This essay discusses the sketching and transformation of parabolas and other curves as areas where learners can exercise and develop control of their mental imagery. (MN)

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…

This study investigated middle school children's ability to form a mental image of a planar figure and to: (1) mentally flip, turn, or slide this representation and then construct the resultant image in correct position ("performing individual motions"), (2) perform two such motions in succession ("composition of motions"), (3) perform the process…

Children aged four through eight performed a series of tasks involving two-dimensional isometrics to determine the amount of compatability between a mathematically-based organization of Euclidean transformation concepts and the existing cognitive structures of the children. Results confirmed that mathematical and cognitive structures are not…

This study investigated the ability of middle school children to perform Euclidean transformations mentally. The results indicated that the tasks were more difficult than Piagetian theory would indicate. (SD)

These 14 research reports are grouped into three broad categories based on the Piagetian level concerned. The articles concerning preoperational concepts focus on problems such as: (1) finding an appropriate mathematical description of some of the primitive mathematical concepts; (2) the role of "activities" in early concept acquisition;…

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 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)