Many worthwhile mathematical activities can be generated by an overgeneralization. Some conjectures and their verification are described, with some exploration of historical procedures. (MNS)

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)

Four different conceptions of error-making from a pedagogical perspective are developed. Using errors as springboards for learning is advocated, so that better understanding of content and of the nature of mathematics results. (MNS)

This is a report of an application of the interpretation of errors and springboards in a real-life situation. If and why we need to reduce fractions is considered. (MNS)

A common mistake in adding fractions involves the confusion betwen the concepts of fraction and ratio. A coherent system to operate with ratios is developed. (MNS)

Several intuitive proofs for evaluating specific infinite expressions are given. Observations on intuition and errors in mathematics are included. (MNS)

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)

Research is reviewed in four categories: teachers' beliefs about mathematics, mathematics learning, and mathematics teaching, and some other important teacher beliefs. Reflections are also included. (MNS)

Illustrated first is the case in which a wrong procedure (with fractions) leads to a correct result. Trying to justify why it works in this case and looking for similar patterns involved interesting algebraic considerations as well as use of computers. (MNS)

A series of common misconceptions with regard to infinite sets is considered. Several notions of infinite numbers proposed by different mathematicians are compared. It is argued that so-called errors should rather be called alternative conceptions. (MNS)

Future research initiatives on learning and instruction are considered to be of most worth if grounded in general systems theory and if multiple research methods are used. Discussed are an information processing theory and a theory for the structure and structuring of stored information. (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)

Research on structural learning theory is reviewed as a base for designing computer-assisted instruction programs. An intelligent "Rule Tutor" emphasizing diagnosis and remediation for whole number concepts is described. (MNS)

Contains a research based discussion of the importance of teacher expectations. Lists 20 suggestions from research that will help facilitate positive and realistic self-concepts in students. (PK)

Presents the major findings identified by a commission that examined research issues in diagnostic and prescriptive mathematics. Addresses the diagnostic process with regard to curriculum, instruction, learners, teacher education, clinics, and the mathematics education community. (TW)