know your edu-terminology

cognitive demand

I'm disheartened to say that I have, this morning, detected yet another obstacle to student achievement in our public schools: the doctrine of "cognitive demand." (pdf file)

The global economy requires that students be provided learning experiences in algebra, geometry, data representation, and statistics that are high in cognitive demand.

High in cognitive demand appears to mean, simply, that the material being enacted (news flash: curricula are now enacted, not taught) is hard for the students to do.

The term “cognitive demand” is used in two ways to describe learning opportunities. The first way is linked with curriculum policy and students’ course-taking options — how much math and which courses. The second way relates to how much thinking is called for in the classroom. Routine memorization involves low cognitive demand, no matter how advanced the content. Understanding mathematical concepts involves high cognitive demand, even for basic content. Both types of cognitive demand are associated with student performance on achievement tests, but they are not substitutes for each other.

This is simply false.

Nearly 3 years into my math self-teaching project (3 years!) I am here to tell you that actually doing math, in the wake of routine memorization, is often far more difficult than understanding it.

Not that I have profound understanding of arithmetic and Algebra 1.

Nevertheless, I do frequently understand a concept fairly well only to discover (discover!) that I can't begin to use it in -- and forgive me for putting it this way -- real life.

next point

I am as certain as a human being can possibly be that the authors of this white paper would construe the sort of understanding I've been doing as not being high in cognitive load. If I can understand a concept better than I can do the concept, how can the concept be high in cognitive load?

answer: it can't

High cognitive load, by definition, comes from understanding, not doing. (Doing depends upon routine memorizing; otherwise you can't remember the steps). If a student is having a harder time with memorizing-doing than he is with understanding, the curriculum-enacter needs to crank up the level of difficulty of the latter.

Which our curricula and curriculum enacters have done!


I give up

I've been thinking about Robert Slavin's observation that ed schools used to focus on direct instruction and teacher effectiveness, once upon a time.

I have to assume he knows what he's talking about.

Which means.....ed schools used to focus on direct instruction and teacher effectiveness. Once upon a time.

Well, when was that time?

And how did it end?

And why was constructivism the next thing?

I'm thinking that the standards and accountability era, which we can provisionally date to 1983, the year that A Nation at Risk appeared, may be the explanation.

Here's the way I make it out (speaking as a person who is not a historian, obviously):

• prior to 1983: public schools a mess, achievement in decline
• after 1983: public clamor for standards and accountability
  
• ed school response: knowledge can't be "transmitted" from teacher to student, and cognitive psychology proves it: people don't "receive" knowledge but, rather, construct knowledge
  
• therefore: students must discover their own knowledge
  

This last point has always been the sudden leap in logic that unhappy parents and mathematicians (and the National Research Council)^* fail to grok.

There's no logical reason to move from the insight that people construct knowledge to the assertion that students must therefore discover knowledge. (And, as I believe instructivist once pointed out, if you're discovering knowledge you're not exactly constructing it, are you? I mean, if it's just lying around on tables and SMART Boards waiting to be discovered.....it's already been constructed. update: yes, instructivist made that very point. And if you have to construct knowledge, not just discover knowledge, then don't you need something to construct it out of? Like some facts or figures or findings or such?)

I remember learning, at Dartmouth, that people construct knowledge.

No one said a word about people therefore having to discover knowledge. That wasn't the point. The point was that when Person B listens to Person A, Person B will use the stuff inside his head - which is different from the stuff inside Person A's head - to make sense of it.

In other words: communication is Playing Telephone.

So is teaching.

There's no discovering.

There's just noise in the channel.

"Discovering" appears to be an ed school add-on.


it's a plot

So I'm thinking..... the invention of constructivism-as-discovery wasn't simply a mistake.

Constructivism-as-discovery was a defense.

The schools had always been about inputs, not outputs.^** Then, suddenly, the public was demanding that educational inputs actually work.

Under the circumstances wouldn't it be helpful to learn that research in cognitive psychology proves it's not possible for teachers to teach?


what would a real historian say?

Ed has been in Brussels since Saturday, so I hadn't had a chance to run this by him.

But when he called today, I asked if this sort of thing is plausible -- is it the sort of explanation a real historian would come up with and be able to support?

He said that, actually, it pretty much is.

He himself (and remember: he headed the California History-Social Science Project back in the early 90s) had attributed the advent of constructivist doctrine to A Nation at Risk, but for a different reason. He had always assumed that professors of education reacted to educational decline by concluding that the traditional methods didn't work.

But he thinks that in fact my hypothesis could be part of it (meaning you could find evidence to support it if you looked).

Of course, I'm not going to go out and find evidence; I'm just going to assume (provisionally) that it's true.

Which is why I give up.

Other people's wrong ideas are one thing.

Other people's defense mechanisms are quite another. You can't talk a person out of a defense mechanism.

If constructivism is in part or in whole a means of defense against the standards and accountability movement .... then parents are going to have to figure out how to teach their kids math themselves.

Math and everything else under the sun.


^* A common misconception regarding “constructivist” theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1994) —even listening to a lecture involves active attempts to construct new knowledge.
National Research Council

^** Clowes: So Project Follow Through confirmed what you had already found about the ineffectiveness of those other programs. Yet those programs still are being promoted in teacher colleges and they still are widely used, while Direct Instruction is not. Why?

Engelmann: The answer is really simple, but it's very difficult for most people to accept: Outcomes have never been a priority in public education, from its inception. That's the way the public education system is. The system is more concerned with the experience of the child: "Let the child explore," "Let the child be his or her self," "Don't interfere with the natural learning process," and so on.
Engelmann, interview