Teaching Note: Using an Unrelated Problem

[fclbrokle]

So much of a student's learning is unrelated to the things we think about when we think about teaching. Lesson plan, the flow of topics, the questions we ask students, how clearly things are explained, these are all important. But so much of a class also depends on each student's mental state, and I think much of a teacher's success comes down to

Comments

[ukelele]

Note, of course, that some of Lemov's techniques do have to do with participation (e.g. Cold Call).

I think...hm. I think you tend to be dealing with students who are intrinsically motivated, and Lemov is dealing with whole-spectrum-of-humanity populations. And in the latter setting, there's a whole lot of stuff you have to deal with in order to create an environment where student participation can happen usefully at all (both motivating students to want to participate at all/constructively, and making an atmosphere where students who do want to participate are willing to/can see their contributions used). So I suspect some of the things you're seeing and finding not useful are just not as relevant with your population, because they're solving problems you rarely encounter. (Also I think some of his stuff is aimed at getting teacher clarity to the point that students can make active use of it; I have no idea the extent to which that is or isn't an issue for your corps.)

Fibonacci: I think that would be lots of fun if your students actually understand what's going on conceptually with symbol manipulation. If they are just shoving symbols around and don't understand why...I guess the question is, is this sort of exercise a bridge from symbol-using to symbol-understanding (yay, the Holy Grail!), or just something that will get people to tune out because they don't get it, or successfully complete the problem but not understand why (I got a pellet but I was incentivized to do something random because I don't know why I got the pellet)?

[fclbrokle]

Whoa! Errrr... I completely misspoke. When I first saw your response, I was thinking, "wait, there was nothing but praise for Doug Lemov in my entry, why are you reading criticism?" until I re-read to see that I had in fact written "But I suspect that much more effective than this [are other techniques]." I have absolutely *no* idea where that came from. I was intending to give an idea of other techniques unrelated to how the material itself is covered to *supplement* what Lemov had proposed. So, errr, yes. My bad. I try to make a policy of not editing my entries, but I'm going to go back and edit this one.

As to the Fibonacci thing: that was definitely an example given for the more motivated; I was eying Splash or perhaps Mathcamp crowds. However, I think that after justifying, say, the Pythagorean theorem, it is perfectly legitimate to do the same thing to re-engage the class.

[arrowedumbrella]

ukelele: I guess the question is, is this sort of exercise a bridge from symbol-using to symbol-understanding (yay, the Holy Grail!), or just something that will get people to tune out because they don't get it, or successfully complete the problem but not understand why (I got a pellet but I was incentivized to do something random because I don't know why I got the pellet)?
fclbrokle: As to the Fibonacci thing: that was definitely an example given for the more motivated; I was eying Splash or perhaps Mathcamp crowds

To me, the Fibonacci example exemplifies a sort of rabbit-out-of-the-hat trick that I delighted in as a student, and that I have had success with at Mathcamp. When I present such tricks in the courses I teach in the academic year, they tend to fall flat. So I am inclined to take issue with the characterization of "motivation" as being the necessary ingredient for appreciating the Fibonacci example even as a bridge between symbol-understanding and symbol-meaning. I think it's more about mathematical maturity, a feeling that things have been too easy so far, and the prior experience of reward for figuring out a mathematical puzzle. Some of my juniors and seniors are motivated in the sense that they will ask many questions in their attempt to figure out the math, and their questions range from surface questions about definitions and variable to deeper questions about concepts. However, they do not appreciate rabbit-out-of-the-hat tricks, because they find math mystifying enough without deliberate obscuring. It takes mathematical maturity to realize that there's something really cool about proving something that looks different at first glance, but is actually the same as what you were looking for. It takes a lot of prior success to have an example like this prompt you to think, "That was unexpected! I wonder how I could have done that myself?" instead of having the reaction, "That was unexpected! I would never be able to do that. Real math is beyond me."

Hmm. On the other hand, thinking about the Fibonacci example more carefully, I can imagine teaching it to my juniors and seniors, but with an extensive discussion afterwards about pathways to coming up with the "trick". But without some teaching of how they themselves could have performed this, I think it runs the danger of being more frustrating than rewarding.

(small note: Lemov's first name is "Doug", not "Dave"... and amusing fact, on google search on my computer "dave lemov" pulls up this entry first!)

[fclbrokle]

Eeek! Fixed, thanks.