Examines the abilities of high school students (n=394) to reflect aspects of 36 cubes that were depicted in 2-dimensional perspective as upright and transparent. The reflections of points, edges, or corners was established through two-sided mirrors variously positioned within each cube. Analysis of the response errors reveals a tendency toward…

A model of qualities of mathematical activity was developed within a framework of learning goals. A clinical application of the model is described, in which ninth-grade students were given assignment projects. A hierarchy of effective guidance was established, permitting diagnostic evaluation and progressive development of mathematical activity.…

Describes observations, written samples, and interviews of (n=24) high school teachers learning concepts of group, subgroup, coset, normality, and quotient group in an Abstract Algebra course. General observations are made about the role of errors and misconceptions in light of an action-process-schema framework. (32 references) (MKR)