Networking: Theory and Teaching Practice Using Lesson Study: (a.k.a. Sensible mathematics: searching for characteristics using lesson study)

This paper describes the search of six Dutch teachers for characteristics of sensible mathematics. The mathematics teachers investigated their theoretically founded classroom practices using lesson study. Two successive research lessons about the introduction of the derivative were jointly planned, implemented, and live observed. The teachers revised and re-teached the research lessons based on collaborative discussions at school and reflections at the university. The results of the study show that making sense of the derivative starts with encouraging students to communicate intuitively using own words. This is followed by the development of visualizations (icons) and finally results in the use of numbers (symbols): operations with numbers and reasoning about operations with numbers