Problem-solving Potential (PsP) in the regular mathematics classroom

A student’s Problem-solving Potential (PsP) is defined by their mindset, their mathematical resilience, and the problem-solving skills they possess. This triad construct of PsP was developed as part of a doctoral study, and investigated amongst six cohorts of highly-able mathematics Transition Year students through an educational intervention. Prior research into mindsets, largely spearheaded by Dweck (2006), found a relationship between achievement and growth-orientated mindsets; which extol the virtues of learning over “looking smart”, and the value of making mistakes, among other attributes. Mathematical resilience is further subdivided into value (belief that mathematics is important), struggle (acknowledgement that struggle is a valuable part of learning mathematics), and growth (referring to growth mindsets) (Kooken et al., 2016). Prior research of mathematical resilience focussed on the development of this concept amongst low-achieving students; whilst our research investigated its development within highly-able students. There is a popular belief amongst educational researchers that mathematics is best learnt through the construction of knowledge by the learner, and mathematical problem-solving is one approach that creates this opportunity for all learners (Mason et al., 2010). Our educational intervention utilised collaborative problem-solving, and was designed to: introduce strategies for problem-solving; encourage reflection on the problem-solving process; provide opportunities for the extension of problems; and develop communication skills. In this paper, we will highlight the benefit of developing PsP in the mathematics classroom for highly-able students by discussing the relevance of each aspect of the construct through the findings of the doctoral study; and also how the development of PsP may impact lower-achieving students.