kitchen table math, the sequel: 5/11/14 - 5/18/14

Thursday, May 15, 2014

Defense of the Sage on the Stage

The joy of lecturing--With a critique of the romantic tradition of education writing (Appendix to How to Teach Mathematics by S.G. Krantz, 2nd edition, Amer. Math. Soc. 1999, pp. 261-271) (Appendix to How to Teach Mathematics by S.G. Krantz, 2nd edition, Amer. Math. Soc. 1999, pp. 261-271) by H. Wu.


"It appears to me that this rejection of the sage-on-the-stage method of instruction is unjustified. There are situations where lectures are very effective, and in fact there are even circumstances which make this method of instruction mandatory..."

Sunday, May 11, 2014

Hainish suggests a 'negg' (and how to write a 4 that doesn't look like a 9)

After I mentioned how impossible I'm finding the project of creating a thesis statement 'algorithm,' Hainish suggested using my mistake as an example of how not to create a thesis statement.

That is essentially the solution Ed came up with today.

Which brings me to something I never got around to mentioning after my time at Morningside Academy's Summer School Institute.

Every day of the two weeks I spent at Morningside brought new revelations, but the two that completely upended my perception of reality were Morningside's focus on anaphora as the critical component of reading comprehension and Kent's explanation of what to do when a student writes 4s that look like 9s and 9s that look like 4s.

So, pop quiz: if you had a student writing 4s that look like 9s and 9s that look like 4s, what would you do?

What I would do -- what I would have done before attending the Institute -- would be to have my student practice writing 4s and 9s.

But no!

That's that wrong answer.

The right answer is to have your student practice seeing 9s and 4s.

More specifically, have the kids practice telling 4s and 9s apart. Give them a worksheet filled with 4s and 9s, and have them "discriminate" 4s and 9s until they can do so fluently.

After that, the kids can write 4s and 9s.

I was gobsmacked.

So Kent explained.

All performance, he said, requires internal inspection. You don't just perform a skill, you watch yourself performing a skill. You inspect your performance as you perform.

And the inspector has to be trained.

The reason students write 4s that look like 9s and 9s that look like 4s isn't that they can't physically write 4s and 9s  They can. They can write other numbers; they can write letters. A child who can write other numbers and letters can write 4s and 9s.

The reason students write 4s that look like 9s and 9s that look like 4s is that they aren't seeing the difference. They aren't discriminating.

Kent said you could make a case all learning is discrimination.

More on this later, but for now: at Morningside, people use Tiemann and Markle's work on curriculum design. To teach a concept, they teach "EGGS" and "NEGGS."

EGGS are examples (thesis statements, in this case), NEGGS are non-examples (non-thesis statements).

More importantly, they give students close-in non-examples.

Make It Stick says pretty much the same thing.

More in a bit.