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Conversations as Learning Tools in Mathematics: What Do Pupils Actually Learn?

  • Ole K. BergemEmail author
  • Kirsti Klette
Part of the Professional Learning and Development in Schools and Higher Education book series (PROD, volume 12)

Abstract

The theme of this chapter is to discuss challenges associated with the use of classroom conversations as learning tools in mathematics in lower secondary school. Conversations as learning tools – be it whole class discussions or conversations in pairs and groups – have received a lot of positive attention within mathematics education over recent decades. Researchers around the world have argued that students generally should be given more opportunities to actively participate in academically related mathematical conversations and discussions (Cobb et al. 1997; Cobb et al. 2000; Sfard 2000, 2001; Sfard and Kieran 2001; Van Oers 2001; Jaworski 2005; Kazemi & Franke, 2004; Lampert and Graziani 2009).

Keywords

Mathematics Education Class Discussion Mathematical Understanding Mathematics Lesson Mathematical Proficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Ball, D. L. (Ed.). (2003). Mathematics proficiency for all students: Towards a strategic research development program in mathematics education. Santa Monica: RAND.Google Scholar
  2. Bauersfeld, H. (1995). Language games in the mathematics classroom: Their function and their effects. In I. P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning (pp. 271–291). Hillsdale: Lawrence Erlbaum Associates.Google Scholar
  3. Bergem, O.K. (2009). Individuelle versus kollektive arbeidsformer. En drøfting av aktuelle utfordringer i matematikkundervisningen i grunnskolen (Individual seat work versus collaborative practices. A discussion of current challenges in the teaching of mathematics in lower secondary school). Unpublished Ph.D. thesis, Faculty of Education, University of Oslo.Google Scholar
  4. Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. Mahwah: Lawrence Erlbaum Associates.Google Scholar
  5. Boaler, J. (2005). Connecting mathematical ideas. Middle school video cases to support teaching and learning. Portsmouth: Heinemann.Google Scholar
  6. Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L. W., & Empson, S. B. (1999). Children’s mathematics: Cognitively guided instruction. Portsmouth: Heinemann.Google Scholar
  7. Cazden, C. B. (2001). Classroom discourse: The language of teaching and learning. Portsmouth: Heinemann.Google Scholar
  8. Cobb, P. (2007). Putting philosophy to work. Coping with multiple theoretical perspectives. In I. F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 3–38). Charlotte: National Council of Teachers of Mathematics, Information Age Publishing.Google Scholar
  9. Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for Research in Mathematics Education, 28(3), 258–277.CrossRefGoogle Scholar
  10. Cobb, P., Yackel, E., & McClain, K. (Eds.). (2000). Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design. Mahwah: Lawrence Erlbaum Associates.Google Scholar
  11. Ernest, P. (1991). The philosophy of mathematics education. Hampshire: The Falmer Press.Google Scholar
  12. Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In I. F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225–256). Charlotte: National Council of Teachers of Mathematics, Information Age Publishing.Google Scholar
  13. Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht: CD-β Press.Google Scholar
  14. Gravemeijer, K., Cobb, P., Bowers, J., & Whitenack, J. (2000). Symbolizing, modeling and instructional design. In I. P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms (pp. 225–273). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  15. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, L., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making sense. Teaching and learning mathematics with understanding. Portsmouth: Heinemann.Google Scholar
  16. Jaworski, B. (2005). Learning communities in mathematics: Creating an inquiry community between teachers and didacticians. In R. Barwell & A. Noyes (Eds.), Papers of the British society for research into learning mathematics, research in mathematics education (Vol. 7, pp. 101–120).Google Scholar
  17. Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7(3), 203–235.CrossRefGoogle Scholar
  18. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: The National Academies Press.Google Scholar
  19. Klette, K., Lie, S., Ødegaard, M., Anmarkrud, Ø., Arnesen, N., Bergem, O. K., & Roe, A. (2008). PISA PLUS: Lærings- og undervisningsstrategier i skolen (Report from the PISA+ video study). Oslo: Norges forskningsråd.Google Scholar
  20. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27(1), 29–63.CrossRefGoogle Scholar
  21. Lampert, M. (2001). Teaching problems and the problem of teaching. New Haven: New University Press.Google Scholar
  22. Lampert, M., & Graziani, F. (2009). Instructional activities as a tool for teachers’ and teacher educators’ learning. The Elementary School Journal, 109(5), 491–509.CrossRefGoogle Scholar
  23. Lerman, S. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education, 27(2), 133–150.CrossRefGoogle Scholar
  24. Nemirovsky, R. (Ed.). (2005). Everyday matters in science and mathematics: Studies of complex classroom events. Mahwah: Lawrence Erlbaum Associates.Google Scholar
  25. Nunes, T. (1999). Mathematics learning as the socialization of the mind. Mind, Culture, and Activity, 6(1), 33–52.CrossRefGoogle Scholar
  26. O’Connor, M. C. (1998). Language socialization in the mathematics classroom: Discourse practices and mathematical thinking. In I. M. Lampter & M. L. Blunk (Eds.), Talking mathematics in schools: Studies of teaching and learning (pp. 17–55). Cambridge: Cambridge University Press.Google Scholar
  27. Sfard, A. (2000). On reform movement and the limits of mathematical discourse. Mathematical Thinking and Learning, 2(3), 157–189.CrossRefGoogle Scholar
  28. Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1), 13–57.CrossRefGoogle Scholar
  29. Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture and Activity, 8(1), 42–76.CrossRefGoogle Scholar
  30. Sfard, A., Nesher, P., Streefland, L., Cobb, P., & Mason, J. (1998). Learning mathematics through conversation: Is It as good as they say? For the Learning of Mathematics, 18(1), 41–51.Google Scholar
  31. Silver, E. A., & Smith, M. S. (1996). Building discourse communities in mathematics classrooms: A worthwhile but challenging journey. In M. J. I Kenney & P. C. Elliott (Eds.), Communication in mathematics, K-12 and beyond. Reston: National Council of Teachers of Mathematics.Google Scholar
  32. Steinbring, H. (2005). The construction of new mathematical knowledge in classroom interaction. An epistemological perspective. New York: Springer.Google Scholar
  33. Stigler, J., Gallimore, R., & Hiebert, J. (2000). Using video surveys to compare classrooms and teaching across cultures: Examples and lessons from the TIMSS video studies. Educational Psychologist, 35(2), 87–100.CrossRefGoogle Scholar
  34. Van Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46(1–3), 59–85.CrossRefGoogle Scholar
  35. Vygotskij, L. S. (1978). Mind in society. The development of higher psychological processes. Cambridge: Harvard University Press.Google Scholar
  36. Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms. Review of Educational Research, 78(3), 516–551.CrossRefGoogle Scholar
  37. Yackel, E. (1995). Children’s talk in inquiry mathematics classroom. In I. P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning. Hillsdale: Lawrence Erlbaum Associates.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of OsloOsloNorway

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