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 a study that investigated linkages between the kinds of mathematical arguments constructed by students and the students’ grasp of the concept of problem solving. It aims to analyze the relationship of data obtained from questionnaires with Likert-style scales and textual data from 30 undergraduate students and 5 graduate students of mathematics education. 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 of the construct. The fragile grasp of the idea of mathematical problem solving uncovered by this study has the potential to inform mathematics instruction.