The intended content of this newsletter is a summary of last week's Brown Bag, but the headlines got firmly pre-empted this afternoon. The department had the joy of celebrating the 95th birthday of Bill Birnbaum, who has been a professor emeritus here since, as he put it, peering over his glasses at the assembled graduate students, "before a lot of you were born", and was on the active faculty list for long before that. Characteristically, he responded to our gift of a celebration with a much more resplendent gift, in this case the gift of reminiscence. His basic theme was an attempt to track down where he caught the bug and how it got sustained. The bug in this case being love of mathematics, which, as he points out, is highly contagious, but must be caught from someone else. He pinpointed the timing to his last year in Gymnasium (=high school) in Lvov, when he had a teacher who managed, while adhering to a strict curriculum involving horrific logarithmic and trigonometric computations ("without any of those little things with buttons that you can hold in your hand"), to make his students aware that mathematics was a very live field, with exciting new developments happening all around, and to entice them (or him at any rate!) into a lively desire to follow those developments. As a testimony to the impact that a good teacher can have on the minds and lives of students, that one is pretty well unbeatable.
But even though one teacher launched this passion, a lot of factors went into sustaining it. The general mathematical ambience of Lvov seems to have been really rich. Birnbaum conjured up a splendid image of the Scottish Cafe, where there was regularly such a crowd of mathematicians that the proprietor became annoyed at the mess they were making of his marble top tables. A compromise was achieved: they converted to using soft enough pencils so that their writing was easy to wipe off "though who knows what wonderful theorems got washed away forever in the process." An alternative mode of discussion was to lean against the large, wood-burning tile stove in the middle of the room. Comfortable on a cold evening, but it did lead to talking around corners. One of the cafe regulars even had all the parts of a proof of Fermat's Last Theorem. Well, all but one. It was like having all the gears and springs from an analogue clock, lacking only that little gadget that makes it go tick-tock!
From Lvov, Birnbaum went on to Göttingen, another phenomenal
mathematical center. He enjoyed the strength of the mathematics
(and contributed to it--not that he mentioned that, but Don Marshall
did in his introduction), and the wisdom and humor that went with
the brilliance of Hilbert. But the final tale he left us with
was of another nature, and such as to be of comfort to those who
worry about the image of our profession as a stodgy bunch of nerds.
It started at the point when he and three friends were gently
evicted from a cafe from which the rest of the clientele had long
gone home, as they had failed to notice because they were too
deep in their mathematical conversation ("What else would
four young men be discussing over a series of glasses of wine?")
The sequel involved a trip up a lamp post, and a 3 AM visit from
a member of the constabulary and...oh, never mind. It was a very
And after that, the original and official topic of this newsletter seems distinctly pedestrian, but I did promise it, so I'll follow through. I had the opportunity last week to become appreciably more informed than I had been on one aspect of the mathematics articulation between high school and university in this state. I summarized that for last week's Brown Bag, and I will now summarize the Brown Bag for this.
First a bit of background: starting a number of years ago, and in response to the NCTM Standards (or more probably to the same forces that launched the Standards) the state of Washington pulled together a bunch of people from many relevant areas to put together the Essential Academic Learning Requirements--a set of benchmarks describing what students ought to know at each of several grade levels in each of several fields including, of course, mathematics. The mathematics benchmarks reflect a lot of the kind of development that CCML is doing its best to support: increased emphasis on mathematics as a field that makes sense and involves thinking rather than one which is to be swallowed whole and involves only computation. A good set, but destined to have no impact at all unless attached to some form of assessment (a discouraging but absolute fact of all academic life, including ours.) Enter the WASLs (= Washington Assessment of Student Learning, I think!) These are the tests you have been reading about off and on in the newspaper, due ultimately to be administered to all fourth, seventh and tenth graders in the state. Not only that, but the tenth grade one is to become the test required for a Certificate of Mastery--meaning a high school diploma (details of that are, I believe, still under negotiation.)
And that's where the conference I was involved in comes in. Because if we have a test all seniors must have passed in order to graduate from high school, that's a start on saying what universities will require. But we obviously need more than what is minimally required to scrape one's way out of high school. How much more? And how do we describe what we need? And how is our description to be used? Not, for a start, in another test-- there are already far too many about. But the need is clear in the abstract, and for the Higher Education Coordinating Board it is clear in the concrete--the Legislature wants to be assured that some criteria are out there.
So last Wednesday I spent the day with representatives from Eastern, Central and Western Washington Universities, and math teachers from two high schools, one on each side of the state, working on just that. The format is that we are producing (actually, they had produced last spring and we were honing down) a list of pieces of mathematical knowledge without which no one, we felt, should be considered for university admission. The teachers will then go and produce problems and projects addressing these pieces of knowledge, and administer them to their students. Then we will gather again and look at the resulting work and decide which of it really represents an adequate grasp of the material. Ultimately a set of these questions, together with representative student work on them (good, bad and indifferent student work, so labeled) will be made available to teachers of high school juniors and seniors, and it will be up to them to make good use of them to teach, advise and recommend students. Two things need to be borne in mind: 1) these represent what is needed IN ADDITION to the tenth grade WASL, and 2) they represent what should be required of someone planning to major in classical ballet, not what is needed to survive calculus. Though on the other hand, as was observed at the Brown Bag, any student really in control of all the material listed would be in fine shape in calculus. And there you get into some of the really murky issues, because we are talking about the difference between "student understands X" and "student really does understand X", which is kind of tricky to write down (and my suggestion of "student does not faint at the sight of the exponential function" somehow didn't get incorporated.)
So there you have the lay of a kind of interesting piece of the land. I have the list we came up with, if anyone is interested in looking at it, and will promise to bear firmly in mind that this is a DRAFT.
And, for a total change of subject, I am going to finish with a book recommendation. I have just come across the English translation of a book I read in Dutch last summer (originally it was German), and I think it's great. It's theoretically designed for kids (middle school age, maybe?), but I would heartily recommend it for any adult who is dubious about mathematics--or, for that matter, who isn't. Profound it's not, but it's got some perfectly respectable mathematics in highly accessible form. It's called The Number Devil, and it's by Hans Magnus Enzenberger. I'll put my copy in the Math Lounge tomorrow.
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