• Nellie Verhoef
  • David Tall
  • Fer Coenders
  • Daan van Smaalen


This study combines the Japanese lesson study approach and mathematics teachers’ professional development. The first year of a 4-year project in which 3 Dutch secondary school teachers worked cooperatively on introducing making sense of the calculus is reported. The analysis focusses on instrumental and relational student understanding of mathematical concepts and the transition between the conceptual embodiment and the operational symbolism of the calculus. This paper reports on 2 cycles of lesson studies that took place in the first project year, the first cycle focussing on the notion of the derivative (introduced for polynomials) and the second on trigonometry (as the concepts shift from ratios in a right-angled triangle to functions in the calculus). The lesson study cycles resulted in changes in the teachers’ educational goals and instructional strategies in relation to student understanding. However, the teachers’ desire to be good teachers, their perceived need to prepare students for standard examinations and their reluctance to use computers impeded their progress in developing a lesson study approach. The introduction of a Japanese lesson study approach into a Dutch context merits further reflection in the later years of the project.

Key words

lesson study making sense of the calculus student understanding teachers’ professional development 


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Copyright information

© National Science Council, Taiwan 2013

Authors and Affiliations

  • Nellie Verhoef
    • 1
  • David Tall
    • 1
  • Fer Coenders
    • 1
  • Daan van Smaalen
    • 1
  1. 1.Warwick UniversityCoventryUnited Kingdom

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