Volume 99 (3), March 1999

Table of Contents

Abstracts

Table of Content

Abstracts

 
The Cereal Box Problem Revisited
Jesse L. M. Wilkins, Virginia Polytechnic Institute and State University


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        The Cereal Box problem is fascinating for students of all levels. Rich in mathematical content, this problem offers students the opportunity to collect data, make conjectures, and derive mathematical models. Using Monte Carlo methods, the Cereal Box problem is investigated in this paper, using both an experimental and theoretical framework. This investigation extends previous considerations of the Cereal Box problem.  Using empirical data, students can discover patterns and relationships that help them understand the origin of the theoretical solution to the problem. Building on experimental findings, a theoretical model is derived, showing that the expected solution of the Cereal Box problem is formed from the sum of successive geometric series.

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One Stateís Self-Study of Initial Certification Programs in Science and Mathematics
Julie A. Luft, University of Arizona
Diane Ebert-May, Michigan State University


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        Creating standards-based teacher education programs for mathematics and science teachers continues to be on the forefront of discussion in US colleges and universities. Yet prior to reforming teacher education programs, self-studies should be conducted to evaluate the status of such programs. This article describes how mathematics and science education specialists in Arizona examined their programs to determine avenues for reform. Both qualitative and quantitative research methods were employed to explore five areas pertaining to initial certification programs in mathematics and science. Mission statements, the composition of initial certification programs, and curriculum, instruction, and assessment practices of faculty were examined. In addition, profiles were created pertaining to faculty, staff, and students who participate in the programs. From this self-study, it became evident that various components of initial certification programs in Arizona may not be consistent with the national reforms in mathematics, science, and teacher education. This paper provides an overview of the self-study and findings and reflects upon the process of self-study.

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The Graphing Calculator: A Survey of Classroom Usage
Eric Milou, Rowan University


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        The purpose of this study was to investigate secondary mathematics teachersí use of the graphing calculator in their classrooms.  The study examined whether algebra teachers are currently using this technology in their classrooms, their perceptions toward the technology, and any changes in the curriculum or instructional practices.  A survey methodology was used in this study.  The findings indicated that the use of the graphing calculator is still controversial to many algebra teachers. Teachers of algebra I were using graphing calculators to a significantly lesser degree than teachers of algebra II.  However, modifications of the algebra curriculum are beginning to appear in classes using graphing calculators.  Finally, a majority of algebra teachers responded that the graphing calculator was a motivational tool.

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Habits of Mind: Integrating the Social and Personal  Characteristics of Doing Science Into the Science Classroom
Mark J. Volkmann and David C. Eichinger
Purdue University


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        Scientific habits of mind are an integral part of contemporary definitions of scientific literacy being presented in national reform documents such as Science For All Americans (American Association for the Advancement of Science, 1989) and the National Science Education Standards (National Research Council, 1996). These scientific habits also serve as an important link between scientific inquiry and science education. This article focuses on three habits associated with personal values and attitudes and one habit associated with the social skills of doing science. These four habits of mind balance the objectivist perspective that misrepresents science as a cold and emotionless abstraction (Pert, 1997) by highlighting a subjective view of scientific activity that is often omitted from school science. The four habits of mind are first illustrated through the story of a modern scientific investigation and then described as the basis of a school laboratory science experience. Implications related to the integration of these four habits of mind into science laboratory reform are discussed.

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Revisiting an Ancient Problem Through Contemporary Discourse
Sergei Abramovich, State University of New York at Potsdam


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        This article presents a computer-mediated discourse on the Pythagorean equation in a university classroom of preservice and in-service teachers. It shows how the use of a spreadsheet as a two-dimensional modeling tool enables students to conjecture the general solution to the Pythagorean equation. A computational approach to the ancient problem improves the well-known off-computer discussion. The environment also provides a kind of a visualization of Fermatís Last Theorem.

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