Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms

Abstract

This article focuses on mathematical tasks as important vehicles for building student capacity for mathematical thinking and reasoning. A stratified random sample of 144 mathematical tasks used during reform-oriented instruction was analyzed in terms of (a) task features (number of solution strategies, number and kind of representations, and communication requirements) and (b) cognitive demands (e.g., memorization, the use of procedures with [and without] connections to concepts, the "doing of mathematics"). The findings suggest that teachers were selecting and setting up the kinds of tasks that reformers argue should lead to the development of students' thinking capacities. During task implementation, the task features tended to remain consistent with how they were set up, but the cognitive demands of high-level tasks had a tendency to decline. The ways in which high-level tasks declined as well as factors associated with task changes from the set-up to implementation phase were explored.