One possible way of evaluating set curricula is to examine the consistency of study programmes with students' psycho-cognitive development. Three theories were used to evaluate matching between developmental theories and content proposed in the mathematics programmes (geometry section) for primary and the beginning of secondary education. These…

This study investigated the geometric cognitive growth of pre-service mathematics teachers in terms of the Van Hiele levels in a technology-enriched environment, as opposed to that of students in a learning environment without any technological enhancements. In order to investigate this, a quasi-experimental non-equivalent comparison group design…

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)

This study investigated middle school children's ability to form a mental image of a planar figure and to: (1) mentally flip, turn, or slide this representation and then construct the resultant image in correct position ("performing individual motions"), (2) perform two such motions in succession ("composition of motions"), (3) perform the process…

The movement to modernize mathematics education is critically examined in the area of instruction of geometry. The author concludes that the elimination of deductive geometry should be reconsidered by mathematics teachers. (MP)

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)

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)

This study investigated the ability of middle school children to perform Euclidean transformations mentally. The results indicated that the tasks were more difficult than Piagetian theory would indicate. (SD)

A system for categorizing components of geometry class discussions is described. The unit of observation is the teacher question; responses are coded at four cognitive levels. The system is easier to use than many in the literature; use of it can help teachers develop questioning techniques. (SD)

These 14 research reports are grouped into three broad categories based on the Piagetian level concerned. The articles concerning preoperational concepts focus on problems such as: (1) finding an appropriate mathematical description of some of the primitive mathematical concepts; (2) the role of "activities" in early concept acquisition;…