Discusses the reduction of the one- and three-dimensional diffusion equation to the difference equation and its stability, convergence, and heat-flow applications under different boundary conditions. Indicates the usefulness of this presentation for beginning students of physics and engineering as well as college teachers. (CC)

Multiple embodiment is explained and discussed, with activities described that might be used to develop concepts in geometry and in arithmetic. A series of questions is raised about the choice, use, and organization of embodiments; suggestions for action research are made. (DT)

Implication of findings for designing an introductory mathematics curriculum are discussed. (Authors)

A study of conservation of length concepts covering the symmetric, asymmetric, reflexive, nonreflexive, and transitive relations. Their order of development was traced during the course of a 15-lesson sequence of related instruction. (MM)

Describes a method utilizing the library system to introduce children to mechanical and mental arithmetic. (RP)

The article presents experiences of the author that lead him to conclude that instructions of a test item sometimes inhibit mathematical activity. The low-ability student is often unable to translate written instructions into action because he is not familiar with acceptable methods. Student reaction to the term proof" receives greatest…