Uses manipulative materials to build and examine geometric models that simulate the self-similarity properties of fractals. Examples are discussed in two dimensions, three dimensions, and the fractal dimension. Discusses how models can be misleading. (Contains 10 references.) (MDH)

Presented is an informal technique for counting the number of different-sized equilateral triangles on an isometric grid. Five activities that relate to this topic are included. (KR)

Describes a geometry course that integrates transformation geometry into traditional high school geometry. Discussion of the scope and sequence of the course includes the topics of proof, congruence, translations, rotations, reflections, dilations, quadrilaterals, parallel lines, and similarity. (MDH)

A selection of 14 tests of five cognitive factors was administered to 95 senior high school geometry students. These cognitive factors were then related to six measures of performance in mathematics and subjected to correlation analysis and stepwise regression. The findings indicated that the selected cognitive factors correlated with all measures…

Examined are the arguments related to whether traditional or new mathematics curricula better prepares students to write proofs. Analyzed are "proofs" presented by students; the author argues that the ability to produce a proof depends upon the cognitive level of the student. (SD)

Five basic skill areas needing more attention in standard high school geometry are discussed. Levels of student mental development in geometry and a need for less emphasis on formal proofs are reviewed. (MP)

In the attempt to improve the quality of geometry instruction in schools, researchers and teachers alike have given considerable attention to the van Hiele theory of geometry learning and development, which proposes a series of cognitive levels through which every geometry student passes. This paper reports a study to determine the extent to which…

These papers presented at a symposium describe how tenth grade students would be taught the slope of a line in geometry using three different approaches to teaching theory: behaviorism, Piagetian cognitive development, and information processing. Analyses of each approach focus on manner of learner cooperation and differing teacher role. (MBR)

Graphical representations of geometrical objects from high school textbooks are categorized according to the implicit conventions underlying their display. The fact that specific illustrations can lead to students' misconceptions about geometric objects is analyzed in relationship to the principle of parallel projection with implications for the…

The ability of tenth grade plane geometry students to structure concepts and relationships from a geometry unit on ratio, proportion and similarity was tested. Analysis of cognitive "maps" of the structural relationships possessed by twenty concrete and twenty formal subjects indicated that formal operational subjects structure subject…

The main thesis of the paper is that geometry deals with mental entities (the so-called geometrical figures) which possess simultaneously conceptual and figural characters. The paper analyzes the internal tensions which may arise in figural concepts because of their double nature, developmental aspects, and didactical implications. (Author/MDH)

Properties of information most likely to attract student attention and how students use information they generate are clarified. Students' expectations of empirical information in geometry and the design of a new version of the Geometric Supposer are discussed. (CW)

This set of five reports and one manual is a product of the Mathemagenic Activities Program (MAP) for early childhood education of the University of Georgia Follow Through Program. Based on Piagetian theory, the MAP provides sequentially structured sets of curriculum materials and processes that are designed to continually challenge children in…

Three activities are presented to assess the level of students' geometric understanding according to van Hiele learning model. The activities--Descriptions, Minimum Properties, and Class Inclusion--are applied to the example of classifying quadrilaterals as squares, rectangles, rhombi, or parallelograms. Implications of this assessment are…

After observing secondary school students having great difficulty learning geometry in their classes, Dutch educators Pierre van Hiele and Dina van Hiele-Geldof developed a theoretical model involving five levels of thought development in geometry. It is the purpose of this monograph to present English translations of some significant works of the…