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March 2003, Volume 34, Issue 2

FEATURES

Improving Education Research: Ideology or Science?
Edward A. Silver
In the United States these days, there is a surprising amount of attention being paid to the improvement of research in education. Calls are heard across the land  for greater rigor in educational research so that scientific evidence and researchbased practices can guide educational improvement. (For more on this, see my editorial in the March 2002 issue [Silver, 2002].) My colleagues in other countries tell me that this rhetoric is also beginning to seep across the borders and oceans surrounding the United States and is finding its way into political and professional  discourse regarding education around the world.

A Modeling Perspective on Students' Mathematical Reasoning About Data
Helen M. Doerr, Lyn D. English
A modeling approach to the teaching and learning of mathematics shifts the focus of the learning activity from finding a solution to a particular problem to creating a system of relationships that is generalizable and reusable. In this article, we discuss the nature of a sequence of tasks that can be used to elicit the development of such systems by  middle school students. We report the results of our research with these tasks at two levels. First, we present a detailed analysis of the mathematical reasoning development of one small group of students across the sequence of tasks. Second, we provide  a macrolevel analysis of the diversity of thinking patterns identified on two of the problem tasks where we incorporate data from multiple groups of students. Student reasoning about the relationships between and among quantities and their application in related situations is discussed. The results suggest that students were able to create generalizable and reusable systems or models for selecting, ranking, and weighting data. Furthermore, the extent of variations in the approaches that students took suggests that there are multiple paths for the development of ideas about ranking data for decision making.

Read how to use this article as part of a Professional Development Experience.

Understanding Learning Systems: Mathematics Education and Complexity Science
Brent Davis, Elaine Simmt
Complexity science may be described as the science of learning systems, where learning is understood in terms of the adaptive behaviors of phenomena that arise in the interactions of multiple agents. Through two examples of complex learning systems, we explore some of the possible contributions of complexity science to discussions of the teaching of mathematics. We focus on two matters in particular: the use of the vocabulary of complexity in the redescription of mathematical communities and the application of principles of complexity to the teaching of mathematics. Through the course of this writing, we attempt to highlight compatible and complementary  discussions that are already represented in the mathematics education literature.

Visions of Problems and Problems of Vision: Enhancing the Messiness of Mathematics in the World
Jeremy A. Kahan, Harold L. Shoen
Problems and problem solving have a long history in mathematics education (Dewey, 1910; National Council of Teachers of Mathematics [NCTM], 1980; Pólya, 1945; Schoenfeld, 1992; Stanic & Kilpatrick, 1988). The Curriculum and Evaluation Standards for School Mathematics asserted, "Problem solving should  be the central focus of the mathematics curriculum" and placed it as Standard 1 (NCTM, 1989, p. 23). The 1990s saw the development of school mathematics  curricula based on various interpretations of these Standards. In most of these curricula, the mathematics emerges from the solution of problems, and there is a  growing body of research evidence supporting the effectiveness of these curricula (Senk & Thompson, 2003). Teaching mathematics through problem solving also continues to be a focus of mathematics educators independent of the curriculum that is used (Schoen & Charles, in press).