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Barrett, Everard – 1991
Examining how students reconstruct stories they've heard can give insights into why students often have difficulty understanding and retaining mathematics. Behavioral psychologists refer to the phenomenon of piecing together a series of events as "chaining." This paper argues that the cognitive capacity to reconstruct a whole contextual…
Descriptors: Cognitive Development, Cognitive Mapping, Concept Formation, Context Effect
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Stipek, Deborah; Salmon, Julie M.; Givvin, Karen B.; Kazemi, Elham; Saxe, Geoffrey; MacGyvers, Valanne L. – Journal for Research in Mathematics Education, 1998
Discusses convergence between instructional practices suggested by research on achievement motivation and practices promoted in mathematics-instruction reform literature by focusing on fourth- through sixth-grade students (N=624) and their teachers (N=24). Concludes that the instructional practices suggested in the literature of both research…
Descriptors: Cognitive Development, Concept Formation, Educational Change, Fractions
Ellerbruch, Lawrence W.; Payne, Joseph N. – NCTM Yearbook, 1978
A teaching sequence provides a guide to instruction on initial concepts of fractions, equivalent fractions, and addition with fractions. (MN)
Descriptors: Addition, Algorithms, Cognitive Development, Computation
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Baroody, Arthur J.; Hume, Janice – Remedial and Special Education (RASE), 1991
The article discusses ways to make mathematics instruction with learning-disabled and other children more developmentally appropriate by building on children's informal understandings in active purposeful learning, using less direct instruction and paper-and-pencil work. Ideas are applied to the teaching of fractions. Instructional materials are…
Descriptors: Cognitive Development, Developmental Stages, Educational Improvement, Elementary Education
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Tzur, Ron – Journal for Research in Mathematics Education, 1999
Studies the co-emergence of teaching and children's construction of specific conceptions that support the generation of improper fractions in a constructivist teaching experiment with two fourth-grade students posing and solving tasks in a computer microworld. Reports that examination of the teacher's adaptation of learning situations (tasks) and…
Descriptors: Cognitive Development, Computer Uses in Education, Concept Formation, Constructivism (Learning)
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Bohan, Harry – Arithmetic Teacher, 1990
Described is a strategy that shows students how one mathematical concept can be connected to another. The emphasis is on both process and product and can lead to creating a learning environment where students do mathematics as mathematicians do. (KR)
Descriptors: Cognitive Development, Cognitive Processes, Elementary Education, Elementary School Mathematics
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Cramer, Kathleen; Bezuk, Nadine – Arithmetic Teacher, 1991
Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)
Descriptors: Cognitive Development, Concept Formation, Elementary Education, Fractions
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Howard, Arthur C. – Mathematics Teacher, 1991
Discussed is why students have the tendency to apply an "add the numerators and add the denominators" approach to adding fractions. Suggested is providing examples exemplifying this intuitive approach from ratio, concentration, and distance problems to demonstrate under what conditions it is applicable in contrast to the addition algorithm. (MDH)
Descriptors: Addition, Cognitive Development, Concept Formation, Elementary School Mathematics
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Campbell, Patricia F., Ed. – Arithmetic Teacher, 1993
Proposes helping students understand fractions by establishing connections between students' informal knowledge of fractions and the mathematical symbols used to represent fractions. Sample dialogues demonstrate how these connections can be made. (MDH)
Descriptors: Cognitive Development, Cognitive Processes, Concept Formation, Discussion (Teaching Technique)
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Bell, Alan – Educational Studies in Mathematics, 1993
Three teaching experiments are reported which study aspects of a diagnostic teaching methodology. An experiment in the field of directional quantities showed a positive relationship between the intensity of discussion and amount of learning; one on fractions and another on geometric reflections showed good two-month retention under the…
Descriptors: Cognitive Development, Diagnostic Teaching, Discussion (Teaching Technique), Fractions
Ball, Deborah Loewenberg – 1990
Learning to teach mathematics for understanding is not easy. First, practice itself is complex. Second, many teachers' traditional experiences with and orientations to mathematics and its pedagogy are additional hindrances. This paper examines teaching practices and reviews some of what is known about prospective and experienced elementary…
Descriptors: Cognitive Development, Cognitive Structures, Elementary Education, Elementary School Mathematics
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Graeber, Anna O.; Baker, Kay M. – Arithmetic Teacher, 1992
Presents teaching methods to rectify the tendency of students and even teachers to divide the smaller number into the larger in problem situations requiring division, while recognizing the impossibility of the answer in the situation. (MDH)
Descriptors: Beliefs, Cognitive Development, Concept Formation, Division
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Ott, Jack M.; And Others – Arithmetic Teacher, 1991
Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)
Descriptors: Cognitive Development, Cognitive Processes, Concept Formation, Division
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Babbitt, Beatrice; Usnick, Virginia – Arithmetic Teacher, 1993
Proposes using a hypermedia authoring program as a method for helping students make connections between definitions, representations, and applications of mathematical concepts. Provides an example involving fractions and discusses the advantages of using hypermedia. (eight references and four resources) (MDH)
Descriptors: Cognitive Development, Cognitive Structures, Computer Assisted Instruction, Concept Formation
Streefland, Leen – 1991
This book has a two-fold purpose. First, it was intended as a description of the development and testing of a primary school fraction program, presently in practice. This project seeks to develop a realistic alternative to the teaching and learning of fractions. The second purpose was to produce a theory on the teaching and learning of fractions…
Descriptors: Cognitive Development, Concept Formation, Curriculum Development, Elementary Education
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