Elements of Effective Tasks in Creating Positive Dispositions: A Capstone Project

Abstract

Research has shown that while the discipline of mathematics focuses on negotiation, interpretation, and uncertainty, classroom mathematics often focus on rigidity, rules, and prescribed algorithms. This misalignment of mathematical practices in the classroom and mathematical practices in the discipline is negatively affecting both students’ learning and students’ dispositions (Boaler and Greeno 2000). Because students’ dispositions develop in response to classroom practices, it is necessary for teachers to look at the ways in which they can better support the development of positive dispositions through task selection and modification. This paper explores a framework of the pivotal elements of task selection and modification, describing how explicit disposition goals can increase the effectiveness of instruction through discourse strategies, appropriate levels of difficulty, differentiation, goal alignment, and context. The paper then evaluates an example of a task from the Interactive Mathematics Program: Year 2 (IMP), showing how modifications to that task can help teachers better develop positive dispositions as well as implement effective instruction.