Instructional Tasks and the Development of Student Capacity to Think and Reason: An Analysis of the Relationship between Teaching and Learning in a Reform Mathematics Project

Abstract In the present study the relationship between teaching and learning was examined using a conceptual framework that links dimensions of instructional tasks with gains in student learning outcomes. The greatest student gains on a performance assessment consisting of tasks that require high levels of mathematical thinking and reasoning were related to the use of instructional tasks that engaged students in the “doing of mathematics” or the use of procedures with connections to meaning. In addition, student performance gains were greater for those sites whose tasks were both set up and implemented to encourage the use of multiple solution strategies, multiple representations, and explanations. Whereas, student performance gains were relatively small for those sites whose tasks tended to be both set up and implemented in a procedural manner and that required a single solution strategy, single representations, and little or no mathematical communication.