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)

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)

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)

Discusses the development of visual thinking in students. Also presents a strategy that incorporates visualization exercises within the framework of traditional mathematics. The technique appears successful for students studying geometry, fractions, and problem solving. Visualization abilities increase understanding and therefore give students…

Secondary geometry students were tested for van Hiele level of thinking, geometry knowledge and achievement, and proof-writing achievement. Proof-writing achievement correlated significantly with van Hiele level entering geometry knowledge and geometry achievement. The predictive validity of the van Hiele model was supported. (Author/DC)

Presented is an alternative method for analyzing the van Hiele level of students' geometrical reasoning. The accuracy of students' answers may afford a description of acquisition and/or expertise for each of the van Hiele levels simultaneously rather than the traditional assignment and evaluation of one level at a time. (JJK)

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)

Some geometric activities are described that teachers can use to give their students experiences that will influence their spatial abilities. It is noted that the goal is to improve spatial abilities, not to increase knowledge, so individual pupil responses should not be used to judge student achievement. (MP)

Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…

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…

Compared are the van Hiele levels of geometric thinking and the geometry curriculum recommended by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Activities which illustrate the various levels are provided by grade level with procedures. (CW)

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…

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)