Didactical designs for students' proportional reasoning: An "open approach" lesson and a "fundamental situation"

Takeshi Miyakawa, Carl Winsløw*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)


In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from different cultural and intellectual environments: lesson study in Japan (implicitly based on the "open approach method") and "didactical engineering" in France (based on the theory of didactical situations). The general aim of our paper is to compare these two environments and their approaches to didactical design, basing our discussion on the concrete designs mentioned above. Clear differences among them are presented, while we also identify links which hold potential for integrating research and practice.

Original languageEnglish
Pages (from-to)199-218
Number of pages20
JournalEducational Studies in Mathematics
Issue number2
Publication statusPublished - 2009 Oct
Externally publishedYes


  • Didactical design
  • Didactical engineering
  • Lesson study
  • Open approach method
  • Proportionality
  • Similarity
  • Theory of didactical situations

ASJC Scopus subject areas

  • Mathematics(all)
  • Education


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