This model is useful in identifying specific learning problems and in providing techniques for the teacher to motivate and teach students at all levels. What it is and how it can be used are discussed, illustrated by specific strategies for geometry and science. (MNS)

Discusses some theorems and properties of figures produced when circles are tangent to one another. (GA)

Presents a model for teaching reasoning using technology in the contexts of algebra and geometry. (MKR)

This material shows how to use basic techniques, principles of counting, and geometry to count squares on geoboards. The methods are elementary in that the proofs are easily conceptualized. A discussion of other approaches illustrates that easily stated problems may lead to very difficult and sophisticated methods. (MP)

Use of prepartitioned models is proposed to help students construct a meaningful concept of fractions. Partitioning, geometric shapes as fractional models, concepts related to successful partitioning, and other benefits from partitioning experiences are discussed. Sample activities are suggested. (CW)

Presents a model that relates Polya's ideas on problem solving to teaching practices that help create a mathematics learning environment in which students are actively involved in doing mathematics. Illustrates the model utilizing a high school geometry problem that asks students to measure the width of a river. (MDH)

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

Suggests a model for teaching mathematics with three dimensions: facts and skills, understanding, and problem solving. Geometric examples are used to illustrate each dimension and suggestions for integrating the teaching of the three dimensions are given. (PK)

U.S. mathematics education has been criticized for being too broad. This article examines ways middle school students use simple problems and situations to foster a deeper understanding of underlying concepts. Presents a sample area and perimeter problem, describes extending the problem using tiles to determine minimum perimeter, and discusses…

Based on research on the geometric understanding of regular and gifted middle school students, this article describes a procedure for assessing geometry readiness in mathematically able middle school students. The procedure utilizes the vanHiele model of stages of geometric understanding and distinguishes between readiness for algebra and…

Instructions are given for constructing two models, one to illustrate the general principles of symmetry in T=1, T=3, and T=4 viruses, and the other to illustrate the disposition of protein subunits in the T=3 plant viruses and the picornaviruses. (Author/CW)

This competency analysis profile contains eight lists of mathematics skills that have been identified by employers and verified by math-certified instructors as being core competencies for eight groups of occupational areas. Each list is organized into subsections dealing with the following: numbers and number relations, measurement, data analysis…

The papers presented in these proceedings are organized into seven categories: (1) number and number operations (13 papers); (2) spatial representation and geometrical understanding (10 papers); (3) developing and/or using models of mathematical learning (15 papers); (4) mathematical concept formation (17 papers); (5) the mathematical learning…

This book presents activities developed for grades 6-10 in creating string designs on polygons and polyhedra. They are designed for use as enrichment materials, each having step-by-step instructions and are arranged from easiest to most difficult, and marked accordingly. The pages are punched and perforated. Many activities are followed by related…

This book provides exemplars of the types of computer-based learning environments represented by the theoretical camps within the field and the practical applications of the theories. The contributors discuss a variety of computer applications to learning, ranging from school-related topics such as geometry, algebra, biology, history, physics, and…