Update on an internet debate

[Myrtle]

In a thread below I had posted about a very long internet debate that was taking place as a result of Keith Devlin (NPR's math guy and Stanford logician/mathematician) telling teachers that teaching kids that multiplication is repeated addition is wrong.

The debate spread across four or five different forums, privately through email, and finally Mark Chu from Good Math/Bad Math picked this up (http://scienceblogs.com/goodmath/2008/07/teaching_multiplication_is_it.php#more). The Good Math/Bad Math blog is the top of the math blog food chain as far as quality and traffic goes and he does a very good job, as usual, of making complex mindless formalism understandable for us chickens.

This whole debate was fascinating to me because 1) it's math ed poltics in real time. Ground zero, baby.

and 2) higher math..as in higher than calculus...gets invoked really quick to come up with a solution and 3) It illustrates what H Wu means when he says that teachers need to have better math educations in order to make better decisions even at very low levels of teaching math.

I'm motivated to keep larnin' and I just wanted to share this with anyone who had been following this on the links I had given earlier.

[HollyinNNV]

In a thread below I had posted about a very long internet debate that was taking place as a result of Keith Devlin (NPR's math guy and Stanford logician/mathematician) telling teachers that teaching kids that multiplication is repeated addition is wrong.




What does Devlin mean by wrong? In what way is it wrong? Are there any studies to back him up?
I'm going to follow your link. This is interesting.
Holly

[HollyinNNV]

OK-well that is an interesting debate. To me, they are arguing two almost separate issues. What is multiplication? and How do you effectively teach multiplication?

Devlin's article was particularly annoying, especially the end of it.:glare:

[Myrtle]

What does Devlin mean by wrong? In what way is it wrong? Are there any studies to back him up?
I'm going to follow your link. This is interesting.
Holly


Holly, Devlin is using some sneaky rhetoric and making both a mathematical claim and a pedogical one all in the same breath.

Pedogogy can be backed up with studies, like you say. But what's really roiled up the math people is that his math is wrong. He's making a claim for something that a junior year math major would know. And that is just astounding considering his math background. A math claim isn't backed up by a study, but by a proof. He hasn't given that either and Mark goes on and on about Devlin's rhetoric. (In math you don't assert over and over again your claim, you actually need to demonstrate what you are saying is correct, so this is why you see an explosion of symbolic vomit on the part of some of the math people in these discussions)

I had one person give me the name of a book which supposedly developed the real numbers, i.e. would give me a demonstration, with some quirky set of axioms but from what I've seen so far it's just very faulty since he uses informal assumptions without proof.

The debates so far have consisted of teachers who don't know the higher math trying to figure out if it might make sense to try to do something new and grad students and math people who are not familiar with what's invovled in teaching the concept to kids, they just look at the math claims, not the teaching claims. Mark is looking at both.

My favorite response so far was in reference to Field's Medalist Tim Gowers saying that it should be taught axiomatically! Technically, that is how it works, but you can't do that with an 8 year old!:lol:

[HollyinNNV]

Holly, Devlin is using some sneaky rhetoric and making both a mathematical claim and a pedogical one all in the same breath.

Pedogogy can be backed up with studies, like you say. But what's really roiled up the math people is that his math is wrong. He's making a claim for something that a junior year math major would know. And that is just astounding considering his math background. A math claim isn't backed up by a study, but by a proof. He hasn't given that either and Mark goes on and on about Devlin's rhetoric. (In math you don't assert over and over again your claim, you actually need to demonstrate what you are saying is correct, so this is why you see an explosion of symbolic vomit on the part of some of the math people in these discussions)

I had one person give me the name of a book which supposedly developed the real numbers, i.e. would give me a demonstration, with some quirky set of axioms but from what I've seen so far it's just very faulty since he uses informal assumptions without proof.

The debates so far have consisted of teachers who don't know the higher math trying to figure out if it might make sense to try to do something new and grad students and math people who are not familiar with what's invovled in teaching the concept to kids, they just look at the math claims, not the teaching claims. Mark is looking at both.

My favorite response so far was in reference to Field's Medalist Tim Gowers saying that it should be taught axiomatically! Technically, that is how it works, but you can't do that with an 8 year old!:lol:

Mathematical vomit aside, I think Devlin must have gone to the same type of elite school as the snarky dude that wrote the article referenced on the general board. Do these guys have too much time on their hands?

On the same note, dh and I listened to an audio book recently on Feynman. Something like, Surely You are Joking....... Anyways, I found one section of the book pretty interesting. He begins to talk about how he spent time reviewing math and science books. Most of them he really abhorred. He had excellent reasons for finding them lacking, but then he never gave suggestions as to what would be a good math/science book. So, after all the chapters on how brilliant he is, and the chapters on the books he hated, he could not give any concrete recommendations? (Maybe he does in another book-or maybe I missed it?) But, I think in many cases it is far easier to tear things down, than build things up.

Holly

[HollyinNNV]

Oh yeah! And I think the surest way to create publicity and buzz is to say, "Hey, you know that thing that everyone does/thinks/eats/believes? It is wrong." And even if all you do is vomit out a bunch of nonsense afterwards, you are guaranteed a bunch of buzz.

[gardenschooler]

Very interesting discussion, you two! I read the Good Math/Bad Math blog, but I'll have to go back and read the rest to get the full picture.

Thanks for bringing this up, Myrtle.