Describes a microcomputer-based system for diagnosing children's multiplication errors which incorporates the knowledge base of all known systematic multiplication errors, and utilizes a modular approach to cope with the program's complexity. Each module's function, how the programs interact, and the design of pupil-machine interaction are…

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

This document is intended to describe several software learning environments in an order that parallels a reasonable sequence of use by students. It also describes a planned an designed, but not yet implemented, extension of these environments from the discrete to the continuous case. Each of the implemented environments was developed in…