Abstract
Research on mathematics teachers’ knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary school teachers of mathematics (PTs). Participants were 149 PTs at a university in Spain. They were at the end of their teacher education program. Data sources consisted of a questionnaire on knowledge of learning PS and a questionnaire on knowledge of teaching PS. Findings indicated that the PTs held combination of different levels of knowledge of PS learning and teaching. Many of them demonstrated appropriate knowledge of many characteristics for (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factor related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, intervention during stuck state in PS, PS assessment, and PS resources. However, there were also contradictions and limitations to their knowledge with implications for teacher education. These combination of appropriate and inappropriate knowledge resulted in some conflicts that are related to teaching actions and would limit student’ learning of PS.
Highlights
We organized the findings in two sections that correspond to the two questionnaires: prospective elementary school teachers of mathematics (PTs)’ knowledge of problem solving (PS) learning and PTs’ knowledge of PS teaching
The PTs’ pedagogical PS knowledge related to PS learning refers to their knowledge of factors that can affect students’ learning of PS. We considered these factors in terms of three categories of knowledge that PTs should hold to support students’ learning of PS: student as a problem-solver, PS as worthwhile task, and non-cognitive factors that affect PS
Building on Chapman’s [3] framework of PS knowledge for teaching, it addressed PTs’ knowledge of: (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factors related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, stuck state in PS, PS assessment, and PS resources
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. While research on mathematics teacher knowledge has received significant attention in the last two decades, the focus has been more on mathematics concepts than mathematical processes. When considering mathematics knowledge for teaching, e.g., [1], content knowledge and pedagogical content knowledge tends to be interpreted as knowledge of mathematics concepts and pedagogical knowledge of mathematics concepts, respectively. As Lin and Rowland [2] pointed out regarding studies on mathematics teacher knowledge reported in the Psychology of Mathematics Education conference proceedings,
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