This paper reports the multimodal resources that attached to students' reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we…

This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…

Development of geometric congruence and motion was studied through tasks that tapped transformational imagery, correspondence matching, measurement operations, and transformation combinations. Results showed even the youngest children studied could generate strategies for verifying congruence. The dominant strategy in younger children was edge…

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…

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 study investigated whether (1) instruction providing for experimental manipulation by students was superior to instruction in which teachers perform the manipulations and children observe, and (2) spatial ability was related to mode of instruction. Participating in the 8-week study were 141 students aged 12-15 in seven intact eighth-grade…

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)