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)

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)

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)

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (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)

Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)

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)

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 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…

This report: (1) describes the mathematics test given to Year 9 students in the Mt. Druitt Longitudinal Study in 1987; (2) describes and discusses the results; (3) analyzes errors made by students; (4) analyzes the responses to items common to the 1986 and 1987 tests; and (5) suggests some interventions to address the errors made by students. The…