kitchen table math, the sequel: again with the critical thinking

Saturday, July 7, 2012

again with the critical thinking

Well, thanks to Texas Republicans including the words "critical thinking" in a statement no one outside a tiny group of public school obsessives actually understands (or cares to understand, apparently), we now have precious NYTimes real estate going to the celebration of non-memorization in schools.

Here, courtesy of the Times, we have the thoughts of a recipient of the Presidential Award for Excellence in Math and Science Teaching and the Distinguished Fulbright Award in Teaching:
I’ve worked for many years with students of varying demographics and learning abilities and what I’ve learned over and over is that nearly all kids love to learn – even those who would like us to believe they hate school. But what they need from their education is more than the memorization of facts – they need great teaching, foundational knowledge, problem solving skills, and the understanding of current issues.

What is a Good Teacher Worth?
July 6, 2012, 10:03 AM
So they're going to acquire "foundational knowledge" but they're not going to memorize any facts. Or not many.

How exactly do you pull that off?

And please don't tell me 'they construct their own knowledge.'

Speaking as a writer, I have constructed knowledge any number of times -- and then promptly forgotten what it was I constructed. For nonfiction writers, forgetting your own ideas is a common occurrence and an occupational hazard. That's why writers keep notebooks.

I do recall, I think, Willingham once saying that we remember knowledge we've figured out for ourselves somewhat better than we do knowledge we've been told by someone else. Assuming that's the case, I surmise that the mechanism is the amount of time you spend trying to figure something out, which amounts to a form of practice or rehearsal as well.

I know for a fact that 'discovering' and 'constructing' your own knowledge is absolutely no guarantee that you will recall your own knowledge later on.

Not even close.

There's only one route to Carnegie Hall.

instructivist weighs in


gasstationwithoutpumps said...

Actually, the quote you pulled out is the one part of the piece that is most correct:
"But what they need from their education is more than the memorization of facts—they need great teaching, foundational knowledge, problem solving skills, and the understanding of current issues."
(Other than that "problem-solving skills" needs a hyphen.)

Memorization is part of "foundational knowledge". I think that disagreements arise about how much foundational knowledge is essential, with people here leaning towards a larger foundation than some school teachers. But that does not mean that students don't need great teaching, problem-solving skills, and an understanding of current issues.

Catherine Johnson said...

Hey gas station --

The piece as a whole uses the word 'memorization' as a negative. Yes, she says that students need 'more' than a "memorized" education, but that 'more' is what makes education good, desirable, and enjoyable.

Here's another passage:

We’re having trouble keeping many of our young people in school because they’re bored and they don’t see the benefit of a memorized education; they want to learn and they want to contribute something meaningful to society.

Students drop out of school because they're bored and "don't see the benefit of a memorized education."

What is the evidence for this claim?

She doesn't offer any, and if you actively value long-term memory and knowledge, which I do, you might make a quite different claim: students drop out when they have failed to memorize the background knowledge that would allow them to understand (and memorize!) the new, more difficult knowledge they encounter in high school.

I haven't spent a lot of time reading the literature on high school completion, but what I have read doesn't comport with the idea that students drop out because they don't see the value in memorized education.

SATVerbalTutor. said...

It's interesting: in principle, I don't dispute what Revkin in saying. Having worked with kids who are accustomed to simply memorizing everything and absolutely allergic to actually thinking, even about very simple things, I can attest to the fact that memorization on its own, as the be-all end-all of education, is not a good idea. It's just as frustrating to work with someone who can't make any real connections between concepts because they don't have the tools to do so, as it is to work with someone who resolutely refuses to read exactly what's on the page. By the way, I'm not talking about kids who are low achievers. The student of mine who most clearly exemplified this phenomenon was admitted to Harvard this year.

On the other hand, though, most of my students could use a serious dose of memorization. They can't make connections between ideas because they simply don't have enough factual knowledge. When Revkin talks about memorization not being enough, those are the kids he's completely overlooking. A lot of teachers seem to be in complete la-la land about their existence.

Catherine Johnson said...

Hi Erica!

I get what you're saying ... but I **think** I'd like to go a bit easier on the "Memorizers."

I keep feeling that kids who are good at memorization should be able to ... feel like they've accomplished something.

Of course, inside actual schools, which still give tests, this is probably a non-issue.

Still and all, I was a terrific memorizer myself, and I did great on short timeline assignments, and I suspect that projects would have been the death of me.

When we were looking at private schools, we found one --- oh gosh, what was the name? I remember sending the link to Vicky S, who had the same reaction I did: THAT'S THE ONE!!

You'd know which one it is....darn. Can't remember the name.

It was a boys school where the boys wore uniforms (pretty sure) and under school philosophy it said, "Our students learn through short timeline assignments."

It came pretty close to saying, outright: YOUR SON WILL NOT BE DOING PROJECTS HERE.

Back to thinking and memorizing...I was a very good memorizer, and I was an active thinker in h.s., too, although I'm not sure whether anyone wanted me to be.

I actually came up with Freud's theory of projection after a couple of run-ins with aggressive popular girls who criticized me for being aggressive---- !)

I'm still having the same problem with the popular girls, come to think of it.

Jen said...

So they're going to acquire "foundational knowledge" but they're not going to memorize anything.

How exactly do you pull that off?"

I'm going with genetic engineering. Manipulated bacteria will deliver the foundational knowledge to their brains directly.

Jen said...

Obviously, JUST memorization is not enough. But:

Gasstation: "Memorization is part of "foundational knowledge". I think that disagreements arise about how much foundational knowledge is essential, with people here leaning towards a larger foundation than some school teachers."

You will find MANY people who argue that little memorization is needed and that foundational knowledge can be acquired solely through discovery and hands-on and group learning.

I know that for myself, memorizing things led to greater understanding YEARS later in many instances. For instance, I knew what procedure was called for and how to do it -- and even had a rudimentary understanding of the why of it all. But things literally clicked in terms of conceptual understanding years later in some cases.

I don't think that that click will ever come without the memorized bits though it could certainly happen in a shorter time frame.

But, while a clear conceptual understanding is what I'd love to leave a kid with, I'd be happy if they just had a good procedural knowledge and ability to determine when to use it. That's better than having...nothing.

Daniel Ethier said...

I think part of the fallacy here is seeing things as memorization vs critical thinking and problem solving.

The truth is more that the rote knowledge and memorized information is the foundation for critical thinking and problem solving.

As a computer science guy who has taught himself a variety of programming languages and how to program a bunch of platforms, I would usually start by imitating code samples exactly. Over time I was able to understand what they were doing, and eventually I was able to be more creative with what I was doing.

I have had similar experiences in other areas. The rote memorized information is the starting point, then comes understanding, finally you can be creative when have deep understanding. Sorry, no short-cuts.

Daniel Willingham made a similar point in the following article:

He calls it inflexible knowledge. It's the required starting point. The flexible thinking builds on it. Again, there are no short-cuts.

SATVerbalTutor. said...

@ Catherine. No, there's absolutely nothing wrong with memorization. I agree 100% that it's the basis for higher order skills. I was also a champion memorizer in high school; I LOVED to memorize things. That's part of why history was my best subject -- it was actually the only subject I got straight As in (speaking of rigorous grading, you may be interested to know that I actually got a C+ one semester in English!) I didn't really learn to "think critically" until I got to college, when I was finally able to put all that factual knowledge to use, and understood why it was so important to have all that factual knowledge in the first place!

But trust me when I say this girl drove me crazy. She was just memorizing things so she could get As on tests; she had no deeper interest in really learning things for their own sake (e.g. she claimed to love French and want to major in it but couldn't even be bothered to spend five or ten minutes a day reading in it, and she made virtually no effort to try to speak it. She literally just wanted to conjugate verbs and got annoyed when she had to do anything less mechanical). Nothing annoys me as much as blatant grade-grubbing.

@Daniel Either. Yes, I agree 100% Factual knowledge is a precondition for higher-level thinking, not its opposite (wow, I really have to do a blog post about that). I learned to write papers in college by reading academic journals and basically imitating how professional scholars wrote. When I work on writing with people (not for the SAT), one of the first things I tell them is that I don't care about whether they're being original or not. A lot of academic writing is about obeying conventions. Once you've mastered those conventions, you have a lot of room to maneuver, but until you understand how to structure a sentence, paragraph, paper, etc., any attempt to be original is likely to turn into a complete mess.

SteveH said...

"But what they need from their education is more than the memorization of facts.."

What schools just have kids memorize facts? Long gone are the days of memorizing the list of presidents, although I can make a good argument for that.

"Last month I asked my students to take a pro or con position on the topic of genetic engineering; one student vociferously announced, “I completely disagree with it."

Where's the "foundational knowledge"?

"She is a recipient of the Presidential Award for Excellence in Math and Science Teaching and the Distinguished Fulbright Award in Teaching."

"Other students thrust their hands into the air anxious to share their point of view, while others simply blurted out their ideas – our classroom was intellectually alive and I was the moderator."

Opinion is NOT foundational knowledge. Apparently, she thinks this demonstrates critical thinking".

"Some adults oppose the teaching of critical thinking skills in our schools, but this is counterproductive."

Nobody opposes critical thinking skills. They oppose twaddle.

Catherine Johnson said...

I was also a champion memorizer in high school; I LOVED to memorize things.

That's the funny thing -- Ed and I went out last night, and I was telling him about the latest Times salvo against memorization, and Ed said, "That's why Asians can do math" (i.e. 'cuz they don't have a gazillion awarding-winning teachers trashing memorization in the newspaper of record).

Then I told him about your student --- who got into Harvard!

And now you tell me you were a great memorizer...

Memorization seems to be pretty strongly predictive of later success ---- !

lgm said...

>>What schools just have kids memorize facts? Long gone are the days of memorizing the list of presidents, although I can make a good argument for that.

Apparently college. My jr's Early College in the High School history class thru S.U.N.Y. Albany devoted 1/4 of the grade to quizzes on data tables. States, capitals, geographical features, people (not in assigned reading but in data table given), major cities, origin of immigrant population, Constitution and amendments (had to know section numbers and summary of each part), supreme court cases and impact on law. The Constitution wasn't discussed in class and it was up to the student to read up on the supreme court and how it comes to a decision.

States and capitals used to be done in elementary school; with full inclusion that was tossed out of the curriculum here. Presidents are still in the honors middle school social studies curriculum here.

lgm said...

Foreign language is also rote memorization. Since it is full inclusion, there is very little reading - the students are told to use the flashcards on the publisher's website to learn the vocab. after it is read to them in class. 7th, 8th, and 9th grade here is all auditory instruction, very little written output.

momof4 said...

In the classical curriculum, the first four years (1-4) comprise the grammar stage, wherein the foundations are laid across the disciplines. This includes lots of memorization - scientific terms, people,places, capitals etc. The next four years comprise the logic stage, which builds on the foundations and establishes connections. The next four years (HS)comprise the rhetoric stage, which also deepens knowledge but stresses analysis and defense/rebuttal of academic positions.

AmyP said...

"7th, 8th, and 9th grade here is all auditory instruction, very little written output."

That is very unfortunate.

With regard to memorization, I'd like to put in a plug here for how they teach poetry in Russia. I don't know how much analysis they do in class, but students are expected to memorize yards of verse during their school careers (I only had to learn two in the US). The virtue of the Russian method is that a lot of students really bond with the material (like the people in Fahrenheit 451 who become books) and some very unlikely individuals (plumbers and electricians) will go all through their adult lives able to quote 19th century Russian Golden Age poets at will. You simply do not see that sort of thing among non-elderly people in the US. I've come to think that that sort of memorization of verse as the surest way to forge a life-long relationship between students and poets, and the most natural way to study verse. (Analysis is good, too, of course, but more people are capable of learning poems than analyzing them well, and memorization has more lasting effects.)

SATVerbalTutor. said...

Memorization seems to be pretty strongly predictive of later success ---- !

That's because you can't do anything without it! If you don't have the factual knowledge at your fingertips, you have no way of putting things together. I learned all my grammar from *years* of rote work in foreign language class: the reason I can spout off about tenses, to take one example, is that I covered them all in French, then in Italian (adding the imperfect subjunctive), and German (adding yet another form of subjunctive for indirect speech). Worksheet after worksheet after worksheet, looking up every word I didn't know. No one even tried to make it fun. It was simply understood that there was no other way to learn a language.

I have no idea what people are expecting when they ask me how to learn vocab: umm... read a whole lot and look up every single unfamiliar word. Everyone wants there to be a shortcut (so they can get to the fun "critical thinking" part), but sometimes there just isn't.

Btw, the student I was talking about is Korean. The whole Asian emphasis on rote learning does have some huge benefits, but it also has some real shortcomings. I'm having to deal with a lot of parents right now who just don't get that boosting a CR score isn't about memorization. They want their kids to be able to sit down and do x,y,z that'll guarantee a score increase, but the reality is that a kid who's basically just learned to memorize things, doesn't read or discuss books on a regular basis, and has very little cultural/contextual knowledge for what they're reading on the SAT is probably not going to be able to pull their score into the 750+ range, no matter how much stuff they memorize. They 1) don't really get the big picture, and 2) miss too many of the nuances. But the parents literally don't get that their kids can't just memorize their way to a high score.

Catherine Johnson said...

Sorry, no short-cuts.

No royal road to geometry!

(Actuallly, I'm interested in shortcuts, and I think there are some...but those 'shortcuts' have to do with efficient teaching & practice....)

Catherine Johnson said...

Ed was saying, last night, that he's really not interested in uninformed opinion at all.

In his classes, during recitation sessions, you do have some debates (over Palestine/Israel situation, he mentioned - I think this may have been in an undergraduate class on...imperialism...)

He sometimes, when that occurs, asks students to argue the position they don't hold.

Catherine Johnson said...

lgm - you just reminded me of something I wanted to post from Bambrick-Santoya's book. He talks about watching one first grade student help another first grade students with flash cards for, I think, 30 minutes.

I think flash cards are a good thing; I have no problem with flash cards. (That said, I never had good luck with flash cards per se....)

But I was a little skeptical of the idea of one student spending 30 minutes helping another student with flash cards ----

Of course, I suppose the student handling the flash cards is also experiencing a practice effect, but it sounded as if that student already knew the material on the cards...

gasstationwithoutpumps said...

It seems to me that people here are prizing what they do best. Those who memorize well are holding up memory work as the foundation for all thought, and those whose expertise is in problem solving hold that as central. (I have never been as good at memory work as at problem solving—history was my worst subject, and I hated it.)

I think that the real situation is that a number of different skills are needed to think well, and that sacrificing some to make one dominant weakens the students. A balance is needed—no, not a single balance, but a different balance of skills for each student, building on their strengths to shore up their weaknesses.

gasstationwithoutpumps said...

has a good post on the use of both higher-level thinking skills and memorization in high school math, written by a math teacher.

gasstationwithoutpumps said...

One of the better defended (and better written) anti-memorization posts I've seen:

momof4 said...

Re: the comment that their 7-8-9th foreign language instruction is essentially all verbal - little written work - because of full inclusion, is appalling.Letting the inclusion of some kids (sounds as if they should have been elsewhere)water down the subject that badly for the rest of the class is just wrong. I'd say educational malpractice, if the ed world was aware of the concept. My kids had regular HS-level Spanish I and II in MS, then went on to Honors Spanish III as freshmen.(there was also regular III). In that class, they finished covering all of the verb tenses - and that class and subsequent Honors IV, AP language and AP lit were all taught in Spanish. Yeah, no one tried to pretend there wasn't lots of memorization, either. There's too much emphasis on "engagement" (whatever that is) and fun and too little on the real effort necessary to learn new material.

Catherine Johnson said...

In all of these discussions there's a problem with definition of terms....

"Memorize" usually means something along the lines of flash cards: intentional, conscious, effortful memorization of specific content.

But there is another form of learning that involves storing content in long-term memory that we don't seem to have a separate term for, and that is repeated exposure.

When you see the same content over and over again, at some point you start to remember it.

I have no idea when students should use flat-out, effortful memorization and when they should use repeated exposure.

This raises another issue that always bugs me.....when ed schools spend their energy denigrating memorization, they aren't spending their energy figure out the best way to move knowledge stored inside a textbook inside students' brains.

Nor are they figuring out which specific content is important to store in long-term memory and which is not.

MagisterGreen said...

Momof4...if you don't mind my asking, what kind of FL program was that which got your kids through HS level II Spanish by the end of 8th grade? I ask because my school is lurching towards something like that but it's being done in such a slovenly fashion that I'm seriously concerned about the students and the program being irrevocably damaged and I've been hunting for successful models.

Catherine Johnson said...

It seems to me that people here are prizing what they do best. Those who memorize well are holding up memory work as the foundation for all thought, and those whose expertise is in problem solving hold that as central.

Not true for me at all!

I think I mentioned in another thread that I worked out Freud's theory of projection independently, for myself, when I was in high school. I was always a 'critical thinker,' naturally so I would say.

As a nonfiction writer my strength is essentially creative: I make connections among studies, findings, and ideas that other people haven't made already (or haven't made in the same way I make the connection....I realize that's vague).

I also (try to) figure out ways to convey these connections that are as striking as possible.

My work involves a form of creativity that is ***completely*** dependent on other people's knowledge.

There's a great saying about this:

"When a man writes from his own mind, he writes very rapidly. The greatest part of a writer's time is spent in reading, in order to write; a man will turn over half a library to make one book."
Boswell: Life

lgm said...

Momof4, your opinion would be viewed as elitist and classist/racist by many in this area. The vocal majority wants success to be available to all who are not classified special education. This means slowing down the courses, so that ELL/poverty can catch up and tutors can fill in gaps. Resources are not to be used on those who are advantaged; they are to dual enroll or go to college early should they find the high school has nothing challenging.

I am the first gen in my family to go to college ancestors came over post Civil War or were Native Americans.....shocking to see that I am considered 'advantaged' and my children can't get the same education I did. I went to a rural school with no AP/IB/Honors, but they knew how to do independent study right.

momof4 said...

lgm: you are unfortunately right, in too many cases. The more/most able kids "will do fine, anyway" - right? Anything for that group is targeted as elitist, classist and racist - despite the fact that those terms are tossed out so often that they are often meaningless; the Hispanic son of two physicians is disadvantaged, the black son of two lawyers is disadvantaged and the son of two Vietnamese "boat people" is advantaged, as is the son of an unemployed coal miner from WV - all people I have known. It's a crazy world. Meanwhile, (far-more-expensive) kids at the other end have rights that trump all others.

Magister Green: That was the regular Spanish sequence (can't remember if they have French, German was DQ'd)at my kids Montgomery County, MD (probably lots of stuff online) MS - I think the program is still the same. They were real HS-level classes, with lots of the class time in Spanish, starting in II. I'm pretty sure they used the same texts as the HS I and II. I think there may have been an honors section for II, but am not sure, and there may have been an option to spread Spanish I over 2 years. At the HS, the same teacher taught all/most sections of III, including honors (wholly in Spanish) and another teacher taught all subsequent honors and AP classes - both were excellent.

I should probably add that all of the courses are supposed to be the same countywide, but this was not always the case - it tended to depend on the demographic/educational level of the catchment area. The school my kids attended was one of the top-end schools and HS level, honors and AP classes were really that level. Is this what you wanted to know?

MagisterGreen said...

Ah, the Montgomery County program. Was this the immersion plan or just the standard sequence?

Jen said...

"the first four years (1-4) comprise the grammar stage, wherein the foundations are laid across the disciplines. This includes lots of memorization - scientific terms, people,places, capitals etc.""

And when you think of this age group -- it's the kind of learning that's exciting to them. This is the age of treasure chests and collections and gathering stuff.

The acquisition of foundational knowledge/basic facts is right up their alley. They want to know multiplication;, they like to gather interesting words.

As Catherine points out, we do seem to be using the term memorization to refer to two different ways of getting things into LT memory. Memorization gets a bad name as just being flash card type drills.

But as I always used to ask kids who didn't know some of the harder basic facts -- what was your kindergarten teacher's name? who was the gym teacher? what's your grandma's phone number? [insert questions about movies, music, etc]

I could prove to them that they do, in fact, have perfectly serviceable memories. It's a matter of exposing them to it often enough (and I'd add in different formats, ONE of which might be classic, flash card style drills) to get it in there for good.

Anonymous said...

Students will memorize what they want to learn, and see a point to learning, much more readily than material they are being forced to take as a graduation requirement. Kids who want to be mechanics can memorize all the parts of a car and how they work. Kids who want to be chefs will memorize hundreds of different cooking procedures and how the various ingredients interact. Kids who are going to end up as talented salespersons hone their abiiity to "read" other people to the nth degree. At some point the issue becomes not whether to memorize, but what to memorize.

palisadesk said...

I don't know if it's a larger trend, or just a local one, but I've seen a noticeably
increased emphasis on the importance of memorization in the last few years. Maybe
it's connected to our curriculum leaders' discovery of Richard Elmore and Hattie's
Visible Learning (if you don't know it, it's a wonderful meta-analysis of effective
practices in teaching -- surprisingly readable). This emphasis on memory work is
apparent across subject areas. I see children memorizing and reciting classic poems
(Stevenson, Lewis Carroll, Robert Frost) and selections from famous speeches
(Lincoln, Martin Luthur King, some of Shakespeare's soliloquys). They are expected
to memorize things like the instruments in the orchestra by family -- woodwinds,
strings etc. -- names and characteristics of particular artists -- Seurat, Picasso,
pointillism, Gauguin came up recently -- not to mention geographic terms, map
locations and so forth. There is less of this than I recall in my elementary years
but far more than in the not-so-distant past, when I would have been bowled over by
an urban ESL third grader explaining pointillism to me, with correct terminology

Where math is concerned, the district (and hence the school) has made developing
foundation skills a priority and we were mandated to devote about 20 minutes daily
to mental math skills -- learning number facts fluently being a prominent goal. I
was surprised to find that first graders are expected to be able to rapidly skip
count forwards, and backwards, to 100 by 1,s, 2,s, 3's, 5's and 10's -- starting at
any point. With lots of practice, that becomes a good foundation for the
multiplication facts.

We have a math coach (responsible for a number of schools) who comes in with
suggestions and materials, but the main thing I have seen is whole-class
teacher-directed practice, often interactive and engaging. They not only use flash
cards but also flash pictures of quantities or equations which the children must
rapidly identify or solve. For instance a card might have a representation of 5
blue dots and 6 red dots (in a sort of random pattern) and children are asked to
rapidly give an equation for the picture -- 5+6=11, or 11-6=5, for instance. They
have to do this fast. Those who need to count on fingers or in their heads are
earmarked for extra practice.

As for general knowledge, I've never heard it deprecated as "mere facts" or
superficial knowledge. Teachers encourage kids to learn and remember "mere facts"
and are favourably impressed when they do this, especially when they do it on their
own, suggesting special interest or commitment. In informal conversations,
colleagues will tell me things like, "Jovaine knows an amazing amount about
reptiles, let's see if we can find some science activities after school for him" or
ask me to help them find resources on some topic that a student was particularly
involved in. Never with any suggestion that "mere facts" were of no importance,
rather that they were a signal that a student might have special aptitude or
interest in something, and we should encourage him.

momof4 said...

Magister Green: The foreign language sequence was not an immersion program - there was none at that school (Frost MS). It was a regular sequence - the one the honors/future AP kids took. The school, and its associated HS (Wootton) does have a lot of very capable and motivated kids - reflection of the local demographics.

Glen said...

I think the two types of memory that people are referring to here would tend to be called long-term declarative memory and procedural memory.

One of the issues when learning a spoken language is that it is a hardcore, real-time skill like playing tennis. Real-time skills rely most heavily on procedural memory. Declarative lookup just isn't "designed" for real-time skills, but it is the easiest type of memory to test objectively.

This produces an unfortunate tendency for schools to teach what is testable (vocabulary & grammar trivia quiz) more than what is most useful (real-time communication habits).

Even more unfortunate is that many educators with a sketchy understanding of this draw the wrong conclusion. They discontinue the fact learning (wrong), and don't do what is needed to cause procedural learning (wrong again), which can't be directly taught.

Procedural learning is an adaptation to pressure, and the pressure needs to be significant and sustained. One way to increase this pressure is by directing the students' attention, and one powerful way of doing that is with--quelle surprise--declarative learning.

If you learn enough vocabulary and grammar to make some sense of what you are hearing, it will capture your attention in a way that gibberish won't. That attention significantly increases the pressure on your procedural memory to adapt.

Of course the best pressure is peer pressure. Put a kid in a class with classmates who are native speakers of the target language, and you have the kind of sustained pressure that languages are built on. Even then, a nice mental dictionary of basic vocabulary and a certain amount of explicit explanation help.

I don't see any practical way to do the peer pressure thing for most students without, dare I say it, much more extensive use of technology in the classroom (video Skype, etc.) We need it.