Experiencing active mathematics learning: Meeting the expectations for teaching and learning in mathematics classrooms

Abstract

Active learning mathematics classrooms incorporate meaningful activities that emphasize reasoning, thinking and active interaction with mathematics. Current mathematics standards and curricula recommend that Mathematics Teacher Educators (MTEs) use elements of active learning in their mathematics content courses specifically designed for Prospective Teachers (PTs) as they prepare PTs to learn and teach mathematics. However, it can be very difficult for PTs to shift their pedagogical dispositions towards instruction associated with active learning because they typically have not experienced mathematics taught in this way. This article focuses on two instructional practices for MTEs to use with PTs. First, selecting tasks that promote reasoning and problem solving. This includes practices to open tasks for multiple entry points or solution strategies, tasks that allow for analysis of examples and counterexamples, and tasks that evaluate multiple strategies. Second, facilitating meaningful mathematical discourse. This includes practices for whole class and small group discourse. When MTEs use active learning strategies with PTs in their mathematics content courses, PTs may begin to shift their beliefs and understandings about what it means to teach and learn mathematics. By highlighting how active learning experiences can enhance PTs' own understanding and their future students' mathematical understanding, MTEs will provide a valuable foundation for PTs to meet the expectations for teaching and learning in mathematics classrooms.