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.

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.

[snip]

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.

How?

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.

Simple!

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.

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 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

High school

Chris Christie January 9:

Let me just clear something up, O.K., about my childhood friend David Wildstein. It is true that I met David in 1977, in high school. He’s a year older than me. David and I were not friends in high school. We were not even acquaintances in high school…. We didn't travel in the same circles in high school. You know, I was the class president and athlete. I don’t know what David was doing during that period of time…. So we went twenty-three years without seeing each other, and in the years we did see each other, we passed in the hallways. So I want to clear that up. It doesn’t make a difference, except that I think some of the stories that’ve been written implied, like, an emotional relationship and closeness between me and David that doesn’t exist. I know David and, you know, I knew that Bill Baroni wanted to hire David to come to the Port Authority, and I gave my permission for him to do it, but that was Bill’s hire. He asked for permission, I gave my permission for him to hire David. But let’s be clear about the relationship, O.K.?

JANUARY 11, 2014 | GOOD SHOW, BUT THIS BRIDGE GOES NOWHERE | POSTED BY HENDRIK HERTZBERG

Apparently Christie has now proposed lengthening the school year and the school day.

Which makes sense because teens need a lot more exposure to the I'm-class-president-and-you're-not peer culture high schools have to offer.

[pause]

Last fall, when the Christie administration closed the lanes, traffic was backed up all the way to Rye. It caused quite a stir. I remember, shortly after the excitement began, ping-ponging back and forth re: Andrew's oxytocin, which comes from a pharmacy in Rye and has to be kept refrigerated.

A: I was glad the pharmacy was delivering as opposed to me driving cross-county to pick it up, but then again B: that didn't solve the problem of a fantastically expensive hormone requiring refrigeration stuck in traffic for 4 hours, which led to C: idle musing about just how long the refrigerated silicon thingies they put inside the mailer stay cold….and as I made the circuit from A to B to C and back again the "backed up all the way to Rye" refrain continued to sound in my kitchen, sparking query D: what did backed-up all the way to Rye, which I figured meant all the North-South corridors here in Westchester County had to be a nightmare, mean for driving East-to-West?

East-to-West in Westchester County is a losing proposition under the best of circumstances; when it comes to driving across the county, as opposed to up and down the county, no roads lead to Rome.

So, with traffic backed up all the way to Rye, what did that mean for Rye to me and me to Rye?

Or me to anywhere, for that matter.

My Bronx semester wasn't starting for a couple of weeks. There wasn't any place I absolutely had to go.

The news stories kept coming; the traffic kept being inexplicably and catastrophically backed-up-to-Rye. The mental imagery was oppressive, and as the days wore on I began to feel like the best course of action was to stay inside my house.

Maybe inside my bedroom.

Possibly forever.

I should probably file a class action suit against the state of New Jersey on behalf of all the people who almost became agoraphobic as a direct result of the Fort Lee lane closings.

the press conference

FAFSA, CSS Profile, and I'm going to shoot myself

I have been putting this off for too long, but now it's nearing completion, although we will have to update the forms when the 2013 numbers are known. Some say that it's better to get the applications in early, but when does financial aid know whether someone has been admitted or not? I suppose they just crank the numbers through a formula so they just do it for all applications. Some schools say they are need blind, but what happens when they crank the numbers for those who are admitted and it comes out too high? I read an article that says that this is a problem for many schools. I don't know how that works if their yield is at 50%.

I like how they all assume that the student is filling out these forms. "You" means the student. Right.

All of my son's schools (save one) require the CSS Profile along with FAFSA. When we went to info sessions, they all talked about how little we might have to pay, even if we make pretty good salaries. There is a potential (no loan) benefit if you get into one of the rich schools, but that doesn't mean that your EFC will not require loans. Also, I don't like how families who are savers get hurt more than families who are not. Although FAFSA doesn't see retirement savings, the CSS Profile schools get those numbers. We should have taken trips and cruises instead of saving.

They also ask you how much you are willing to pay each year towards your child's college education. Um, zero? Is this a trap for the gullible? We should have paid more attention to those full ride offers from other universities. What is the future value of $100K not spent?

Any comments from experienced parents to us financial aid "newbies"? The one I learned too late is that some colleges require early financial aid information for Early Action. Fortunately, the one that my son chose was one of the few that had a late EA financial aid deadline. He was deferred so it was moot. Our high school had an open meeting about FAFSA, but said little about the CSS Profile.

Happy New Year!

Chris's friend D. snapped a quick Christmas photo of us in the drizzle this weekend, and I see Andrew has a pretty serious frowny-face. (For passers-by, Andrew & Jimmy - in front - have autism.)

I will do better next year!

The law of universal linearity

Interesting discussion

I was struck by this passage:

In terms of implementing this in practice, I think that college is way too late, and also quite difficult because college math (and STEM) courses tend to be mostly about transmitting massive amounts of boring technical content and technical skills, leaving little to no room for actual ideas or ways of thinking. Nevertheless, I do think it would be an interesting experiment to have students keep something akin to a "vocabulary notebook" where they record the meaning (as opposed to the formal definition) of the various kinds of expressions they run in to. For example, a fraction ab is supposed to mean "a number which when multiplied by b gives a"; it is short and illuminating work to figure out from this (using distributivity of multiplication over addition, which we definitely want numbers to satisfy) that ab+cd=ad+bcbd, that there is no number meant by a0, and that 00 can mean any number). This of course, presupposes that somebody takes the time and makes sure that the language in which these meanings are explained is coherent, so it would be a lot of work to design a course around this method.

---

I did in fact once successfully disabuse a(n Honors Calculus) student of "the Law of Universal Linearity" using these ideas. The particular instance concerned manipulating the Fibonacci sequence, and the student had made the error of writing something like Fx+Fx=F2x. What I did is explain the stuff above and had the student apply them by analyzing the meaning of the various expressions he had written down was, and then ask whether that equality was justified based on what he knew the expressions meant. That seemed to make an impression on the student, but I personally believe it was an impression made ten years too late...

Speaking of 'instructionism'...

...which I was doing a couple of hours ago, Chris's best friend from NYU was here today, in need of a brief session of instructionism himself.

Chris had been telling me his friend -- D. -- "can't do commas."

(I don't absolutely know Chris can do commas, by the way, though I think that, on the punctuation front, he's pretty much arrived. Will have to ask Ed, who's been advising Chris on history papers this year. Suffice it to say Chris knows enough about commas to be able to copy-edit D's papers.)

UPDATE 1/12/2014: Ed says Chris's punctuation is fine. It was basically fine by the time he graduated high school.

Anyway, I'd been mulling D's situation, and had decided I could probably fix all of D's comma problems in a couple of weeks, max.

The reason I was pretty sure all of D's comma problems could be remedied in a couple of weeks is that I've just about got sentence punctuation boiled down to the absolute, bare minimum of things you need to know in order to punctuate declarative sentences in college papers, and guess what?

There are only 8 basic sentence punctuation patterns.

That's not very many, eight.

To learn the 8 patterns, you need to know:

• Finite and nonfinite verbs
• Independent and dependent clauses
• Restrictive and nonrestrictive modifiers (how to tell them apart)
• Coordinators
• Subordinators (aka dependent marker words)
• Adverbial conjunctions (which I call "fancy FANBOYS" in class)

If you are a native speaker (D. is), you already know these things nonconsciously (though I'm not sure that's true of the distinction between restrictive versus nonrestrictive modifiers), no matter how random your commas.

So I figured I could simply tell a smart kid like D. how to use commas in sentences, and he would know. His writing is good -- I've seen it -- it really is just the commas that are the problem.

So today Chris and D. did Hunter College's Exercise B, and I looked it over.

Turned out D. had never heard of "comma splices."

Or dependent clauses.

Never, in 13 years of public-school English class and 1 year of writing instruction at NYU (tuition $48k).

His only tactic for deploying commas was to listen for pauses as he wrote. Listening for pauses is a good idea as far as it goes, but, as D. pointed out, it's not going to fix comma splices. It's going to cause comma splices.

I suspect that listening for pauses may have caused both of the mistakes he was making:

• He was hearing the pause between sentences loud and clear, and was inserting naked commas^* between sentences he wanted to join. 
• He wasn't hearing the pause between opening dependent clauses and main clauses -- or, more likely, he was hearing the pause but was experiencing it, correctly, as softer than the pause between sentences. So he was failing to place commas after "introductory elements."

The instant I explained to D. that, generally speaking, in college prose you're not supposed to use  commas to join sentences, he got it. He correctly punctuated the last four sentences on the page without further ado. 

I'm pretty sure he instantly got introductory subordinate clauses as well. I told him that, with "introductory elements," you can just listen for the pause and use a comma or not, depending. 

I'm pretty sure that observation is true (once someone tells you that introductory elements are usually followed by commas). At least, it seems to be true with my students, but take it with a grain of salt. Somehow, for native speakers, hearing introductory elements appears to be natural even for students who have never in their lives placed a comma after an introductory dependent clause. So it seems to me. 

In any event, D. was having no trouble hearing the pause. He heard the non-pause that results when you move the dependent clause to the end of the sentence, too:

• When you get to the corner, turn right. [slight pause between clauses]
• Turn right when you get to the corner. [no pause between clauses]

We didn't have time to get into restrictive versus nonrestrictive clauses, which is a challenge for my students.

D., by the way, is very smart. Had all 4s and 5s in multiple AP classes; wrote his friends' college admission essays. And didn't know what a comma splice is.

Someone should have just told him. It simply is not the case that smart people -- or good readers -- "pick up" punctuation by osmosis. We're not built that way. We're built to register the gist of a sentence, not the particulars.

Plus which …. there's nothing magical or even important about commas versus semicolons. Using semicolons instead of commas to join sentences is a convention; twenty years from now comma splices will probably be  correct. So just tell students what the convention is and move on.

But somehow, telling is not possible.

Not even at the college level, not even in a full year of college-level writing instruction.

^* "naked commas" meaning commas unaccompanied by a coordinator (and, but, or, so, nor, yet, for: the FANBOYS)

Over and over

To recap, the list of people with really bad ideas thus far:

• Kofi Annan
• David Brooks
• The Daily
• Barry Eichengreen
• Reed Hastings
• President Obama
• Larry Summers
• Robert Shiller

It's annoying enough that policy elites have to have bad ideas, but why do they always have to have the same bad idea?

Kofi Annan has a really bad idea

re: One Laptop Per Child

"This is not just a matter of giving a laptop to each child, as if bestowing on them some magical charm. The magic lies within -- within each child, within each scientist, scholar, or just plain citizen in the making. This initiative is meant to bring it forth into the light of day."
—Kofi Annan

"Instructionism" defined

Instructionism refers to all of the educational theories based on the idea of the teacher teaching, usually according to a predetermined schedule, rather than on students learning from their own experiences at their own pace. This includes any form of rote learning, and most forms of book learning in actual use, as well as drill and practice.

Instructionism | One Laptop Per Child

Compare and contrast:

The scientific laboratory is a place for exploration and discovery, where the principal topic of investigation is human ignorance in whatever form it currently takes, using the sharpest tools and brightest lights that human ingenuity can bring to bear. The school laboratory is almost always a place for regimented repetition of "experiments" whose outcome is known in advance. Similarly, a research library is a different sort of place to explore human ignorance about other kinds of questions. Here we look for interpretations of what has previously been recorded, often by comparing differing source accounts, often by finding questions that we can attempt to answer by other means. The school library is more often a place for looking up the "right" answer. A textbook can be an account of the frontiers of knowledge and understanding, presenting conflicting theories and attempts to find evidence to distinguish among them, or it can be a compendium of socially approved "facts".

Instructionism | One Laptop Per Child

Polar vortex la-la-la

Every few months I'll learn some horrible new thing I have never heard of in my entire life, which at this point is starting to seem weird, and a little bit creepy. Are there a lot of horrible things I don't know about? Not obscure horrible things--I'd just as soon not know about those--but regular horrible things, the kind of horrible things you can find on Wikipedia?

Things like Miller Fisher Syndrome, for instance. Until 2013 I had not heard even the words "Miller Fisher Syndrome." Then one Wednesday my next-door neighbor and friend started coming down with a cold and by Friday she was completely paralyzed.

Paralyzed.

I had spent years avoiding spinal cord injuries by not riding a lot of horses or bicycles, and come to find out all it takes to end up helpless and hallucinating in the ICU is catching the wrong kind of cold.

(My neighbor is fine now, thank God. She recovered quickly, too, much more quickly than I expected after a couple of sessions with Google.)

Anyway, Miller Fisher Syndrome. A new one on me.

Then yesterday I read the news and found….polar vortex.

I grew up a a farm, for pete's sake. My dad's crops lived or died by the weather. I thought I knew every catastrophic, life-altering storm and/or temperature change on the menu; in fact, I was confident I did. Yet somehow, in all these years, the words "polar vortex" never came up.

What next?

They do what they do

In the Times:

Only weeks before a chemistry experiment sent a plume of fire across a Manhattan high school science lab, engulfing two students and leaving one with life-threatening burns, a federal safety agency issued a video warning of the dangers of the very same experiment, a common one across the country.

The agency, the United States Chemical Safety Board, distributed the video warning to its 60,000 subscribers, a spokeswoman, Hillary Cohen, said Friday, but it had no sure way to reach individual teachers at schools like Beacon High School on the Upper West Side. There on Thursday, Anna Poole, a young science teacher known for safety consciousness, used methanol as an accelerant to burn dishes of different minerals in the chemistry demonstration known as the Rainbow.

With about 30 students watching from their desks, a snakelike flame tore through the air, missing the students closest to the teacher’s desk, but enveloping Alonzo Yanes, 16, searing and melting the skin on his face and body, according to witnesses. He was in critical condition on Friday in the burn unit of NewYork-Presbyterian Hospital/Weill Cornell Medical Center, Myrna Manners, a hospital spokeswoman, said.

Another student, Julia Saltonstall, 16, saw her thin T-shirt burned off her torso in an instant as some of her long dark hair went up in smoke, her father said. Though she was no farther from the demonstration than Alonzo, she escaped with only first-degree burns.

[snip]

The safety board’s video, and an accompanying message, did not say the Rainbow demonstration should be banned, but warned that accidents have repeatedly occurred because of the volatile material involved.


“What we need to look at is why is this accident keeps happening across the country,” said Mary Beth Mulcahy, a former high school science teacher who is now an investigator with the safety board, which has documented at least seven similar accidents, including a 2006 case featured in the video that left a 15-year-old girl in Ohio, Calais Weber, with severe burns over more than 48 percent of her body. “What do we need to do to stop the cycle?”

As a 23-year-old teacher, Dr. Mulcahy added, she herself did the rainbow demonstration, unaware of the potential dangers. The visually exciting demonstration shows how different substances produce flames of different colors because of their varying properties. But she added, “I can’t imagine a teacher would do this demonstration if they knew the potential risk they were putting students in.”

Said Ms. Weber, now a pre-med student in Boston: “I read this article last night about the New York students and honestly, I cried. I can’t believe this keeps happening.”

NYTIMES

Barry's book is out!!!!!

Letters from John Dewey/Letters from Huck Finn: A Look at Math Education from the Inside by Barry Garelick

Go order it right this minute!

I'm a sucker for Apple ads...

I'm 100% certain I shouldn't like this, but I do.

Revised post

For any of you getting posts by email …. I hit "Publish" too soon on the previous post, which is now finished:

5 years on