336 THE PROB LEMS OF EDUCATION ARE NOT GE NE TICDewey was also less interested in what a child learned, the offi cial school
outcomes, than that the child learned how to learn.^30 Th is would seem of
increasing importance in preparation for a changing but demo cratic
society.
Aft er all, human learning evolved for knowledge abstraction in so-
cially meaningful contexts. Concepts are learned because they are in-
trinsic to goals shared globally in a group, as well as between novice and
expert, teacher and learner. Countless complex social rules and customs
are acquired in such a supportive framework. It is the kind of learning-
for- cooperation that our uniquely huge human brains evolved for. Par-
ents do not send their children to school to learn how to speak.
When people, and children, really want to learn something for a so-
cially relevant activity, they do so, with their “good enough” systems, very
quickly and easily. Th e widely used example is that of human language,
consisting of highly abstract grammar and other rules of use that the vast
majority of infants have acquired before starting school. Indeed, adult
experts in a domain, including practicing mathematicians, scientists, and
engineers, will oft en say how they found the subjects diffi cult in school,
but learning later fl ourished in real contexts.
Taking school math as an example, David Carraher and Analucia
Schliemann have pointed out (as I also noted above) that the emphasis in
school math is on the computational rules and seldom on the meaning of
the pro cess. In contrast, informal math (as in young street traders) pre-
serves meaning, and is used and expressed in a diversity of ways for dif-
fer ent prob lems. Th e math knowledge may thus be quite diff er ent across
the two situations and thus transfer to novel prob lems with diff er ent ease.
Practical math was the form in which it was passed across generations
long before formal schooling. In a modern world, we need both sides of
the coin, the practical and the abstract. But in the typical curriculum,
it has become too one sided. Schooled individuals are coached in rules,
but the search for rules can be a source of improved per for mance when
meaning plays a more impor tant role, Carraher and Schliemann say.
A teaching approach that combines both aspects would obviously ap-
proximate, rather more closely, math knowledge as it has evolved among
mathematicians and is used in science and engineering and other prac-
tical goals.^31
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