It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

There has been a large amount of research about the impact of dynamic geometry software (DGS) on the learning of mathematics mainly related to different representations of mathematical concepts and functional dependences. This paper goes beyond these investigations by suggesting meaningful connection and integration of DGS with physical resources…

This article gives an example for using Dynamic Geometry Software to encourage making conjectures, reasoning, and experiencing mathematics as a process.

Interactive or Dynamic Geometry System (DGS) is a tool that help to teach and learn geometry using a computer-based interactive environment. Traditionally, the interaction with DGS is based on keyboard and mouse events where the functionalities are accessed using a menu of icons. Nevertheless, recent findings suggest that such a traditional model…

Reports, in French, an investigation on the use of graphic representations in problem-solving tasks of the type in Spanish Mathematical Olympiads. Analysis showed that the choice and interpretation of the first graphic representation played a decisive role in the discovery of the solution. (34 references) (Author/MKR)

Explores the role of proof in mathematics education and provides justification for its importance in the curriculum. Discusses three applications of dynamic geometry software--heuristics, exploration, and visualization--as tools in the teaching of proof and as potential challenges to the importance of proof. (Author/MM)

Reports on a long-term teaching experiment carried out in the 9th and 10th grades of a scientific high school as part of a larger research project. Aims to clarify the role of a particular software, Cabri Geometry, in the teaching/learning process. Focuses on the social construction of knowledge. (Author/MM)

Presents an activity suitable for rainy days in which students solve a story problem to determine how fast a person should run in the rain to get the least wet. (MDH)

Discusses geometry and Dynamical Geometry Software (DGS). Analyses the way DGS-use influences traditional geometry. Highlights changes in the interactions between geometry, computers, and DGS and human users, focusing on changes in the teaching and learning of geometry. Concludes that DGS deeply changes geometry if it is taken as a human activity…

The article discusses the classic problem: "Given an equilateral triangle and a point P inside the triangle, what is the sum of the distances from P to the three sides?" The problem is used to illustrate the generative nature of problem-posing using the heuristic "What happens if...?" (PK)

Presents thinking-aloud protocols from secondary pupils solving arithmetic story and geometrical problems and analyzes their protocols by using interpretation models founded on a general problem-solving model. A word problem solving simulation is also used to further explicate processes pupils use to solve mathematical tasks. (Author/MBR)

Described and evaluated are microcomputers as a tool for construction in geometry education and heuristic theorem finding through interactive continuous variation of geometric configurations. Numerous examples of theorem finding processes are provided using the prototype graphics system CABRI-Geometer. (MDH)

This report describes an analysis of the segments and shows of the first season's production of "Square One TV" in terms of its elaborated goals. It includes charts and graphs showing the treatment of objectives for the series' goals across the 75 shows of the series. The goals of the series are: (1) to promote positive attitudes toward,…

This study examined whether analogy or means-ends strategies (heuristics) would be used to solve geometric puzzle-like problems, which were generated by a microcomputer. The subjects in the two-group experiment were undergraduate students enrolled in an introductory psychology course at Potsdam College (New York). One group of subjects learned…