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…

Algebra word problems were analyzed in terms of the information integration tasks that are required to solve the problems. These tasks were classified into three levels: value assignment, value derivation, and equation construction. Novices (35 first year algebra students) and experts (13 analytic geometry students) were compared on the proportion…

On the Australian Mathematics Competition, boys responded correctly to more questions than did girls, but this difference came largely from a handful of questions. Responses to questions where sex differences occurred are discussed. (MNS)

In order to determine the knowledge and skills needed by novice programmers to successfully learn computer programming, four studies were conducted using a clinical interview technique. The first study determined that many systematic errors in programming were due to programmers' high-level misconceptions of the nature of the computer and of the…

Four methods of solutions and 12 calculative strategies were found from introspective reports of 15 skilled and 15 unskilled students in grades 11 and 12 doing mental multiplication. Unskilled students used strategies more suited to written than mental computation, while skilled students used strategies based on number properties. (MNS)

Summarizes information processing models of the mind based on a literature review; describes a prototypical model of college learning; examines links between mental models and cognitive errors; reviews cognitive science students; and identifies six factors contributing to cognitive error production. (104 references) (Author/MBR)

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.…

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be…

A collection of student distortions, represented by student-invented variations of theorems, are presented. They were drawn from examination papers of 17-year-old students in Israel. (MNS)

An overall schema of interpretation for programming instructors is given, so that the misconceptions students develop in programming can be determined more readily. Types of language-independent and -dependent bugs, how they can be identified, and how to help students overcome them are addressed. (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)

High school students' misunderstandings of the conceptual machine of the BASIC programming language were examined using a screening test and structured interviews to determine their understanding of fundamental concepts such as variables, assignments, loops, flow and control, and tracing and debugging. (MBR)