Download e-book for iPad: Humans-with-Media and the Reorganization of Mathematical by Marcelo C. Borba

By Marcelo C. Borba

ISBN-10: 0387242635

ISBN-13: 9780387242637

ISBN-10: 0387242643

ISBN-13: 9780387242644

This e-book bargains a brand new conceptual framework for reflecting at the function of knowledge and conversation expertise in arithmetic schooling. Borba and Villarreal supply examples from examine performed on the point of simple and university-level schooling, built via their study workforce dependent in Brazil, and talk about their findings within the mild of the appropriate literature. Arguing that diverse media reorganize mathematical pondering in several methods, they speak about how pcs, writing and oral discourse remodel schooling at an epistemological in addition to a political point. Modeling and experimentation are noticeable as pedagogical techniques that are in concord with alterations caused by means of the presence of data and verbal exchange expertise in academic settings. Examples of study approximately online arithmetic schooling classes, and net utilized in standard arithmetic classes, are offered and mentioned at a theoretical point. during this publication, mathematical wisdom is visible as constructed via collectives of humans-with-media. The authors suggest that wisdom isn't developed completely via people, yet through collectives of people and applied sciences of intelligence. Theoretical dialogue built within the booklet, including new examples, shed new gentle on discussions relating to visualization, experimentation and a number of representations in arithmetic schooling. Insightful examples from academic perform open up new paths for the reader.

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Extra info for Humans-with-Media and the Reorganization of Mathematical Thinking: Information and Communication Technologies, Modeling, Visualization and Experimentation

Example text

The focus of our attention should thus be directed to what happens when humans-computer systems solve problems. In this sense, when features of the computer are incorporated into the search process of humans, when the ’search’ process of the computer is used in combination with that developed by humans, and the various forms of feedback provided by the computer contribute to the emergence of new problems, one can apply the metaphor of reorganization to describe what happens to thinking. If computers are used to solve problems and/or generate new problems, one can say that reorganization of thinking has occurred, but of course this reorganization does not preclude a pedagogical discussion.

But the obvious question then becomes: What is the alternative? How can we view technology in a way in which it is not so dichotomized? In the previous discussion in this chapter regarding Tikhomirov (1981) and Borba (1993), a slight distinction between computers (a type of technology) and humans could be perceived in the views of both authors. Noss and Hoyles (1996) described the mediating role of the computer in mathematical learning as structuring, and being structured by, the activity of the learners, when a particular type of software is used.

In such a view, mathematical knowledge is independent of the medium, and the job of the educator is to try to use the computer in a way that does not affect mathematics. We believe that this leads to the domestication of this new medium, and efforts to reproduce practices and styles from other media. We claim that a new technology of intelligence results in a new collective that produces new knowledge, which is qualitatively different from the knowledge produced by other collectives. Once writing was introduced, orality was also transformed.

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Humans-with-Media and the Reorganization of Mathematical Thinking: Information and Communication Technologies, Modeling, Visualization and Experimentation by Marcelo C. Borba

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