>In my opinion, quantitative measurement is highly useful in the >physical world: [...stuff deleted...] Unfortunately, human behavior >bears very little reliable resemblance to buying carpet or brewing >beer. Education is not a product. Learning is very difficult, if not >impossible, to quantify in a way that I find useful. Why? Because in >the context of education, what would be useful would be to find the >replicable conditions, measure them to a satisfactory degree of >accuracy, and (this is the kicker) then REPLICATE them.
>But any experienced and reflective teacher will tell you that very little >is replicable in the classroom. Like the ancient Greek philosopher >(Heraclitus?) said, "You can't step into the same river twice." Because >neither you nor the river is the same, I would argue. And thus, it is >impossible to teach the same lesson twice (assuming that so doing were >desirable).
I think this is a misconception of what quantifiable, replicable data ARE. Human biology is unpredictable, ever-changing -- not everyone responds to the same drug or therapy the same, and the even same person may respond differently on different days, depending on a swarm of minor variations in background conditions. This hardly means that quantitative methods may not be applied!
In less exact sciences than medicine, physics or accounting, the nature of quantitative data may be different -- it may take a great many experiments, each with its own noise and error to give the sort of convergence of evidence needed to establish the *general* validity of a hypothesis. But that's hardly the same as saying quantitative evidence shouldn't be sought.
>Numbers will not settle this debate definitively because what we're dealing >with, student learning, is quite nebulous.
I could agree with a weaker statement here, that reasonable people might differ about the objectives of education. So one might argue that a particular quantitative measure doesn't accurately reflect the goals of one's teaching. Note this is different than saying quantitative methods are invalid because every class is different!
But saying that learning is nebulous doesn't quite cut it -- certainly not not when talking about larger groups of students, say a school-district full, or a state-load. What do you expect most people to be able to understand? What do you expect them to be able to DO? What do you expect the *best* students to be able to understand and do? Is there NO way to quantify these things? Everyone's different, sure, and no matter what test you use, some people's scores won't accurately reflect their ability, but still, can nothing specific or measurable be said?
>At some point, for me the educational debate comes down to the fact >that every fiber of my being and experience as a learner and a teacher >tells me that approaches like that of John Saxon to the difficulties >of learning mathematics are a soul-less, quick fix; and that >approaches to mathematics education similar to those of the NCTM >Standards are, while not THE answer, an approach much more in tune >with what makes intellectual pursuits worthwhile and humans as >learners interesting.
OK. Now go and quantify! Part of the beauty of mathematics and statistics (and I shouldn't need to tell this to a math teacher!) stems precisely from its ability to get beyond subjective, visceral (fibrous?) feelings. We can sit and argue aesthetics all day; we can point to successes or failures with individual students; we can make analogies between teaching and how Shakespeare wrote his plays, or how a village raises a child, or whatnot. Numeric measures may be biased, or may not measure quite the right quantity, and one may argue about how to improve the measures, or interpret the scores -- but without them, it's all wind.