ed.), Handbook of research in mathematics teaching and learning (pp. 209–239). New York: Macmillan.Google Scholar
  4. Brown, T., & McNamara, O. (2011). Becoming a mathematics teacher – Identities and identifications. New York: Springer.CrossRefGoogle Scholar
  5. Chapman, O. (2008). Narratives in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), Tools and processes in mathematics teacher education, vol 2 of T. Wood (Series Ed.), International handbook of mathematics teacher education (pp. 15–38). Dordrecht: Sense Publishers.Google Scholar
  6. Chapman, O. (1997). Metaphors in the teaching of mathematical problem solving. Educational Studies in Mathematics, 32, 201–208.CrossRefGoogle Scholar
  7. Chapman, O. (2002). Belief structure and inservice high school mathematics teachers’ growth. In G. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 177–194). Dordrecht: Kluwer Academic Publishers.Google Scholar
  8. Chapman, O. (2004). Helping pre-service elementary teachers develop flexibility in using word problems in their teaching. In D. McDougall & A. Ross (Eds.), Proceedings of the 26th North American Chapter of PME, 3, 1175–1182.Google Scholar
  9. Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT: Research and Practice in Mathematics, Science and Technology Education, 3(1), 19–36.Google Scholar
  10. Charalambous, C. Y., Hill, H. C., & Ball, D. L. (2011). Prospective teachers’ learning to provide instructional explanations: how does it look and what might it take. Journal of Mathematics Teacher Education, 14, 441–463.CrossRefGoogle Scholar
  11. Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.CrossRefGoogle Scholar
  12. Darling-Hammond, L., & Rothman, R. (Eds.). (2011). Teacher and leader effectiveness in high-performing education systems. Washington, DC: Alliance for Excellent Education, and Stanford, CA: Stanford Centre for Opportunity Policy in Education.Google Scholar
  13. Drake, C. (2006). Turning points: Using teachers’ mathematics life stories to understand the implementation of mathematics education reform. Journal of Mathematics Teacher Education, 9, 579–608.CrossRefGoogle Scholar
  14. Feiman-Nemser, S., & Featherstone, H. (1992). The student, the teacher, and the moon. In S. Feiman & H. Featherstone (Eds.), Exploring teaching: Reinventing an introductory course (pp. 59–85). New York: Teachers College Press.Google Scholar
  15. Glesne, C. (1999). Becoming qualitative researchers: An introduction (2nd edn.). New York: Longman.Google Scholar
  16. Green, T. F. (1971). The activities of teaching. New York: McGraw-Hill Book Co.Google Scholar
  17. Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. New York: Routledge.Google Scholar
  18. Jaworski, B., & Gellert, U. (2003). Educating new mathematics teachers: Integrating theory and practice, and the roles of practicing teachers. In A. Bishop, M. A. Clements, C. Keitel-Kreidt, J. Kilpatrick & F.K.S. Leung (Eds.), Second handbook of mathematics education (pp. 829–875). New York: Springer.CrossRefGoogle Scholar
  19. Kaasila, R. (2007). Using narrative inquiry for investigating the becoming of a mathematics teacher. Zentralblatt für Didaktik der Mathematik, 39(3), 205–213.CrossRefGoogle Scholar
  20. Kaur, B. (2008). Problem solving in the mathematics classroom (Secondary). Singapore: National Institute of Education & Association of Mathematics Educators.Google Scholar
  21. Kaur, B., & Toh, T. L. (2011). Mathematical problem solving: Linking theory and practice. In O. Zaslavsky & P. Sullivan (Eds.), Constructing knowledge for teaching secondary mathematics (pp. 177–188). New York: Springer.CrossRefGoogle Scholar
  22. Kennedy, M. M. (1999). The role of preservice teacher education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of teaching and policy (pp. 54–86). San Francisco: Jossey Bass.Google Scholar
  23. Kinach, B. M. (2002). Understanding and learning-to-explain by representing mathematics. Epistemological dilemmas facing teacher educators in the secondary “methods” course. Journal of Mathematics Teacher Education, 5, 153–186.CrossRefGoogle Scholar
  24. Lampert, M., & Ball, D. L. (1998). Teaching, multimedia and mathematics. New York: Teachers College Press.Google Scholar
  25. Leinhardt, G., Putnam, R. T., Stein, M. K., & Baxter, J. (1991). Where subject knowledge matters. In J. Brophy (Ed.), Advances in research in teaching (vol. 2, pp. 87–113). London: JAI Press Inc.Google Scholar
  26. Liljedahl, P., Rolka, K., & Rösken, B. (2007). Affecting affect: The reeducation of preservice teachers’ beliefs about mathematics and mathematics learning and teaching. In W. G. Martin, M. E. Strutchens & P. C. Elliot (Eds.), The learning of mathematics (pp. 319–330). Reston: National Council of Teachers of Mathematics.Google Scholar
  27. Martin, J. R. (1970). Explaining, understanding and teaching. New York: McGraw-Hill.Google Scholar
  28. Mewborn, D. S. (1999). Reflective thinking among preservice elementary mathematics teachers. Journal for Research in Mathematics Education, 30, 316–341.CrossRefGoogle Scholar
  29. Miller, L. D. (1992). Teacher benefit from impromptu writing in algebra classes. Journal for Research in Mathematics Education, 23(4), 329–340.CrossRefGoogle Scholar
  30. Ministry of Education (2012). O-level, N(A)-level & N(T)-level mathematics teaching and learning syllabus. Singapore: Author.Google Scholar
  31. Mkomange, W. C., & Ajagbe, M. A. (2012). Prospective secondary teachers’ beliefs about mathematical problem solving. International Journal of Research in Management and Technology, 2(2), 154–163.Google Scholar
  32. Mok, I.A.C., & Kaur, B. (2006). ‘Learning task’ lesson events. In D. J. Clarke, J. Emanuelsson, E. Jablonka & I.A.C. Mok (Eds.), Making connections: Comparing classrooms around the world (pp. 147–164). Rotterdam: Sense Publishers.Google Scholar
  33. Nührenbörger, M., & Steinberg, H. (2008). Manipulatives as tools in mathematics teacher education. In D. Tirosh & T. Wood (Eds.), Tools and processes in mathematics teacher education, vol 2 of T. Wood (Series Ed.), International handbook of mathematics teacher education (pp. 157–181). Dordrecht: Sense Publishers.Google Scholar
  34. Op’t Eynde, P., de Corte, E., & Verschaffel, L. (2001). Problem solving in the mathematics classroom: A socio-constructivist account of the role of students’ emotions. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the twenty-fifth annual conference of the International Group for the Psychology of Mathematics Education (vol. 4, pp. 25–32). Utrecht: PME.Google Scholar
  35. Polya, G. (1973). How to solve it. Princeton: Princeton University Press.Google Scholar
  36. Ponte, J., & Brunheira, L. (2001). Analysing practice in preservice mathematics teacher education. Mathematics Education Research Journal, 3, 16–27.Google Scholar
  37. Ponte, J., & Chapman, O. (2008). Preservice mathematics teachers’ knowledge and development. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 223–261). Routledge.Google Scholar
  38. Ponte, J., & Chapman, O. (2016). Prospective mathematics teachers’ learning and knowledge for teaching. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (pp. 275–296). Routledge.Google Scholar
  39. Prediger, S. (2010). How to develop mathematics-for-teaching and for understanding: The case of meanings of the equal sign. Journal of Mathematics Teacher Education, 13(1), 73–93.CrossRefGoogle Scholar
  40. Ryve, A. (2007). What is actually discussed in problem-solving courses for prospective teachers? Journal of Mathematics Teacher Education, 10(1), 43–61.CrossRefGoogle Scholar
  41. Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  42. Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.Google Scholar
  43. Steele, M. D., Hillen, A. F., & Smith, M. S. (2013). Developing mathematical knowledge for teaching in a methods course: The case of function. Journal of Mathematics Teacher Education, 16(6), 451–482.CrossRefGoogle Scholar
  44. Wasserman, N. H., & Ham, E. (2013). Beginning teachers’ perspectives on attributes for teaching secondary mathematics: Reflections on teacher education. Mathematics Teacher Education and Development, 15(2), 70–96.Google Scholar
  45. Weber, R. P. (1990). Basic content analysis. Newbury Park: Sage.CrossRefGoogle Scholar
  46. Zaslavsky, O. (2008). Meeting the challenges of mathematics teacher education through design and use of tasks that facilitate teacher learning. In B. Jaworski & T. Wood (Eds.), The mathematics teacher educator as a developing professional, vol 4 of T. Wood (Series Ed.), International handbook of mathematics teacher education (pp. 93–114). Dordrecht: Sense Publishers.Google Scholar
  47. Zaslavsky, O., & Sullivan, P. (2011). Setting the stage: A conceptual framework for examining and developing tasks for mathematics teacher education. In O. Zaslavsky & P. Sullivan (Eds.), Constructing knowledge for teaching secondary mathematics (pp. 1–19). New York: Springer.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  1. 1.National Institute of EducationNanyang Technological UniversitySingaporeSingapore

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