Volume 105 (5), May 2005

Table of Contents

Abstract

Students’ Retention of Mathematical Knowledge and Skills in Differential Equations "Students’ Retention of Mathematical Knowledge and Skills in Differential Equations"

Oh Nam Kwon, Seoul National University 

Chris Rasmussen, San Diego State

Karen Allen, Michigan State University

This study investigates students’ retention of mathematical knowledge and skills in two differential equations classes. Posttests and delayed posttests after 1 year were administered to students in inquiry-oriented and traditional classes. The results show that students in the inquiry-oriented class retained conceptual knowledge, as seen by their performance on modeling problems, and retained equal proficiency in procedural problems, when compared with students in the traditionally taught classes. The results of this study add additional support to the claim that teaching for conceptual understanding can lead to longer retention of mathematical knowledge.

Exploring Mathematics in Imaginative Places: Rethinking What Counts as Meaningful Contexts for Learning Mathematics "Exploring Mathematics in Imaginative Places\: Rethinking What Counts as Meaningful Contexts for Learning Mathematics" 

Cynthia Nicol, University of British Columbia

Sandra Crespo, Michigan State University

This paper explores what happens when students engage with mathematical tasks that make no attempt to be connected with students’ everyday life experiences. The investigation draws on the work of educators who call for a broader view of what might count as real and relevant contexts for studying mathematics. It investigates students’ experiences with two imaginative tasks and reports on the students’ intellectual and emotional engagement. This engagement is examined and described in terms of the character and quality of the class and group discussions generated. Findings suggest that students can indeed engage productively with mathematics when it is explored in imaginative settings and that such contexts can help students support and sustain their engagement with the mathematics in the task.

The Winds Are Variable: Student Intuitions About Variation "The Winds Are Variable\: Student Intuitions About Variation"

Jane M. Watson and Ben A. Kelly  

University of Tasmania

This study uses the context of the weather to explore the development of students’ intuitive ideas of variation from pre-Grade 1 to Grade 9. Three aspects of understanding these intuitions associated with variation are explored in individual videotaped interviews with 73 students: explanations, suggestions of data, and graphing. The development of these three aspects across grades is explored, as well as the associations among them. Fifty-eight of the students also answered a general question on the definitions of “variation” and “variable,” and these responses are discussed and compared with responses to the weather task. The interview protocol may prove useful for teachers, particularly with younger children, to appreciate students’ developing understanding of variation and provide starting points for classroom work of a more specific nature, either with respect to weather or other contextual topics.

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