Re: Math and all that

Tibor Benke (benke@SFU.CA)
Tue, 18 Apr 1995 09:57:34 -0700

>Tibor Benke has mentioned the possibility of looking at mathematical
>pedagogy. A good idea, I think. At this point, I am aware of two
>approaches that haven't worked too well as far as I can see, and one
>that has worked, a bit, for me.
>One that didn't work too well is the classic drum it in by doing lots
>of problems. Here ideas get lost in the minutiae of technique and
>unless the problems are directly relevant to something a student is
>interested in, doing them is just a pain, period.
>Another was the "New math." Knowing a bit of set theory is surely not
>a bad thing, but again lack of relevance makes it chore and too easy
>to forget.
>For me the first revelation came when taking a course in formal logic
>and trying to parse arguments phrased in natural language to abstract
>their logical structure. The second came from approaching math
>historically, reading about the lives of mathematicians and why they
>got excited about the problems they worked on.Both led to the
>realization that math is a way of thinking about the world in more
>sophisticated ways than commonsense offers and an art who's results
>are often as surprising and beautiful as great poems or works of

I want to thank John, for finally pulling this thread in the direction I
was hoping it would take. Thank you John Mcreery!

It seems to me, however, that it is not up to us as anthropologists, to
worry too much about either the benefits of the mathematical enterprise, as
such; nor need we worry about which technique of mathematical pedagogy is
most effective - mathematicians and pedagougues are probably the people who
should lead in addressing these issues. (Though, of course, as we use
mathematics in our own work, we raise an interesting example of recursion.)
Rather, we need to form a detailed and dynamic picture on the social
function of the mathematical enterprise, and the social meaning of
mathematics, mathematical thought, the semantic value of the mathematical
and the mathematicised (i.e. neutrality, authoritativeness, right/wrong
orientation), being endowed with more mathematical learning or talent
then someone else, etc. - in short, an anthropology of mathematics on
lines analogous to a sociology of knowledge.

What would such a sub-subdiscipline look like? For all I know, something
like this might already exist. If so, I hope that someone on the list will
bring my attention to it. But right now, I suspect, much data exists
hidden in the fragmented literature of the four fields. Physical
anthropologists may be able to understand the neuro-scientists and
cognitive scientists and what they may tell us about the evolution of
intelligence and how mathematical activity (e.g. matching one to one,
verbal enumeration, etc.) can be both a product and a cause of this
evolution. Archeologists can tell us about the prehistory of mathematical
artifacts and the role of simple mathematics in the development of the
achievements of the neolithic (the role of geometry in agriculture, the
role of arithmetic in pastoralism and trade - we certainly can't imagine
these activities now without mathematics, but some of them must have been
carried out without such some time - or must they?). The linguists, who
possibly have made the most progress in looking at mathematics from their
discipline's perspective, need to be drawn back to anthropology, since, as
I understand these things, most of them have fled to Cognitive Science and
elsewhere. Finally, Socio-Cultural Anthropologists and ethnohistorians, it
seems to me, have the most work ahead of them. For example, both methods
of mathematical pedagogy John gave of things that didn't work, had social
consequences. Anthropologists would not assume that they didn't work any
more, then they would assume that magical practices didn't work. Though a
magical procedure may not achieve the purpose it is said by the 'natives'
to achieve, it may achieve results which might be 'functional'; similarly,
the practice of teaching mathematics a certain way, has social
consequences. Given any particular constellation of methods, definite
(though not neccessarily measurable) results will obtain. How much does
the steretype of the boring accountant or engineer have to do with the
"classic drum it in" school of mathematical pedagogy? Does 'new math' have
a class bias ? I know very little mathematics (never made it past trig )
but I could come up with hundreds of questions along this line.

I know the information is out there, but can it be pulled together? How
about a ROMdisc anthology project on the Anthropology of Mathematics?


>@> Tibor Benke / (^)%(#)
>@> Graduate Student (MA program)
>@> Department of Sociology and Anthropology
>@> Simon Fraser University,
>@> Burnaby, B.C., Canada. V5A 1S6