Discards the blinders that have hampered the traditional teaching of calculus and reexamines some of the intuitive ideas that underlie this subject matter. Analyzes the various indeterminate forms that arise through the blind application of algebraic operations. (Author/ASK)

Originally written near the beginning of the "new math" movement, this article reflects on the role of student discovery, intuition, mathematics as an analytic language, and the problem of student readiness. (MKR)

An activity in a college statistics class had students go to a field of grass and clover and use a variety of estimation, probability, sampling, distribution, and calculation techniques for determining the number of flowers in the field. The activity focused on the discovery process, encouraged abstract reasoning, and was pleasurable. (MSE)

Several intuitive proofs for evaluating specific infinite expressions are given. Observations on intuition and errors in mathematics are included. (MNS)

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)

Counterintuitive moments in the classroom challenge common sense and practice and can be used to help mathematics students appreciate the need to explore, reflect, and reason. Proposed are four examples involving geometry, systems of equations, and matrices as counterintuitive instances. (MDH)

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)

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

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…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)