Once again a triple-header, with the final head being an AWM column. I'll keep the other two brief.
Event the first was an expedition. In late April,
thanks to support from the VIGRE project, three graduate students and I
attended the annual Washington Community College Math Conference. Since
this was the quintennial joint meeting with Oregon and other NW states,
the meeting was held at Skamania, just across the Columbia from Oregon
-- quite a trek, but between good weather and good company, a very
pleasant one. For me these conferences are always a delight, because I
see so many folks that I knew as graduate students, many of them people
whose interest in teaching I enjoyed fostering. On top of it, this time
the programming was the most interesting to me that it ever has been,
partly because of a very lively development of interest in teaching
future elementary school teachers, with an increasing number of
programs designed to do so. Not only am I interested in the programs
themselves, but apparently the existence and activities of WaToToM were
helpful at several stages -- a distinct boost to the morale!
The three graduate students had very different
perspectives, which made it interesting to compare notes. One had
accepted a position two days before at Green River Community College,
whose faculty was attending en masse. He was, needless to say,
ecstatic. The other two were either definitely or potentially
interested in community college teaching, and explored and observed
accordingly.
And to top it all off, at a session on hands-on
teaching I learned the best introductory statistics activity I have
ever seen, which I fully intend to use as soon and as often as I
possibly can. Too bulky a description to throw into an already long
newsletter, but I'd be happy to write it out if you drop me a note.
The next event followed right on the heels of that
one, but was less stellar. It was a follow-up Brown Bag in which I
hoped to continue what had been a pretty civil discussion of the
current scene in K-12 mathematics teaching. Unfortunately it proved not
to be possible to maintain the tenor I had hoped to. The causes were
many, and it would be of no benefit to spread them out here. Many of us
on both sides, definitely including myself, became highly emphatic in
ways that were mystifying to the many colleagues whose interest in
learning about the situation I so much appreciated. I'll leave it at
that.
The final event is an AWM Education column. It's
final in a couple of senses: after nine years as the education editor,
I decided it was time somebody else got a word in edgewise. An
excellent triumvirate, or rather triumfeminate, will be taking over
after this issue. So this (relatively frivolous) column is my swan song
on the AWM front. Here goes:
The catalyst for this column was, oddly, the winter
Olympics. Somewhat to my surprise I found myself listening one
evening to some of the late night coverage featuring various American
athletes. First came some general comments, later interviews with the
athletes themselves. My ear was caught by a repeated theme: the
comments would include somewhat disparaging quotations from athletes of
other nations to the effect that these athletes couldn't be taken
seriously because they were just there to have fun. And in the
interviews, sure enough, the athletes would sparkle about how much fun
they were having. Pushed a little further, they would supply some
details about their fun, which had in part to do with being surrounded
by fellow athletes in an exciting place, but more to do with putting in
a particularly satisfying performance on some particular race, or
observing what other people's performances could teach them. Not that
they were denying the pleasure of winning an Olympic medal, but
improving on a personal best appeared to be what they were defining as
fun. It took me back some years to the time a friend's son, interviewed
after taking part in, and losing, a kayaking race in the summer
Olympics, made his mother extremely proud by replying to an interviewer
that he would stick with kayaking as long as he was still learning.
Clearly that was what made it fun for him.
This in turn took me back to one of the first
teacher workshops I helped to lead. I commented in a class discussion
that it seemed to me important that the kids should have fun. One of
the teachers immediately countered with a volley of negative remarks
that left me nonplussed (and probably speechless.) His remarks
have been sitting around more or less undigested at the back of my mind
in the decades since, and resurfaced after the Olympic interviews with
the label "Fun is getting a bad rap!" As I have tried to articulate
that thought, though, I have realized that my analysis had only
scratched the surface. It's not fun that's getting a bad rap, it's
learning itself. Think of the games and computer programs that
advertise "Makes learning fun!" I once even saw "Makes creativity
fun!", but that was an extreme case. Fun, in other words, is the
sugar-coating for something unappealing, if not downright distasteful.
Learning distasteful? That's serious. But it's a
message deeply embedded in our culture. Yesterday I toured Monticello,
and the guide, by way of jollying the children in the group along,
checked that they were all on spring break "because if you were cutting
school I would have to make you learn something and give you a quiz at
the end." Then, to do her justice, she gave a tour with plenty of
tidbits of just the type likely to intrigue a child, and since they
were motivated by interest and not requirement, I suspect a number of
the tidbits will stick with them and pique their interest in Jefferson
and his times. Me, I enjoyed the tidbits, too, but remained, as I
frequently do, a bit chilled by the introduction.
The place, of course, where this message is most
firmly focused and solidly entrenched is in the schools themselves.
This is not new – consider Shakespeare's "…". Furthermore,
some aspects of it really are inevitable – week after week there
is no alternative to getting up and out of the house at a specified
hour, which can be painful to some. On the other hand, other aspects
are evitable and should indeed be evitted (or avoided, if one wishes to
treat the English language more kindly).
I am not at all a lone voice crying out this
message. In effect it underlies the whole move away from the "sit down,
shut up and learn what I tell you to learn" mode of teaching. The Dutch
Realistische Wiskunde", which came over to us as Math in Context, uses
the world outside of school – maps and trips and building
materials – to provide problems that students solve from interest
rather than by professorial edict. The movement to use hands-on
materials provides tangible mathematical objects, many of them
highly engaging, to set up situations which, when well used, can give a
very solid foundation to vital mathematical concepts. On the other
hand, no theory, no curriculum, no materials can overcome on its own
the impact of a teacher whose own beliefs include a conviction that
mathematics itself, "real mathematics", is hard and painful to learn,
and that part of his or her obligation as a loving teacher is to
protect the class from pain.
All of this, as usual, circles back to the
question: "Well, what can we do about all this?" To me, the answer
crystallizes into two components. One has to do with the teachers'
image of their classes. They need to see their students – not
just somebody's, but their own – completely engrossed in a game
or puzzle or problem, motivated solely by their desire to figure out
the strategy or the solution. That's something we can do. We have
access to a world of games and puzzles and problems, and we know enough
to distinguish the ones with mathematical content. If we play our cards
right we can capture a class's attention and keep it captured for long
enough for its teacher to see her or his students working with an
intensity she or he has never associated with mathematics.
The second component comes into play when we have an
opportunity to teach present or future teachers some mathematics. All
of us are painfully aware how many gaps there are in the mathematical
knowledge of the average teacher, and given the opportunity we will
rush to fill in those gaps. It seems to me vital that we also
stay conscious of the need for the teachers we teach to experience the
joy and excitement that the learning of mathematics can provide. How
else are they to know what to aim for in their classes? My favorite
example of such teaching comes from the special topics course on Knot
Theory that a colleague of mine taught. She had successfully attracted
a highly diverse collection of students, including one who was heading
into teaching after some years of another career, and who was rusty and
perennially petrified. It was a triumph, therefore, to hear this
student saying, a few weeks into the quarter, "I don't believe this. A
two and a half hour class and I don't want to take the break that was
offered. In a Math course!"