Compares a teaching program designed to enhance schema acquisition with one of worked examples, traditionally used to teach geometry. Shows that both groups of subjects had improvements in the number of problems solved, with those exposed to non-goal-specific procedures demonstrating greater rates of improvement and greater efficacy in…

Presents an activity using geoboards to recognize similar and different relationships of triangles. (ASK)

Recognizing geometric shapes and noting their special properties are important steps in learning geometry. Offers the use of geoboards and emphasizes that much of what teachers want students to learn about squares, rectangles, and trapezoids can be accomplished with geoboard figures. Presents activities on quadrilaterals using geoboards. (ASK)

Presents a framework for differentiating between five levels of extension of knowledge: basic features, forms, rules, application, and elaboration. Comparison of the extent of knowledge use exhibited by (n=14) Year-11 Australian students on a range of plane geometry problems found that high-achieving students exhibited greater extension of…

Documents students' use of Cabri-Geometry to work on tasks that led them to construct particular relationships and explore and connect different mathematical themes or ideas. (Author/MM)

Surveys recent literature on the use and value of the history of geometry in mathematics education. Makes the case that arguments can be divided into conceptual, (multi-) cultural and motivational ones. Details about content and purpose of the literature surveyed are presented in two appendices. (Author/MM)

Presents an activity that uses square-foot tiles as a coordinate system on which human geometric models are constructed. (ASK)

Uses colored cube combinations to investigate surface area, volume, and axes of symmetry. (ASK)

Describes how origami can be used to help elementary school students learn geometrical concepts of shapes in two and three dimensions. Discusses equilateral triangles, Stars of David, rhombuses, and spirals. (MM)

Geometrical representations can help students generalize arithmetic to algebra. Includes several examples including triangle numbers and models of cubes. (Author/MM)

Humans are endowed with cognitive modules specialised in processing information about the class of natural things. Due to their naturalness, fractal art and design can contribute to developing these modules, and trigger affective responses that are associated with certain natural objects. It is argued that exposure to fractals in an art and design…

Thousands of years ago, mathematicians thought about numbers in terms of geometry. Numbers had shapes, and by thinking about the shapes, mathematicians could do a lot of things with numbers that are now recognized as algebra. This document contains a lesson plan for students to learn the relationship between numbers--all while developing algebraic…

With both "Cabri" and "Autograph" now venturing into 3D, the dimension that previously was only demonstrated in the classroom with a lot of arm waving and crude wire cages can now be explored dynamically on screen. "Cabri 3D" concentrates on constructions, using the principles of Euclidian geometry, whereas "Autograph" creates objects using a…

This article discusses how paper folding can be used in the classroom to introduce the standard results of school geometry, such as the transversal and parallel lines results, along with results concerning angles in convex polygons and centres of triangles, for example. Angle bisectors, midpoints, perpendiculars are all straightforward…

Several examples proved Van Hiele theory to be a useful ingredient in teaching of a summer course for high school students who had failed geometry during the school year are discussed. The theory provided a framework to help organize and reflect upon instruction for some key concepts in geometry.