Volume 99 (1), January 1999

Table of Contents

Abstracts

Table of Contents

Abstracts

 
• Teaching Length Measurement: Research Challenges

Douglas H. Clements, State University of New York at Buffalo


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        Many publications and curriculum materials promote a specific instructional sequence for introducing length measure: gross comparisons of length, measurement with nonstandard units such as paper clips, measurement with manipulative standard units, and finally measurement with standard instruments such as rulers. Several recent studies, however, imply that aspects of this traditional approach may not match childrenís developmental progression. This article describes several studies that challenge conventional wisdom regarding the teaching and learning of nonstandard and standard units, rulers, and measurement sense and draws educational implications from their results.

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• The Development and Validation of the Measure of Acceptance of the Theory of Evolution Instrument

Michael L. Rutledge, Middle Tennessee State University
Melissa A. Warden, Ball State University


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        A biology teacherís acceptance or rejection of evolutionary theory as a scientifically valid explanation is potentially important to the role that evolution takes in the high school biology curriculum. Due to the nature of available instrumentation, our understanding of teacher acceptance of this complex over-reaching biological theory may be incomplete or confounded. This paper describes the development and validation of the Measure of Acceptance of the Theory of Evolution (MATE)óa 20-item Likert-scaled instrument that assesses teachersí overall acceptance of evolutionary theory. Chronbach alpha reliability of the MATE is also reported.

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• Using Concept Maps and Interpretive Essays for Assessment in Mathematics

Linda A. Bolte, Eastern Washington University


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        This study explored the use of student-constructed concept maps in conjunction with written interpretive essays as an additional method of assessment in three undergraduate mathematics courses. The primary objectives of this study were to evaluate the benefits of using concept maps and written essays to assess the "connectedness" of studentsí knowledge; to measure the correlation between studentsí scores on the concept maps and written essays, course exams, and final grade; and to document studentsí perception of the effect of this approach on their mathematical knowledge. Results indicated that concept maps, when combined with written essays, are viable tools for assessing studentsí organization of mathematical knowledge. In addition, students perceive this approach as enhancing their mathematical knowledge.

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• Mathematical Dimensions of Studentsí Use of Proportional Reasoning In High School Physics

Ayo Harriet Akatugba and John Wallace
Curtin University of Technology


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        This study examines the mathematical processes used by students when solving physics tasks requiring proportional reasoning. The study investigates studentsí understanding and explanations of their mathematical processes. A qualitative and interpretive case study was conducted with 6 students from a coeducational urban high school for 5 months. Students were engaged with some high school physics tasks requiring proportional reasoning, during which a hermeneutic dialectic design was used to investigate their processes, understandings, and difficulties. Research techniques such as interviews, dialectical discourses, journal dialogue, and video and audio recordings were employed to generate, analyze, and interpret data. Results of the study indicate that the students employed mathematical proportional reasoning patterns and algorithms which they could not explain. Students also had difficulties translating physics tasks into mathematical statements, symbols, and relations. Students could not perform mathematical operations that were not directly obvious from the physics tasks, and some had difficulty with division. Students did not have adequate understanding of the mathematical processes involved in proportional reasoning.

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• The Task-Technique Matrix: An Alternative System for Classifying Research in Mathematics Education

Eileen F. Donoghue, Columbia University


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        This paper introduces a schema for classifying research in mathematics education that deepens and extends the Romberg/Bourne model. It employs dual hierarchical systems, one relating to the research task and the other to the research technique. The six task categoriesódescriptive, interpretive, prescriptive, analytic, synthetic, and theoreticóare defined with respect to breadth, depth, and scope of a study. The six technique categoriesóreflective, referential, evidential, clinical, empirical, and experimentalóare defined in terms of utilization of resources and design intentions of the investigator. The pairing of task categories with technique categories permits the creation of a classification matrix for research in mathematics education. By examining the location of studies within this task-technique matrix, both producers and consumers of research in mathematics education can discern historical trends influencing current and future investigations.

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