Twelve middle school students, working in pairs, used a computer microworld to explore introductory geometric transformational concepts. Despite a tendency for symbolic overgeneralization, the students were able to use visual feedback from the microworld and discussions with partners to correct their own mistakes. (Author/JJK)

One class of interactive, computer-based learning environments (microworlds) for the exploration of school mathematics (and science) entails the incorporation of appropriate concepts within the engaging context of self-directed discovery learning. The objective of this research was to investigate and describe in detail the constructive learning…

Utilizes LOGO to teach the concept of inequalities by programing the turtle to take random walks in the coordinate plane restricted to predetermined regions defined by inequalities. The students task is to discover the inequalities that define the illegal areas into which the turtle must not move. Provides examples and corresponding computer…

Describes an activity intended to incorporate investigation into learning of mathematics. The example cited involved having fourth graders study perimeter and area of rectangles using Logo. The author suggests that what began as a simple exercise in investigating geometric concepts became an exciting exploration that touched on many topics. (PK)

Used 2 12-year-old children to investigate deductive and inductive reasoning in plane geometry. A LOGO microworld was programmed to measure distances and turns relative to points on the plane. Learning environments like this may enhance formation of inductive geometrical understandings. (Contains 44 references.) (LDR)

N:4$2 N:4$N Reported are results of a Technical Education Research Centers (TERC) project describing telecommunication interactions between groups of students using the computer software unit "Connectany." Polygons are formed through repetitive "jumps" between points on a circle. Investigation questions and results are shared…

Describes activities that use the geometric construction capabilities of the Geometer's Sketchpad computer software to explore triangles. Topics investigated include angle measurement, the sum of the measures of the angles of a triangle and a five-pointed star, triangle classification, and area and perimeter of a triangle. (MDH)

Presents activities employing LOGO to help create situations that enable students to make meaningful cognitive connections while exploring mathematical relationships. Activities explore the concepts of angles and rotations, progressing from off-line to on-line activities with suggested extensions. (MDH)

This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school…

This paper examines a range of studies done on the "Geometric Supposer" software and its use since the mid-1980s. It describes how the "Geometric Supposer" is a response to the call for reform by the mathematics community to create classroom environments that allow students to construct their own knowledge. This approach to…

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" (the "Standards"), provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. This book, one in a series…