Skip to main content

Advertisement

SpringerLink
Log in

Functions of Interactive Visual Representations in Interactive Mathematical Textbooks

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

Abstract

The paper explores changes in technology that have implications for the teaching and learning of school mathematics. To this end, it examines aspects of interactive mathematical textbooks; specifically it analyzes functions authors may intend to be carried out by embedded interactive diagrams. The paper analyzes theoretical as well as practical lessons that I learned while designing such a book. It is the purpose of this article to provide a rough, preliminary collection of categories of diagram function that would allow an orderly discussion of the subject. While this is not an empirical study, the hypotheses about student practices with interactive diagrams are based on a long series of studies related to the learning of algebra in a technologically-rich environment.

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

  • F. Arzarello F. Olivero D. Paola O. Robutti (2002) ArticleTitleA cognitive analysis of dragging practises in cabri environments Zentralblatt Fur Didaktik Der Mathematik 34 IssueID3 66–72

    Google Scholar 

  • L.D. Ball K.D. Cohen (1996) ArticleTitleReform by the book: What is- or might be- the role of curriculum materials in teacher learning and instructional reform? Educational Researcher 25 IssueID9 6–8

    Google Scholar 

  • M.C. Borba J. Confrey (1996) ArticleTitleA student’s construction of transformations of functions in a multiple representational environment Educational Studies in Mathematics 31 319–337 Occurrence Handle10.1007/BF00376325

    Article  Google Scholar 

  • D. Chazan (2000) Beyond Formulas in Mathematics and Teaching: Dynamics of the High School Algebra Classroom Teachers College Press NY

    Google Scholar 

  • D. Chazan M. Yerushalmy (2003) On appreciating the cognitive complexity of school algebra: Research on algebra learning and directions of curricular change J. Kilpatrick D. Schifter G. Martin (Eds) A Research Companion to the Principles and Standards for School Mathematics NCTM Reston 123–135

    Google Scholar 

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

  • L.D. Edwards (1998) ArticleTitleEmbodying mathematics and science: Microworlds as representations Journal of Mathematical Behavior 17 IssueID1 53–78 Occurrence Handle10.1016/S0732-3123(99)80061-3

    Article  Google Scholar 

  • H. Freudenthal (1973) Mathematics as an Educational Task Reidel Dordrecht

    Google Scholar 

  • Gilead, S. and Yerushalmy, M. (2001). Deep structures of algebra word problems: Is it approach (in)dependent? Proceedings of the 25th Annual meeting of the International Group of Psychology of Mathematics Education, Utrecht

  • P.E. Goldenberg (1999) ArticleTitlePrinciples, arts, and craft in curriculum design: The case of connected geometry International Journal of Computers for Mathematical Learning 4 191–224 Occurrence Handle10.1023/A:1009878903774

    Article  Google Scholar 

  • Hershkovitz, R. (1987). The acquisition of concepts and misconceptions in basic geometry – or when a little learning is a dangerous thing. In Novak, J.D. (Eds), Proceedings of the Second International Seminar on Misconceptions and Educational Strategies in Science and Mathematics 3 (pp. 238–251). Ithaca NY.

  • R. Hershkovitz B.B. Schwarz (1999) ArticleTitleReflective processes in a technology-based mathematics classroom Cognition and Instruction 17 665–91

    Google Scholar 

  • R. Hershkovitz T. Dreyfus D. Ben-Zvi A. Freidlander N. Hadas T. Resnick M. Tabach B. Schwarz (2002) Mathematics curriculum development for computerized environments: A designer-researcher-teacher-learner-activity L. English (Eds) Handbook of International Research in Mathematics Education Lawrence Erlbaum Associates Mahwah, New Jersey & London

    Google Scholar 

  • R. Holzl (1996) ArticleTitleHow does “Dragging” affect the learning of geometry International Journal of Computers for Mathematical Learning 1 IssueID2 169–187

    Google Scholar 

  • Hoyles, C. (1993). Microworlds/Schoolworlds: The transformation of an innovation. In C. Keitel and K. Ruthven (Eds), Learning from Computers: Mathematics Education and Technology. pp 1–16

  • Hoyles, C. and Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education. innovation . In A.J. Bishop, M.A. Clements, C. Keitel, J. Kilpatrick and F.K.S. Leung (Eds), Second International Handbook of Mathematics Education Dordrecht, Vol. 1. (pp. 323–350) Kluwer

  • C. Jewitt R. Oyama (2001) Visual meaning: A social semiotic approach T. Leeuwen Particlevan C. Jewitt (Eds) Handbook of Visual Analysis SAGE Publications Thousand Oaks, CA

    Google Scholar 

  • Kieran, C. and Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey and H. Shick (Eds), ICMI Studies in Algebra (Chapter 5)

  • G. Kress T. Leeuwen Particlevan (1996) Reading Images The Grammar of Visual Design Routledge London

    Google Scholar 

  • G. Kress (2003) Literacy in the New Media Age Routledge London

    Google Scholar 

  • C. Laborde (2001) ArticleTitleIntegration of technology in the design of geometry tasks with cabri-geometry International Journal of Computers for Mathematical Learning. 6 IssueID3 283–317 Occurrence Handle10.1023/A:1013309728825

    Article  Google Scholar 

  • J.-B. Lagrange M. Artigue et al. (2003) Technology and Math Education: A Multidimensional Study of the Evolution of Research and Innovation. The 2nd International Handbook of Mathematics Education Kluwer Academic Publisher Netherlands

    Google Scholar 

  • Lemke J.L. (1998). Multiplying meaning: visual and verbal semiotics in scientific text. London: Routledge (pp. 87–113) In J.R. martin and R. Veel (Eds), Reading Science. Routledge

  • Leikin, R. and Dinur, S. (2003). Patterns of flexibility: Teachers’ behavior in mathematical discussion. In Electronic Proceedings of the Third Conference of the European Society for Research in Mathematics Education. (10 p.) http://www.dm.unipi.it/~didattica/CERME3/WG11/papers_pdf/TG11_Leikin.pdf

  • Levin, J.R. (1989). A transfer- appropriate-processing perspective of pictures in prose. In H. Mandl and J.R. Levin (Eds), Knowledge Acquisition from Text and Pictures. Elsevier Science Publishers B.V. 58.

  • E. Love D. Pimm (1996) This is so: A text on texts A.J. Bishop (Eds) International Handbook of Mathematics Education Kluwer Academic Publisher Netherlands 371–409

    Google Scholar 

  • H. Mandl J.R. Levin (1989) Knowledge Acquisition from Text and Pictures Elsevier Science Publishers Amsterdam

    Google Scholar 

  • Molitor, S. and Ballstaedt, S.-P. (1989). Problems in knowledge acquisition from text and pictures. In H. Mandl and J.R. Levin (Eds), Knowledge Acquisition from text and Pictures. vol. 58. (pp. 3–35) Elsevier Science Publishers B.V.

  • C. Morgan (Eds) (1998) Writing mathematically, The Discourse of Investigation Falmer Press London

    Google Scholar 

  • K. Nunokawa (1994) ArticleTitleImproving diagrams gradually: One approach to using diagrams in problem solving For the Learning of Mathematics 14 IssueID1 34–38

    Google Scholar 

  • R. Netz (1999) The Shaping of Deduction in Greek Mathematics Cambridge University Press UK

    Google Scholar 

  • T.A. Romberg E. Fennema T. Carpenter (1993) Integrating Research on Graphical Representations of Functions Erlbaum Inc NJ

    Google Scholar 

  • B. Shternberg M. Yerushalmy (2003) Models of functions and models of situations: On design of a modeling based learning environment H.M. Doerr R. Lesh (Eds) Beyond Constructivism: A Model and Modeling Perspective on Teaching, Learning, and Problem Solving in Mathematics Education Lawrence Album Mahwah, NJ 479–500

    Google Scholar 

  • S. Vinner (1983) ArticleTitleConcept definition, concept image and the notion of function International Journal of Mathematical Education in Science and Technology 14 293–305

    Google Scholar 

  • S. Vinner T. Dreyfus (1989) ArticleTitleImages and definitions for the concept of function Journal for Research in Mathematics Education 20 356–366

    Google Scholar 

  • Visual-Mathematics (1995) Algebra and functions, (Curriculum In Hebrew) Center for Educational Technology, Tel-Aviv. http://www.cet.ac.il/math-international/visualizing.htm

  • M. Yerushalmy (2000) ArticleTitleProblem Solving Strategies and Mathematical Resources: A Longitudinal View on Problem Solving in a Functional Based Approach to Algebra Educational Studies in Mathematics 43 125–147 Occurrence Handle10.1023/A:1017566031373

    Article  Google Scholar 

  • M. Yerushalmy (1999) ArticleTitleMaking exploration visible: On software design and school algebra curriculum International Journal of Computers for Mathematical Learning 4 169–184

    Google Scholar 

  • M. Yerushalmy (1997a) ArticleTitleReaching the unreachable: Technology and the semantics of asymptotes International Jounral of Computers for Mathematical Learning. 2 1–25

    Google Scholar 

  • M. Yerushalmy (1997b) ArticleTitleMathematizing qualitative verbal descriptions of situations: A language to support modeling Cognition and Instruction 15 IssueID2 207–264

    Google Scholar 

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

    Google Scholar 

  • M. Yerushalmy D. Chazan (2002) Flux in school algebra: Curricular change, graphing technology, and research on student learning and teacher knowledge L.D. English (Eds) Handbook of International Research in Mathematics Education. Lawrence Erlbaum Associates Mahwah, New Jersey and London 725–755

    Google Scholar 

  • M. Yerushalmy D. Chazan (1990) ArticleTitleOvercoming visual obstacles with the aid of the supposer Educational Studies in Mathematics 21 199–219 Occurrence Handle10.1007/BF00305090

    Article  Google Scholar 

  • Yerushalmy, M., Katriel, H. and Shternberg, B. (2002). The Function Web-book. http://www.cet.ac.il/math/function/english

  • Yerushalmy, M and Gafni, R. (1992). Syntactic Manipulations and Semantic Interpretations in Algebra: The Effect of Graphic Representation. Learning and Instruction. Vol. 2. (pp. 303–319) Pergamon Press Ltd.

  • M. Yerushalmy J.L. Schwartz (1993) Seizing the opportunity to make algebra mathematically and pedagogically interesting T.A. Romberg E. Fennema T. Carpenter (Eds) Integrating Research on Graphical Representations of Functions Erlbaum Inc NJ

    Google Scholar 

  • Yerushalmy, M. and Shternberg, B. (2001). A visual course to functions. In Cuoco, A.A. and Curcio, F. (Eds), The Roles of Representations in School Mathematics (pp. 125–147). NTCM Yearbook.

Download references

Author information

Authors and Affiliations

  1. Department of Education, University of Haifa, Haifa, Israel

    Michal Yerushalmy

Authors
  1. Michal Yerushalmy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michal Yerushalmy.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yerushalmy, M. Functions of Interactive Visual Representations in Interactive Mathematical Textbooks. Int J Comput Math Learning 10, 217–249 (2005). https://doi.org/10.1007/s10758-005-0538-2

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10758-005-0538-2

Keywords

Search

Navigation