Examines the abilities of high school students (n=394) to reflect aspects of 36 cubes that were depicted in 2-dimensional perspective as upright and transparent. The reflections of points, edges, or corners was established through two-sided mirrors variously positioned within each cube. Analysis of the response errors reveals a tendency toward…

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…

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)

Three studies were conducted in order to determine the source and frequency of children's difficulties in subtraction and to examine different approaches to remediation. In the first study, third-grade children were asked to solve subtraction problems and were observed and questioned about their solution processes. Children who had difficulty…

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…

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)

Reports on a study to determine if having students write about the work required in doing three types of exercises from elementary algebraic fractions would affect the students' error patterns on quizzes. The study involved six developmental studies in elementary algebra classes. (PK)

The literature on proportional reasoning is reviewed. After methodology is discussed, strategies used to solve proportion problems, variables that influence performance, and training studies are each considered. (MNS)

Suggests that student errors in mathematics be used as motivational devices and starting points for mathematical explorations, involving problem solving and problem posing activities. It is further suggested that errors can foster a deeper and more complete understanding of mathematical content and nature of mathematics itself. (PK)

These proceedings include two lectures followed by working group and topic group contributions in reduced format. The two lectures were by Heinrich Bauersfeld, speaking on contributions to a fundamental theory of mathematics learning and teaching, and Henry Pollak, speaking on the relationship between applications of mathematics and the teaching…

The study was undertaken to investigate the errors made by high and low achievers in a mathematics test administered to students in their second year of high school. The focus of the study was to determine whether any common error types existed within or between the two groups or whether there were error strategies which differed between the two…

This issue contains abstracts and critical comments for 11 articles. Three articles focus on problem solving; the remainder concern understanding of the equals sign, mathematical structure, mathematical abilities, the role of language in tasks involving sets, sex differences in mathematical errors, subtraction, algorithms as schemes, and…

A theory of how people learn certain procedural skills is presented. It is based on the idea that the teaching and learning that goes on in a classroom is like an ordinary conversation. The speaker (teacher) compresses a non-linear knowledge structure (the target procedure) into a linear sequence of utterances (lessons). The listener (student)…

A student was observed practicing arithmetic with a computer-assisted instruction (CAI) system. She enjoyed practice and believed that it helped. However, she consistently failed to solve problems on the computer that she could do with pencil and paper. This paper suggests reasons for her problems and draws implications for CAI. (Author/PK)

This report: (1) describes the mathematics test given to Year 8 students in the Mt. Druitt Longitudinal Study in 1986; (2) describes and discusses the results; (3) analyzes errors made by the students; and (4) suggests some possible interventions to address the errors made by students. The study dates from 1975 when funds were obtained to provide…