The degree to which second and third grade children learn transformational geometry concepts under specific instructional conditions and the effects of transformational geometry instruction upon the children's spatial abilities are studied. Results imply that the students learned aspects of transformational geometry but that their spatial…

This study investigated the ways in which the technological tool, The Geometer's Sketchpad, mediated the understandings that high school Honors Geometry students developed about geometric transformations by focusing on their uses of technological affordances and the ways in which they interpreted technological results in terms of figure and…

Creation of materials for a geometry course using transformations is briefly summarized, then research on its effect upon student learning of geometry concepts and student attitudes towards mathematics is discussed. Implementation and other related questions are considered informally. (DT)

The ability of students in grades 1-12 to generate proofs of theorems in an unfamiliar, one axiom, abstract system was investigated. There were no significant differences in performance of two levels of secondary students; fourth- through sixth-grade students were also able to develop proofs, but needed more time. (SD)

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…

The effect of direction of motion on the difficulty of slides, flips, and turns for first, third, and fifth graders was examined. The study considered only students with no training in transformation tasks. The investigation found that the sex main effect was not significant. (Author/MP)

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)

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)

Investigates whether elementary school students can construct operations of thought for integers and integer addition crucial for understanding elementary algebra. Two sixth graders were taught using a computer. Results included both students being able to construct mental operations for negating arbitrary integers and determining sign and…