kitchen table math, the sequel: 1/19/14 - 1/26/14

Saturday, January 25, 2014

Doing versus explaining and the process method

Fabulous comments on the Should math students explain their answer in words post. I'll try to get as many as I can pulled up front…

In the thread, Allison points out the irony that good teachers are the people who actually know consciously the nonconscious steps experts use to do what they do, and yet teachers are the one category of human being expected to stand aside while students figure things on their own out by deploying strategies and asking three before me.

Which brings me to my own experience teaching college composition.

I know I've said this a number of times but it bears repeating, I think: when I returned to teaching three years ago, I was chronically stymied by the fact that while I knew how to write myself, I had no idea how to explain what I did to my students.

In fact, it was worse than that. The problem wasn't just that I had no idea how to explain what I did when I wrote. The real problem was that I had no idea what that was. What was I doing when I wrote that was different from what they were doing?

All I really knew about what I did was that I wrote by ear. And so I would tell my students, frequently, that writing by ear was an option, and that the way to develop an ear for college writing was to do all their assigned college reading (and hope for the best).

Beyond that, I was stumped.

I didn't particularly want to tell freshman writers just how obsessive the process of writing entirely by ear actually was.

Writing by ear, for me, meant I would write something that sounded bad; I would hear that it sounded bad (that seemed to be the critical element, hearing badness); and I would then spend endless hours writing and rewriting and rewriting again (and again and again), trying to make what I'd written a) stop sounding bad and, only then, once that was achieved, b) start sounding good.

I did this for hours on end.

Until things sounded right.

So what does writing-by-ear translate to inside a composition class?

I'll tell you what it translates to: it translates to the process method, which I think is a lousy way to teach writing.

The Process Method, by the way, seems to have originated in the Bay Area Writing Project, now called the National Writing Project. Ed was somehow connected with the Bay Area Writing Project & has spoken disapprovingly of it for lo these many years. I'll have to get him to brief me again…

In the process method, students write something bad, then have their peers tell them it's bad, then revise the bad thing they've written to make it …. better.

Then, if they happen to be in a class taught by Peter Elbow, they find a volunteer copy editor to fix all the things that still need fixing.

OK, time to cook vegetables.

Will finish up later.

Tuesday, January 21, 2014

And here's to you, Mrs. Malaprop

I love student malapropisms.

I love student logic misfires just as much.

From Ignorance is Blitz: Mangled Moments of History From Actual College Students Paperback by Anders Henriksson:
Judyism was the first monolithic religion. It had one big God named 'Yahoo'.

Noah's ark came to it's end near Mt. Arafat.

These pre-Socratics lived long before Plato and were not decisively influenced by his work.

Eventually Christian started the new religion with sayings like, 'The mice shall inherit the earth'. Later Christians fortunately abandoned this idea.

Romans persacuted Christians by lionizing them in public stadiums.

Without the discovery of the flying buttock it would have been an impossible job to build the Gothic cathedral.

(Regarding the Black Plague): "Death rates exceeded 100% in some towns."

This was a time of stunned growth. The plague also helped the emergence of English as the national language of England, France, and Italy.

Renaissance merchants were beautiful and almost lifelike. They enriched themselves by planting wool and selling it for clothing. They increased these profets by paying interest to people who borrowed money from them. This produced even more grits for the mills of change.

Hitler, who had become depressed for some reason, crawled under Berlin. Here he had his wife Evita put to sleep, and then shot himself in the bonker.

Stalin, Rosevelt, Churchill, and Truman were known as the 'big three'.
And this:
It is now the age of now. This concept grinds our critical, seething minds to a halt.
You can say that again.

Should math students explain their answers in words?

Complex information, such as that required for motor skills, can be learned implicitly, without awareness.


Imagine you are riding a bicycle, and you start falling to the right. How would you avoid the impending crash? Many cyclists say they would compensate by leaning towards the left, but that action would precipitate the fall. When responding to the same situation while actually riding a bicycle, these same cyclists would turn their handlebars in the direction of the fall. The example (from Ref. 1) highlights the distinction between implicit and explicit knowledge*. Implicit learning refers to the ability to learn complex information (e.g. skills such as bicycle riding) in the absence of explicit awareness. Anecdotes such as the bicycle example offer subjectively compelling demonstrations for the existence of implicit forms of knowledge that are distinct from (and possibly in conflict with) explicit knowledge, but the existence of such learning without awareness has been difficult to prove scientifically.

Implicit learning revealed by the method of opposition
Tim Curran
TRENDS in Cognitive Sciences Vol.5 No.12 December 2001
It's an article of faith, inside schools of education, that procedural learning is dumb.

Having spent a great deal of time immersed in the literature on the basal ganglia, which handle  procedural learning, I'm pretty sure that assumption is wrong. Possibly very wrong.

The emerging research on the intelligence of nonconscious learning and the cognitive unconscious hasn't surprised me at all, mainly because, years ago, I read Arthur Reber's Implicit Learning and Tacit Knowledge: An Essay on the Cognitive Unconscious. Reber's book was so world-altering that I have kept it on my desk ever since.

As I recall (it's time to re-read), Reber opens his book with the question of expertise: how to transmit expert knowledge from one generation to the next.

In other words, he opens with the question of education.

e.g.: We have, today, people who know how to perform open-heart surgery. We will need, tomorrow, people who also know how to perform open-heart surgery. Since the people who know how to perform open-heart surgery today will grow old and die, we need to transfer their knowledge to the next generation.


People's first thought (again, I haven't read Reber's book in years, so take my summary with a grain of salt)…. People's first thought was that experts should simply tell novices how they do what they do.


But that didn't work out.

The reason it didn't work out: experts don't know how they do what they do.

That fundamental insight into the nature of expertise has never left me.

Experts don't know how they do what they do.

The fact that experts don't know how they do what they do has made me highly skeptical of "explain your answer" questions as the sine qua non of math achievement and comprehension. As far as I can tell, adults who are really good at what they do have an enormous amount of nonconscious knowledge and comprehension, so shouldn't that also be the case with children who are good at math?

I don't think the second proposition necessarily follows from the first. Perhaps math students should be able to explain, in words, why they did what they did in order to arrive at a correct answer. However, anecdotally I do see "math kids" who "just get it" -- and, anecdotally, those kids always look like the good-at-math kids to me.

In any event, I was tickled to discover that people who know how to ride a bicycle not only don't know how they do what they do but in many cases consciously believe they do exactly the opposite of what they actually do.

"Sluggish attentional shifting" in dyslexia

Have just come across this paper in my travels today:
Apart from their reading difficulties, dyslexic subjects often suffer from a variety of subtle sensory and motor deficits.Whether these deficits have a causal relationship to the reading disorder, form additional risk factors, or are totally independent of the reading problem, is under vivid debate. In this article, we review the evidence and suggest that ‘sluggish attentional shifting’ (SAS) can account for the impaired processing of rapid stimulus sequences in dyslexia. Within this novel framework attention-related prolongation of input chunks is decisive for many small deficits found in dyslexic subjects.

Impaired processing of rapid stimulus sequences in dyslexia
Riitta Hari and Hanna Renvall
TRENDS in Cognitive Sciences Vol.5 No.12 December 2001
For years now I've been hoping to find time to dig into the literature on dyslexia.

One of these days.

Hari & Renvall open with an arresting observation by Scott Adams:
‘It might seem impossible for you to convey that time doesn’t always march in one direction, bringing with it a perfectly ordered sequence of causes and effects, but it is not hard for me to imagine it, because I’m dyslexic. When I hear a phone number spoken quickly, I hear all the numbers but don’t have any impression in what order they were spoken. It’s as if they came in all at once.’
Scott Adams in The Dilbert Future (2000), Boxtree, p. 233.
The authors remark that:
This description from the famous cartoonist fits nicely with findings on dyslexic adults who seem to have a prolonged ‘cognitive window’ (or ‘time or input chunk’1) within which the temporal order of successive items is easily confused 2–4.

Monday, January 20, 2014

Debbie's book - Today Show - Spreecast !

Debbie's pub date is coming up, and things are getting exciting. She's had incredible response to the book; the blurbs are incredible. So I'm expecting good things.

The biggest news so far is that Debbie and Ethan will be on the Today Show on February 25.

And, on February 12 Debbie will be doing a "Spreecast." (Actually, it's the 2 of us; I'm the interviewer/sidekick).

You can sign up here, and I hope lots of you will---!

Neil Postman's 1990 prediction

School teachers, for example, will, in the long run, probably be made obsolete by television, as blacksmiths were made obsolete by the automobile, as balladeers were made obsolete by the printing press.

Informing Ourselves to Death by Neil Postman1990 | speech excerpted by Memoria Press
The technologies that were going to make teachers obsolete thus far:
  • movies
  • film strips
  • TV
  • CDs
  • desktops/laptops/iPads 
  • internet
  • educational software
The technology that's going to make teachers obsolete will have to be much more radical than any of these things, I think.

Some kind of knowledge implant, a la The Matrix….

Sunday, January 19, 2014

Sunday reading - horselaugh edition

I'm a huge fan of bad sci fi (Ed, too).

I'm also a fan of funny writing about bad sci fi, which goes with the territory. Any day that brings an Anthony Lane review of a movie starring Tom Cruise is a good one.

Yesterday, via the magic of Google, I discovered Ricki Lewis's post on SyFy Channel's Helix. She is hilarious.

Her piece was so funny I insisted on reading practically the whole thing out loud to Ed while he was trying to read something else.

I was laughing and guffawing throughout, which I'm sure added to the entertainment value.

SyFy’s Helix: Tired Plot, Bad Science, Fun
By Ricki Lewis, PhD
Posted: January 16, 2014