Learning In and Out of School

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Consider the arithmetic knowledge of M, a 12-year-old coconut vendor on the streets of Recife in northern Brazil. We visit him at his stand one day and ask him how much it will cost to buy 10 coconuts that cost 35 cents each. Let's listen in as he computes his answer:

CUSTOMER: How much is one coconut?

M: Thirty-five.

CUSTOMER: I'd like ten. How much is that?

M: [Pause] Three will be one hundred and five; with three more, that will be two hundred and ten. [Pause] I need four more. That is ... [Pause] three hundred and fifteen...I think it is three hundred and fifty

As you can see, M correctly computes that 10 times 35 is 350. However, he doesn't use the procedure taught in Brazilian schools of simply placing a zero to the right of any number that is being multiplied by 10. Instead, he converts multiplication into repeated addition by threes 105 + 105 + 105 + 35. This is an example of an invented strategy used on an informal test of arithmetic.

M has had some schooling and currently is in the third grade. Suppose we visit him in school one day, give him a pencil and paper, and dictate some arithmetic problems and words problems to him. This is a formal test of arithmetic. For example, for the problem 35 X 4 = ________, M writes the answer "200." He explains his answer as follows:

Four times five is twenty, carry the two; two plus three is five, times four is twenty

As you can see, M is trying to use the school-taught procedure but because it is meaningless to him, he tends to makes some errors in applying it

This example comes from a study by Nunes, Schliemann, and Carraher (1993) in which they compare the performance of five children—all street vendors between ages 9 and 15—on formal and informal tests of arithmetic.The street vendors were nearly errorless in computing answers to arithmetic problems in the street but performed much more poorly when equivalent problems were presented in school-like form. In short, children who are "capable of solving a computational problem in the natural situation" often "fail to solve the same problem when it is taken out of context" (Nunes et al., 1993, p. 23).

What can we conclude from studies of Brazilian street vendors' These results demonstrate that "daily problem solving may be accomplished by routines different from those taught in schools" (Nunes et al., 1993, p. 26). In spite of the fact that the children in this study had received formal instruction in arithmetic computational procedures, they invented their own procedures to solve computational problems in the context of their roles as street vendors. Although they had difficulty in correctly applying school-taught procedures in a formal school-like context, they were highly successful in applying their own invented procedures in an informal everyday context These findings "raise doubts about the pedagogical practice of teaching children how to solve mathematical operations simply with numbers" (p. 25) and point to the role of cultural context in learning. In short, there is some support for students' claims that they do not use school-taught math outside of school.