Addressing the affective domain to increase effectiveness of mathematical thinking and problem solving

In England, groups of post-16 mathematics students seeking to develop mathematical thinking and problem solving often contain students who experience high mathematics anxiety, and low mathematical resilience. Mathematics anxiety, a prevalent, acquired, disabling and treatable condition, can be thought of as “an emotional handbrake” on mathematical thinking and problem solving. Thus, in order to develop mathematical thinking and problem solving as effectively as possible across post-16 provision, it is important to enable learners to address any mathematics anxiety. In this paper, it is argued that doing so explicitly will have a longer term impact than doing so implicitly. Some interventions have been found effective in reducing mathematical anxiety, and some in building mathematical resilience. Exposure to problem solving can have short-term impact on ability to manage the affective domain whilst learners are seeking to solve problems. Exposure to the growth zone model can have long-term impact on ability to manage the affective domain. The paper draws on the work of several teachers undertaking post-graduate study at the University of Warwick to illustrate the underlying premise. Teachers such as Silversides, Chisholm and King have found the growth model to have high efficacy in enabling learners to communicate and learn to manage feelings when learning to problem solve. Interviews with students reveal that most find the growth zone model effective to build resilience and communicate emotions. This is important, since success in mathematics is heavily dependent on emotion. We conjecture that explicit use of a tool such as the ‘growth zone model’ is most effective when combined with artefacts such as a ‘stuck’ poster