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…

Analyzes one student's thinking using the Van Hiele levels of geometric thinking. (KHR)

Theory and research concerning the development of spatial concepts by young children are discussed. Results of Martin and Kidder are compared with those of Piaget. (SD)

Performance of first and second graders on measurement problems indicated that they are unable to relate the measurements of objects using different units to visual comparisons of quantities. (SD)

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the…

When primary children were interviewed to determine their perceptions of embedded triangles, they failed to observe overlapping triangles. Possible explanations for this and other response patterns are discussed, and implications for schooling are explored. (SD)

Development of geometric congruence and motion was studied through tasks that tapped transformational imagery, correspondence matching, measurement operations, and transformation combinations. Results showed even the youngest children studied could generate strategies for verifying congruence. The dominant strategy in younger children was edge…

Seymour Papert, creator of LOGO, explains how he came to create this important problem-solving language and how he intended it to be used to foster learning among children. What children can do with turtle geometry (indicated to be a natural approach to mathematics) is one topic considered. (Author/JN)

Describes young children's thinking about geometric shapes and discusses implications for teaching and learning. (KHR)

Performance of over 200 third and fourth graders on a post test and a two-month follow-up measure showed that groups receiving lessons based on a task analysis instructional design performed significantly better than groups receiving placebo lessons at two levels of advanced mastery for the concepts, "equilateral triangle" and…

Investigates uses of interactive geometry software to enhance students' understanding and reasoning about two-dimensional shapes. Describes basic principles that underlie high-quality geometry instruction. Presents examples that illustrate how appropriate use of dynamic software can enhance students' geometric reasoning. (KHR)

Examines aspects of Navajo cosmology relevant to understanding Navajo spatial representations. Compares Navajo children's spatial knowledge with Piaget's findings about the development of geometric concepts in Swiss children. Describes classroom activities whereby Navajo children explore the geometry inherent in their cultural and physical…

Presented is a study which focused on using turtle graphics programing for geometric problem solving. The goal was to investigate changes in children's mathematical knowledge and results indicate that the LOGO environment enriched children's geometric conceptualizations and sophistication of their geometric thinking. (KR)

Using case studies that are functionalist in orientation and computational in technique, the role of control knowledge in developing constructive thinking is illustrated. Further, the integration of related knowledge structures, emanating from diverse sensory modes and pertaining to both place value in addition and angle relationships in geometry,…

This book examines the Navajo system of spatial knowledge and describes a culture-based curriculum for the development of an intuitive geometry based on the child's experience of the physical world. Aspects of the Navajo cosmology relevant to spatial knowledge are discussed: the structure of the world; the dynamic nature of the universe;…