A major component of student difficulty with algebra is the inability to make sense of the algebra symbol system as a language. Accordingly, remedies should be sought by considering algebra in a linguistic sense. (PK)

Discusses insufficiency of the linear method and some informal practices (or heuristics) used by expositors in trying to alleviate it. Uses the Cantor-Bernstein theorem to illustrate the linear proof, structuring, and the structure proof. Argues that the informal practices considered be consistently applied to the presentation of pivots and…

Describes basic problem-solving skills and presents a protocol of a student solving a problem. Discusses some of the difficulties in obtaining a correct solution. Lists basic prompts for problem solving. (YP)

Suggests that it is possible to apply the principles of literary criticism to the mathematical text. Discussed are the areas of rhetoric, metaphor, and metonymy. (PK)

Described are the difficulties in translating word sentences between English and Algebra. Two classic sentences that typically produce student errors are presented with explanations that can be shared with the students on overcoming these translation difficulties. (MDH)

Reports on the findings of an examination of 32 linear algebra textbooks. The examination, to determine existing approaches to teaching the topics, was in preparation for developing a linear algebra program for high school students. (PK)

Described is the development and implementation of a course on the history of irrational numbers for inservice mathematics teachers in Israel. Some of the materials included in the course are discussed. (RH)

Investigates children's behaviors and conceptual achievements in the transition from informal calculation strategies to a written division algorithm. Describes five different strategies observed in the solution of division problems. Discusses the implications of the children's behavior. (YP)

The constructivist perspective, which holds that children's learning of subject matter is an interaction between what they are taught and what they bring to a learning situation, could be used to improve mathematics teacher education. (PK)

Historical issues concerning the role of mathematics in the school curriculum are considered, with numerous examples illustrating varying emphases. (MNS)

The roles of skills and meaning in mathematics are discussed, with concern expressed over the little time spent on developing understanding. Approaches to proportion are described, levels of meaning are proposed, and proportion as a unifying idea for geometry are among the topics discussed. (MNS)

Advantages and disadvantages of the modern definition of function, understanding the concept of function, procedures used in a study of the understandings of ninth graders, and detailed results of the study are discussed. (MNS)

The teaching of negative numbers poses problems at the school level. A historical account of the intellectual difficulties in the evolution of negative numbers and a method of viewing negative numbers as an extension of the number system to help overcome these difficulties are presented. (MDH)

This paper on the language of zero (1) deals with the spoken and written symbols used to convey the concepts of zero; (2) considers computational algorithms and the exception behavior of zero which illustrate much language of and about zero; and (3) the historical evolution of the language of zero. (JN)

Described are the background, structure, themes, methodology, projects, and assessment for the course. A list of themes is provided. Results of the piloting of the course are discussed. (CW)