Skip to main content
SpringerLink
Log in

On teachers' mathematical knowledge and student exploration: A personal story about teaching a technologically supported approach to school algebra

  • Published:
International Journal of Computers for Mathematical Learning Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  • Ball, D. L. (1992). Teaching mathematics for understanding: What do teachers need to know about the subject matter. In M. Kennedy (Ed.), Teaching Academic Subjects to Diverse Learners (pp. 63–83). New York: Teachers College.

    Google Scholar 

  • Ball, D. L. (1993a). Halves pieces, and twoths: Constructing and using representational contexts in teaching fractions. In T. Carpenter and E. Fennema (Eds), Learning, Teaching, and Assessing Rational Number Constructs (pp. 157–195). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Ball, D. L. (1993b). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics, The Elementary School Journal 93(4): 373–397.

    Article  Google Scholar 

  • Van Barneveld, G. and Krabbendam, H. (Eds) (1982). Conference on Functions: Report 1. Enschede, The Netherlands: Foundation for Curriculum Development.

    Google Scholar 

  • Bednarz, N., Kieran, C. and Lee, L. (Eds) (1996). Approaches to Algebra: Perspectives for Research and Teaching. Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Bracey, Gerald (1992, June 12). If you ask me – cut out algebra! Mostly it's a useless, impractical exercise. Washington Post.

  • California State Department of Education (1992). Mathematics Framework for California Public Schools. Sacramento: Author.

    Google Scholar 

  • Chazan, D. (1992). Knowing school mathematics: A personal reflection on NCTM's teaching standards, Mathematics Teacher 85: 371–375.

    Google Scholar 

  • Chazan, D. (1993). F(x) = G(x)?: An approach to modeling with algebra, For the Learning of Mathematics 13(3): 22–26.

    Google Scholar 

  • Chazan, D. (1996). Algebra for all students? Journal of Mathematical Behavior 15(3): 455–477.

    Article  Google Scholar 

  • Chazan, D. and Bethell, S. (1998). Working with algebra. In Mathematical Sciences Education Board (Ed.), High School Mathematics at Work: Essays and Examples from Workplace Contexts to Strengthen the Mathematical Education of All Students. Washington, DC: National Research Council.

    Google Scholar 

  • Cohen, D., McLaughlin, M. and Talbot, J. (Eds) (1993). Teaching for Understanding: Challenges for Policy and Practice. San Francisco: Jossey-Bass.

    Google Scholar 

  • Computer-Intensive Curricula in Elementary Algebra (1991). Computer-Intensive Curricula in Elementary Algebra. The University of Maryland and The Pennsylvania State University.

  • Confrey, J. and Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions, Journal for Research in Mathematics Education 26(1): 66–86.

    Article  Google Scholar 

  • Cuban, L. (1993). How Teachers Taught: Constancy and Change in American Classrooms 1890–1990, 2nd edn, New York: Teachers College.

    Google Scholar 

  • Cuoco, A. (1990). Investigations in Algebra. Cambridge, MA: MIT.

    Google Scholar 

  • Dewey, J. (1902/1990). The School and Society; The Child and the Curriculum. Chicago: University of Chicago.

    Google Scholar 

  • Dolciani, M. and Wooton, W. (1970/73). Modern Algebra, Book One: Structure and Method. Boston: Houghton-Mifflin.

    Google Scholar 

  • Dugdale, S. and Kibbey, D. (1986). Interpreting Graphs. Pleasantville, NY: Sunburst.

    Google Scholar 

  • Fey, J. (1989). School algebra for the year 2000. In S. Wagner and C. Kieran (Eds), Research Issues in the Learning and Teaching of Algebra. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Goldenberg, P. (1988). Mathematics, metaphors, and human factors: Mathematical, technical, and pedagogical challenges in the educational use of graphical representations of functions, Journal of Mathematical Behavior 7: 135–173.

    Google Scholar 

  • Hewitt, D. (1995). Imagery as a tool to assist the teaching of algebra. In R. Sutherland and J. Mason (Eds), Exploiting Mental Imagery with Computers in Mathematics Education. Berlin: Springer-Verlag.

    Google Scholar 

  • Hirsch, E. D. (1996). The School We Need and Why We Don't Have Them. New York: Doubleday.

    Google Scholar 

  • Jaworski, B. (1994). Investigating Mathematics Teaching: A Constructivist Enquiry. London: Falmer.

    Google Scholar 

  • Kieran, C., Boileau, A. and Garancon, M. (1996). Introducing algebra by means of a technology-supported, functional approach. In N. Bednarz, C. Kieran and L. Lee (Eds), Approaches to Algebra: Perspectives for Research and Teaching (pp. 257–293). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Lacampagne, C., Blair, W. and Kaput, J. (Eds) (1995). The Algebra Initiative Colloquium. Washington: U.S. Department of Education.

    Google Scholar 

  • Lampert, M. (1989). Choosing and using mathematical tools in classroom discourse. In J. Brophy (Ed.), Advances in Research on Teaching, Vol. 1 (pp. 223–264). Greenwich, CT: JAI Press.

    Google Scholar 

  • Lampert, M. (1990). When the problem is not the question and the solution is not the answer: mathematical knowing and teaching, American Educational Research Journal 27(1): 29–63.

    Article  Google Scholar 

  • Lee, L. (1996). Algebraic understanding: The search for a model in the mathematics education community. Unpublished Dissertation, Universite du Quebec a Montreal, Montreal.

  • Lester, F. and Garofalo, J. (Eds) (1982). Mathematical Problem Solving: Issues in Research. Philadelphia: Frankline Institute Press.

    Google Scholar 

  • Love, E. (1988). Evaluating mathematical activity. In D. Pimm (Ed.), Mathematics, Teachers and Children (pp. 249–263). London: Hodder and Stoughton.

    Google Scholar 

  • Mason, J. (1996). Expressing generality and roots of Algebra. In N. Bednarz, C. Kieran and L. Lee (Eds), Approaches to Algebra: Perspectives for Research and Teaching (pp. 65–86). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • McCarthy, C. (1991, April 20). Who needs algebra? Washington Post.

  • Morgan, C. (1998). Writing Mathematically: The Discourse of Investigations. London: Falmer.

    Google Scholar 

  • Moschkovich, J., Schoenfeld, A. H. and Arcavi, A. (1993). Aspects of understanding: On multiple perspectives and representations of linear relations and connections among them. In T. A. Romberg, E. Fennema and T. P. Carpenter (Eds), Integrating Research on the Graphical Representation of Function (pp. 69–100). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA.

  • National Council of Teachers of Mathematics (1991). Professional Standards for Teaching Mathematics. Reston, VA.

  • National Council of Teachers of Mathematics (1994, September). A Framework for Constructing a Vision of Algebra: Working Draft. Reston, VA.

  • Peterson, P. L., Fennema, E. and Carpenter, T. (1991). Using children's mathematical knowledge. In B. Means, C. Chelemer,and M. S. Knapp (Eds), Teaching Advanced Skills to At-Risk Students: Views from Research and Practice (pp. 68–101). San Francisco, CA: Jossey-Bass.

    Google Scholar 

  • Pimm, D. (1995). Symbols and Meanings in School Mathematics. London: Routledge.

    Google Scholar 

  • Rojano, T. (1996). Developing algebraic aspects of problem solving within a spreadsheet environment. In N. Bednarz, C. Kieran and L. Lee (Eds), Approaches to Algebra: Perspectives for Research and Teaching (pp. 137–147). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Roberts, Wayne (1991, April 27). Algebra is not just math, its the language of science, Minneapolis Star Tribune.

  • Schoenfeld, A., Smith, J. and Arcavi, A. (1990). Learning: The microgenetic analysis of one student's understanding of a complex subject matter domain. In R. Glaser (Ed.), Advances in Instructional Psychology, Vol. 4. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Schwartz, J., Yerushalmy, M. and Educational Development Center. (1989). The Function Supposer: Explorations in Algebra. Pleasantville, NY: Sunburst.

    Google Scholar 

  • Schwartz, J. and Yerushalmy, M. (1992). Getting students to function in and with algebra. In G. H. and E. Dubinsky (Eds), The Concept of Function: Aspects of Epistemology and Pedagogy. Washington: Mathematical Association of America.

    Google Scholar 

  • Schwartz, J. and Yerushalmy, M. (1995). On the need for a bridging language for mathematical modeling, For the Learning of Mathematics 15(2): 29–35.

    Google Scholar 

  • Sizer, T. (1992). Horace's School: Redesigning the American High School. Boston: Houghton Mifflin.

    Google Scholar 

  • Thompson, P. (1993). Quantitative reasoning, complexity, and additive structures, Educational Studies in Mathematics 25: 165–208.

    Article  Google Scholar 

  • Tikhomirov, O. K. (1972/1981). The psychological consequences of computerization. In J. V. Wertsch (Ed.), The Concept of Activity in Soviet Psychology (pp. 256–278). New York: M.E. Sharpe.

    Google Scholar 

  • Usiskin, Z. (1987).Why elementary algebra can, should, and must be an eight-grade course for average students, Mathematics Teacher 80(6): 428–438.

    Google Scholar 

  • Wheeler, D. (1993). Knowledge at the crossroads, For the Learning of Mathematics 13(1): 53–55.

    Google Scholar 

  • Wood, T., Cobb, P., Yackel, E. and Dillon, D. (Eds). (1993). Rethinking elementary school mathematics: Insights and issues, Journal for Research in Mathematics Education 6.

  • Yerushalmy, M. (1991). Effects of computerized feedback on performing and debugging algebraic transformations, Journal of Educational Computing Research 7: 309–330.

    Article  Google Scholar 

  • Yerushalmy, M., and Schwartz, J. (1993). Seizing the opportunity to make algebra mathematically and pedagogically interesting. In E. Fennema, T. Romberg, and T. Carpenter (Eds), Integrating Research on the Graphical Representation of Function. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Yerushalmy, M. and Gafni, R. (1992). Syntactic manipulations and semantic interpretations in algebra: The effect of graphic representation, Learning and Instruction 2: 303–319.

    Article  Google Scholar 

  • Yerushalmy, M. and Gilead, S. (1997). Solving equations in a technological environment: Seeing and manipulating, Mathematics Teacher 90(2): 156–163.

    Google Scholar 

  • Yerushalmy, M. and Schwartz, J. (1997). A Procedural Approach to Explorations in Calculus. Haifa, Israel: Haifa University.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Michigan State University, 116L Erickson Hall, East Lansing, MI, 48824, U.S.A

    Daniel Chazan

Authors
  1. Daniel Chazan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chazan, D. On teachers' mathematical knowledge and student exploration: A personal story about teaching a technologically supported approach to school algebra. International Journal of Computers for Mathematical Learning 4, 121–149 (1999). https://doi.org/10.1023/A:1009875213030

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009875213030

Keywords

Search

Navigation