A couple months ago, I was invited to give a couple talks at a school. This was, to say the least, a surprise. Although I used to give such talks every other week, I had not been approached since around the time I wrote off the MAV as a cabal of censorious tossers and resigned from the whole popularisation thing. Now, many years later, there appears this invitation, from a teacher I do not know or know of and who seemingly knows little about me. Strange.
Stranger still was the teacher contacting me through this blog, which one would not imagine being an enticing advertisement for the blog’s author to come meet the kiddies. Did she really want me to come yell at her students, “Learn your friggin’ tables”? If not, what was she expecting? It was difficult to tell.
It also didn’t matter much what the teacher wanted, since anyway I always pretty much do what I want. It’s always the same sermons, with slightly varying jokes. Also, the truth was that I also didn’t much want to do anything. When I received the teacher’s email, my heart sank more than a little.
Post-MAV, I have had zero interest in doing school talks, and even beforehand I had seldom much enjoyed the trips. Although I had done at least a hundred of the things, the trips always involved a lot of stress, before and during. The teachers in the PD sessions always gave strong vibes of wanting to be elsewhere, clearly unconvinced that I had anything to offer, and with me far from convinced that they were wrong. And one was never sure how the kids would react and behave: mathematics is not an easy sell to a large sceptical room, and attentiveness and good manners are now anything but the norm. So, although I might possess a good bag of tricks and a quirky style, the stress of needing to perform, to try to be memorable in a properly meaningful manner, inevitably resulted in days of work and worry. Added to this, it had been so long since I’d done the school thing I had diminished faith in the tricks and my style; it seemed entirely plausible that the visit would be a debacle. Nonetheless, I said yes. Because I pretty much always say yes.
It was a very enjoyable and rewarding trip.
The teacher who invited me was an excellent, attentive host, and the school was a small, pleasingly proper girls’ school. The middle year students to whom I presented were charming, good humoured and well-mannered and engaged. The PD was what such PDs are, but I was loud and told jokes and I came armed with a hammer. I hammered away, figuratively and literally.
It was interesting and nostalgic to do it all again, and I’m very grateful to the teacher for the opportunity. I’m also very grateful to be back in retirement.
It is always great when things coincide; audience, mood, and surroundings.
And then there’s the opposite …
Like you, it has been a long time since I was in a classroom until about a week ago when I gave a talk at a summer camp. The topic was getting kids to look at geometry from a transformation perspective, one of the problems being the following: an equilateral triangle abuts a square, all side of the same length 1; what is the radius of the circle that goes through the vertex of the square not on the triangle and the two vertices of the square not on the triangle. (Hint: let the triangle slide down to the opposite side of the square.) What makes the session work well is some kid to offer a solution or ask a question, because it is the interaction sparked that makes it move along (and sometimes even change direction.)
I admire the teacher who invited you, Marty, because she was willing to risk the unknown. I think what makes a lot of teachers diffident about going off script is that they are not confident that they can handle the situation (a couple of teachers made this explicit) when kids ask questions or make a comment whose validity they cannot assess. Some kids are quick to see a situation but unable to articulate it, so part of the game is to give them a voice.
For those of you who visit classrooms, here is something that I have found works well because there is a fairly evident entry point but it is hard for most classes to get the complete story in the period. There are six segments joining pairs of four points in the plane. Find all the configurations for which the six lengths take one or two distinct values. The square is put on the table pretty quickly, and this helps define the problem for the kids who are not sure what is being asked. There are six possibilities, and the ones that most classes do not get is an isosceles trapezoid. However, one on occasion, this was the first example given. When I asked the kid about it, he responded that you take a regular pentagon and remove on vertex.
Another one is the following. Let n be a positive integer exceeding 2. Show that 4/n can be written as the sum of three distinct positive integer reciprocals. This is actually the Erdos-Strauss conjecture. But a typical class can dispose of all the cases except the outstanding one in which n = 24k + 1. The kids take off once someone gets the key fact that 1/n = 1/(n+1) + 1/[n(n+1)].
If you can hit on something where the kids have to chase down stuff and there are a couple of quick entry points, then you are usually off to the races.
Ed, Do the three positive integers have to be distinct?
Thanks very much, Ed.
I think summer schools and regular, say weekly, extension classes are fundamentally different from the kind of talk I just did, and tended to do (although I’ve done some of the regular stuff as well). Although I definitely try to have participation and back and forth, and to present some deeper ideas and questions, a presentation to 100+ all-abilities kids cannot be much more than an advertisement for the real thing.
As to what should go into the real thing, I’m a genuine amateur, and am alway looking to learn from guys like you and, vale, Tony, as well as some strong teacher-friends I know in Victoria. I’ve just put up this post, which hasn’t received much attention, for suggestions for primary school. Perhaps I should do a companion secondary school post?
Once back on …
Nope.