Mathematical Identity and the Use of High-Leverage Thinking Moves During Problem-Solving Activities

Abstract

This case study explored the relationship between a student's mathematical identity and their understanding of statistical concepts through four individuals in an AP Statistics course in a Midwest metropolitan suburban high school. A primary framework was used to examine the connections between mathematical identity and thinking moves during problem-solving activities. Within the primary framework, one secondary framework was used to investigate mathematical identities though two lenses: (1) current identities, which are identities in the form of stories, generally told in the present tense, about the actual state of affairs; and (2) designated identities, which are identities in the form of stories, told in the future tense or in a way that expresses aspirations or needs about a state of affairs expected to be the case either presently or in the future. Moreover, a second secondary framework was used to reveal mathematical understanding through the demonstration of thinking moves during problem-solving activities. In the end, the research framework guided the investigation of the association between the mathematical identities (i.e., current identity and designated identity) and the use of thinking moves during problem-solving activities. The results indicate that while there were differences between the patterns of thinking moves used during the group activities, there was little difference between the thinking moves used on the individual work on selected exam questions. During the group activities, individuals who had mostly positive feelings and experiences related to mathematics, who viewed themselves as confident students of mathematics, and who saw themselves as central members of the mathematics classroom demonstrated more extensive use of the eight thinking moves and the use of thinking moves that reside in all three thinking categories. In addition, approaches to learning that are focused on understanding the material (i.e., a substantial approach) and are consistent with discourse-for-oneself status are linked to the use of a larger variety of thinking moves and the use of thinking moves which reside in all three thinking categories. An important implication of the research is that classroom teachers need to create learning environments that nurture vibrant student relationships with mathematics.