Volume 97 (3), March 1997

Table of Contents

Abstracts

Table of Contents

Abstracts

 
• Measurement of Length: The Need for a Better Approach to Teaching

Constance Kamii, The University of Alabama at Birmingham
Faye B. Clark, Samford University


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        Three hundred and eighty-three children in grades 1-5 were individually interviewed to find out at when they construct unit iteration out of transitive reasoning as described by Piaget, Inhelder, and Szeminska (1960). The results indicated that most children (72%) construct unit iteration out of transitive reasoning by fourth grade. The article explains why traditional instruction produces the poor results revealed by the National Assessment of Educational Progress. It also suggests a better approach to the teaching of measurement that presents problems and encourages children to modify their ways of thinking.

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• Successful Students' Perceptions of Secondary School Science

John Eichinger, California State University, Los Angeles


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        The attitudinal perceptions of successful college science students regarding their junior high and high school science experiences were compared with those of successful nonscience students. Particular attention was paid to recollections of teacher personality attributes and instructional methodology. Results indicate that science students were especially motivated by knowledgeable, enthusiastic, communicative, committed, friendly, competent, and creative science teachers, whereas the nonscience group preferred patient, knowledgeabel, congenial, friendly, supportive, and enthusiastic instructors. Both groups agreed that, although traditional methods (textbooks, lectures, quizzes/tests) dominated their science experiences, their preferred instructional strategies included more dynamic methods, including laboratory activities, teacher demonstrations, and discussions. Both groups also agreed that high school science courses provided a closer match than did junior high/middle school courses in providing their preferred teacher attributes and instructional methods. Results supported the observation that, even for these academically gifted students, interest in science is relatively depressed during the junior high/middle school years. It was concluded that, although endogenous variables act in concert, the quality of the student-teacher interaction exerts the greatest influence on student attitudes, particularly if those students are not already "science-friendly." Instructional implications are discussed.

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• Fibonacci Numbers and an Area Puzzle: Connecting Geometry and Algebra in the Mathematics Classroom

Mary M. Sullivan, Curry College
Regina M. Panasuk, University of Massachusetts-Lowell


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        A mathematical puzzle that asks about "missing" area leads to an exploration of the Fibonacci sequence as well as genuine inquiry in plane geometry connected to algebra. This article discusses the inquiry, the concepts, the solution, and an extension that deepens all students' understanding of connections between algebra and geometry.

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• Student-Invented Numeration Systems: Pattern-Analysis and Mathematical Understanding

Elizabeth S. Senger, Auburn University


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        Thirteen fifth graders were given an assignment to invent their own numeration systems, following a unit on bases and a look at early events in the history of numbers. The task presented options that required the students to make decisions (such as whether to use a base, which base to use, design of symbols, etc.), and build a rationale for the elements of their system. Analyses of patterns embedded in their invented systems provided an assessment of student understanding of numeration. The progression of more and less complex thinking related to the student's choice of a base other than 10, consistency of logic throughout the system in words and symbols, rationale for change, and perception of real life examples that would change if the system was adopted. The invention task is presented as another way to make connections.

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• Lakatos' Proofs and Refutations Comes Alive in an Elementary Classroom

Sandra L. Atkins, University of Central Florida


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        This paper presents an alternative pedagogy implicit in Imre Lakatos' Proofs and Refutations: the Logic of Mathematical Discovery. Through the voices of his characters, Lakatos reveals that learning mathematics is a discourse laden activity. In this approach it is acceptable, if not preferable, to refute a conjecture. Examples of the use of a Lakatosian approach in an elementary classroom are given. In this classroom setting students are able to propose more mature solutions, through posing and refuting conjectures.

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• The Teaching of General Solution Methods to Pattern Finding Problems Through Focusing on an Evaluation and Improvement Process

Junichi Ishida, Yokohama National University


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        This study examined the effects of a teaching strategy in which fifth-grade students evaluated the strengths or weaknesses of solution methods to pattern finding problems. The experimental and control group each consisted of theiry four elementary students in Japan who took the pre, post and retention tests. The experimental group showed a significantly better performance on the retention test although no significant differences were observed on the pre and post tests. This result suggests that the evaluation and improvement activity was important as a teaching strategy.

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