Two experiments investigated children's strategies for solving geometric matrices that were correctly or incorrectly completed and that varied in number of elements and number of transformations. Examining the relationship between working memory and item complexity, the first experiment tested 90 boys and girls of 7, 10, and 13 years of age for…

This study examines the extent to which modeling facilitates transformational problem solving in mathematics for children in kindergarten and first grade. Subjects were 20 children selected from each level. They responded to two problems for each of four problem types (counting on, story problems, quantitative comparisons, and ordination) under…

Discussed is an application of number theory to cryptology that can be used with secondary school students. Background on the topics is given first, followed by an explanation for use of the topic. (MNS)

Geometric matrix problems were presented to 11- and 14-year-olds and adults to investigate latency to solution as a function of number of elements (1-3) and of transformations (0-2) that had to be considered for correct solution. At all ages latencies increased as the number of elements and number of transformations increased. (Author/DB)

The transformation assigning to every point its inverse with respect to a circle with given radius and center is called an inversion. Discusses inversion with respect to points, circles, angles, distances, space, and the parallel postulate. Exercises related to these topics are included. (MDH)

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…

Presents a series of solution methods to the Eight Queens Problem of placing eight queens on a chess board so that no one queen can capture another. Solution methods progress from empirical approaches to the use of computer algorithms. Geometric transformations are used to find other solutions. (MDH)

Argues that Turtle Geometry has a great deal to offer mathematics teaching and learning. Suggests that it helps develop general problem-solving strategies and encourages new approaches to teaching and learning. (PK)

Two studies to determine how students interact with two microworlds that reflect a constructivist view of learning investigated students' goals during interaction, strategies utilized to achieve their goals, changes in goals during interaction, and common patterns of interaction and learning. Concludes that well-designed games enable students to…

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)

This paper considers how the algebra curriculum in secondary mathematics might be reformulated by rethinking both the content of algebra and the approaches to teaching and learning algebraic concepts. It considers how the concept of function can be made a central theme of the algebra curriculum and further suggests that computer software, when…

This guide is designed to help classroom teachers implement the Alabama Course of Study: Mathematics K-12. It is inclusive also of the objectives tested by the Stanford Achievement Tests and the Alabama Basic Competency Tests. One characteristic of the curriculum guide is that it clearly states what students should learn in each grade level. These…

This unit is 1 of 12 developed for the university classroom portion of the Mathematics-Methods Program (MMP), created by the Indiana University Mathematics Education Development Center (MEDC) as an innovative program for the mathematics training of prospective elementary school teachers (PSTs). Each unit is written in an activity format that…