By Erna Yackel, Koeno Gravemeijer, Anna Sfard, Paul Cobb
This ebook offers rules built by way of Paul Cobb and his colleagues that experience considerably prompted the sphere of arithmetic schooling during the last 3 a long time. during this quantity, they're introduced jointly for readers to offer a transparent view of the way the sphere 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 bunch of faculty academics, and to a faculty district with all its academics, academics' lecturers and principals. It used to be his desire to make a true distinction and his continually revised knowing of what it takes to take action that dictated this slow broadening of the unit of study. This improvement is gifted during this ebook with assistance from chronologically geared up formerly released papers, each one of which represents a special degree during this highbrow trip and is preceded via a brand new statement that sheds extra gentle at the approaches of reconceptualization and therefore is helping the reader to appreciate the explanations, mechanisms, and results of researchers’ consistent pursuit of recent insights. This booklet therefore demonstrates how examine develops and evolves whilst conception and perform are taken as together informing elements of the researcher’s paintings. during this feel, the quantity is proper to audiences essentially drawn to useful features of arithmetic schooling in addition to to these whose basic pursuits lie in theoretical developments.
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Extra info for A Journey in Mathematics Education Research: Insights from the Work of Paul Cobb
1929/1958). Experience and nature. New York: Dober. Fish, S. E. (1980). Is there a text in this class? Cambridge, MA: Harvard University Press. Kuhn, T. S. (1962). ). Chicago: University of Chicago Press. Latour, B. (1987). Science in action. Cambridge: Harvard University Press. Peirce, C. S. (1958). The fixation of belief. In P. P. ), Values in a universe of choice: Selected writings of Charles S. Peirce. Stanford, CA: Stanford University Press. 2 Introduction 17 Putnam, H. (1987). The many faces of realism.
Model Building in a Teaching Experiment We contend that children’s mathematical knowledge can be modeled in terms of coordinated schemes of actions and operations (von Glasersfeld, 1980). Our goal is to specify these schemes and to intervene in an attempt to help the children as they build more sophisticated and powerful schemes. We offer a brief glimpse of the steps that Jason, a six-year-old child in 1980, took when constructing his counting scheme. We also mention some of our concomitant intentions when teaching Jason.
P. Steffe Even though the developmental model of counting types had an experiential basis, it did not indicate how we might help children make progress. A new teaching experiment was called for to fill out and, if necessary, refine the skeleton of some possible courses of development specified by the developmental model. When we formulated the model, we were primarily concerned with the form and structure of the counting scheme at various points in its development. The teaching experiment allowed us to conduct an analysis of the steps the children took when making progress in the construction of more sophisticated unit items.
A Journey in Mathematics Education Research: Insights from the Work of Paul Cobb by Erna Yackel, Koeno Gravemeijer, Anna Sfard, Paul Cobb