In this study Piaget's method of the clinical interview was used to examine children's understanding of rotation about apoint at three age levels (6, 7, and 8). In two half-hour sessions, subjects (N = 108) were given four tasks: (1) an adaptation of Piaget's locus and circular motion experiment, and tasks concerned with (2) the circle as a locus…

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…

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;…

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)

Describes a geometry course that integrates transformation geometry into traditional high school geometry. Discussion of the scope and sequence of the course includes the topics of proof, congruence, translations, rotations, reflections, dilations, quadrilaterals, parallel lines, and similarity. (MDH)