Presented are three cases for intuitive understanding in secondary and college level geometry. Four ways to develop the intuition (physical experience, mutable manipulatives, visualization, and looking back) step are discussed. (YP)

This document suggests ways of using children's intuitive ideas about mathematics as a starting point for an elementary curriculum. Ways are discussed to capitalize on what children already know: to cultivate rather than discourage students' intuitive mathematical sense, and to help students make connections between what they know and what they…

This article explores the multiple representations (verbal, algebraic, graphical, and numerical) that can be used to study the golden ratio. Emphasis is placed on using technology (both calculators and computers) to investigate the algebraic, graphical, and numerical representations. (JAF)

The learning difficulties that students experience with fractions begin immediately when they are shown fraction symbols with one numeral written above the other and told that the "top number" is called the numerator and the "bottom number" is called the denominator. This introduction to fractions will usually include a few visual diagrams to help…

To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within…