Learning from history for teaching in the future

L. Streefland, Marja Van Den Heuvel-Panhuizen*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


Reflecting on the learning process of topologist Stephen Smale, certain properties and characteristics of that process are selected and analysed: the question and anticipation of future mathematics, the generalising potential thereof, and the shift from after-image or 'model of ...' to pre-image or 'model for ...'. These features are explored for the benefit of the design of learning-teaching sequences in mathematics education, and are illustrated in a variety of examples.

Original languageEnglish
Pages (from-to)37-62
Number of pages26
JournalEducational Studies in Mathematics
Issue number1
Publication statusPublished - 2003


  • Equations
  • Estimation
  • Formulas
  • Fractions
  • Graphs
  • Mathematicians' and students' learning processes
  • Mathematization
  • Measurement
  • Models of and models for
  • Number
  • Ratio and scale
  • Sine functions


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