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Gagnon, Joseph Calvin; Maccini, Paula – TEACHING Exceptional Children, 2001
This article presents specific instructional approaches and examples to develop the algebraic reasoning skills of middle and secondary students with mild disabilities. Discussion of the National Council of Teachers of Mathematics standards identifies general principles, content standards, and process standards. Discussion of effective instruction…
Descriptors: Abstract Reasoning, Academic Standards, Algebra, Educational Principles

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

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

Shaw, Jean M. – Arithmetic Teacher, 1993
Preservice elementary teachers worked cooperatively to explore the relationship between the measure of the central angle and the number of sides of regular polygons using the reflection of a line in a hinged mirror. The experience involved conjecture and experimentation, communication, and building connections between science, geometry, and…
Descriptors: Abstract Reasoning, Discovery Learning, Discovery Processes, Elementary Education

Rezba, Richard J.; And Others – Science Scope, 1992
Presents three typical lab activities involving the breathing rate of fish, the behavior of electromagnets, and tests for water hardness to demonstrate how labs can be modified to teach process skills. Discusses how basic concepts about experimentation are developed and ways of generating and improving science experiments. Includes a laboratory…
Descriptors: Abstract Reasoning, Acids, Biological Sciences, Chemistry
Peterson, Susan K.; And Others – 1987
This study compared the acquisition of an initial place value skill when presented in a concrete, semiconcrete, abstract teaching sequence to acquisition of the same skill when presented at the abstract level only. The 24 subjects were elementary and middle school students (ages 8-13) with learning disabilities who were randomly assigned to…
Descriptors: Abstract Reasoning, Arithmetic, Concept Formation, Educational Principles