Studying and Remedying Students’ Modelling Competencies: Routine Behaviour or Adaptive Expertise

Abstract

First, we summarise some studies on students’ overuse of the linear model when solving problems in various domains of mathematics, showing to what extent they are led by routine behaviour in mathematical modelling. Second, we discuss a teaching experiment that aimed at enabling 8th graders to adaptively choose between a linear, a quadratic or a cubic model while solving geometry problems. The results show that, after the experiment, the students applied the linear model less automatically, but tended to switch back and forth between applying it either “everywhere” or “nowhere”, indiscriminately.