Assessing children's mathematical thinking in practical modelling situations

Abstract

This paper reports on research into the development of mathematical thinking skills using practical modelling activities. An action research group of 12 teachers from six secondary schools in Wales was created to investigate the use of mathematical modelling tasks in years seven and eight (11 and 12 years old). Twelve intervention classes were matched with 12 equivalent control classes as part of a quasi-experiment to investigate the impact of such activities. The experimental design was based on the use of written pre-tests, post-tests and delayed tests. However, in addition to the written tests, 48 pupils—two from each class—engaged in mathematical modelling tasks during one to one semi-structured interviews with the researchers. The interviews used a form of dynamic assessment to analyse the development of pupils' mathematical thinking at each assessment point. This paper focuses on the interview data and reports on the extent to which some pupils proved to be naturally mindful and the extent to which metacognitive thinking might be taught in the early years of secondary school.