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.…

A test of logic using implicational and disjunctive sentences was given to Chinese and English speakers. No differences were found on "if-then" sentences, but differences were found on "or" sentences. (MNS)

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)

The literature on proportional reasoning is reviewed. After methodology is discussed, strategies used to solve proportion problems, variables that influence performance, and training studies are each considered. (MNS)