This article endeavours to define how the application of incorrect or wrong solutions to mathematical equations or problems can be used to help stimulate students to perform a critical analysis of the mathematics being applied or the context of the equations used. The context of the application is discussed together with the specific learning…

In the early stages of working with dynamical geometry environments, students make many more mistakes than if they thought out and implemented the same constructions on paper. Most Czech teachers have very little experience of doing geometry using computers. A methodology which could help them to teach students to avoid mistakes dependent on the…

Computation errors that may occur by expanded use of calculators are discussed. Potential errors with five exact arithmetic examples are described as they are translated into approximate processes. (MNS)

Discusses errors made by remedial intermediate algebra students in factoring polynomials in light of student definitions of factoring. Found certain beliefs about factoring to logically imply many of the errors made. Suggests that belief-based teaching can be successful in teaching factoring. (16 references) (Author/MKR)

Illustrates, categorizes, and analyzes typical mathematical errors in algebra and trigonometry made by high school and lower division college students. (16 references) (Author/MKR)

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…

Several examples of mathematical diagnosis using microcomputer software are presented, with possible future considerations suggested. Three limitations of the software are discussed. (MNS)

The performance of 60 fourth form pupils who had been taught to solve algebraic equations by the algorithmic or flow chart method was studied. A sizeable number of pupils were not using the flow chart method. Other types of errors are noted. (MNS)

Evidence was collected to support previous research findings that children prefer quantitative to formal methods of solving linear equations. They find formal methods difficult. How to help them become more receptive to learning formal methods is discussed. (MNS)

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)

This article, a reprint from 1930, offers an interesting perspective on the importance of diagnostic and prescriptive teaching as well as the role of drill and the use of objectives in mathematics. (Author/MK)

An approach to teaching factors and terms is offered that builds directly on students' knowledge of arithmetic. Errors arising from factor and term confusions are noted, followed by the pedagogical strategy of exploration, invention, and discovery. (MNS)

Errant mathematical views are widely found among teachers, their students, and authors of applied mathematics texts. Suggests classroom experimentation, both to confirm the occurrence of these errors, and to apply the appropriate corrective teaching. (Author/ASK)

Structuring the algebra course to provide a link between a student's existing knowledge and the new topic being presented is discussed. Developing relationships among topics is suggested through examples describing a mathematical problem and effective teaching approaches. Stress is placed on teachers reflecting on mistakes pupils are likely to…

A lesson in editing was learned from a study of errors made on a national mathematics test in Israel. Analysis indicated that the errors were often caused by careless printing of the test, misleading figures, poor designations, or ambiguous phrasing. (MNS)