Skip to main content
Log in

The teacher’s role in supporting students’ connections between realistic situations and conventional symbol systems

  • Articles
  • Published:
Mathematics Education Research Journal Aims and scope Submit manuscript

Abstract

We use the notion offocusing phenomena to help explain how a teacher’s actions were connected to her students’ interpretations of a linear equation. This study was conducted in a high-school classroom that regularly emphasised dependency relationships in real-world situations. Seven interviews revealed a majority view ofy = b + mx as astorage container—a place to insert b and m values—rather than as a relationship between x- and y-values. Classroom analysis revealed how the teacher directed attention away from functional relationships with increasing frequency as she moved from realistic situations to conventional representations.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Australian Education Council. (1990).A national statement on mathematics for Australian schools. Melbourne: Curriculum Corporation.

    Google Scholar 

  • Bernard, H. E. (1988).Research methods in cultural anthropology. Beverly Hills, CA: Sage.

    Google Scholar 

  • Bowers, J. S., & Nickerson, S. (2000). Students’ changing views of rates and graphs when working with a simulation microworld.Focus on Learning Problems in Mathematics, 22(3 & 4), 10–27.

    Google Scholar 

  • Coxford, A. F., Fey, J. T., Hirsh, C. R., Schoen, H. L., Burrill, G., & Hart, E. W. (1998).Contemporary mathematics in context: A unified approach, Course 1, Part A. Chicago, IL: Everyday Learning Corporation.

    Google Scholar 

  • English, L., & Warren, E. (1995). General reasoning processes and elementary algebraic understanding: Implications for instruction.Focus on Learning Problems in Mathematics, 17(4), 1–19.

    Google Scholar 

  • Fey, J. T. (1990). Quantity. In L. A. Steen (Ed.),On the shoulders of giants (pp. 61–94). Washington, DC: National Academy Press.

    Google Scholar 

  • Frorer, P., Hazzan, O., & Manes, M. (1997). Revealing the many faces of abstraction.International Journal of Computers for Mathematical Learning, 2(3), 217–228.

    Article  Google Scholar 

  • Glaser, B. G., & Strauss, A. L. (1967).The discovery of grounded theory: Strategies for qualitative research. Chicago, IL: Aldine Publishing Company.

    Google Scholar 

  • Gravemeijer, K., Cobb, P., Bowers, J., & Whitenack, J. (2000). Symbolizing, modeling, and instructional design. In P. Cobb, E. Yackel, & K. McClain (Eds.),Symbolizing and communicating in mathematics classrooms (pp. 225–273). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions.Journal for Research in Mathematics Education, 32(2), 195–222.

    Article  Google Scholar 

  • Huntley, M. A., Rasmussen, C., Villarubi, R., Sangton, J., & Fey, J. (2000). Effects of standardsbased mathematics education: A study of the Core-Plus Mathematics Project Algebra/Functions Strand.Journal for Research in Mathematics Education, 31, 328–361.

    Article  Google Scholar 

  • Kaput, J. J. (1994). The representational roles of technology in connecting mathematics with authentic experience. In R. Biehler, R. W. Scholz, R. Sträßer, & B. Winkelmann (Eds.),Didactics of mathematics as a scientific discipline (pp. 379–397). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Kaput, J. J., & Nemirovsky, R. (1995). Moving to the next level: A mathematics of change theme throughout the K-16 curriculum.Undergraduate Mathematics Education Trends, 6(6), 20–21.

    Google Scholar 

  • Kieran, C. (1993). Functions, graphing, and technology: Integrating research on learning and instruction. In T. A. Romberg, E. Fennema, & T. P. Carpenter (Eds.),Integrating research on the graphical representation of functions (pp. 189–238). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Lee, L. (1996). An initiation into algebraic culture through generalization activities. In N. Bednarz, C. Kieran, & L. Lee (Eds.),Approaches to algebra (pp. 87–106). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Lobato, J., Ellis, A., & Muñoz, R. (in press). How “focusing phenomena” in the instructional environment afford students’ generalizations.Mathematical Thinking and Learning.

  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.),Approaches to algebra (pp. 65–86). Dordrecht, The Netherlands: Kluwer.

    Google Scholar 

  • Mathematical Sciences Education Board. (1998).High school mathematics at work. Washington, DC: National Academy Press.

    Google Scholar 

  • Miles, M. B., & Huberman, A. M. (1994).Qualitative data analysis (2nd ed.). Thousand Oaks, CA: Sage Publications.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989).Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • National Council of Teachers of Mathematics. (2000).Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • National Research Council. (1990).Reshaping school mathematics: A philosophy and framework for curriculum. Washington, DC: National Academy Press.

    Google Scholar 

  • Nemirovsky, R., Tierney, C., & Wright, T. (1998). Body motion and graphing.Cognition and Instruction, 16, 119–172.

    Article  Google Scholar 

  • Orton, A., & Orton, J. (1994). Students’ perception and use of pattern and generalization. In J. P. da Ponto & J. F. Matos (Eds.),Proceedings of the 18th International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 407–414). Lisbon, Portugal: PME Program Committee.

    Google Scholar 

  • Pegg, J., & Redden, E. (1990). Procedures for, and experiences in, introducing algebra in New South Wales.Mathematics Teacher, 83(5), 386–391.

    Google Scholar 

  • Reeuwijk, M. van (2002). Early school algebra: A Dutch perspective. In J. Kaput (Ed.),Employing children’s natural powers to build algebraic reasoning in the content of elementary mathematics. Manuscript in preparation. Available: http://www.simcalc.umassd.edu/NewWebsite/EABookChapters.html

  • Reeuwijk, M. van, & Wijers, M. (1997). Students’ construction of formulas in context.Mathematics Teaching in the Middle School, 2(4), 230–236.

    Google Scholar 

  • Reid, D. (2002). Conjectures and refutations in grade 5 mathematics.Journal for Research in Mathematics Education, 33(1), 5–29.

    Article  Google Scholar 

  • Schatzman, L., & Strauss, A.L. (1973).Field research. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Schliemann, A.D., Carraher, D.W., & Brizuela, B.M. (2001). When tables become function tables. In M. van den Heuvel-Panhuizen (Ed.),Proceedings of the XXV Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 145–152). Utrecht, The Netherlands: Freudenthal Institute.

    Google Scholar 

  • Sfard, A. (2000). Symbolizing mathematical reality into being—or how mathematical discourse and mathematical objects create each other. In P. Cobb, E. Yackel, & K. McClain (Eds.),Symbolizing and communicating in mathematics classrooms (pp. 37–98). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Stacey, K. (1989). Finding and using patterns in linear generalising problems.Educational Studies in Mathematics, 20, 147–164.

    Article  Google Scholar 

  • Stacey, K., & MacGregor, M. (1997). Ideas about symbolism that students bring to algebra.Mathematics Teacher, 90(3), 110–113.

    Google Scholar 

  • Strauss, A., & Corbin, C. (1990).Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park, CA: Sage Publications.

    Google Scholar 

  • Streefland, L. (1995, April).Developing instructional activities in which algebra might arise naturally. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.

  • Szombathelyi, A., & Szarvas, T. (1998). Ideas for developing students’ reasoning: A Hungarian perspective.Mathematics Teacher, 91(8), 677–681.

    Google Scholar 

  • Thompson, P. W. (1995). Notation, convention, and quantity in elementary mathematics. In J. T. Sowder & B. P. Schappelle (Eds.),Providing a foundation for teaching mathematics in the middle grades (pp. 199–222). Albany, NY: State University of New York Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lobato, J., Ellis, A.B. The teacher’s role in supporting students’ connections between realistic situations and conventional symbol systems. Math Ed Res J 14, 99–120 (2002). https://doi.org/10.1007/BF03217356

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03217356

Keywords

Navigation