This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.

This document focuses on a series of studies that viewed aspects of conditional reasoning. The investigations were concerned with the processes children use to acquire patterns of deductive inference and logical relationships pertaining to propositional reasoning. The first experiment, involving 96 children each in grades 2 and 5, investigated the…

Presented are abstracts of 14 research reports. Topics covered include: (1) the effects of games on mathematics skills and concepts; (2) the use of problem-solving heuristics in the playing of games involving mathematics; (3) sex differences in electing mathematics; (4) the origins of sex differences in high school mathematics achievement and…

This study provides an integrated investigation of creative thinking, mathematical and nonmathematical problem solving, and transfer of training among secondary-school students. Fifty-two geometry students participated in a two-week Divergent Thinking Activities program developed by the experimenter. In addition to this group, 30 geometry students…

This yearbook presents many aspects of mathematics learning by children between the ages of three and eight. Addressed to teachers of primary school children, the book begins with chapters discussing learning and cognition, the primary curriculum, and research on mathematics learning at this age level. Eight subsequent chapters deal with the…

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

Description of the field of robotics and its possible use in high school computational geometry classes emphasizes motion planning exercises and computer graphics displays. Eleven geometrical problems based on robotics are presented along with the correct solutions and explanations. (LRW)

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)

Some examples are given of geometric exploration and problem solving in which Logo is the primary tool and turtle graphics is the mathematical environment. Students can explore and develop important patterns while building visual intuition. (MNS)

Develops a classification scheme for mathematical problem-solving activities. Presents problems generated in solid and plane geometry and fractions. (JM)

This paper will discuss some findings from a study investigating the development of the proving process in a dynamic geometry environment. Through a detailed analysis of students' processes when working with open geometry problems involving conjecturing and proving in Cabri, an analytical and explanatory framework has been developed. This paper…

Math Sense consists of five books that develop from basic to more advanced math skills. This document contains a placement test used with Math Sense to help students and their teachers decide into which Math Sense book to begin working. The placement test is divided into six parts, each consisting of 10 to 22 problems, and is based on exit skill…

This book was developed for teachers, youth group leaders, after-school child care providers, and parents, who may not have the time or the expertise to develop strategies for preparing students to be effective problem solvers. The content is organized in a pyramid style to make it easy to locate and grasp the information provided. Information on…

Properties of the harmonic number triangle are listed, and ways of generating the elements of harmonic triangles are described. (MNS)

Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)