Doorman, Drijvers, Gravemeijer, Boon, & Reed (2012)

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Tool Use and the Development of the Function Concept: From Repeated Calculations to Functional Thinking


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.

Outline of Headings

  • Introduction
  • Theoretical Framework
    • The Concept of Function
    • Emergent Modeling
    • Tools and Instrumentation
  • Methods
    • Design Phase
    • Teaching Experiments and Data Collection
    • Analysis
  • Results
    • The Initial Cell Phone Offer Task: Organizing Calculations
    • Introducing Arrow Chains: Visualize Functions
    • Using the Computer Tool to Create Arrow Chains
    • Using the computer tool to create reverse chains
    • Whole-class Discussion Capitalizing on Hands-on Experience
    • A Different View on Function
    • Backing Up Case Study Findings
    • Overview of the Findings
  • Conclusion and Discussion
    • Conclusion
    • Discussion


Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Tool use and the development of the function concept: From repeated calculations to functional thinking. International Journal of Science and Mathematics Education, 10(6), 1243–1267. doi:10.1007/s10763-012-9329-0
author = {Doorman, Michiel and Drijvers, Paul and Gravemeijer, Koeno and Boon, Peter and Reed, Helen},
doi = {10.1007/s10763-012-9329-0},
journal = {International Journal of Science and Mathematics Education},
keywords = {emergent modeling,function concept,instrumentation,mathematics education,technology},
number = {6},
pages = {1243--1267},
title = {{Tool use and the development of the function concept: From repeated calculations to functional thinking}},
url = {},
volume = {10},
year = {2012}