Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching

Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching

Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching

Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching

Synopsis

This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age.

Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work:

http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/

This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.

Excerpt

This chapter describes instructional modules that are based on a models and modeling perspective, and that were designed to meet goals that are unusual compared with those driving the development of most commercially produced materials for instruction or assessment. First, the modules were designed to provide rich research sites for investigating the interacting development of students and teachers. Therefore, they are modularized so that components can be easily deleted, extended, modified, or re-sequenced to suit the needs of researchers (or teachers) representing a variety of theoretical perspectives, purposes, and student populations. Second, to make it possible to observe processes that influence the development of students' and teachers' ways of thinking, the modules were designed to be thought revealing (Lesh, Hoover, Hole, Kelly, & Post, 2000) and to be efficient for producing maximum results using minimum investments of time and other resources. Consequently, from the perspective of teachers, they have the unusual characteristic of seeming to be small-but-easy-to-extend rather than being large-and-difficult-to-reduce. Third, they were designed to emphasize important understandings and abilities that are needed for success beyond schools in a technology-based age of information.

Even though many of the big ideas that are especially powerful in everyday situations have long traditions of being treated as foundation-level ideas in elementary mathematics, it will be clear, in transcripts that are given throughout this book, that many others are not. Also, the activities that we'll be describing often give special attention to levels and types of understanding (and ability) that seldom have been emphasized in traditional textbooks, tests, or teaching. Consequently, by emphasizing an unusually broad range of understandings and abilities, a broader range of students typically emerge as being highly capable; and, many of these students are surprisingly young or were formerly labeled . . .

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