BOX 3.8 Everyday and Formal Math

The importance of building on previous experiences is relevant for adults as well as children. A mathematics instructor describes his realization of his mother’s knowledge (Fasheh, 1990:21–22):

Math was necessary for my mother in a much more sense than it was for me. Unable to read or write, my mother routinely took rectangles of fabric and, with few measurements and no patterns, cut them and turned them into perfectly fitted clothing for people…I realized that the mathematics she was using was beyond my comprehension. Moreover, although mathematics was a subject matter that I studied and taught, for her it was basic to the operation of her understanding. What she was doing was math in the sense that it embodied order, pattern, relations, and measurement. It was math because she was breaking a whole into smaller parts and constructing a new whole out of most of the pieces, a new whole that had its own style, shape, size, and that had to fit a specific person. Mistakes in her math entailed practical consequences, unlike mistakes in my math.

Imagine Fasheh’s mother enrolling in a course on formal mathematics. The structure of many courses would fail to provide the kinds of support that could help her make contact with her rich set of informal knowledge. Would the mother’s learning of formal mathematics be enhanced if it were connected to this knowledge? The literature on learning and transfer suggests that this is an important question to pursue.

Building on Existing Knowledge

Children’s early mathematics knowledge illustrates the benefits of helping students draw on relevant knowledge that can serve as a source of transfer. By the time children begin school, most have built a considerable knowledge store relevant to arithmetic. They have experiences of adding and subtracting numbers of items in their everyday play, although they lack the symbolic representations of addition and subtraction that are taught in school. If children’s knowledge is tapped and built on as teachers attempt to teach them the formal operations of addition and subtraction, it is likely that children will acquire a more coherent and thorough understanding of these processes than if they taught them as isolated abstractions. Without specific guidance from teachers, students may fail to connect everyday knowledge to subjects taught in school.

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