Date of Completion

12-1992

Document Type

Open Access Capstone

Degree Name

Master of Arts (MA)

First Advisor

Patricia S. Davidson

Second Advisor

John R. Murray

Third Advisor

Judy A. Clark

Abstract

Recent critiques of mathematics education have resulted in proposals to restructure learning and teaching for mathematical power. The new vision pictures the classroom as a community of learners where mathematics come alive as a useful tool in our technological society. However, many high school mathematics teachers are struggling to understand and implement the fundamental instructional change inherent in the vision. Written from the perspective of a high school teacher for experienced high school mathematics teachers, this thesis attempts to bridge vision and practice. To clarify the vision, current literature on reform in mathematics education is synthesized into a framework of eight instructional targets. Four of the targets focus on student behavior indicative of mathematical power: deep understanding of concepts and schemas, mathematical thinking, communication about mathematics and a positive disposition toward mathematics. The other four targets focus on the instructional setting: student-centered tasks, a variety of work formats, mathematical tools and assessment alternatives. Suggestions for each target help teachers generate ideas for implementation. The framework is based on seven learning principles synthesized from current research: 1) knowledge is constructed: 2) all students can grapple with complex ideas; 3) conceptual learning is effective; 4) prior knowledge influences learning; 5) learning is a social act; 6) change in cognitive structure is a goal of teaching; and 7) students must be actively engaged to learn. To implement the vision, the recommended strategy for experienced teachers is to expand their repertoire of instructional methods by focusing on teaching thinking. Guidelines for a model of thinking, levels of curriculum planning and relevant issues in cognitive education are incorporated into a lesson plan model. As tactical examples of the implementation strategy, three techniques designed to develop ;the thinking processes of classifying, pattern finding and concept formation are modeled using Algebra I content. The presentation of the techniques is structured to emphasize general instructional decisions made by the teacher in order to enhance transfer to particular classrooms. Two underlying convictions are: experienced teachers attempting reform must focus on the process of instruction; and successful reform depends on teacher reflection leading to ownership of the vision.

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