math facts & letter facts

Susan J left this comment:

Maybe we need another term besides "math facts." They are much more fundamental than contingent facts like, say, dates when certain historical events occurred.

Do kids still learn "letter facts" like the names of the letters and alphabetical order?

That's a terrific point. The term "math facts" does lend itself to the view that "math facts" are on a par with historical dates.

I'm going to start using the terms fundamental versus contingent to talk about the math facts.

(I guess we could call them math fundamentals...on occasion.)


here's Barry:

Call them something exotic so the reformers at large will think it's higher order thinking skills. Call them theorems, because that's what they are. 3 + 2 = 5 is a theorem which can be proven using Peano's axioms. And like all theorems, once proven, it can be used without having to re-prove it, thus alleviating our kids from having to draw clusters and go back to first principles each and every time they add, subtract, multiply or divide lest anyone think they were doing things by rote.

Steve H

I've never liked this either. I think it's a carfully-selected term used to degrade the importance of the knowledge. when I told my son's Kindergarten teacher (years ago) that I supported an educational approach that emphasized basic knowledge and skills, she said that I would like one of the second grade teachers who required each child to give her a "math fact" to enter the room.

They are just clueless.

From his first grade teacher I learned about "superficial knowledge". I wanted to tell her that it is fundamental knowledge.

Basic knowledge and skills are the foundation of education. You build from the bottom up rather than the top down. Somehow they think that education should be thematic or top down; that kids can learn basic knowledge and skills by osmosis.

Basic facts and skills require hard work.

Hard work is a filter.

The only point I would add here is that achieving expertise requires hard work and expert teaching.

I've been trying to make my way through the research on expertise, with limited success. It is vast.

However, I've managed to do some mighty skimming.

As far as I can tell, expertise is expertise; the mechanisms by which one acquires expertise are (largely) the same.

These days I think about athletics and athletes when I'm confused by an issue in K-12 education.

There's a reason you never, ever, see an Olympic athlete who is self-taught.

That reason is that expertise requires superb teaching.

I'm not sure whether the strong form of this statement is correct.* Certainly I've seen many people who are self-taught (I taught myself to write).

There must be a literature somewhere on self-teaching.

Nevertheless, the weak form of the statement is certainly true.

Our kids need expert teachers who themselves take the development of expertise seriously. Hard work isn't enough.

I would rewrite every school mission statement in this country to reflect this understanding.

I'd take out all the "lifelong learners" and "critical thinkers" and "all children can learn" foofaraw.

I'd insert the word expertise.

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* One of the reasons why I'm not sure is that procedural learning and knowledge, which I believe is dominant in athletics, seems to follow a slightly different set of rules than declarative knowledge, which is dominant in academic disciplines.

Procedural knowledge seems to be much more vulnerable to error. Once you learn a procedure - a golf swing, say - the wrong way, you can't unlearn it.

As far as I can tell, declarative knowledge is less vulnerable. If you mislearn a fact, you can overwrite it in memory. I'm guessing it's possible to learn from error in declarative knowledge.

caveat: I don't "know" these things. This is what I surmise based in many years' surfing literature on memory.