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Evans, David – Early Child Development and Care, 1983
Discusses three problems preschool teachers should consider when aiming to facilitate children's mathematical activity: (1) How may young children relate to the necessarily abstract basis of mathematics? (2) When is a child's activity mathematical? (3) How may "mathematical" language, concepts, and experiences be appropriately defined?…
Descriptors: Abstract Reasoning, Mathematical Concepts, Mathematics Instruction, Preschool Children
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Book, Ronald V. – American Mathematical Monthly, 1988
The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)
Descriptors: Abstract Reasoning, Algebra, Algorithms, College Mathematics
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Magill, K. D., Jr. – American Mathematical Monthly, 1988
The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)
Descriptors: Abstract Reasoning, Algebra, College Mathematics, Geometry
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Nugent, Wendy – Mathematics in School, 1990
Presents young children's concepts related to probability grouped by definite, possible, and definitely not. Discusses the teaching methods of the probability concepts. (YP)
Descriptors: Abstract Reasoning, Concept Formation, Early Childhood Education, Fundamental Concepts
Giordano, Gerard – Academic Therapy, 1987
Ten remedial mathematics exercises are provided for children who have failed to integrate or apply their math skills. The exercises provide remediation through systematic experimentation, rather than abstract drills, by using number-configuration distinction with blocks, fractioned candy bars, decimal match sticks, graphed pictures, etc. (JDD)
Descriptors: Abstract Reasoning, Concept Formation, Elementary Secondary Education, Experiential Learning
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Cawley, John F.; Parmar, Rene S. – Remedial and Special Education (RASE), 1992
Concepts from cognitive psychology are presented as an alternative framework to arithmetic instruction for students with disabilities. The approach, which emphasizes reasoning, communication, and problem solving, is applied to addition, division, multiplication, subtraction, and word problems. The purpose of arithmetic instruction is asserted to…
Descriptors: Abstract Reasoning, Cognitive Psychology, Computation, Disabilities
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Cramer, Kathleen; Post, Thomas – Arithmetic Teacher, 1993
Defines the mathematical concept of proportionality. Uses graphs of linear relationships to explore and make generalizations about the characteristics of proportional situations to help students critically evaluate problems involving proportions. (MDH)
Descriptors: Abstract Reasoning, Formal Operations, Graphs, Mathematical Applications
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Carroll, William M. – Mathematics Teaching in the Middle School, 1998
Describes several short geometry tasks that go beyond the simple recognition of figures and properties. Presents scoring rubrics and questions that might be useful to middle school teachers developing short open-ended questions that encourage and assess students' thinking. (ASK)
Descriptors: Abstract Reasoning, Evaluation Criteria, Geometric Concepts, Geometry
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Battista, Michael J., Ed.; Clements, Douglas H. – Arithmetic Teacher, 1990
Described is how using LOGO tools for manipulating embodiments of geometric objects helps students construct more abstract and coherent concepts. Discussions are included on developing verbal definitions versus constructing concepts, tasks for integrating turns and angles, group discussions, and maze tasks. (KR)
Descriptors: Abstract Reasoning, Cognitive Processes, Computer Assisted Instruction, Computer Uses in Education