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Journal of Mathematics Teacher Education

, Volume 14, Issue 4, pp 285–304 | Cite as

Using technology to explore mathematical relationships: a framework for orienting mathematics courses for prospective teachers

  • Janet S. Bowers
  • Becky Stephens
Article

Abstract

The technological revolution that has finally permeated K-12 education has direct implications for modern teacher educators whose “Hippocratic oath” is to best prepare future teachers for twenty-first-century classrooms. The goal of this article is to suggest that the heart of sound technological implementation is to encourage students to use whatever tools are available to explain the mathematical relations that underlie what they observe on the screen. We suggest ways in which Mishra and Koehler’s construct of Technological Pedagogical Content Knowledge may be customized to provide a framework for guiding prospective teachers’ efforts to develop and assess lesson plans that use technology in novel and effective ways. Data are presented in the form of two contrasting case studies to illustrate the differing degrees to which prospective mathematics teachers leveraged technology to teach themselves and their future students to explain the mathematics behind various topics.

Keywords

TPACK Technological knowledge Content knowledge Technology 

References

  1. Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14–17. 20–22, 43–46.Google Scholar
  2. 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
  3. Battista, M. (2008). Development of the shape makers geometry microworld: Design principles and research. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Vol 2. Cases and perspectives (pp. 131–156). Charlotte, NC: Information Age Publishing, Inc.Google Scholar
  4. Bowers, J., & Nickerson, S. D. (2001). Identifying cyclic patterns of interaction to study individual and collective learning. Mathematical Thinking and Learning, 3(1), 1–28.Google Scholar
  5. Bowers, J., Nickerson, S., & Kenehan, G. (2002). Using technology to teach concepts of speed. In B. H. Litwiller (Ed.), Making sense of fractions, ratios, and proportions: The 2002 yearbook of the national council of teachers of mathematics (pp. 176–187). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  6. Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, 2(2), 141–178.CrossRefGoogle Scholar
  7. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  8. Cobb, P., & Yackel, E. (1996). Constructivist, ermergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175–190.CrossRefGoogle Scholar
  9. Confrey, J. (1999). Voice, perspective, bias and stance: Applying and modifying Piagetian theory in mathematics education. In B. Leone (Ed.), Learning mathematics: From hierarchies to networks (pp. 3–20). London: Falmer Press.Google Scholar
  10. Confrey, J., & Maloney, A. (2008). Research-design interactions in building function probe software. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Vol 2. Cases and perspectives (pp. 183–210). Charlotte, NC: Information Age Publishing, Inc.Google Scholar
  11. De Villiers, M. (1998). An alternative approach to proof with dynamic geometry. In D. C. R. Lehrer (Ed.), New directions in teaching and learning geometry. Mahwah, NJ: Erlbaum.Google Scholar
  12. De Villiers, M. (1999). Rethinking proof with geometer’s sketchpad. Berkeley, CA: Key Curriculum Press.Google Scholar
  13. Dick, T., & Edwards, B. (2008). Multiple representations and local linearity-research influences on the use of technology in calculus curriculum reform. In G. Blume & K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Vol 2 Cases and perspectives (pp. 255–278). Charlotte, NC: Information Age Publishing, Inc.Google Scholar
  14. Goldenberg, E. P., Scher, D., & Feurzeig, N. (2008). What lies behind dynamic interactive geometry software. In K. G. Blume & K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Vol 2. Cases and perspectives (pp. 53–88). Charlotte, NC: Information Age Publishing, Inc.Google Scholar
  15. Goos, M., & Bennison, A. (2002). Building learning communities to support beginning teachers’ use of technology. Paper presented at the annual conference of the australian association for research in education. Retrieved July 21, 2010, from http://www.aare.edu.au/02pap/goo02058.htm.
  16. Hall, G. E., & Hord, S. M. (2006). Implementing change: Patterns, principles, and potholes (2nd ed.). Boston: Pearson/Allyn & Bacon.Google Scholar
  17. Hart, E., Keller, S., Martin, W., Midgett, C., & Gorski, S. (2005). Using the internet to illuminate NCTM’s principles and standards for school mathematics. In W. Masalski & P. Elliott (Eds.), Technology-supported mathematics learning environments (pp. 221–240). Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  18. Herbst, P. (2002). Establishing a custom of proving in American school geometry: Evolution of the two-column proof in the early twentieth century. Educational Studies in Mathematics, 49(1), 283–312.CrossRefGoogle Scholar
  19. Hill, H., Ball, D. L., & Schilling, S. (2008). Unpacking “pedagogical content knowledge”: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.Google Scholar
  20. IGI Global. (2010, March 30). Classrooms becoming more revolutionized one whiteboard at a time. Retrieved June 10, 2010, from IGI Global: Disseminator of knowledge www.igi-global.com/blogs/main/10-03-30.
  21. Jackiw, N. (2001). The geometer’s sketchpad, version 4.0 [computer software]. Emeryville, CA: Key Curriculum Press.Google Scholar
  22. Kaput, J. (1993). Overcoming physicality and the eternal present: Cybernetic manipulatives. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in education (pp. 220–248). Berlin: Springer.Google Scholar
  23. Konold, C., & Miller, C. (2009). TinkerPlots, version 1.1 [computer software]. Emeryville, CA: Key Curriculum Press.Google Scholar
  24. Meel, D. E. (2003). Models and theories of mathematical understanding: Comparing Pirie and Kieren’s model of the growth of mathematical understanding and APOS theory. CBMS Issues in Mathematics Education, 12, 132–181.Google Scholar
  25. Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A new framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054.CrossRefGoogle Scholar
  26. Moyer-Packenham, P. S., Salkind, G., & Bolyard, J. J. (2008). Virtual manipulatives used by K-8 teachers for mathematics instruction: Considering mathematical, cognitive, and pedagogical fidelity. Contemporary Issues in Technology and Teacher Education, 8(3), 202–218.Google Scholar
  27. National Council of Teachers of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Teachers of Mathematics.Google Scholar
  28. Papert, S. (1993). The children’s machine: Rethinking school in the age of the computer. New York: Basic Books.Google Scholar
  29. Patsiomitou, S. (2008, December 15–19). Do geometrical constructions in a dynamic geometry enviroment affect students’ algebraic expressions? Retrieved June 2010, from electronic proceedings of the thirteenth Asian technology conference in mathematics http://atcm.mathandtech.org/EP2008/papers_full/2412008_15001.pdf.
  30. Pirie, S., & Kieren, T. (1994). Growth of mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26(2–3), 165–190.CrossRefGoogle Scholar
  31. Project Tomorrow. (2010). Creating our future: Students speak up about their vision for 21st century learning. Retrieved June 15, 2010, from Project Tomorrow http://www.tomorrow.org/speakup/pdfs/SU09NationalFindingsStudents&Parents.pdf.
  32. Roschelle, J., & Kaput, J. (1996). SimCalc Mathworlds for the mathematics of change. Communications of the ACM, 39, 97–99.CrossRefGoogle Scholar
  33. Schulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1–22.Google Scholar
  34. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.CrossRefGoogle Scholar
  35. Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  36. Sfard, A., & McClain, K. (2002). Analyzing tools: Perspectives on the role of designed artifacts in mathematics learning. Journal of the Learning Sciences, 11(2), 153–161.CrossRefGoogle Scholar
  37. Sinclair, N. (2003). Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52, 289–317.CrossRefGoogle Scholar
  38. Underwood, J., Hoadley, C., Lee, H., Hollebrands, K., DiGiano, C., & Renninger, K. A. (2005). IDEA: Identifying design principles in educational applets. Educational Technology Research and Development, 53(2), 99–112.CrossRefGoogle Scholar
  39. Wertsch, J. (2002). Computer mediation, PBL, and dialogicality. Distance Education, 23(1), 105–108.CrossRefGoogle Scholar
  40. Zbiek, R. M., & Hollebrands, K. (2008). Incorporating mathematics technology into classroom practice. In K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics (Vol. I, pp. 287–344). Charlotte, NC: Information Age Publishing, Inc.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSan Diego State UniversitySan DiegoUSA

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