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Resnick, Lauren B.; And Others – 1988
Considered is a conceptual analog of buggy algorithms and rule-based mathematical development. The investigations consider whether children's efforts to make conceptual sense of new mathematics instruction in terms of their available knowledge may sometimes lead them to make systematic errors. In particular, the possibility is explored that…
Descriptors: Arithmetic, Concept Formation, Decimal Fractions, Educational Research
Davis, Robert B. – 1983
The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…
Descriptors: Algorithms, Cognitive Processes, Educational Research, Elementary Secondary Education
LeFevre, Patricia – 1986
This exploratory study describes fourth-grade students' opinions and knowledge about fractions. A coherent and elaborate fraction knowledge base results when students establish connections between their conceptual knowledge and procedural knowledge of fractions. One possible juncture between concepts and procedures might involve establishing…
Descriptors: Case Studies, Cognitive Processes, Educational Research, Elementary School Mathematics
Peer reviewed Peer reviewed
Behr, Merlyn J.; And Others – Journal for Research in Mathematics Education, 1984
Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in 132 interviews during an 18-week teaching experiment. Six children were instructed individually and as a group at two sites, with instruction relying heavily on manipulative aids. Strategies used to compare fractions were identified. (MNS)
Descriptors: Cognitive Processes, Educational Research, Elementary Education, Elementary School Mathematics
Peer reviewed Peer reviewed
Tirosh, Dina; Graeber, Anna O. – Journal for Research in Mathematics Education, 1990
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.…
Descriptors: Arithmetic, College Mathematics, Computation, Division
Peer reviewed Peer reviewed
Thipkong, Siriporn; Davis, Edward J. – School Science and Mathematics, 1991
A study on the impact of misconceptions on preservice elementary teachers' processes in solving problems involving multiplication and division of decimals is described. Included are the purpose of the study, a description of the subjects, instruments, and interviews, the findings, and discussion. (KR)
Descriptors: Algorithms, Arithmetic, Decimal Fractions, Elementary Education
Peer reviewed Peer reviewed
Erickson, Donna Bird – School Science and Mathematics, 1991
The ability of students to sort cards based on surface features and deep patterns is investigated. The effect of the presence of variables and what makes a pattern difficult or easy for students to recognize are discussed. Study revealed that students are unsuccessful at making connections between expressions, sentences, and sequences which share…
Descriptors: Algebra, Arithmetic, Attention, Fractions
Peer reviewed Peer reviewed
Greer, Brian – Journal for Research in Mathematics Education, 1987
Investigated was how easily pupils aged 12 and 13 who were initially unaware of the invariance of an operation (with decimals) modeling a situation could be led to such awareness. Results from clinical interviews are reviewed and a protocol presented. It appeared difficult to induce conservation. (MNS)
Descriptors: Cognitive Processes, Conservation (Concept), Decimal Fractions, Division
Ball, Deborah Loewenberg – 1988
This paper presents results from a study of 19 teacher education students' knowledge of mathematics and discusses an analytic framework for examing and appraising teachers' and prospective teachers' subject matter knowledge. Participants in the study were 10 elementary education majors and 9 mathematics majors or minors who were preparing to teach…
Descriptors: Algebra, Concept Formation, Division, Educational Research
Peer reviewed Peer reviewed
Hasselbring, Ted; And Others – Journal of Educational Technology Systems, 1988
Describes study designed to evaluate the effectiveness of interactive videodisc program Mastering Fractions. The videodisc program is compared with traditional fractions curriculum and teaching methods in sixth grade classes; pretests, posttests, and mastery tests used are discussed; and results of the study are analyzed. (LRW)
Descriptors: Analysis of Covariance, Curriculum Evaluation, Fractions, Grade 6