kitchen table math, the sequel: uh-oh

Sunday, March 6, 2011


"when A.P. testing began in 1956, memorization was not yet a dirty word"

Rethinking Advanced Placement
Published: January 7, 2011
In theory, the new A.P. courses are going to replace "memorization" with "critical thinking."

In reality, critical thinking depends on memorization: you can't think critically without something to think about, and that something has to be stored in long-term memory. If you're going to think critically, you have to know (i.e. remember) what you're thinking about.

What happens when you try to think critically about a subject without memorizing its terms and concepts first?

What happens is that you can think about 4 items at most. That is the number of new, discrete elements you can hold in conscious, "working memory"* at one time. Four. And four may be pushing it.

Of course, when it comes to critical thinking, 4 is a tiny number. Experts think critically about far more elements at one time; being able to think about a vast amount of complex material is pretty much the definition of an expert, as a matter of fact:
The sine qua non of skilled cognitive performance is the ability to access large amounts of domain specific information [i.e. knowledge]. For example, it is estimated that chess masters have access to as many as 100,000 familiar configurations of chess pieces (Chase & Simon, 1973). As another example, in order to make sense of what he or she is reading, a reader must have access to information gained from previously read text. This is particularly true when reading complex technical material filled with jargon.
summary of Ericsson, K. A., & Kintsch, W. (1995). Long-term working memory. Psychological Review, 102, 211-245.
David Zach Hambrick, 1998,

basal ganglia lollapalooza

Here's an example from my own life.

As a nonfiction writer, I'm essentially a permanent student: I am constantly trying to write interesting articles and books (mostly books) about material that may be brand-new to me. My current project involves the basal ganglia, which I knew nothing about going in. The vocabulary alone is overwhelming: nucleus accumbens, orbitofrontal circuit, putamen, striatum --- and that's just for starters.

So here's the question. How exactly am I to (a) understand and (b) think critically about a passage that contains these four terms if I haven't memorized what these terms mean and how they are related to each other first?

The answer is: I can't.

If I don't memorize vocabulary, I have to look up the definitions and then try to hold the definitions in mind while also reading and trying to think about what I'm reading.

It can't be done, and the reason I know it can't be done is that I've spent a lot of time trying to do it. I always make the same mistake with each new project I tackle. Somehow I think I can just look things up (Google!) and remember them while I read a complex study or article.

But I can't. No one can. Looking up four new words and remembering four new meanings maxes out working memory. There's no capacity left to read and understand a text using those four new words and four new meanings, let alone think.

I don't know why this is. Logically speaking, shouldn't it take just as much working memory to hold 4 memorized terms in mind as it does to hold 4 non-memorized terms in mind?

The answer is no: knowledge - content stored in long-term memory - extends working memory.

When you know a lot about a subject - when you have a great deal of knowledge stored in long-term memory - you can think about more than just 4 things at once.

blackboards vs PowerPoints

* Working memory is essentially consciousness: it's what you're thinking about and/or remembering right now. When you hold a phone number in memory while dialing it, you're using working memory.


Catherine Johnson said...

Working memory is so much larger for subjects you know well that for a time researchers like Ericsson were talking about "long-term working memory."

I don't understand that concept well, and I **think** cognitive science has moved on to a different understanding of why working memory is so much bigger in your area of expertise.

But take that with a grain of salt.

Daniel Ethier said...

Cognitive load theory has much to say about the educational implications of our limited working memory on learning.

As I read various papers on cognitive load theory, I keep having aha moments as I find reasons for things I see in the classroom.

The key to getting around our limited working memory is automaticity. If you know something well enough to not have to think about it, it does not take up working memory. And so you are free to think about the problem you're trying to solve.

Use Google Scholar and read some of the many papers about various aspects of cognitive load theory. Well worth the time.

Catherine Johnson said...

btw - & I don't think I've ever pointed this out - because of our kids' autism, we've seen physicians who are world experts in the field.

The amount of knowledge a world expert can bring to bear on a subject (or a diagnosis or treatment plan) is staggering.

Sometimes I wonder how many education-world people have ever dealt face-to-face with a real expert.

I suspect that once you've seen an honest-to-god world expert in action, you couldn't minimize the importance of memory and memorization.

Catherine Johnson said...

Looks like long-term working memory is still a viable concept.

ChemProf said...

And a broad knowledge base also helps. Last year, one of my chem major seniors ran into papers that talked about "spiked samples." She had never heard of spiking punch or similar terms, so couldn't make sense of the papers. Since it was such a general term, she also found google was useless.

A spiked sample, by the way, is one where a known amount of a standard that isn't present in the original sample is added. The technical term is an internal standard, but it is often just called spiking.

Glen said...

I suspect that once you've seen an honest-to-god world expert in action, you couldn't minimize the importance of memory and memorization.

Unfortunately, I don't think you're right about this, because unlike you, Catherine, most people don't understand what the expert is doing when they watch him do it. They don't know enough about cognition. They think he's reasoning when he's mostly recognizing. The expert himself may not realize it if his field isn't related to brain function. They never show "Dr. House" studying, only pondering. That's how people, even experts, see experts.

Allison said...

I'm with Glen on this one. Not only do they not recognize an expert when they watch "him" do it, they don't recognize their own expertise when they themselves do it. In fact, this is PART OF CHUNKING! When you've really backgrounded the process, and you really aren't spending any working memory on it anymore, because you've chunked so much, you can't accurately even describe what you do--because consciously you do not know. You've memorized enough that you aren't thinking about it, and therefore, aren't conscious of what you're doing. Few people then abstract along that line of thinking to realize what must be happening cognitively.

Consider the excellent reader. Readers have read numerous books, websites, magazines, and the like and are EXPERTS at reading, having spent 20-50 some years doing it. We do it a lot differently than we did when we were young. Do most expert readers have any sense that we aren't reasoning, but we're recognizing? That we've chunked entire sentences and sentence structures?

Or the expert car driver. Or the expert cook. You need not be Michael Schumacher or Martha Stewart or 6 sigma away from the mean; just 3 sigma away is enough different to show how significant memory is, but most people can't even tell you what they are doing when they drive--no idea where their hands really are, or when they check mirrors, or what they actually did when they downshifted and then switched lanes, say. It would take a lot to convince people that they've "memorized" driving in this sense, because they didn't learn it by flash cards, nor did they actually repeatedly practice every scenario in closed conditions. But the brain has memorized, and has chunked the information.

btw, your statement about working memory being "essentially consciousness" is not at all a good description. Consciousness requires a self-awareness, an ability to observe the process of experiencing and deciding, and influence at that meta-level. Concepts in working memory may be what you are currently conscious OF, but that's not the same process as consciousness, which requires far more than just elements in working memory, including but not limited to this ability to self-refer, self-limit, self-control the thoughts one is having in working memory. Mice have working memory too. But that's not consciousness.

Allison said...

--I don't know why this is. Logically speaking, shouldn't it take just as much working memory to hold 4 memorized terms in mind as it does to hold 4 non-memorized terms in mind?

I think you're using a kind of physical analogy for memory that doesn't really apply.

In computer science, you can think about the physical memory that a byte of data is held in; and computer programs were once written to "look" in that location of memory, whether that was a location on a tape, or a sector on a hard drive, or a cel in an array.

But then computer scientists moved on to addressing memory not by its physical location, but with more abstract means. One was an arrow, or a pointer. You don't need to ask what's in location 134. Now you ask what's my pointer pointing to, and it could even point to other pointers.

Once you accept the abstraction, then you realize that pointers don't need to point to atoms of information, but can point to be structures of it. A pointer need not point to 134, but can point to "the recipe for bread pudding" or "the set of actions needed to slow the car down".

Other abstractions for handing data in memory work, too. One nice one is a "thunk". It's a way of handling a very long (or infinite) list. The ingenious part is that instead of actually trying to hold the WHOLE list in working memory, you just hold two items: the first element of the list, and a promise to return the rest of the list if you really need it.

Think about that for a while--the "promise" ensures that you know you can get the data if you have to, BECAUSE IT'S ALREADY STORED AND ORDERED IN SOME MEANINGFUL WAY. And so, if necessary, you actually can return the whole list, one element at a time, if need be, but you never need to have more than two elements in working memory at a time.

So, this is one way that content "Extends" working memory: it structures your knowledge your brain can return a "thunk" to you instead of having to actually return you all of your knowledge right now.

Allison said...

When you're learning something, especially new content, you don't have a structure for it to fit in. You don't have a schema. Some concepts fit well in a tree structure--"here are biological processes, off those processes we hang branches labeling the organs responsible for those processes, off that we explain the mediating step, or the key regulatory mechanism that organ achieves", or "here are strategies, off of those we hang tactics, off of those tactics we hang materiel needed to employ said tactics." Other structures are more appropriate to other ideas.

But when you're looking at new ideas, you don't have a place to hang anything yet, because you haven't understood well enough to organize it. So you have to keep learning those definitions, keep re learning those concepts to mastery until your brain finally starts organizing the content in a meaningful way rather than just "oh, stuff it in the file cabinet somewhere". That takes practice, and we know that *retrieval* supports that organization. And our brains RE ORGANIZE as we learn, and experts have re organized in multiple ways, overlaying more mappings on top of the other ones, connecting to other concepts with something like those pointers pointing to whole structures at a time.

This isn't to say that at the wet level of brains, we've got pointers or thunks per se, but that various models of abstraction of how the mind works are useful for understanding why we're not as limited as the physical underpinnings of "4 items in memory" sounds.