By Richard A. Lesh, Helen M. Doerr
This ebook has basic objectives. at the point of concept improvement, the booklet clarifies the character of an rising "models and modeling point of view" approximately educating, studying, and challenge fixing in arithmetic and technological know-how schooling. at the point of emphasizing useful difficulties, it clarifies the character of a few of crucial elementary-but-powerful mathematical or clinical understandings and skills that american citizens tend to want as foundations for fulfillment within the current and destiny technology-based info age. past Constructivism: versions and Modeling views on arithmetic challenge fixing, studying, and educating good points an cutting edge site housing on-line appendices for every bankruptcy, designed to complement the print chapters with electronic assets that come with instance difficulties, appropriate learn instruments and videos, in addition to transcripts and different samples of scholars' paintings: http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/ this can be a vital quantity for graduate-level classes in arithmetic and technological know-how schooling, cognition and studying, and significant and inventive pondering, in addition to a worthwhile source for researchers and practitioners in those components.
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Extra info for Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching
Lesh et. al, 2000; Lesh, Hoover, & Kelly, 1993). In general, they are similar to the case studies that are used for both instruction and assessment in future-oriented graduate programs and professional schools—in fields ranging from aeronautical engineering, to business management, to agricultural sciences—at universities such as Purdue, Syracuse, Minnesota, or Wisconsin. In these graduate programs and professional schools, many of the most important goals of instruction involve helping future leaders develop powerful models and conceptual tools for making (and making sense of) complex systems.
In elementary science, it is clear that, independently from the influence of schools, children often develop models (perhaps in the form of experience-based metaphors that may be expressed using natural language and child-generated diagrams and notations) for making sense of everyday experiences involving phenomena such as gravity, electricity, light, magnetism, or buoyancy. Furthermore, it is also obvious that, to help children develop beyond primitive ways of thinking about such phenomena, it is seldom enough to introduce new facts and skills.
Nevertheless, it is somewhat difficult to illustrate how children's conceptual systems (or models) tend to be less like rigid and stable worlds than they are like loosely related and shifting collections of tectonic plates. These plates exist as relatively fuzzy, undifferentiated, and disintegrated fragments that yield piecemeal ways of thinking, which are often remarkably barren, distorted, and inconsistent from one moment to the next. 1. FOUNDATIONS OF MODELS AND MODELING PERSPECTIVE 19 MODELING OFTEN INVOLVES LOCAL CONCEPTUAL DEVELOPMENT Following the Big Foot Problem in Appendix A, two more model-eliciting activities also are given that involve proportional reasoning (A/B = C/D); and, for each of these model-eliciting activities, transcripts are given of videotaped problem-solving sessions that show typical solution processes used by average ability middle school students.
Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching by Richard A. Lesh, Helen M. Doerr