Describes a classroom activity featuring a simple stay-switch probability game. Contends that the exercise helps students see the importance of empirically validating beliefs. Includes full instructions for conducting and discussing the exercise. (CFR)

Asserts that the sudden insights that characterize intuitive thinking are as important in effectuating learning as analytical thinking. Claims that intuitive thinking enables students to comprehend complex relationships better, to put things into better perspective, to generate new ideas, and to perceive more ways to integrate facts, concepts, and…

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…