Roger Shank's arguments against the relevance, or at least against an
exaggerated obsession with usefulness of mathematics, in the school
curriculum can be read at:
http://www.ils.nwu.edu/information/edoutrage2.html
And here is my private reply to Roger's institute group:
Since I am about to visit ILS, I thought I'd send along a few reactions to
Roger's Shank's rage against established educational "wisdom".
I certainly agree that a lot of what gets done in schools is determined by
networks of interdependencies among many factors not usually considered in
curriculum planning -- like class size, book costs, testing paradigms,
cultural ideologies, social class privileges, teacher training systems,
etc., etc. Schooling is after all a technology, and all technologies
survive only as parts of such extensive networks (ask Bruno Latour, or most
historians of science and technology).
I also agree that most of what is in the traditional curriculum is of
dubious practical value in most people's real lives. And almost none of it
(at least beyond about grade 6) has ever been validated by empirical
studies of what kinds of knowledge people really do most often need. That
certainly includes algebra and trigonometry.
But curriculum is not just about reproducing the past or facilitating the
present; it is also about engineering the future. Not that I personally
believe one can engineer it very much beyond fairly short timescales or
over fairly local networks of influence ... but still, our culture really
believes in trying to shape a better future.
So what about mathematics? is there anything in the math curriculum that is
plausibly of widespread potential value for our social-technological
future? Factoring polynomials probably isn't ... but maybe probabilistic
reasoning, or elementary statistical literacy is. More generally, there
would seem to be a number of quantitative reasoning skills that are
necessary to think effectively about any sort of material or social
phenomena that varies quasi-continuously or by degree, and a number of
supporting networks of concepts for doing so systematically. I would
probably nominate some such as: ratio and proportion, functional
dependence, probability, graphical representation of covariation,
correlation, some statistical inference, interpolation and extrapolation,
linear vs. nonlinear qualitative properties of systems ... There is
probably no definitive list, but one could imagine empirical analysis of
good reasoning about material and social phenomena that might produce a
similar list.
A study I read a few years ago (I think by Ed Tufte) noted that data
graphs and other visual representations of quantitative relationships were
vastly more common in Japanese newspapers than in US ones, even those for
the best educated US readers. A cultural preference in part, but also an
issue of social choice: would we like to be a country where more citizens
are good at quantitative reasoning, at following and critiqueing
quantitative arguments? I'd rather hope so, if only as a defense against
all the bad arguments now used to justify interested decisions.
A case can also be made I think that many qualitative categorial forms of
reasoning (e.g. about race, about gender and sexuality, about ethnic
groupings, about social class) are socially dangerous if they are not
embedded in quantitative thinking about degrees of membership in these
groups, about the multidimensionality of such categories, with matters of
degree on every dimension.
Finally, I will make a case on my visit to ILS that we ought to regard the
fundamental function of mathematics as building a semiotic bridge between
visual-spatial-motor forms of meaning-making (pictures, diagrams, graphs,
gestures, action movements) and verbal-categorial-conceptual ones; as well
as between the representation of quasi-continuously variable phenomena
(matters of degree) and more categorial ones (matters of kind). In that
role it seems a rather essential part of the toolkit for doing serious,
data-based thinking about almost anything at all.
But of course not ALL of mathematics, and perhaps not any specific piece of
mathematics for all.
Once again I do agree that the uniformitarianism of the curricular model of
schooling is something of a historical-technological accident, or at least
merely contingent and not logically or socially necessary. In fact I think
we'd all be a lot better off if more students spent more time studying what
they found interesting and relevant, with some efforts to introduce them to
new domains of experience, and a reasonable amount of guidance in finding
the connections and relevancies of new areas to ones they are already
pursuing.
Shank doesn't say so, but I assume we also agree that new information and
communication technologies may make this more individualized view of
education more economically practical. There is already a cultural
foundation for such an ideal. The main obstacle is the sedimented social
structures of schools and their many parasitic institutions (text
publishers, teacher education programs, real estate deals, taxation
systems, testing empires, a tried-and-true formula for legitimating the
privileges of the better off, etc.).
History (and ecology) does show, however, that such apparently highly
stable networks of people and things can sometimes change radically, and
quite quickly, with just a little bit of the right re-wiring of
connections. Just don't try to predict the consequences!
JAY LEMKE.
PS. Maybe a big part of the educational problem in schools is that the real
"inmates" (the students) are NOT running the asylum.
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JAY L. LEMKE
PROFESSOR OF EDUCATION
CITY UNIVERSITY OF NEW YORK
JLLBC who-is-at CUNYVM.CUNY.EDU
<http://academic.brooklyn.cuny.edu/education/jlemke/index.htm>
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