Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)

Studied were the misconceptions that preservice elementary teachers have about multiplication and division. Results indicated that they are influenced by the same primitive models as students; the most common errors made by both groups are quite similar. (MNS)

Discusses how student errors can be utilized to understand the nature of the conceptions that underlie students' mathematical activity. Looks at why errors are made in mathematics, how teachers and students perceive errors, and how to use errors in the classroom. (MDH)

Discusses geometrical reasoning in the framework of the theory of Figural Concepts to highlight the interaction between the figural and conceptual components of geometrical concepts. Examples of students' difficulties and errors in geometrical reasoning are interpreted according to the internal tension that appears in figural concepts resulting…

Focuses on the language used by elementary mathematics teachers and its relationship to students' understanding of mathematical concepts, as well as their misconceptions. Describes eight situations in which the use of precise, formal mathematical terms could be replaced by informal language, particularly when introducing new concepts. (TW)

Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)

Reviews the logic underlying mathematical induction and presents 10 tasks designed to help students develop a conceptual framework for mathematical induction. (Contains 20 references.) (MDH)

The concept of probability is not an easy concept for high school and college students to understand. This paper identifies and analyzes the students' alternative frameworks from the viewpoint of constructivism. There are various interpretations of probability through mathematical history: classical, frequentist, and subjectivist interpretation.…

Reports misconceptions identified in students with respect to the topic of parallel lines and the teaching strategies found to be useful in challenging those misconceptions. (11 references) (MDH)

Examined fifth-grade students' survey responses to investigate incorrect rules that derive from children's efforts to interpret decimals as integers or as fractions. Regarding fractions, difficulties arise because only the whole-part approach to fractions is presented in elementary school. (Author/MDH)

Diagnoses of students' performance on procedural mathematical tasks need to display a certain level of stability and robustness if they are to be used as the basis for remediation, particularly with computer-delivered instruction. The purpose of this study was to compare two diagnostic approaches for describing students' (n=231) errors in algebra…