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Catherine,

this is a great post... I'm going to have to think this stuff over for a while.

I was reminded yesterday of an experience I had in high school drama, of all things. I'd been given a part in a short play called ... I can't remember what it was called, but maybe someone else will. Anyway, it was about a bedridden rich woman who overhears, on her phone, a man plotting a murder. She tries calling the police, they blow her off, she tries calling her husband, he blows her off, everyone blows her off, and at the end of the play it turns out to have been a hit ordered on her, by her husband.

So I played the bedridden woman, the center of the action. Other people at the other end of the phone appear in spotlights on corners of the stage.

I was terrified because I could not remember all the darned meaningless exchanges and phone numbers. I was constantly saying things like "operator, please give me Murray Hill 3, oh 6 oh 9", and I couldn't just make them up at random, because I had to say the same ones several times.

In retrospect, I think that's how my anxiety disorder began. Although it worked very well for that part.

If I were an adult now, I'd know it was a huge challenge and I'd have some strategies to apply. At the time, I didn't know what to do, and I had no help, either.

I expect this is how a kid who hasn't memorized the multiplication tables feels, the entire way through school. No wonder they avoid math as much as possible.

-- CarolynJohnston - 11 Oct 2005

oh my gosh!

what an incredible story!

-- CatherineJohnson - 11 Oct 2005

I have some books on memory strategies that are supposed to be fantastic. They're tough to read, because, for me, reading about memory just isn't gripping the way reading about a lot of other things is.

But I've started to use the strategies I have managed to read about.

A few years ago I went to a friend's 40th birthday party, where the only person I knew was her.

I used a visualization device to remember every name of every person there, and pretty soon I was the Party Entertainment; people were standing around watching me Remember Names.

It was hilarious.

-- CatherineJohnson - 11 Oct 2005

One of the issues that constantly gets jumbled up in talking about math ed is the "simple" issue of REMEMBERING math.

You can understand math perfectly, and still not remember it.

They're not separate issues either biologically (I don't think) or 'professionally' (professional meaning teachers figuring out how best to teach). (For instance, I've seen research, which I believe, showing that conceptual understanding helps memory; when you understand a concept you remember it better, too.)

But functionally speaking, in everyday life, I think it pays to see them as separate and distinct.

HAS CHRISTOPHER PRACTICED THIS CONCEPT/ALGORITHM/DEFINITION ENOUGH THAT HE CAN REMEMBER IT?

AND: HAS HE PRACTICED IT ENOUGH THAT HE CAN REMEMBER IT ON DEMAND.

-- CatherineJohnson - 11 Oct 2005

ON DEMAND AND FAST

-- CatherineJohnson - 11 Oct 2005

I like Zig's observation about Hirsh:

Hirsch's case is very weak. He has an underlying message that makes sense, which is that students must learn a base of knowledge if they are to perform on a range of unanticipated tasks. The reason I have taken issue with the details of his orientation, however, is that they are not scientific. They lack respect for the importance of bottom-line classroom data, which show what works and what doesn't. (emphasis mine)

By basing all our rules and decisions on what actually goes on the classroom, we avoid tarnishing our understanding and relying on questionable theories. And that's the whole point that Feynman tried to make in his chapter: The goal of scientific investigation is to be honest and not to be influenced by what we would like to believe, what people have said we should believe, what is politically correct to believe, and above all what seems believable. To yield to these influences is to buy a ticket to the cargo cults.

Zig is of course the grandfather of direct instruction and it has taken him many years to hone his curriculum by constantly testing lesons in the classroom, observing the results, and erfining the lessons until the kids are learning what they are supposed to.

-- KDeRosa - 11 Oct 2005

KDeRosa

Fabulous!

That's exactly the way I feel about it.

I gobble up every cog-sci text I can get to, but when push comes to shove you have to look clearly at what exactly is happening when you're trying to teach or learn.

-- CatherineJohnson - 11 Oct 2005

This is why I'm not a diehard advocate of 'science' & 'research' as the answer to our prayers....

Somebody out there (and it could have been Hirsch himself) drew a terrific distinction between craft & science, or maybe it was between craft & profession.

He pointed out that long before architecture was formalized into a professional discipline, people knew how to build houses. Building houses was a craft.

He wasn't saying that it's a bad thing to formalize a craft into a profession.

He was saying, instead, that when a craft is formalized into a discipline in fact you don't throw out the knowledge craftsmen possess.

Their knowledge is real.

You build on it, and extend it.

Good teachers today know how to teach. It's a craft.

Good research will, in the years to come I hope, extend & formalize the knowledge good teachers possess.

What that tells me is that I need to look at what good teachers are doing.

I need to find those teachers, and pay attention.

And when someone like Carolyn, who did a very good job learning math herself, and who is now doing a brilliant job teaching math to a child with a significant disability, tells me that math has to 'get into a child's fingers,' I pay attention.

-- CatherineJohnson - 11 Oct 2005

Conceptual understanding only gets you so far. Even a great deal of conceptual understanding is no substitute for knowing something on demand and fast. Unless your conceptual understanding is so high that you can in fact recall things on demand and quickly.

I have taken many exams where I have undertood the material conceptually and could even derive material I had not memorized, but it takes a tremendous amount of mental energy to do this and then determine the correct procedure for solving the problems in a timed exam. Ultimately, you are forced to rush, leading to silly mistakes, and increasing the stress level. Better to have mastered the facts and procedure to automaticity. Less mistakes and far less stress. There just is no substitute for repeated practice beforehand.

-- KDeRosa - 11 Oct 2005

"And when someone like Carolyn, who did a very good job learning math herself, and who is now doing a brilliant job teaching math to a child with a significant disability, tells me that math has to 'get into a child's fingers,' I pay attention."

Golly. Like Gomer said. Thank you!

I really do think that the standard algorithms and algebraic manipulations need to become part of motor memory, like riding a bicycle, in order to become automatic. Doing them by hand is an aid to this process; that's how I expect the processes that pull something into motor memory are triggered.

I have no hard evidence for that, however.

Here's an interesting idea for an experiment. Take someone with demonstrable expertise in math, with selective brain damage to parts of the brain other than motor memory, where procedural knowledge resides (frontal lobes? Catherine?). How much of the ability to do those grade-school algorithms do they retain?

-- CarolynJohnston - 11 Oct 2005

Although the experiment would be all messed up if they'd lost their domain knowledge of numbers. You need both.

-- CarolynJohnston - 11 Oct 2005

The great book on Carolyn's experiment (in the realm, at least) is:

Memory'S Ghost : The Nature Of Memory And The Strange Tale Of Mr. M

I still haven't read it, probably because I find it too upsetting.

We loved the movie about the guy with no short-term memory, though.

What the he** was its name???

I'll think of it.

-- CatherineJohnson - 11 Oct 2005

Here's a short write-up on Patient H.M.

-- CatherineJohnson - 11 Oct 2005

Memento

Brilliant, brilliant film.

-- CatherineJohnson - 11 Oct 2005

Here's the Memento flash site

-- CatherineJohnson - 11 Oct 2005

AND O MY GOD--HERE'S ANDY KLEIN, A FRIEND FROM GRAD SCHOOL WHO I HAVEN'T TALKED TO SINCE, WRITING ABOUT MEMENTO AT SALON

Everything You Wanted to Know about Memento

oh boy

that was weird

I'm going to have to go lie down

-- CatherineJohnson - 11 Oct 2005

Not everyone may wish to go quite as far as I have -- four theatrical viewings, three of them with copious note taking; a fifth viewing on videotape, with lots of whipping back and forth to check for differences in "repeated" shots, and slo-mo attention to quick-cut subliminal moments; reading the published script and comparing it to the film; reading the short story, "Memento Mori," written by Nolan's brother Jonathan and credited as the film's source; and a few trips through www.otnemem.com, the film's official Web site, also by Jonathan Nolan. More than anything, I'm grateful to everyone who posted ideas about "Memento" in the movie conference of the Well -- you know, "America's pioneering online community, see www.well.com" -- a whole gang of enthusiastic, contentious, brilliant, pigheaded and articulate fans, who have more than once opened up for me some movie that I simply did not get.

wow

that sounds like Andy

-- CatherineJohnson - 11 Oct 2005

can't wait to show this to Ed

-- CatherineJohnson - 11 Oct 2005

ok, i don't need to lie down

i need to go for a run

-- CatherineJohnson - 11 Oct 2005

"CAD students can't draw" "I think Carolyn may have finally solved a problem I've been puzzling over, which has to do with something Temple has told me many, many times. Temple says that students in her architectural drawing class who've never learned to make scale drawings by hand, but only on the computer, can't do it."

What is "it"?

If you are talking about drafting, then these students haven't been taught. They have been taught how to use a program, like AutoCAD^?. Old-time designers spent a long time learning how to draft and some of their drawings are like works of art. Not only that, they are drawn so that others can understand them; different line thicknesses and styles, proper dimensioning, and many detail views. This can be done in CAD, but it takes time and that is not what is taught in school. I also don't think the solution is to first learn drafting by hand. CAD doesn't preclude good drafting, but it is pretty good at distracting people from the real subject. Think about people learning to write who spend more time on learning how to use a word processor (pictures and fonts), than learning how to communicate. I don't think there is a need to write with paper and pencil first. I just think that the tools become an end in themselves and reduce the amount of time applied to what you really need to learn. Some students might become good CAD jockeys, but not very good architects. (They could have gone to a technical school.) Colleges have to be very careful about getting distracted by the tools.

If you are talking about design (engineering, form, fit, and function), then many students are not taught that either. The holy grail of computer-aided design is 3D modeling first and then derive the construction information from that automatically. Solid modelers are now set up to automatically generate dimensioned, exploded views and to automatically generate dimensioned traditional 2D scale drawings. Unfortunately, many of these programs leave a lot to be desired and the students aren't taught to focus on the end product and not the process. If the program can't do it, then they won't learn it. Once again, students are distracted from the real topic of architecture. They may be able to produce a 3D model of a building in record time and generate nicely rendered views set against a digital background of the building site, but the building might be a failure.

The problem is not learning how to draft by hand first. The problem is that they are not taught what they need to know. There are too many distractions. CAD (the process) becomes the end and not the means to an end. CAD distracts; it doesn't impair.

One has to be careful about thinking that everything has to be done by hand first before using the calculator or computer. However, let me state categorically what I have said before. I see no need to use a calculator for math before 6th or even 8th grade. I could probably come up with some good examples, but it sure isn't necessary. I have also said that using computers or calculators at any level of schooling should raise expectations, not lower them. Many modern math curricula see calculators as avoidance tools, not as a means to tackle more complicated real-world problems that couldn't be done by hand.

I have been writing CAD programs for 30 years and I have dealt with customers at both ends; the older designer who learned everything by hand, and the younger person who only knows the computer ways. Many of the younger people are beginning to understand that there is a big difference between being a CAD jockey in an architectural office and being the lead architect. And, many of the older designers are realizing that their lack of CAD knowledge limits their ability to be competitive and to try new things.

As for the process of learning, hand drafting (even CAD drafting) isn't the goal. I have met some amazing designers who couldn't draw a straight line with a ruler.

-- SteveH - 11 Oct 2005

"But math is hard, and that, I think, is a core truth about math & about teaching math, which tells me we should constantly be looking for ways to do exactly what Carolyn did: ..."

In the middle of a discussion of cognitive issues it hits me. I find myself thinking about how our public schools still use MathLand and CMP. I remember that about 50 percent of fourth graders don't know how many fourths are in a whole. Math is hard, but it's not that hard. I think back on the math open houses where the math teachers talk about cognitive issues. Then I think about how they let the kids slide from grade to grade, trying to get them to master their adds and subtracts to 20 in third grade, and trying to get them to master their times tables in fifth grade. I stop thinking about cognitive issues and start thinking about ignorance, incompetence, and arrogance.

-- SteveH - 11 Oct 2005

Teaching is not yet a mature profession. They talk a good talk when it comes to the science of teachiing and cognitive issues, but they stubornly refuse to abandon their fads and cognitively unsound practices. No amount of empirical data or scientific evidence will dissuade them. In fact, I don't even think they can distinguish between real science and junk science. Accountability, fixed goals, and government sinecures are part of the problem, but the real problem lies much deeper. In mature professions, practioneers cannot afford to become enamored of failed theories because products need to be developed, built, and shipped in working condition by fixed deadlines.

-- KDeRosa - 11 Oct 2005

Steve -- From what Temple tells me, her students don't know how to do proportional scale drawings, if that's the correct term.

They'll click on icons, put them on the screen, and then assume from looking at the image that their design works.

They'll make mistakes like creating a chute that's only 1 foot across.

I imagine they also don't know how to design (assuming I know what 'design' means)....but from what Temple says, these students are making elementary errors in math, measurement, and proportion.

-- CatherineJohnson - 11 Oct 2005

I have also said that using computers or calculators at any level of schooling should raise expectations, not lower them.

I think I should put that in 'Wit and Wisdom.

Also, I'm looking for something you said one day (I wish to heck I'd bookmarked it that minute): engineers aren't looking for the right answer, but for the best answer.

Do you have any idea where you left that Comment?

(I haven't done a Comments search yet--if I find it, I'll tell you.)

-- CatherineJohnson - 11 Oct 2005

I found it:

multiple answer math

-- CatherineJohnson - 11 Oct 2005

Catherine,

You're way too fast for me. You've come and gone before I know what is going on.

-- SteveH - 12 Oct 2005

carolyn's play sounds like sorry, wrong number.
movie-ized with barbara stanwyck, iirc. memento rocks.

-- VlorbikDotCom - 12 Oct 2005

I think "Sorry Wrong Number" is correct.

It's a sad commentary on the state of my memory that even when prompted -- I can't be certain.

-- CarolynJohnston - 12 Oct 2005