The Teacher-Text Interaction in Mathematics Instruction: Elementary and Middle School Teachers Redesign Mathematics Exercises to Increase Cognitive Demand

Abstract

Mathematics teachers modify problems for use in their classrooms but we know little about what exercises they choose to modify, in what ways they typically modify them, and what role teaching experience plays. Additionally, the modification of pre-written tasks can impact the mathematics students have the opportunity to learn, so it is important to learn more about this phenomenon. This qualitative, empirical study explored the ways that K-8 teachers interacted with mathematics curriculum materials with the goal of redesigning exercises into more cognitively demanding tasks. Seventy early career and experienced teachers participated in the study, which took place over the course of a school year. Data were collected in two stages, first from early career teachers and then with more experienced teachers. The collected data consisted of the original and redesigned tasks, teachers’ written reflections on the work that they did, audio-recorded work sessions of third and sixth-grade teacher groups, and the researcher’s reflective journal. Analysis occurred within and between grade bands and teacher experience levels. Findings indicate that teachers tended to choose simple exercises to modify and typically redesigned them by making structural changes to the task, or by opening them up to become student explorations. Results of this study indicate that teachers may benefit from frameworks that detail a hierarchy of how children best develop the mathematical understanding of concepts beyond basic number operations.