Declarative knowledge is knowledge you can declare.

I declare that 2 + 2 = 4

It took me about 2 seconds to check--and I could check simply by trying it out on a simple fraction problem and seeing if I got the right answer--then I had it. Procedural knowledge is sturdy stuff.

So I always remember what procedural knowledge is.

But I came across a definition I'd never heard before over at Wikipedia; procedural knowledge is know-how. I love that.

Know-how is a useful term in more ways than one, I think. Your Core American respects know-how. Even more importantly, your Core American does not respect eggheads & pointy-headed intellectuals.

I say we let radical constructivists yammer on about critical thinking skills.

We're talking math know-how.

consigning 'rote memory' to the Banned Words & Phrases bin

No more In defense of 'Mindless Rote' essays. Please.

What distinguishes our position from radical constructivism is not that we believe in rote knowledge. We do not. (I do not, make that.)

We (I!) believe in:

• domain knowledge, aka declarative knowledge (A cognitive scientist probably would not equate these two, for reasons I'll get to in another post. However, in general, I'm going to tend to use these terms as rough synonyms.)

and

• procedural knowledge (more qualifications: I can't tell whether cognitive scientists universally use the term procedural knowledge or procedural memory to apply to intellectual procedures, like adding & subtracting. Normally you see procedural memory applied to motor skills, like knowing how to ride a bicycle. I'm going to check around. Still, Liping Ma uses the term procedural to describe fluency with the algorithms, and that's good enough for me.

Willingham on rote memory

What is Rote Knowledge?

Much of what is commonly taken to be rote knowledge is in fact not rote knowledge. Rather, what we often think of as rote is, instead, inflexible knowledge, which is a normal product of learning and a common part of the journey toward expertise.

In his book Anguished English, Richard Lederer reports that one student provided this definition of "equator": "A managerie lion running around the Earth through Africa." How has the student so grossly misunderstood the definition? And how fragmented and disjointed must the remainder of the student’s knowledge of planetary science be if he or she doesn’t notice that this "fact" doesn’t seem to fit into the other material learned?

All teachers occasionally see this sort of answer, and they are probably fairly confident that they know what has happened. The definition of "equator" has been memorized as rote knowledge. An informal definition of rote knowledge might be "memorizing form in the absence of meaning." This student didn’t even memorize words: The student took the memorization down to the level of sounds and so "imaginary line" became "managerie lion."

"Rote knowledge" has become a bogeyman of education, and with good reason. We rightly want students to understand; we seek to train creative problem solvers, not parrots. Insofar as we can prevent students from absorbing knowledge in a rote form, we should do so. I will address what we know about this problem, and how to avert it, in a future column.

But a more benign cousin to rote knowledge is what I would call "inflexible" knowledge. On the surface it may appear rote, but it’s not. And, it’s absolutely vital to students’ education: Inflexible knowledge seems to be the unavoidable foundation of expertise, including that part of expertise that enables individuals to solve novel problems by applying existing knowledge to new situations--sometimes known popularly as "problem-solving" skills.

more t/k

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