Geography Reference
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To say that “'mathematics' is the product of social work and symbolic fashioning”
(Lave 1988:126) means that it stems from human constructions and creates new
concepts (Piatelli-Palmarini 1980 as cited in Crump 1992:28). It also means that
there is more than one universal grammar of number (Chomsky 1980). In order
to assert what these grammars, understandings, and concepts are, our gaze is here
directed to the discrepancies between experience and incorrigible beliefs which can
render intelligible what happens when 1 + 1
2, the so-called “mistakes” (Pollner
1974 as cited in Lave 1988:126). In other words, looking at discrepancies and
discontinuities found within arithmetical practices and in situations that require
mathematical reasoning would allow us to understand why central Brazilian peoples
and other ethnic minorities are challenged by mathematics. The recent “Numbers
Crunch” series ( New York Times 2013) shows that entrenched stereotypes about who
does well in science and mathematics also work against minorities in classrooms.
Too many teachers give up easily on ethnically diverse students, girls in particular,
simply because they are not expected to do as well as white students.
The large disparity found between arithmetic test performance and arithmetic
procedures carried out in daily lives (Carraher et al. 1991, Cole et al. 1971,
D'Ambrosio 1990, King 1967) points to the “conception of problem-solving activity
from a value-free, context-free technology of means, to a value-laden, conflict-
driven, situationally-specific direct form of experience” (Lave 1988:139). The use
of problem solving as a key concept in cognitive theory, that is, as a measure of
“intelligence,” has serious implications. 22
The authors of the polemic topic Bell Curve , for instance, see the coming century
dominated by a “Cognitive Elite” rather than by lower IQ “cabinetmakers or
ditchdiggers” (Herrnstein & Murray 1994:25,54). Professions requiring mathematics
skills (engineers, accountants, computer science) are “high-IQ professions,”
positioned “at the top of the American labor market.” Furthermore, such “cognitive
partitioning” is genetically determined: “high cognitive ability means, more than
ever before, that the chances of success in life are good and getting better all the
time. Putting it all together, success and failure in the American economy, and all that
goes with it, are increasingly a matter of the genes that people inherit” (Herrnstein
& Murray 1994:91). The “end result,” according to the authors, is “prosperity
[high incomes] for those lucky enough to be intelligent” (Herrnstein & Murray
1994:100). The “unlucky,” on the other hand, are “criminal offenders,” “illegitimate
childbearers,” “poverty-stricken individuals,” and the like.
The gift is the continuing theme of both the Bell Curve and The Gift , works that
bear on social structure and public policy. What a gift means in each work, however,
is vastly different. To the authors of the first, it is a high IQ:
To be intellectually gifted is indeed a gift. Nobody “deserves” it. The monetary
and social rewards that accrue to being intellectually gifted are growing all
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