Skip to main content
SpringerLink
Log in

Models in Mathematics Education Research: A Broader View of Research Results

  • Chapter
Mathematics Education as a Research Domain: A Search for Identity

Part of the book series: New ICMI Studies Series ((NISS,volume 4))

Abstract

It may seem strange to some to imagine models as research results. How are research results defined? Narrowly, in the sense of empirical findings, or more broadly as the products of research endeavors -that are in some way linked to empirical work. At international conferences of mathematics education researchers, for example, the International Group for the Psychology of Mathematics Education (PME), one finds in the guidelines for conference proposals two categories of research reports: empirical and theoretical. But the separation between empirical and theoretical work in mathematics education research may, in fact, be a false one — especially with respect to models. At the least, the dividing line between the two is blurring.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bartolini Bussi, M. G.: 1994, ‘Theoretical and Empirical Approaches to Classroom Interaction’, in R. Biehler, R. W. Scholz, R. Sträβer & B. Winkelmann (eds.), Didactics of Mathematics as a Scientific Discipline, Springer Science+Business Media Dordrecht, Dordrecht, 121–132.

    Google Scholar 

  • Behr, M. J., Wachsmuth, I. & Post, T. R.: 1985, ‘Construct a Sum: A Measure of Children’s Understanding of Fraction Size’, Journal for Research in Mathematics Education 16, 120–131.

    Article  Google Scholar 

  • Bergeron, J. C. & Herscovics, N.: 1989, ‘A Model to Describe the Construction of Mathematical Concepts from an Epistemological Perspective’, in L. Pereira-Mendoza & M. Quigley (eds.), Proceedings of the 1989 Annual Meeting of the Canadian Mathematics Education Study Group, Memorial University of Newfoundland, St. John’s, 99–114.

    Google Scholar 

  • Brousseau, G.: 1972(February), ‘Processus de Mathématisation’, Bulletin de l’association des professeurs de mathématiques de l’enseignement public, 282, 57–84.

    Google Scholar 

  • Brousseau, G.: 1986, Théorisation des Phénomenes d’Enseignement des Mathématiques. Unpublished postdoctoral dissertation, University of Bordeaux, France.

    Google Scholar 

  • Davis, R. B.: 1975, ‘Cognitive Processes Involved in Solving Simple Algebraic Equations’, Journal of Children’ s Mathematical Behavior 1(3), 7–35.

    Google Scholar 

  • Davis, R. B.: 1984, Learning Mathematics: The Cognitive Science Approach to Mathematics Education, Routledge, London.

    Google Scholar 

  • Davis, R. B.: 1990, ‘The Knowledge of Cats: Epistemological Foundations of Mathematics Education’, in G. Booker, P. Cobb & T. N. de Mendicuti (eds.), Proceedings of the 14th International Conference for the Psychology of Mathematics Education, PME Program Committee, Oaxtepec, Mexico, PI.1–PI.24.

    Google Scholar 

  • Davis, R. B.: 1992, ‘Understanding “Understanding”’, Journal of Mathematical Behavior 11, 225–241.

    Google Scholar 

  • Douady, R.: 1985, ‘The Interplay between Different Settings: Tool-Object Dialectic in the Extension of Mathematical Ability — Examples from Elementary School Teaching’, in L. Streefland (ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education, State University of Utrecht, The Netherlands, Vol. 2, 33–52.

    Google Scholar 

  • Dreyfus, T.: 1990, ‘Advanced Mathematical Thinking’, in P. Nesher & J. Kilpatrick (eds.), Mathematics and Cognition: A Research Synthesis by the International Group for the Psychology of Mathematics Education, Cambridge University Press, Cambridge, 113–134.

    Chapter  Google Scholar 

  • Dubinsky, E.: 1991, ‘Reflective Abstraction in Advanced Mathematical Thinking’, in D. Tall (ed.), Advanced Mathematical Thinking, Springer Science+Business Media Dordrecht, Dordrecht, 95–123.

    Google Scholar 

  • Filloy, E.: 1990, ‘PME Algebra Research. A Working Perspective’, in G. Booker, P. Cobb & T. N. de Mendicuti (eds.), Proceedings of the 14th International Conference for the Psychology of Mathematics Education, PME Program Committee, Oaxtepec, Mexico, Vol. I, PII.1–PII.33.

    Google Scholar 

  • Fischbein, E.: 1994, ‘The Interaction Between the Formal, the Algorithmic, and the Intuitive Components in a Mathematical Activity’, in R. Biehler, R. W. Scholz, R. Sträβer & B. Winkel mann (eds.), Didactics of Mathematics as a Scientific Discipline, Springer Science+Business Media Dordrecht, Dordrecht, 231–245.

    Google Scholar 

  • Fischbein, E., Deri, M., Nello, M. S. & Marino, M. S.: 1985, ‘The Role of Implicit Models in Solving Problems in Multiplication and Division’, Journal for Research in Mathematics Education 16, 3–17.

    Article  Google Scholar 

  • Fischbein, E., Tirosh, D., Stavy, R. & Oster, A.: 1990, ‘The Autonomy of Mental Models’, Eor the Learning of Mathematics 10(1), 23–29.

    Google Scholar 

  • Goldin, G. A.: 1992, ‘On Developing a Unified Model for the Psychology of Mathematical Learning and Problem Solving’, in W. Geeslin & K. Graham (eds.), Proceedings of the 16th International Conference for the Psychology of Mathematics Education, PME Program Committee, Durham, NH, Vol. III, 235–261.

    Google Scholar 

  • Gray, E. M. & Tall, D. O.: 1994, ‘Duality, Ambiguity, and Flexibility: A “Proceptual” View of Simple Arithmetic’, Journal for Research in Mathematics Education 25, 116–140.

    Article  Google Scholar 

  • Harel, G.: 1985, Teaching Linear Algebra in High School. Unpublished doctoral dissertation, Ben-Gurion University of the Negev, Beer-Sheva, Israel.

    Google Scholar 

  • Harel, G. & Kaput, J.: 1991, ‘The Role of Conceptual Entities and their Symbols in Building Advanced Mathematical Concepts’, in D. Tall (ed.), Advanced Mathematical Thinking, Springer Science+Business Media Dordrecht, Dordrecht, 82–94.

    Google Scholar 

  • Hart, K. (ed.): 1981, Children’s Understanding of Mathematics 11-16, John Murray, London.

    Google Scholar 

  • Herscovics, N. & Bergeron, J. C.: 1983, ‘Models of Understanding’, Zentralblatt für Didaktik der Mathematik 15, 75–83.

    Google Scholar 

  • Kaput, J. J.: 1991, ‘Notations and Representations as Mediators of Constructive Processes’, in E. von Glasersfeld (ed.), Radical Constructivism in Mathematics Education, Springer Science+Business Media Dordrecht, Dordrecht, 53–74.

    Google Scholar 

  • Lesh, R. & Kelly A. E.: 1994, ‘Action-Theoretic and Phenomenological Approaches to Research in Mathematics Education: Studies of Continually Developing Experts’, in R. Biehler, R. W. Scholz, R. Sträβer, & B. Winkelmann (eds.), Didactics of Mathematics as a Scientific Discipline, Kluwer, Dordrecht, 277–286.

    Google Scholar 

  • Pirie, S. E. B. & Kieren, T. E.: 1992, ‘Watching Sandy’s Understanding Grow’, Journal of Mathematical Behavior 11, 243–257.

    Google Scholar 

  • Richards, J.: 1979, ‘Modeling and Theorizing in Mathematics Education’, in K. C. Fuson & W. E. Geeslin (eds.), Explorations in the Modeling of the Learning of Mathematics, ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Ohio State University, Columbus, 5–26.

    Google Scholar 

  • Rouse, W. G., & Morris, N. M.: 1985, On Looking into the Black Box: Prospects and Limits in the Search for Mental Models (Research report), Georgia Institute of Technology and Systems Engineering (ERIC Document Reproduction Service No ED 268 131)

    Google Scholar 

  • Sfard, A.: 1987, ‘Two Conceptions of Mathematical Notions: Operational and Structural’, in J. C. Bergeron, N. Herscovics & C. Kieran (eds.), Proceedings of the 11th International Conference for the Psychology of Mathematics Education, Université de Montréal, Canada, Vol. III, 162–169.

    Google Scholar 

  • Sfard, A.: 1989, ‘Transition from Operational to Structural Conception: The Notion of Function Revisited’, in G. Vergnaud, J. Rogalski & M. Artigue (eds.), Proceedings of the 13th International Conference for the Psychology of Mathematics Education, G. R. Didactique, CNRS, Paris, Vol. 3, 151–158.

    Google Scholar 

  • Sfard, A.: 1991, ‘On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same Coin’, Educational Studies in Mathematics 22, 1–36.

    Article  Google Scholar 

  • Soloway, E., Lochhead, J. & Clement, J.: 1982, ‘Does Computer Programming Enhance Problem Solving Ability? Some Positive Evidence on Algebra Word Problems’, in R. J. Seidel, R. E. Anderson & B. Hunter (eds.), Computer Literacy, Academic Press, New York, 171–185.

    Google Scholar 

  • Steffe, L. P.: 1983, ‘The Teaching Experiment Methodology in a Constructivist Research Program’, in M. Zweng, T. Green, J. Kilpatrick, H. Pollak & M. Suydam (eds.), Proceedings of the Fourth International Congress on Mathematical Education, Birkhäuser, Boston, 469–471.

    Google Scholar 

  • Steffe, L. P., Richards, J. & von Glasersfeld, E.: 1979, ‘Experimental Models for the Child’s Acquisition of Counting and of Addition and Subtraction’, in K. C. Fuson & W. E. Geeslin (eds.), Explorations in the Modeling of the Learning of Mathematics, ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Ohio State University, Columbus, Ohio, 27–44.

    Google Scholar 

  • Thompson, P. W.: 1985, ‘Experience, Problem Solving, and Learning Mathematics: Considerations in Developing Mathematics Curricula’, in E. A. Silver (ed.), Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives, Lawrence Erlbaum, Hillsdale, NJ, 189–236.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématiques, Université du Québec à Montréal, Montréal, QC, H3C 3P8, Canada

    Carolyn Kieran

Authors
  1. Carolyn Kieran
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Concordia University, Montreal, Quebec, Canada

    Anna Sierpinska

  2. University of Georgia, Athens, Georgia, USA

    Jeremy Kilpatrick

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media New York

About this chapter

Cite this chapter

Kieran, C. (1998). Models in Mathematics Education Research: A Broader View of Research Results. In: Sierpinska, A., Kilpatrick, J. (eds) Mathematics Education as a Research Domain: A Search for Identity. New ICMI Studies Series, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5470-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5470-3_14

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-4600-5

  • Online ISBN: 978-94-011-5470-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation