This report describes a program for increasing students' ability to simplify square roots. The targeted population consisted of high school students in a rural community in a midwestern plains state. The problem of the ability to understand the abstract algebraic process of simplifying square roots was documented through teacher-made tests,…

In this study Piaget's method of the clinical interview was used to examine children's understanding of rotation about apoint at three age levels (6, 7, and 8). In two half-hour sessions, subjects (N = 108) were given four tasks: (1) an adaptation of Piaget's locus and circular motion experiment, and tasks concerned with (2) the circle as a locus…

This report describes a program for increasing adolescent visualization and understanding of geometry problems. The targeted population consisted of high school students in two geometry classes in a growing middle-class community. The inability of students to adequately visualize and understand geometry problems was documented through teacher-made…

This study was designed to determine if a group of five- and eight-year-old students' understanding of selected geometric ideas paralleled Piaget's topological, projective, and Euclidean thesis. Additional purposes were to investigate which geometric ideas the group learned easiest, and to examine the relationships between geometric understanding…

This study was undertaken to explore the problem solving processes of secondary-school students. Geometry students were given an experimenter-constructed test of convergent and divergent thinking and classified as high on both, high convergent, high divergent, or low on both. Of these 105 students, 49 were selected for individual observation as…

This report describes a program for improving attitudes towards mathematics and problem solving in order to improve performance in these areas. The targeted population consists of two high school geometry classes. The school is located in a western suburb of a major mid-western city. The problems of negative attitudes towards mathematics and…

This study was designed to test the effects of a geometry course incorporating large-group, small-group, and individualized instruction on the achievement and attitudes of students. Three of six classes and teachers were randomly assigned to experimental instruction, the remainder serving as controls. Pretest measures included IQ and attitude…

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…

The purpose of the project was to determine the effects of journal writing on the thinking skills of high school geometry students. The research supports the idea that writing can enhance a student's metacognitive ability. The results show that the journals served effectively in various capacities. Each student became actively involved in his or…

Three methods of instructing third graders about geometric concepts are compared in this study. Methods were all presented in programed instruction packages; but differed in the types of activities incorporated: paper and pencil activities (Treatment W), activities with manipulatives such as geoboard and paper folding (Treatment M), and…