Riding the Mathematical Merry-Go-Round to Foster Conceptual Understanding of Angle

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This article presents playful activities for fostering students' conceptual understanding of angle--a root concept in mathematics--that revolve around the Mathematical Merry-Go-Round game. The authors focus on activities for two reasons. On one hand, NCTM's Principles and Standards for School Mathematics (2000) stresses the central role of student activity in coming to understand mathematics. This emphasis is consistent with a constructivist stance (Piaget 1971) about learning as an active process. On the other hand, typical activities used for teaching angle, in which an introduction of the definition is followed by operations on angles, such as measuring, adding, comparing, and classifying, seem to leave many students unclear about the "thing" on which they operate. In this article, the authors present components of a lesson outline (two to three class periods) that combines activities used by several teachers. They describe the Mathematical Merry-Go-Round game and how a teacher can explain it, present follow-up prompts, and guide a whole-class discussion.