Discussed are "moves" in teaching mathematics that can serve as a basis for defining understanding. How to characterize and use moves is discussed, with specific examples and research evidence. (MP)

Some suggestions are given of how various decimal concepts can be introduced using Multibase Arithmetic Blocks, base ten. (MN)

Using a pegboard and different colored pegs, students were able to visualize mathematical concepts, generate and solve problems, and test hypotheses. Illustrations included. (MA)

Reasoning patterns and learning difficulties of six students are illustrated in support of the contention that language and notation often disguise thought. (MN)

Thirty-nine elementary education majors used manipulative aids to work laboratory exercises while thirty-nine control subjects completed the same exercises without the use of manipulative materials. No significant differences were found between groups in demonstrating numerical and structural properties of the four basic arithmetic operations…

In the study of mathematics instruction the focus has changed from the outcomes of learning to the cognitive processes involved in mathematics learning. This new emphasis presents a serious challenge for curriculum design, but it may also lead to more success for students in learning mathematics. (Author/VM)

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

Considers the problem of constructing Venn diagrams for more than three sets. Presents an unusual geometric display of a Venn diagram for five sets. (PK)

Computing pi efficiently has been of great interest to mathematicians for centuries. This article presents an algorithm to solve this problem through skillful computer use. (PK)

Presents ideas that are intended to convey new insights on familiar topics and to enhance pedagogy. The mathematical topics addressed are applications of transformations to numerical integration, the golden ratio, Cramer's rule, a counting problem, and the general form of the arithmetic-geometric mean inequality. (PK)

Reports that students frequently confuse meanings of terms and misunderstand function-related concepts. Also, providing mental images of functions is often limited to elementary algebra examples. This article describes a game which can help create conceptual links between the function properties and their various representations. (PK)

Describes a method that will easily generate any number of triangles of equal area and perimeter, and also geometrically characterize such triangles. (PK)

Narrates an account of teaching mathematical concepts to junior high school students using manipulative materials and small and large group games. The following concepts are explained through game descriptions using numeration or Dienes blocks: regrouping decimals, and place value. (DST)

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)

Compares the similar mathematical problems of molecular vibrational calculations (at any intermediate level of sophistication) and molecular orbital calculations (at the Huckel level). Discusses how the generalizations of Huckel treatment of molecular orbitals apply to vibrational theory. (TW)