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.
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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
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).