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Nasca, Donald – Arithmetic Teacher, 1978
Three components of a curriculum organized to facilitate a concept acquisition process are discussed. These are concrete experiences related to a concept, skill development activities and applications. (MP)
Descriptors: Cognitive Development, Concept Formation, Curriculum, Elementary Education

Callahan, Leroy G., Ed. – Arithmetic Teacher, 1987
Metacognition is described and suggestions for teachers about developing and improving metacognitive skills in performing mathematical tasks are given. (MNS)
Descriptors: Cognitive Development, Elementary Education, Elementary School Mathematics, Mathematics Instruction

Heddens, James W. – Arithmetic Teacher, 1986
Discusses how teachers can help students make the transition from using manipulative materials to abstract mathematical symbols. Includes: (1) a definition of the transition state; (2) ways to bridge the gap (by asking questions and by using activities); and (3) a specific example (teaching place value). (JN)
Descriptors: Cognitive Development, Developmental Stages, Elementary Education, Elementary School Mathematics

Young, Jerry L. – Arithmetic Teacher, 1982
Some geometric activities are described that teachers can use to give their students experiences that will influence their spatial abilities. It is noted that the goal is to improve spatial abilities, not to increase knowledge, so individual pupil responses should not be used to judge student achievement. (MP)
Descriptors: Cognitive Development, Elementary Secondary Education, Geometric Concepts, Geometry

Harrison, Marilyn; Harrison, Bruce – Arithmetic Teacher, 1986
Presents activities that have been used successfully in leading students from concrete experiences through pictorial and symbolic representations of important numeration concepts and patterns, including place value, multiples, and rounding. Each activity includes concept or skill fostered, list of materials needed, recommended grade level, and…
Descriptors: Cognitive Development, Concept Formation, Elementary Education, Elementary School Mathematics

Taback, Stanley F. – Arithmetic Teacher, 1975
Three examples of teacher and student exchanges in mathematics classes are presented which typify the qualitative difference between children's thinking and adult's thinking. The cases explored also illustrate differences caused by cultural factors. (JP)
Descriptors: Cognitive Development, Cultural Influences, Elementary Education, Elementary School Mathematics

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

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

Liedtke, Werner – Arithmetic Teacher, 1988
Argues that "student talk" is an important developmental activity in mathematics. Gives suggestions that will facilitate student talk. (PK)
Descriptors: Classroom Communication, Cognitive Development, Concept Formation, Discussion (Teaching Technique)

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)

Carey, Deborah A.; Campbell, Patricia F., Ed. – Arithmetic Teacher, 1992
Relates research findings on the way primary-grade students communicate mathematical ideas through the use of symbols to a framework for students to investigate the part-whole relationship of quantity. Discusses children's problem-solving abilities, linking word problems and symbols, the importance of context for understanding symbols, and the…
Descriptors: Addition, Cognitive Development, Cognitive Processes, Cognitive Style

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

Ford, Margaret I. – Arithmetic Teacher, 1990
Described is a strategy where students write stories to help in the process of solving problems. The strategy is a five-step process which includes prewriting, writing, conference, revising and editing, and publication. (KR)
Descriptors: Cognitive Development, Elementary Education, Elementary School Mathematics, Learning Strategies

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

Kieran, Carolyn – Arithmetic Teacher, 1991
Instructional strategies are presented that illustrate ways of developing students' understanding of nonnumerical notation that are compatible with a constructivist stance. The concepts of using letters to represent a range of values and those used to represent unknowns are discussed. (KR)
Descriptors: Algebra, Cognitive Development, Concept Formation, Elementary Education
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