You are here:

Computer as a medium for overcoming misconceptions in solving inequalities
Article

, State University of New York at Potsdam, United States ; , Tel Aviv University, Israel

JCMST Volume 26, Number 3, ISSN 0731-9258 Publisher: Association for the Advancement of Computing in Education (AACE), Waynesville, NC USA

Full Text

Abstract

Inequalities are considered among the most useful tools of investigation in pure and applied mathematics; yet their didactical aspects have not received much attention in mathematics education research until recently. An important aspect of teaching problem solving at the secondary level deals with the notion of equivalence of algebraic transformations used in replacing inequalities by equations. This paper shows that the appropriate use of computer graphing software has the potential to avoid errors and overcome misconceptions associated with the notion of equivalence in solving inequalities. It demonstrates how mathematical visualization provides learners with a conceptual insight into the sources of errors typical for the secondary mathematics classroom.

Citation

Abramovich, S. & Ehrlich, A. (2007). Computer as a medium for overcoming misconceptions in solving inequalities. Journal of Computers in Mathematics and Science Teaching, 26(3), 181-196. Waynesville, NC USA: Association for the Advancement of Computing in Education (AACE). Retrieved December 8, 2023 from .

© 2007 Association for the Advancement of Computing in Education (AACE)

Keywords

References

View References & Citations Map
  1. Abramovich, S. (2005). How to “check the result”? Discourse revisited. International Journal of Mathematical Education in Science and Technology, 36(4), 414-423.
  2. Abramovich, S., & Ehrlich, A. (1993). Computer-assisted instruction through the visualization of erroneous thinking. Paper presented at the 5th European Conference for Research on Learning and Instruction. Aix-en-Provence, France.
  3. Abramovich. S., & Norton, A. (2006). Equations with parameters: A locus approach. Journal of Computers in Mathematics and Science Teaching, 25(1), 5-28.
  4. Balacheff, N. (1990). Towards a problématique é ématique for research on mathematics teaching. Journal for Research in Mathematics Education, 21(4), 258-272.
  5. Batanero, C., Godino, J.D., Vallecillos, A., Green, D.R., & Holmes, P. (1994). Errors and difficulties in understanding elementary statistical concepts. International Journal of Mathematics Education in Science and Technology, 25(4), 527-547.
  6. Boero, P., & Bazzini, L. (2004). Inequalities in mathematics education: The need for complementary perspectives. In M.J. Hoines & A.B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (vol. 1, pp. 139-143). Bergen, Norway:
  7. Demb, A.B. (1973). Instructional uses of computers in higher education: A survey of higher education in Massachusetts. Paper presented at the EDUCOM Fall Conference, Toronto, Ontario (ERIC Document Reproduction Service No. ED 097028)
  8. DeSoto, C.B., London, M., & Handel, S. (1965). Social reasoning and spatial paralogic. Journal of Personality and Social Psychology, 2(4), 513-521.
  9. Dobbs, D.E., & Peterson, J.C. (1991). The sign-chart method for solving inequalities. Mathematics Teacher, 84(8), 657-664.
  10. Eisenberg, T., & Dreyfus, T. (1991). On the reluctance to visualize in mathematics. In W. Zimmermann& S. Cunningham (Eds.), Visualization in teaching and learning mathematics (pp. 158-164). Washington, DC: Mathematical
  11. Matz, M. (1982). Towards a process model for high school algebra errors. In D. Sleeman & J.S. Brown (Eds.), Intelligent tutoring systems (pp. 25-50).
  12. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  13. Parish, C.R. (1992). Inequalities, absolute value, and logical connectives. Mathematics Teacher, 85(9), 756-757.
  14. Radatz, H. (1979). Error analysis in mathematics education. Journal for Research in Mathematics Education, 10(3), 163-172.
  15. Sackur-Grisvard, C., & Leonard, F. (1985). Intermediate cognitive organization in the process of learning a mathematical concept: The order of positive decimal numbers. Cognition and Instruction, 2(2), 157-174.
  16. Schwartz, J.L. (1993). Software to think with: The case of algebra. In D.L. Ferguson (Ed.) Advanced educational technologies for mathematics and science (pp. 469-495). Berlin: Springer-Verlag.
  17. Shaw, D.E. (1997). Report to the President on the use of technology to strengthen K-12 education in the United States. Washington, DC: President’s Committee of Advisors on Science and Technology, Panel on Educational Technology.
  18. Sleeman, D. (1984). Mis-generalization: An explanation of observed mal-rules. In Proceedings of the Sixth Annual Conference of the Cognitive Science Society (pp. 51-56). Boulder, CO: Cognitive Science Society.
  19. Sleeman, D., & Brown, J.S. (1982). Intelligent tutoring systems. London: Academic Press.
  20. Steinberg, R.M., Sleeman, D.H., & Ktorza, D. (1990). Algebra students’ knowledge of equivalence of equations. Journal for Research in Mathematics Education, 22(2), 112-121.
  21. Tall, D.O. (2004). Reflections on research and teaching of equations and inequalities. In M.J. Hoines & A.B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, (vol. 1, pp. 158-161). Bergen, Norway: Bergen University College.
  22. Thompson, P.W. (1989). Artificial intelligence, advanced technology, and learning and teaching algebra. In C. Kieran& S. Wagner (Eds.), Research issues in the learning and teaching of algebra (pp. 135-161). Hillsdale, NJ: Lawrence Erlbaum.
  23. Tsamir, P., Tirosh, D., & Tiano, S. (2004). “New errors” and “old errors”: The case of quadratic inequalities. In M.J. Hoines & A.B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (vol.1, pp. 155-158). Bergen, Norway:

These references have been extracted automatically and may have some errors. Signed in users can suggest corrections to these mistakes.

Suggest Corrections to References