This document contains 15 research papers presented at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics. The papers are organized into four sections. In part I, four position papers by Romberg, Engelhardt, Ashlock, and Heddens reflect research ideas which underlie the Council. Part II…

Reports results obtained when 24 14-year-old students were presented with algebra tasks by a computer-based modeling system and, four months later, comparable paper and pencil tests together with detailed interviews. Comparison of the results revealed profound misunderstandings of algebraic notation and identified classes of strategies used by…

Evidence on learning problems due to dyscalculia is surveyed. Definitions, factors responsible for dyscalculia, split-brain research and hemispheric roles, mathematics learning problems and personality, materials for instruction, and levels of knowing mathematics are among the topics discussed with an extensive list of references. (MNS)

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…

This document contains 14 papers selected from those presented at the Seventh Annual Conference of the Research Council for Diagnostic and Prescriptive Mathematics. Categorized as interdisciplinary studies are reports on "Mathematics as an Activity of Our Intelligence" by Skemp and a study on "The Brain Basis of Developing…

The work of Ladislav Kosc on dyscalculia is presented. His work on meanings, forms, terminology, diagnosis, correction principles, factors in mathematical ability, language dysfunctions, and publications are each included. (MNS)

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.…

How computers have affected diagnosis in mathematics is discussed. A distinction is made between errors and mistakes, followed by consideration of computers as a diagnostic tool. The development of algorithms to diagnose errors and of models of student performance is described. (MNS)

Analysis of errors children make is modeled both with and without computers. Patterns of thinking are traced for a fifth grader, with the discussion focused on getting clues for remedial instruction by analyzing the dialog. (MNS)

This study sought to evaluate a measure of dyscalculia to determine its validity and reliability. It also tested use of the instrument with seventh graders and ascertained where errors attributed to dyscalculia were also present in an average sample of seventh graders. Results varied. (MNS)

Documented are major categories of errors that appear as children learn decimal fractions. Then the conceptual sources of these errors are established. Different curriculum sequences influence the probability that these classes of errors will appear. They can be used as diagnostic tools to detect children's understanding of mathematics topics.…