Skip to main content
Log in

The World According to Johnny; A Coping Perspective in Mathematics Education

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Students in mathematical problem-solving situations often experience confusion and loss of meaning. In these situations, affective and social factors are as much part of the student's thinking and behavior as are cognitive factors. These additional factors might include, for example, the need to make sense and the need to meet expectations of the authority figure involved (e.g., teacher or researcher). In this paper we attempt to analyze students' productions, taking into account such additional affective and social factors. To this end, we have tried to reproduce the student's voice in what we call virtual monologue. It consists of a monologue in the student's voice given in first person language, in which we try to describe as vividly and as faithfully as we can our picture of what might be going on in the student's mind during such situations.

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

  • Beth, E.W. and Piaget, J.: 1966, Mathematical Epistemology and Psychology, D. Reidel Publishing Company.

  • Bruner, J. and Haste, H. (eds.): 1987, Making Sense, Methuen, London.

    Google Scholar 

  • Clement, J.: 1982, ‘Algebra word problem solutions: Thought processes underlying a common misconception’, Journal for Research in Mathematics Education 13, 16–30.

    Google Scholar 

  • Cobb, P., Yackel, E. and Wood, T.: 1989, ‘Young children's emotional acts while doing mathematical problem solving’, In McLeod, D. B and Adams, V. M. (eds.). Affect and Mathematical Problem Solving, Springer-Verlag, New-York, 117–148.

    Google Scholar 

  • Confrey, J.: 1995–6, ‘A theory of intellectual development’, For the Learning of Mathematics, Part I: 14, 2–8; Part II: 15, 38–48; Part III: 15, 36–45.

    Google Scholar 

  • Davis, R.B. and Maher, C.A.: 1990, ‘What do we do when we “do mathematics”?’, Journal for Research in Mathematics Education, Monograph number 4, 65–78.

  • Davis, R.B, Maher, C.A. and Noddings, N. (eds.): 1990, Journal for Research in Mathematics Education — Monograph No. 4 — Constrctivist Views on the Teaching and Learning of Mathematics.

  • Donaldson, M.: 1978, Children's Minds, William Collins Sons and Co Ltd, Great Britain.

    Google Scholar 

  • Dubinsky, E., Leron, U., Dautermann, J. and Zazkis, R.: 1994, ‘On learning fundamental concepts of group theory’, Educational Studies in Mathematics 27, 267–305.

    Google Scholar 

  • Duffin, J. and Simpson, A.: in press, ‘A theory, a story, its analysis and some implications’, Journal of Mathematical Behavior.

  • Ericsson, K.A. and Simon, H.A.: 1980, ‘Verbal reports as data’, Psychological Review 87, 215–251.

    Google Scholar 

  • Erlwanger, S.H.: 1973, ‘Benny's conception of rules and answers in IPI mathematics’, The Journal of Children's Mathematical Behavior 1, 7–26.

    Google Scholar 

  • Even, R.: 1992, ‘The inverse function: Prospective teachers’ use of'undoing”, International Journal of Mathematics Education in Science and Technology 23, 557–562.

    Google Scholar 

  • Feyerabend, P.: 1991, Three Dialogues on Knowledge, Blackwell, Oxford.

    Google Scholar 

  • Hardy, T. and Wilson, D.: 1995, ‘Working with ‘the discipline of noticing’: An authenticating experience?’, Philosophy of Mathematics Education Newsletter 8, 10–12.

    Google Scholar 

  • Hazzan, O.: 1995, Undergraduate Students' Understanding of Concepts in Abstract Algebra, Doctoral thesis (Hebrew), Technion — Israel Institute of Technology.

  • Hazzan, O. and Leron, U.: 1996, ‘Students' use and misuse of mathematical theorems: The case of Lagrange's theorem’, For the Learning of Mathematics 16, 23–26.

    Google Scholar 

  • Hilgard, E.R. and Bower, G.H.: 1966, Theories of Learning (third edition), Meredith Publishing Company.

  • Jerman, M.: 1973, ‘Problem length as a structural variable in verbal arithmetic problems’, Educational Studies in Mathematics 5, 109–123.

    Google Scholar 

  • Kilpatrick, J.: 1987, ‘What constructivism might be in mathematics education’, Proceedings of the 11th PME, Vol. 1, 3–27.

    Google Scholar 

  • Kilpatrick, J: 1992, ‘A history of research in mathematics education’, In D.A. Grouws (ed.). Handbook of Research on Mathematics Teaching and Learning, Macmillan Publishing Company, NY, 3–38.

    Google Scholar 

  • Lester, F.K. and Garofalo, J.: 1982, ‘Metacognitive aspects of elementary students' performance on arithmetic tasks’. Paper presented at The annual meeting of the American Educational Research Association, New-York.

  • Leron, U. and Dubinsky, E.: 1995, ‘An abstract algebra story’, The American Mathematical Monthly 102, 227–242.

    Google Scholar 

  • Leron, U., Hazzan, O. and Zazkis, R.: 1995, ‘Learning group isomorphism: A crossroads of many concepts’. Educational Studies in Mathematics 29, 153–174.

    Google Scholar 

  • Mandler, G: 1989a, ‘Affect and learning: Causes and consequences of emotional interactions’. In McLeod, D.B and Adams, V.M. (eds.). Affect and Mathematical Problem Solving, Springer-Verlag, New-York, 3–19.

    Google Scholar 

  • Mandler, G: 1989b, ‘Affect and learning: Reflections and prospects’, In McLeod, D. B and Adams, V. M. (eds.). Affect and Mathematical Problem Solving, Springer-Verlag, New-York, 237–244.

    Google Scholar 

  • Mason, J.: 1994, ‘Researching from the inside in mathematics education — locating an I-you relationship’, Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education, Lisbon, Portugal, Vol. 1, 176–194.

    Google Scholar 

  • McLeod, D.B.: 1989, ‘The role of affect in mathematical problem solving’, In McLeod, D.B. and Adams, V.M. (eds.). Affect and Mathematical Problem Solving, Springer-Verlag, New-York, pp. 20–36.

    Google Scholar 

  • McLeod, D.B.: 1990, ‘Information-processing theories and mathematical learning: The role of affect’, International Journal of Educational Research 14, 13–29.

    Google Scholar 

  • McLeod, D.B.: 1994, ‘Research on affect and mathematics learning in the JRME from 1970 to the present’, Journal for Research in Mathematics Education 25, 637–647.

    Google Scholar 

  • McLeod, D.B and Adams, V.M. (eds.): 1989, Affect and Mathematical Problem Solving, Springer-Verlag, New-York.

    Google Scholar 

  • Nesher, P. and Teubal, E.: 1975, ‘Verbal cues as an interfering factor in verbal problem solving, Educational Studies in Mathematics 6, 41–51.

    Google Scholar 

  • Nesher, P.: 1980, ‘The stereotyped nature of school word problems’, For the Learning of Mathematics 1, 41–48.

    Google Scholar 

  • Nisbett, R.E. and Wilson, T.: 1977, ‘Telling more than we know: Verbal reports on mental processes’, Psychological Review 84, 231–260.

    Google Scholar 

  • Papert, S.: 1980, Mindstorms — Children, Computers, and Powerful Ideas, Basic Books, Inc. Publishers, New-York.

    Google Scholar 

  • Prawat and Anderson: 1994, ‘The affective experiences of children during mathematics’, Journal of Mathematical Behavior 13, 201–222.

    Google Scholar 

  • Schiefele, U. and Csikszentmihalyi, M.: 1995, ‘Motivation and ability as factors in mathematics experience and achievement’, Journal for Research in Mathematics Education 26, 163–181.

    Google Scholar 

  • Schoenfeld, A.H.: 1985a, Mathematical Problem Solving, Academic press.

  • Schoenfeld, A.H.: 1985b, ‘Making sense of ‘out loud’ problem-solving protocols’, The Journal of Mathematical Behavior 4, 171–191.

    Google Scholar 

  • Schon, D.: 1987, Educating the Reflective Practitioner: Towards a New Design for Teaching and Learning in The Profession, San Francisco: Jossey-Bass.

    Google Scholar 

  • Selden, A. and Selden, J.: 1987, ‘Errors and misconceptions in college level theorem proving’, in Proceedings of the Second International Seminar — Misconceptions and Educational Strategies in Science and Mathematics, Cornell University, NY.

  • Selden, A. and Selden, J.: 1993, ‘Collegiate mathematics education research: What would that be like?, The College Mathematics Journal 24, 431–445.

    Google Scholar 

  • Sfard, A.: 1992, ‘Operational origins of mathematical objects and the quandary of reification — the case of function’, in G. Harel and E. Dubinsky: The Concept of Function — aspects of Epistemology and Pedagogy, 59–84.

  • Sfard, A. and Linchevski, L: 1994, ‘The gains and the pitfalls of reification — The case of algebra’, Educational Studies in Mathematics 26, 191–228.

    Google Scholar 

  • Sfard, A.: in print, ‘The development of the concept of concept development: From God's eye view to what can be seen with the mind's eye’, to appear in the Proceedings of the Seventh Carinthian Symposium for Mathematics education on Trends and Perspectives, Klagenfurt.

  • Skemp, R.R.: 1976, ‘Relational understanding and instrumental understanding’, Mathematics Teaching, December, 20–26.

  • Smith, J.P., diSessa, A.A. and Roschelle, J.: 1993, ‘Misconceptions reconceived: A constructivist analysis of knowledge in transition’, The Journal of the Learning Sciences 3, 115–163.

    Google Scholar 

  • Vygotsky, L.S.: 1962, Thought and Language, (E. Hanfmann, ed. and G. Vaker, trans.). Cambridge, MA: Massachusetts Institute of Technology Press.

    Google Scholar 

  • Wheatley, G.H.: 1991, ‘Constructivist perspectives on science and mathematics learning’, Science Education 75, 9–21.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leron, U., Hazzan, O. The World According to Johnny; A Coping Perspective in Mathematics Education. Educational Studies in Mathematics 32, 265–292 (1997). https://doi.org/10.1023/A:1002908608251

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1002908608251

Keywords

Navigation