Using technology to explore mathematical relationships: a framework for orienting mathematics courses for prospective teachers
- 961 Downloads
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.
KeywordsTPACK Technological knowledge Content knowledge Technology
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- De Villiers, M. (1999). Rethinking proof with geometer’s sketchpad. Berkeley, CA: Key Curriculum Press.Google Scholar
- 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
- 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
- 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.
- Hall, G. E., & Hord, S. M. (2006). Implementing change: Patterns, principles, and potholes (2nd ed.). Boston: Pearson/Allyn & Bacon.Google Scholar
- 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
- 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
- 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.
- Jackiw, N. (2001). The geometer’s sketchpad, version 4.0 [computer software]. Emeryville, CA: Key Curriculum Press.Google Scholar
- 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
- Konold, C., & Miller, C. (2009). TinkerPlots, version 1.1 [computer software]. Emeryville, CA: Key Curriculum Press.Google Scholar
- 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
- 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
- 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
- Papert, S. (1993). The children’s machine: Rethinking school in the age of the computer. New York: Basic Books.Google Scholar
- 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.
- 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.
- Schulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1–22.Google Scholar
- 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