In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students' concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition--concept image as reported by Tall and Vinner ("Educational Studies in Mathematics" 12:151-169, 1981), a…

This paper reports on concept images of 38 secondary school mathematics prospective teachers, regarding the evenness of numbers. Written assignments, individual interviews, and lesson transcripts uncover salient, erroneous concept images of even numbers as numbers that are two times "something" (i.e., "2i" is an even number),…

Students react similarly to a wide variety of conceptually unrelated situations. Describes a rule that is manifested when two systems are equal with respect to certain quantity A, but differ in another quantity B. Indicates that in such situations students often argue that the same amount of A implies the same amount of B. (Contains 30…

Presents a joint work of mathematics and science educators that suggests that many responses that literature describes as alternative conceptions are interpreted as if they evolved from a small number of intuitive rules. Demonstrates the explanatory and predictive power of these intuitive rules. (Contains 36 references.) (Author/ASK)

This book reports on students' reactions to different situations in mathematics and science education. A theory is presented to explain and predict students' responses which is based on these observations. The identified rules of the theory of intuitive rules is explained. Chapters include: (1) "How Children and Adults Use the Intuitive Rule 'More…

Investigated was whether preservice teachers' success in solving division word problems was effected by the type of problem or by the common misconceptions related to primitive models of division. Preservice teachers' ways of thinking about division were also examined. Sample division problems, results, discussion, and implications are included.…

Discusses an attempt to promote the development of prospective elementary teachers' own subject-matter knowledge of the division of fractions as well as their awareness of nature and likely sources of related common misconceptions held by children. Indicates that before the described mathematics methods course, most participants knew how to divide…

Investigated was the use of cognitive conflict to probe the misconceptions held by preservice elementary teachers that in a division problem the quotient must be less than the dividend. Explains how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding support their misconceptions.…

Described is a computer-based tutoring program that helped to improve computational performance for 16 preservice elementary teachers by effectively increasing their awareness of a tendency to divide consistently by the smaller of 2 numbers presented within division word problems. (JJK)

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

Described are the conceptions held by United States and Israeli students about multiplication and division that may impede their work with decimals. Included are the introduction, method, division and multiplication task results, and the implications for education and textbook development. (KR)

Assessed are the extent to which the beliefs, "multiplication always makes bigger" and "division always makes smaller," are explicitly held by preservice elementary teachers. Insight into the sources of preservice teachers' beliefs and into the relationship among preservice teachers' beliefs, computational skills, and performance on word problems…

Discusses a system of classification for students' inconsistent ideas in mathematics, the sources of students' mathematical inconsistency, and instructional strategies for helping students to resolve apparent learning inconsistencies. Language, curriculum, and instruction are included in the discussion. (KR)