Hi Kirby,

Given this is 8th grade, I look at it as first exposure or a first pass. Some stuff will go over their heads, some will stick. It's not necessary that they be complete masters of everything they see. I think a lot of education is previewing. What I dislike about most math curricula is how it's taboo to look ahead and see where we're going. "Looking ahead" is an underdeveloped strain in most curricula, I'm sure. It's partly in the (traditional use) of the word curriculum: a path from a defined outset to a well-defined goal.

Given limited time and the pressure of written examinations teachers tend to shorten those interesting but time-consuming overview sessions in favor of more exercises (at least it happens to me often enough, learning _my_ lessons as a teacher, <sigh>). Another thing: Only an expert will be able to do a meaningful preview, so it's a lecture which mainly reaches the more interested students (who will appreciate it and learn from listening) but leaves the rest with nothing to _do_. So I don't think it is a taboo that these connections with future themes are understressed. It is just hard to do this right for larger audiences (classes). Still, I think you are right: It is a good thing to (quietly) stick in more than the linear curriculum stuff, even things which will go over their heads. I _am_ doing this here, for instance using the words 'object' or 'method' without "explaining it", only introducing a vocabulary through usage. On the other hand, I want to have a very clear picture in my head of _those_ ideas which will be spelled out step by step and which will be in the tests.

I understand the Sony robot dog has Python bindings but have no details. Sony should send me a sample. :-D

If they send samples, I want one too... ;-))

I started out talking about types e.g. type(2), type(2.0) and type('hello'). Thinking in terms of types makes plenty of sense, because what Python provides is "an extensible type system" i.e. you get the primitive types out of the box, then you build your own, adding to the types ( = classes) available.

Having looked at smalltalk (squeak) a little in the past year: in this aspect Python is not nearly as uniform (difference between primitive types/user classes) as smalltalk is. I understand that much work is going on to address this issue...

I use a projector, boost IDLE to like 20 point (Comic Sans these days) and have kids follow along at their own workstations as I "doodle" i.e. write simple functions and stuff. Other times I hand out stuff on paper and walk around the room, helping where needed.

I often use the projector in exactly the same way (apart from the Comic Sans, will try that out next time)

I continue to think programming is a very motivating way to get into mathematics. Yes. And Python together with Idle (doodling up functions) is a wonderful tool. In the pre-college years, I wouldn't be unhappy to see programming move into the foreground. To make it sound radical and provoke anxiety, I'd say my position is: drop math completely as traditionally taught, and teach computer science instead -- but in a different way that preserves most of the old math content (plus adds a lot of new stuff). I could imagine that, too. But in a centralized school system it doesn't look like anything like this is going to happen here soon.

A less radical position: offer this as an alternative "track" running in parallel and let it compete with traditional math. That's actually a crueler option (means slow death of traditional math vs. a quick transition to these better methods).

In our system pupils are obliged to choose an optional subject (with 3 lesson-hours a 45 min per week) in grade nine and ten. This can be another foreign language or a combination like biology/chemistry or maths/computer. The latter is chosen rather often with different motivations: a) I like playing around with computers ('cause I like computer games) and it sounds less dull and less hard than, say French b) Computers will be important in a later professional life (often the parents' view) c) I like maths and want more of that So some have this on top of their regular maths-class (also 3 lesson-hours per week). Although many have chosen it with motive a) rather than c) I think one can say that all profit from getting exposed to more maths. (Nearly all of them will go on to high-school-level later, where maths (calculus, vectors, probability) is obligatory for everyone.) I can't help but think that 3 weekly lesson-hours (from around 32) for maths is not enough. The German system has always promoted _many_ different subjects at the same time on the grounds that only general education is the goal of the schools. I liked this as a pupil (with many different interests). But as a teacher I feel that today just too many pupils get only very superficial bits of knowledge here and there. Zapping through school subjects like checking through 30 TV channels. Concentrating hard on less subjects could turn out to be more educating. Cheers, Christian