Eastern Ontario Pre-Service Intermediate-Senior Mathematics Teachers' Beliefs About Problem Solving

Abstract

Problem solving in the Ontario mathematics curricula is described as central to learning mathematics. Scholars of mathematics education similarly stress the importance of problem solving, noting its potential to develop students’ academic ability in mathematics and prepare students to be effective lifelong learners. However, despite the value attributed to problem solving in the learning of mathematics, little is known about how pre-service teachers are thinking about problem solving. Given that beliefs are a fundamental domain of cognition, the first step in addressing this gap in the literature is to explore pre-service teachers’ beliefs about problem solving. Hence, the purpose of this mixed methods study was to explore Eastern Ontario pre-service intermediate-senior mathematics teachers’ beliefs about mathematics problem solving.

Following a pragmatic mixed methods approach, quantitative questionnaire data were collected from a sample of 44 pre-service teachers in an Eastern Ontario teacher education program, and qualitative interview data were collected from a subsample of four pre-service teachers. Both types of data were collected at the beginning and end of the Fall 2016 academic term. Analysis followed a convergent parallel design, where quantitative and qualitative data were analyzed separately then merged to enable the identification of key features being converged upon by the two data sets.

Analysis of the qualitative interview data identified and described the pre-service teachers’ ontological and epistemological beliefs about mathematics problem solving (i.e., beliefs about what mathematics problem solving is and how mathematics problem-solving knowledge is acquired, respectively). Additionally, analysis of the quantitative questionnaire data identified statistically significant differences in the pre-teachers’ beliefs about problem solving with respect to experience in the teacher education program and teacher-related variables. Finally, by comparing and integrating the questionnaire and interview findings, it was possible to characterize the prominent features of problem solving the pre-service teachers emphasized when communicating their thoughts about problem solving. The implications for mathematics educators focus on opportunities for recognizing the complex conceptualization of problem solving espoused by pre-service intermediate-senior mathematics teachers. Recommendations for future research highlight the need to expand the scope of this initial investigation and to investigate pre-service teachers’ knowledge of problem solving.