Student teachers’ conceptualizations of mathematical problem solving and the nature of their warrants

Abstract

Absence of inquiry about meaning of mathematical objects learners deal with has permeated the school mathematics curriculum. Deep learning through questioning situations can be achieved if learners are helped to embrace the argumentation discourse in their problem solving efforts. This paper reports on a study that investigated linkages between the kinds of mathematical arguments constructed by students and the students’ grasp of the concept of problem solving. With the overall goal of teasing out such linkages a questionnaire that elicited likert-style and textual data was administered to 30 undergraduate and 5 postgraduate mathematics education students. The two data sources were triangulated with reflective interviews guided by students’ written responses and their validations on likert items. Descriptive statistics were applied to likert data and directed content analysis was used to analyze and interpret the qualitative data. The study concluded that students lacked appropriate conceptions of the notion of problem solving and in particular their thinking as reflected in their arguments that contradicted current understandings on the construct. The fragile grasp of the idea of mathematical problem solving uncovered by this study has the potential to inform mathematics instruction.