Skip to main content
SpringerLink
Log in

Relations between Types of Reasoning and Computational Representations

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

Abstract

This paper examines the idea that particular representations differentially support and enhance different cognitive processes, in particular different types of reasoning. Five case studies were conducted consisting of detailed observations of pairs of middle-school students interacting with a computer-based learning environment. The software environment, called NumberSpeed, deals with kinematics concepts by having students construct various motion scenarios by adjusting numerical motion parameters: position, velocity and acceleration. NumberSpeed provides feedback about the student-specified motion using two representations: the motion representation and the number-lists representation. Two distinct types of reasoning were recognized in students’ learning while interacting with NumberSpeed: (1) model-based reasoning and (2) constraint-based reasoning. These two types of reasoning are characterized in detail and their roles in problem-solving are analyzed. A cross-analysis between the types of reasoning and the use of particular NumberSpeed representations reveals a correlation between type of reasoning and representational choice. These findings are explained by analyzing the representations’ characteristics and the ways they may differentially support and enhance particular types of reasoning.

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

Similar content being viewed by others

References

  • S. Adams A.A. diSessa (1991) ArticleTitleLearning by “Cheating”: Students’ inventive ways of using a boxer motion microworld Journal of Mathematical Behavior 10 79–89

    Google Scholar 

  • S. Ainsworth (1999) ArticleTitleThe functions of multiple representations Computers & Education. 33 IssueID(2–3) 131–152

    Google Scholar 

  • J. De Kleer J.S. Brown (1983) Assumptions and ambiguities in mechanistic mental models. D. Gentner A.L. Stevens (Eds) Mental Models Erlbaum Hillsdale, New Jessey

    Google Scholar 

  • A.A. diSessa (1995) The many faces of a computational medium: teaching the mathematics of motion. A.A. diSessa C. Hoyles R. Noss L. Edwards (Eds) Computers and Exploratory Learning Springer Verlag Berlin 337–359

    Google Scholar 

  • A.A. diSessa (2000) Changing Minds: Computers, Learning, and Literacy. MIT Press Cambridge, MA

    Google Scholar 

  • A.A. diSessa H. Abelson (1986) ArticleTitleBoxer: A reconstructible computational medium Communications of the ACM 29 IssueID9 859–868 Occurrence Handle10.1145/6592.6595

    Article  Google Scholar 

  • diSessa, A.A. and Sherin, B. (1995). Discrete models and radical reformulation of physics for instruction. Unpublished paper presented at AERA 1995.

  • K. Forbus (1983) Qualitative reasoning about space & motion. D. Gentner A.L. Stevens (Eds) Mental Models Erlbaum Hillsdale, N J

    Google Scholar 

  • Ford, M., Frederickson, A. and Martin, L. (2000). The interpretation of symbol schemes in a computational medium. Unpublished paper presented at the annual meeting of the American Educational Research Association. New Orleans, LA.

  • J.R. Frederiksen B.Y. White J. Gutwill (1999) ArticleTitleDynamic mental models in learning science Journal of Research in Science Teaching 36 IssueID7 806–836 Occurrence Handle10.1002/(SICI)1098-2736(199909)36:7<806::AID-TEA5>3.0.CO;2-2

    Article  Google Scholar 

  • J. Kaput (1989) Linking representations in the symbol systems of algebra C. Kieran S. Wagner (Eds) Research Agenda for Mathematics Education: Research Issues in the Learning and Teaching of Algebra Lawrence Erlbaum Publishers Hillsdale, New Jersy 167–194

    Google Scholar 

  • J. Larkin H. Simon (1987) ArticleTitleWhy a diagram is (sometimes) worth ten thousand words Cognitive Science 11 65–99

    Google Scholar 

  • R. Nachmias A. Arcavi (1990) ArticleTitleA parallel representation of linear functions using a microcomputer-based environment Journal of Computers in Mathematics and Science Teaching 9 IssueID4 79–88

    Google Scholar 

  • M.J. Nathan W. Kintsch E. Young (1992) ArticleTitleA theory of algebra word problem comprehension and its implications for the design of computer learning environments Cognition and Instruction 9 IssueID4 329–389

    Google Scholar 

  • R. Nemirovsky (1994) ArticleTitleOn ways of symbolizing: the case of Laura and velocity sign The Journal of Mathematical Behavior 13 389–422 Occurrence Handle10.1016/0732-3123(94)90002-7

    Article  Google Scholar 

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

    Google Scholar 

  • Parnafes, O. (2001). Patterns of Learning and Thinking in a Computer-based Learning Environment. Unpublished Masters thesis. UC Berkeley, Berkeley, California.

  • R.D. Pea (1987) Cognitive technologies for mathematics education A. Schoenfeld (Eds) Cognitive Science and Mathematics Education Lawrence Erlbaum Associates Hillsdale, New Jessey 89–122

    Google Scholar 

  • R.D. Pea (1993) Practices of distributed intelligence and designs for education G. Salomon (Eds) Distributed cognition: Psychological and educational considerations Lawrence Erlbaum Associates Mahwah, New Jersey 47–87

    Google Scholar 

  • D.L. Schwartz J.B. Black (1996) ArticleTitleShuttling between depictive models and abstract rules: induction and fall-back Cognitive Science 20 457–497 Occurrence Handle10.1016/S0364-0213(99)80012-3

    Article  Google Scholar 

  • R.N. Shepard (1978) ArticleTitleThe mental image American Psychologist 33 125–137 Occurrence Handle10.1037//0003-066X.33.2.125

    Article  Google Scholar 

  • R.K. Thornton D.R. Sokoloff (1990) ArticleTitleLearning motion concepts using real-time microcomputer-based laboratory tools American Journal of Physics 58 858–867

    Google Scholar 

  • D.E. Trowbridge L.C. McDermott (1980) ArticleTitleInvestigation of student understanding of the concept of velocity in one dimension American Journal of Physics 48 IssueID12 1020–1028 Occurrence Handle10.1119/1.12298

    Article  Google Scholar 

  • R.A. Wilson F.C. Keil (1999) The MIT encyclopedia of the cognitive sciences. MIT Press Cambridge, Massachusetts

    Google Scholar 

  • M. Yerushalmy (1991) ArticleTitleStudent perceptions of aspects of algebraic function using multiple representation software Journal of Computer Assisted Learning 7 42–57

    Google Scholar 

  • J. Zhang (1997) ArticleTitleThe nature of external representations in problem solving Cognitive Science 21 IssueID2 179–217 Occurrence Handle10.1016/S0364-0213(99)80022-6

    Article  Google Scholar 

  • J. Zhang D. Norman (1994) ArticleTitleRepresentations in distributed cognitive tasks Cognitive Science 18 IssueID1 87–122 Occurrence Handle10.1016/0364-0213(94)90021-3

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Education, University of California, Berkeley, USA

    Orit Parnafes & Andrea Disessa

Authors
  1. Orit Parnafes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Disessa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Orit Parnafes.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Parnafes, O., Disessa, A. Relations between Types of Reasoning and Computational Representations. Int J Comput Math Learning 9, 251–280 (2004). https://doi.org/10.1007/s10758-004-3794-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10758-004-3794-7

Keywords

Search

Navigation