TOOL USE AND THE DEVELOPMENT OF THE FUNCTION CONCEPT: FROM REPEATED CALCULATIONS TO FUNCTIONAL THINKING

  • Michiel Doorman
  • Paul Drijvers
  • Koeno Gravemeijer
  • Peter Boon
  • Helen Reed
Open AccessArticle

DOI: 10.1007/s10763-012-9329-0

Cite this article as:
Doorman, M., Drijvers, P., Gravemeijer, K. et al. Int J of Sci and Math Educ (2012) 10: 1243. doi:10.1007/s10763-012-9329-0

ABSTRACT

The concept of function is a central but difficult topic in secondary school mathematics curricula, which encompasses a transition from an operational to a structural view. The question in this paper is how the use of computer tools may foster this transition. With domain-specific pedagogical knowledge on the learning of function as a point of departure and the notions of emergent modeling and instrumentation as design heuristics, a potentially rich technology-intensive learning arrangement for grade 8 students was designed and field-tested. The results suggest that the relationship between tool use and conceptual development benefits from preliminary activities, from tools offering representations that allow for progressively increasing levels of reasoning, and from intertwinement with paper-and-pencil work.

KEY WORDS

emergent modelingfunction conceptinstrumentationmathematics educationtechnology
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© The Author(s) 2012

Authors and Affiliations

  • Michiel Doorman
    • 1
  • Paul Drijvers
    • 1
  • Koeno Gravemeijer
    • 1
  • Peter Boon
    • 1
  • Helen Reed
    • 1
  1. 1.Freudenthal Institute for Science and Mathematics EducationUtrecht UniversityUtrechtThe Netherlands