Does mathematical learning occur in going from concrete to abstract or in going from abstract to concrete? [An article from: Journal of Mathematical Behavior]

This digital document is a journal article from Journal of Mathematical Behavior, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The notions of abstract and concrete are central to the conceptualization of mathematical knowing and learning. It is generally accepted that development goes from concrete toward the abstract; but dialectical theorists maintain just the opposite: development consists of an ascension from the abstract to the concrete. In this article, we reformulate the relationship of abstract and concrete consistent with a dialectical materialist approach to conscious human activity, as it was developed in the line of cultural-historical psychology. Our reformulation of development in and through interpretation shows that rather than being a movement from concrete to abstract or from abstract to concrete, development occurs in a double ascension that simultaneously moves in both direction: it is a passage of one in the other. In the proposed approach, the theoretical contradictions of earlier approaches to the issue of abstract have been eliminated.