Ten seventh-grade students were interviewed to provide information about the conceptual frameworks they have about points and lines. Their responses are discussed and compared to those given by 10 elementary education seniors. Implications of responses for mathematics instruction are addressed. (JN)

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…

Discusses students' writing in mathematics, focusing on (1) creating stories; (2) writing mathematical essays; (3) expressing feelings and beliefs about mathematics through diaries and anecdotes; and (4) the use of dialogs. The strategies considered have been used at the high school and remedial college levels. (JN)

Provides definitions of "attitudes" and discusses these attitude measures: (1) Thurstone (equal-appearing) scales; (2) Likert scales; (3) (Osgood's) semantic differential scale; (4) inventories and checklists; (5) preference rankings; (6) projective techniques; (7) enrollments; (8) clinical and anthropological observations; and (9)…

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)

Presented is an edited transcript of an interview with Dr. Caleb Gattegno exploring the teaching approaches used in a film of the same name. (MP)

A discussion of the history of error analysis in mathematics education research provides an overview of research published in German and Anglo-American publications since the early 1900s. (MP)

Mathematics education is viewed as a process imbedded in social interaction. Alternatives to seven widely recognized modeling perspectives that provide conceptual foundations for mathematics learning are discussed. (MP)

Failure of most children to solve word problems beyond the simplest is seen to stem from two causes: failure to understand applied arithmetic and failure to relate problems to the real world. Relevant research is reviewed, and a route for new research is proposed. (MP)

The roles and uses of symbols in mathematical thinking are discussed. The thinking process is further subdivided into specialization, generalization, and reasoning. (MP)

A general model of teacher-student interaction is expanded specifically to mathematics. Mathematics appears to lead to idiosyncratic forms of language and communication in the classroom. (MP)

An attempt is made to link the domain of mathematics and the natures and abilities of mathematicians to that which is perceptual, presentational, and implicit. (MP)

Analysis of the clinical interview procedure as employed in psychological research on mathematical thinking is presented. It is noted that there are three clinical methods, each designed for a different research purpose. (MP)

This review illustrates aspects of cognitive psychology relevant to the understanding of how people think mathematically. Developments in memory research, artificial intelligence, visually mediated processes, and problem-solving research are discussed. (MP)

The need for improving the dialog between teacher and student is promoted as an important step towards improving the mathematics curriculum. (MP)