DOI QR코드

DOI QR Code

Secondary Mathematics Teachers' Perceptions of Rate of Change

  • Noh, Jihwa (Department of Mathematics Education Pusan National University)
  • 투고 : 2017.08.22
  • 심사 : 2017.08.26
  • 발행 : 2017.08.31

초록

This is a descriptive study with the intent of providing a rich characterization of teachers' perceptions of rate of change. The nature of teachers' perceptions and differences among teachers were examined by collecting data through a survey on teachers' conceptions of rate of change in terms of learning goals, prerequisites, and beliefs about teaching and learning of rate of change, and an interview individually assessing teachers' concept images and definitions. The participating 13 teachers were selected to provide a range of similar and contrasting levels of experiences based on the teachers' educational background and the number of years they had been teaching. Findings and implications of this study are discussed.

키워드

참고문헌

  1. Behr, M. J., Lesh, R., Post, T. R., & Silver, E. A. (1983). Rational-number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91-126). New York: Academic Press.
  2. Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33 (5), 352-378. https://doi.org/10.2307/4149958
  3. Dreyfus, T. (1991). Advanced mathematical thinking processes. In D. Tall (Ed.), Advanced mathematical thinking (pp. 25-41). Dordrecht, The Netherlands: Kluwer.
  4. Herbert, S., & Pierce, R. (2008). An 'Emergent Model' for rate of change. International Journal of Computers for Mathematical Learning, 13 (3), 231-249. https://doi.org/10.1007/s10758-008-9140-8
  5. Kalchman, M., Moss, J., & Case, R. (2001). Psychological models for the development of mathematical understanding: Rational numbers and functions. NY: Lawrence Erlbaum Associates, Inc.
  6. Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60 (1), 1-64. https://doi.org/10.3102/00346543060001001
  7. Monk. G. S. (1992). Students' understanding of function given by a physical model. In G. Harel & E. Dubinsky (Eds.), The concept of function: Aspects of epistemology and pedagogy (Vol. 25, pp. 175-193). Washington, DC: Mathematical Association of America.
  8. Monk, G. S., & Nemirovsky, R. (1994). The case of Dan: Student construction of a functional situation through visual attributes. CBMS Issues in Mathematics Education, 4 , 139-168: American mathematical Society,
  9. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics . Reston, VA: National Council of Teachers of Mathematics.
  10. Noble, T., Nemirovsky, R., Wright, T., & Tierney, C. (2001). Experiencing change: The mathematics of change in multiple environments. Journal for Research in Mathematics Education, 32 (1), 85-108. https://doi.org/10.2307/749622
  11. Reys, R., & Reys, R. (2009). Two high school mathematics curricular paths-Which one to take? Mathematics Teacher, 102( 8). 568-570.
  12. Schoenfeld, A. H., Smith, J. P., & Arcavi, A. (1993). Learning: The microgenetic analysis of one student's evolving understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 4, pp. 55-175). Hillsdale, NJ: Lawrence Erlbaum.
  13. Stewart, I. (1990). Change. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 183-217). Washington, DC: National Academy Press.
  14. Stump, S. L. (2001). High school precalculus students' understanding of slope as measure. School Science and Mathematics, 101 (2), 81-89. https://doi.org/10.1111/j.1949-8594.2001.tb18009.x
  15. Sullivan, M., & Sullivan M. III. (2006). Precalculus enhanced with graphing utilities. 4th ed. Engle- wood Cliffs, NJ: Pearson Prentice Hall.
  16. Teuscher, D., & Reys, R. (2010). Slope, rate of change, and steepness: Do students understand these concepts? Mathematics Teacher, 103 (7), 519-524.
  17. Thompson, A. G., & Thompson, P. W. (1996). Talking about rates conceptually, Part II: Mathematical knowledge for teaching. Journal for Research in Mathematics Education, 27 (1), 2-24. https://doi.org/10.2307/749194
  18. Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26 (2-3), 229-274. https://doi.org/10.1007/BF01273664
  19. Ubuz, B. (2007). Interpreting a graph and constructing its derivative graph: Stability and change in students' conceptions. International Journal of Mathematical Education in Science and Technology, 38 (5), 609-637. https://doi.org/10.1080/00207390701359313
  20. Vinner, S. (1989). The avoidance of visual considerations on calculus students. Focus on Learning Problems in Mathematics, 11 (2), 149-156.
  21. Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20 , 356-366. https://doi.org/10.2307/749441
  22. Wilhelm, J, & Confrey, J. (2003). Projecting rate of change in the context of motion onto the context of money. International Journal of Mathematical Education in Science and Technology, 34 (6), 887-904. https://doi.org/10.1080/00207390310001606660