A couple of weeks ago when I told someone (at a campus ministry I still attend) that I was going to start teaching, she asked me what my teaching philosophy was. My answer: "Um...uh...what do you mean, exactly?"
Since then, I've come across the word "automaticity" (which, yes, I had not heard before *hangs head*) in an education article, and I liked it because it helped me to verbalize my answer to the math wars.
People vehemently against constructivism point out examples of students taught with a discovery-based curriculum that still can't do things like basic multiplication facts (7x4) as fast as those taught with direct instruction. But what is the point in memorizing 7x4=28 in these days of calculators?
Don't get me wrong - I am NOT saying that basic arithmetic facts don't need to be learned. I constantly get frustrated with high school and college students that can't do basic arithmetic, because it hampers the teaching of higher-order thinking skills when we have to break stride to cover fractions or negatives.
No, I think that being fluent in arithmetic is very important. But I also believe that in a calculator-filled world, there is no fundamental difference between someone who doesn't know 7x4, and someone who has memorized 7x4=28 because they copied it repeatedly on 500 worksheets.
Memorization has been made obsolete, but automaticity is more important than ever. Wikipedia's article on automaticity describes it as the point where a skill is learned so well that the lower level thinking is no longer needed - it has become automatic like driving or riding a bike. I no longer spell out C-A-T when I see cat, and I no longer add 7+7+7+7 to get 7x4, but I do understand how to start over from the beginning to explain my thinking to myself or others if I need to. And that is what gives me deep fluency in both English and math.
If my algebra kids know 7x4=28 but don't know why, it doesn't help us when we get to factoring, or finding common denominators, or finding areas and volumes, or any of that. Memorized facts can only be used in a few narrow ways.
But the DI people are right about one thing. A student that can explain 7x4 as 7+7+7+7, and 4+4+4+4+4+4+4, and the number of squares in a rectangle 7 units long and 4 units across....but still has to punch it into the calculator, is almost as (if not equally) hampered as the one who memorized the phrase "Sayvun thymes foe-rr ees tventi aight."
Discovery by itself isn't enough. Memorization by itself isn't...well, anything, unless you're Amish. But a teaching philosophy that promotes going from discovery to automaticity can prepare students for the world.
There's my teaching philosophy: DTA. Discovery To Automaticity. Let's see how long it lasts!
Lonely Math Teachers
15 hours ago