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Mathematics Education Research Journal

, Volume 27, Issue 2, pp 165–182 | Cite as

Knowledge concerning the mathematical horizon: a close view

  • Raisa Guberman
  • Dvora Gorev
Original Article
First Online:

Abstract

The main objective of this study is to identify components of teachers’ mathematical knowledge for teaching, associated with the knowledge of mathematical horizon (KMH) in order to describe this type of knowledge from the viewpoint of elementary school mathematics teachers. The research population of this study consisted of 118 elementary school mathematics teachers who responded to an open-ended questionnaire. Findings of this study illustrate that KMH can be considered as a separate category according to teachers’ voice. An analysis of teachers’ utterances resulted in three KMH characteristics: insight of subject matter, mathematical connections, and understanding of meta-mathematics.

Keywords

Mathematical knowledge for teaching Teachers’ knowledge Teachers’ voice 
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References

  1. Aubrey, C. (1997). Mathematics teaching in the early years: an investigation of teachers’ subject knowledge. London: The Falmer Press.Google Scholar
  2. Ball, D. L. & Bass, H. (2009). With an eye on the mathematical horizon: knowing mathematics for teaching to learners’ mathematical futures. Paper prepared based on keynote address at the 43rd Jahrestagung für Didaktik der Mathematik held in Oldenburg, Germany.Google Scholar
  3. Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching. American Educator, 29(1), 14–17. 20–22, 43–46.Google Scholar
  4. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  5. Bass, H., & Ball, D. L. (2004). A practice-based theory of mathematical knowledge for teaching: the case of mathematical reasoning. In W. Jianpan & X. Binyan (Eds.), Trends and challenges in mathematics education (pp. 107–123). Shanghai: East China Normal University Press.Google Scholar
  6. Begle, E. (1972). Teacher knowledge and student achievement in algebra. School Mathematics Study Group Reports, Number 9. Washington, D.C: Stanford University, California School Mathematics Study Group, National Science Foundation.Google Scholar
  7. Begle, E., & Geeslin, W. (1972). Teacher effectiveness in mathematics instruction. N. 28. Washington D.C.: NCTM.Google Scholar
  8. Bruner, J. (1986). Actual minds, possible worlds. Cambridge, MA: Harvard University Press.Google Scholar
  9. Butts, R. F., & Cremin, L. A. (1953). A History of Education in American Culture. New York: Henry Holt and Company.Google Scholar
  10. Charalambous, C., Panaoura, A., & Philippou, G. (2009). Using the history of mathematics to induce changes in preservice teachers’ beliefs and attitudes: insights from evaluating a teacher education program. Educational Studies in Mathematics, 71(2), 161–180.CrossRefGoogle Scholar
  11. Clemente, M., & Ramirez, E. (2008). How teachers express their knowledge through narrative. Teaching and Teacher Education: An International Journal of Research and Studies, 24(5), 1244–1258.CrossRefGoogle Scholar
  12. Cooper, P., & McIntyre, D. (1996). Effective teaching and learning: teachers’ and students’ perspectives. Buckingham: Open University Press.Google Scholar
  13. de Freitas, E. (2004). Plotting intersections along the political axis: the interior voice of dissenting mathematics teachers. Educational Studies in Mathematics, 55(1–3), 259–274.CrossRefGoogle Scholar
  14. Drake, C. (2006). Turning points: Using teachers’ mathematics life stories to understand implementation of mathematics education reform materials. Journal of Mathematics Teacher Education, 9(6), 579–608.CrossRefGoogle Scholar
  15. Eisenberg, T. (1977). Begle revisited: teacher knowledge and student achievement in algebra. Journal of Research in Mathematics Education, 8(3), 216–222.CrossRefGoogle Scholar
  16. Fennema, E., & Franke, M. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147–164). New York: Macmillan.Google Scholar
  17. Fernández, S., Figueiras, L., Deulofeu, J., & Martinez, M. (2011). Re-defining HCK to approach transition. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 2640–2649). Poland: University of Rzeszów.Google Scholar
  18. Foster, C. (2011). Peripheral mathematical knowledge. For the Learning of Mathematics, 31(3), 24–26.Google Scholar
  19. Grossman, P. L., Wilson, S. M., & Shulman, L. S. (1989). Teachers of substance: subject matter knowledge for teaching. In M. C. Reynolds (Ed.), Knowledge base for the beginning teacher (pp. 23–36). New York: Pergamon.Google Scholar
  20. Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers’ mathematical knowledge: what knowledge matters and what evidence counts? In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111–155). Charlotte, NC: Information Age Publishing.Google Scholar
  21. Hsieh, H.-F., & Shannon, S. E. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15(9), 1277–1288.CrossRefGoogle Scholar
  22. Kaasila, R. (2007). Mathematical biography and key rhetoric. Educational Studies in Mathematics, 66(3), 373–384.CrossRefGoogle Scholar
  23. Kaasila, R., Hannula, M. S., Laine, A., & Pehkonen, E. (2008). Socio-emotional orientations and teacher change. Educational Studies in Mathematics, 67(2), 111–123.CrossRefGoogle Scholar
  24. Kennedy, M. (2004). Reform ideals and teachers’ practical intentions. Education Policy Analysis Archives, 12(13). Retrieved from http://epaa.asu.edu/ojs/article/view/168.
  25. Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 3–38). New York: Macmillan Publishing Company.Google Scholar
  26. Klein, F. (1932). Elementary mathematics from an advanced standpoint. Arithmetic, Algebra, Analysis. Translated from the third German edition by E. R. Hedrick & C. A. Noble. New York: Macmillan.Google Scholar
  27. Leikin, R. (2006). Learning by teaching: the case of Sieve of Eratosthenes and one elementary school teacher. In R. Zazkis & S. Campbell (Eds.), Number Theory in Mathematics Education: Perspectives and Prospects (pp. 115–140). Mahwah, NJ: Erlbaum.Google Scholar
  28. Mamolo, A., & Zazkis, R. (2011). Reaching out to the horizon: teachers’ use of advanced mathematical knowledge. Portland, Oregon: Proceedings of the 14th annual conference on Research in undergraduate mathematics education.Google Scholar
  29. Nardi, E., Biza, I., & Zachariades, T. (2011). ‘Warrant’ revisited: integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation. Educational Studies in Mathematics, 79(2), 157–173.CrossRefGoogle Scholar
  30. Oslund, J. A. (2012). Mathematics-for-teaching: what can be learned from the ethnopoetics of teachers’ stories? Educational Studies in Mathematics, 79, 293–309.CrossRefGoogle Scholar
  31. Phelps, C. M. (2010). Factors that pre-service elementary teachers perceive as affecting their motivational profiles in mathematics. Educational Studies in Mathematics, 75(3), 293–309.CrossRefGoogle Scholar
  32. 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
  33. Roche, A., & Clarke, D. M. (2013). Primary teachers’ representations of division: assessing mathematical knowledge that has pedagogical potential. Mathematics Education Research Journal, 25(2), 257–278.CrossRefGoogle Scholar
  34. Ross, S., & Pratt-Coffer, M. (1999). Subtraction in the United States: an historical perspective. The Mathematics Educator, 10(2), 49–56.Google Scholar
  35. Sabar Ben-Yehoshua, N. (1997). Qualitative research in teaching and learning. Tel Aviv: Moden Publishing. [Hebrew].Google Scholar
  36. Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a theory of proficiency in teaching mathematics. In D. Tirosh & T. Wood (Eds.), International handbook of mathematics teacher education (tools and processes in mathematics teacher education, Vol. 2, pp. 321–354). Rotterdam, Netherlands: Sense Publishers.Google Scholar
  37. Scott, A., Clarkson, P., & McDonough, A. (2012). Professional learning and action research: early career teachers reflect on their practice. Mathematics Education Research Journal, 24(2), 129–151.CrossRefGoogle Scholar
  38. Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  39. Strauss, A., & Corbin, J. (1990). Basics of qualitative research: grounded theory procedures and techniques. Newbury Park, CA: Sage.Google Scholar
  40. Van der Valk, T. A. E., & Broekman, H. G. B. (1999). The lesson preparation method: a way of investigating pre-service teachers’ pedagogical content knowledge. European Journal of Teacher Education, 22(1), 11–22.CrossRefGoogle Scholar
  41. Wilson, S. M., Shulman, L. S., & Richert, A. (1987). “150 different ways of knowing”: representations of knowledge in teaching. In J. Calderhead (Ed.), Exploring teacher thinking (pp. 104–124). Sussex, UK: Holt, Rinehart and Winston.Google Scholar
  42. Zazkis, R., & Mamolo, A. (2011). Reconceptualising knowledge at the mathematical horizon. For the Learning of Mathematics, 31(2), 8–13.Google Scholar
  43. Zazkis, R., & Mamolo, A. (2012). Continuing conversations towards the horizon. For the Learning of Mathematics, 32(1), 22–25.Google Scholar
  44. Zhang, O., & Stephens, M. (2013). Utilising a construct of teacher capacity to examine national curriculum reform in mathematics. Mathematics Education Research Journal, 25(4), 481–502.CrossRefGoogle Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2014

Authors and Affiliations

  1. 1.Department of MathematicsAchva Academic CollegePOB, ShikmimIsrael

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