Hoping I’m not behind, just on a different path

Oh, thank you Kate, for your latest post, from which all this flows. It’s reassuring that the luminaries, the veterans of this biz, are facing some of the same demons I am. It’s also profoundly scary to know that they will not go away (the demons, not the luminaries). At any rate, musing on her post made me think about the various ways that we are all tacking against strong prevailing winds.

And isn’t that a noble calling: to buck the system, to stick it to The Man? Sure is, but it only counts if what we do actually works. And that’s why good assessment is such a sterilizing light; as the punk said, we gots to know.

So, to the nitty-gritty. I teach “regular” stats; my colleague teaches “honors” stats. He sent me some problems he was giving to his kids. Here’s one:

A market research company employs a large number of typists to enter data into a computer. The time taken for new typists to learn the computer system is known to have a normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes. The proportion of new typists that take more than two hours to learn the computer system is

A) 0.048

B) 0.394

C) 0.452

D) 0.548

E) 0.952

If you are appalled, let me say that it is not his fault: if you were an AP Stat teacher, you would recognize this sort of thing as preparation for the AP exam. The Normal distribution is Chapter 2 in the book, and the exam has questions like this.

But if you are not appalled, let me try to convince you at least to be uncomfortable: Who are they kidding? Do you really think that some company knows this mean and standard deviation? How do they assess when a typist “knows” the new computer system? Do they really have enough data to establish whether the distribution is Normal? And why, in this day and age, does this company use an army of typists for data entry? [see note at end of post]

Doesn’t that argument sound good? Yeah! All power to realistic contexts! Promote authenticity! Stick it to The Man!

But here’s what really went on in my head when I read that problem:

“OMG, I’m so far behind.”

Where in the world did that come from? I may be a newbie as a classroom teacher, but I’ve been working for over 25 years as a progressive math and science educator (I’m a reverse Dan Meyer, getting less experienced as the years pass). I’ve supported depth over breadth. I ought to be able to stand up for taking it slowly, especially with the “regular” students. Let the honors kids zoom through Normal calculations; what do we care? I have my class “mission statement.” It has stood the test of time—three weeks so far. Normal calculations do not particularly support it. I shouldn’t care a whit whether the honors kids know what normalcdf means.

But oh man, there’s something buried deep in there. For me, it’s a fear not just of being behind, but a fear that my kids will leave my class not having learned something essential. More damningly, what if the stuff I have been doing is all fluff and nonsense, a kind of mathematical holding pattern, a waste of the kids’ valuable time? I bet that morass is part of what pulls us towards the security blanket of the textbook, the odd-numbered problems, the inexorable march of two-page spreads—and averaging the scores to decide on grades.

I’m not going there, of course. But I do need to keep convincing myself that my direction is good, or at least plausible, if only for me and my class right now. Writing here helps clarify, which is part of the point. Good assessment will help too.

So: While the honors kids have been learning about the Normal distribution, what the heck have we been up to? That was what I was going to write about when I sat down, but this preamble is enough for one post. Stay tuned for the next exciting episode…

(note)

In the question-constructor’s defense, I admit that it’s at least an attempt to wrap Normal calculations in a context. But looking deeper, why is the Normal so important? It used to be essential in the era of the slide rule. But because we have better computing machinery, we can approach the mechanics of stats using randomization, relegating the Normal distribution to a less-central role.