Pre-Service Mathematics Teachers’ Web of Knowledge Recalled for Mathematically Rich and Contextually Realistic Problems

Abstract

This study aimed to elicit middle school preservice mathematics teachers' self-reported web of knowledge recalled in generating mathematically rich and contextually realistic problems. We designed this study as multi-tier design research incorporated into two teacher education courses in which 40 preservice teachers enrolled in total. Preservice teachers worked in small groups and recorded the characteristics of mathematically rich and contextually realistic problems. They were also asked to produce webs of knowledge recalled in this process. Preservice teachers' individual reflection papers, audio records of their group discussions and interviews were analyzed to understand how different types of knowledge in their web of knowledge function in relation to the mathematical richness and contextual realness aspects of the problems. The findings indicated that preservice teachers could identify various characteristics for mathematical richness and contextual realistic aspects of the problems. In relation to those characteristics, the preservice teachers' self-reported web of knowledge produced three core knowledge types for ensuring mathematical richness (i.e., knowledge of content, curriculum, and pedagogy) and two aspects of realistic contexts (i.e., real life knowledge and interdisciplinary knowledge). Furthermore, although they included common knowledge types, the webs of knowledge were in different shapes and indicated various relationships (i.e., hierarchical, categorical, influential, and holistic.). Considering the various relations indicated by the webs of knowledge, we claimed that teachers needed an interconnected knowledge base for mathematically rich and contextually realistic problems, the implications of which we discussed for mathematics teacher education.