
Re: Getting students to take responsibility
Posted:
Oct 10, 1995 5:01 PM


roitman@oberon.math.ukans.edu writes
>You've got to be kidding. A lot of numeric measures seem to be all wind.
>Anyway, mathematics is a lot more than numeric measures. For example the >notion of a partial order would be very helpful (and humbling) in trying to >compare things, and the notion of nontransitivity would be even more >useful in certain situations.
As it happens, some of my research relates to partial orders and generalized measurement (including measurement structures with intransitivities). I'm most familiar with applications in utility theory and risk assessment than statistical analysis, but, it's not hard to come up with partially ordered measures of educational goals that yield to statistical assessment. Heck, even the SAT, with its TWO scores (Verbal, Math) yields a partial ordering  if my math score is higher, but your verbal score is, we are "incomparable". (I'm not arguing for the SAT as the right measure, just pointing out that there's nothing magical about partial orders  ALL partial orders may be represented as the "conjunction" of a collection of total orders.)
I agree that numbers and statistics can be created and used mindlessly or falsely, but at least they present a solid target! Someone who argues that it is impossible to measure any portion of the effects of his/her proposals  or that there's no need to measure because he/she "feels it in his/her bones"!  is certainly outside the realm of emprirical science, accepting no evidence to the possibility he/she might be wrong.
I also agree that math is about more than measurement. I hope I never stated otherwise. But the remarkable utility of math in the world is not limited to buying carpet or building bridges.
Ted Alper alper@ockham.stanford.edu

