Download e-book for iPad: A Journey in Mathematics Education Research: Insights from by Erna Yackel, Koeno Gravemeijer, Anna Sfard, Paul Cobb

By Erna Yackel, Koeno Gravemeijer, Anna Sfard, Paul Cobb

ISBN-10: 9048197287

ISBN-13: 9789048197286

ISBN-10: 9048197295

ISBN-13: 9789048197293

This ebook offers principles built via Paul Cobb and his colleagues that experience considerably encouraged the sphere of arithmetic schooling over the last 3 many years. during this quantity, they're introduced jointly for readers to provide a transparent view of ways the sector has replaced in the course of that point. in the course of his profession Cobb moved from taking a look at a unmarried kid's mathematical reasoning, to a category studying a selected mathematical subject, to a gaggle of college lecturers, and to a faculty district with all its academics, lecturers' academics and principals. It used to be his desire to make a true distinction and his continually revised figuring out of what it takes to take action that dictated this slow broadening of the unit of research. This improvement is gifted during this e-book with assistance from chronologically prepared formerly released papers, each one of which represents a unique degree during this highbrow trip and is preceded through a brand new remark that sheds extra gentle at the tactics of reconceptualization and hence is helping the reader to appreciate the explanations, mechanisms, and results of researchers’ consistent pursuit of latest insights. This booklet therefore demonstrates how study develops and evolves while concept and perform are taken as jointly informing elements of the researcher’s paintings. during this feel, the quantity is suitable to audiences essentially attracted to sensible features of arithmetic schooling in addition to to these whose fundamental pursuits lie in theoretical developments.

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Additional resources for A Journey in Mathematics Education Research: Insights from the Work of Paul Cobb

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For their part, researchers conducting a design experiment frame the development of instructional designs for supporting students’ mathematical learning as an explicit goal. There are a number of additional points of contact between the two methodologies. For example, we clarify in the reprinted chapter that our intent when conducting 2 Introduction 13 a constructivist teaching experiment was to test and revise conjectures about students’ mathematical reasoning. This conjecture-testing process foreshadowed the tightly integrated cycles of design and analysis that characterize design research.

Given our focus on children’s constructive activity, it is clear that constructivist teaching experiments are microschemes. Constructivist and Nonconstructivist Microschemes Kantowski’s outstanding investigation exemplifies a characteristic shared by nonconstructivist teaching experiments. The processes studied are determined a priori to be the ones of interest. Alternative processes are of secondary importance. This characteristic reflects beliefs about how learning and teaching are related. Menchinskaya (1969b) states the Soviet position succinctly when she says that “neither scientific nor everyday concepts spring forth spontaneously; both are formed under the influence of adult teaching,” (p.

Counting was an expression of numerical structure. For example, in an interview in November 1981, he counted 16 units beyond 14 to find the sum of 14 and 16 by sequentially putting up fingers in synchrony with uttering “16-17-. -31” 3 The Constructivist Researcher as Teacher and Model Builder 27 (he stopped at 31 because of an executive error). He intentionally kept track of his utterances. Moreover, he counted backwards “16-15-14---13” to find how many marbles were left in a tube containing 16 after 3 had been removed, which had been completely beyond him in April.

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A Journey in Mathematics Education Research: Insights from the Work of Paul Cobb by Erna Yackel, Koeno Gravemeijer, Anna Sfard, Paul Cobb

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