Volume 99 (5), May 1999

Table of Contents

Abstracts

Table of Contents

Abstracts

 
Analogies and Reconstruction of Probability Knowledge

Gerald R. Fast
University of Wisconsin Oshkosh


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        The effectiveness of utilizing analogies to effect conceptual change in studentsí alternative probability concepts was investigated. Forty-one senior high school mathematics students were engaged in a knowledge reconstruction process regarding their beliefs about common everyday probability situations, such as sports events or lotteries. The students were given situations similar to those shown in previous research to reveal alternative mathematical conceptions. They were also given analogous researcher-generated anchoring situations that had been pretested and found to elicit mathematically acceptable responses. The cognitive dissonance produced by the conflicting responses motivated students to reconstruct their knowledge. The results of the investigation showed that analogies can be effective in producing a desired conceptual change in high school studentsí probability concepts.

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Meeting the Needs of Diverse Student Populations: Comprehensive Professional Development in Science, Math, and Technology for Teachers of Students With Disabilities

Howard Kimmel and Fadi P. Deek, New Jersey Institute of Technology
Mary L. Farrell, Fairleigh Dickinson University

Mark OíShea, California State University Monterey Bay


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        Professional development for teachers has become a key component for reform in teaching, learning, and curriculum change. This report describes a model of professional development designed to improve the skills and knowledge of teams of special education and regular education teachers in science, mathematics, and technology instruction. The comprehensive model included summer and academic year content and methodology-focused workshops and summer "practicum" experiences. It was designed to link those factors impacting teacher practices and interventions with teachersí beliefs in instruction. The training component for teachers included opportunities for collaborative teaching, upgrading knowledge of math and science subject matter, and identifying, integrating, and practicing alternative approaches for teaching science and math that address the needs of special education students, with a focus on techniques for adapting instruction to specific disabilities. The program led to development of coping skills and persistence in the teaching of science and math for all students. As a result, strong efficacy expectations have been developed through repeated experiences of success with children in a classroom environment. Remaining issues still to be addressed include classroom management, teaching in a heterogeneous classroom, and further improvement of content expertise of teachers.

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Preservice Teachersí Use of Multiple Representations In Solving Arithmetic Mean Problems

Mary K. Gfeller, Margaret L. Niess, & Norman G. Lederman
Oregon State University


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        The development of preservice teachersí views of various mathematical concepts involves building a repertoire of flexible representations of the concepts they teach. In this study, science and mathematics preservice teachers (n = 19) were asked to solve graphical and numerical problems involving the arithmetic mean and to provide two different solutions for each problem. Background information about the preservice teachers was obtained, including subject area specialty, type of statistics courses previously taken, type of science laboratory courses previously taken, and prior experience with real data outside the classroom. In solving the problems, some participants presented two different methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing deviations to solve the problems but not in the use of the computational algorithm.

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