In Praise of Drilling

Boys and girls, today we have a problem. I'm currently teaching division at LoLMEECoA, and it's starting to frustrate me. Dear readers, nobody has drilled these kids on their multiplication tables.

I used to think that drilling and repetition of things like multiplication tables, single-digit subtraction and addition, and the various other math drills that we halfheartedly repeated in elementary school were relics of a time when teachers didn't know any better. Problem is, those drills prepared us for higher math.

I can instantly tell you the product of any two one-digit numbers, and drilling in elementary school (along with my grandparents giving me a plastic game/contraption that had all the times tables from 1-9 on semi-opaque square buttons, and which would show me the product when I pushed down on each semi-opaque button). My students, well, let's just say that they have a hard time telling me what the word "product" means.

We're currently working on division in my classes, and it has been a disaster up till now. I guess disaster is a vague word. Let's say it's more '89 SF earthquake and less huge tsunami in the Pacific. Given that my students don't know their multiplication tables, they have a tough time with division. "Tough time," in this context, means that I can sit at their table for 45 minutes working on two simple division problems (I'm talking single-digit number into triple-digit number) and by the time they're finished they still don't know why the answer is what it is.

Monday was the first time I've been so exhausted by class that I just wanted to crawl into bed and pull my legs up to my chest and fall asleep afterward. Attempting to teach division to kids who can't do multiplication is like trying to teach the Hindenberg blimp not to explode: You know it wants to not explode, but it's just so full of hydrogen and there are so many damn sparks flying around, it's gonna explode eventually, and people will read about it in the paper. Put another way: I'm trying to show these kids how to write diaries in cursive before teaching them how to spell.

The average session attempting to teach division goes something like this:

Teacher (Me): Alright, what's 156 divided by 3?

My Precious Petunia of a Student: I don't know.

T: Alright, what's the first step?

MPPS: I don't know.

T: What numbers are we dividing?

MPPS: 3 divided by 186.

T: Well, no, you copied that wrong. Look at the board again. Good. We're actually dividing 156 by 3. Do you know what that means? We're trying to find out how many times 3 will go into 156. Okay, first step, can 3 go into 1?

MPPS: Yes.

T: You can put three gallons of water into a one gallon jug?


T: Then can 3 go into 1?

MPPS: Yes.

T: (Eyebrow raised in confusion)

MPPS: No, no.

T: Correct. Alright, so let's move over one place. Can 3 go into 15?


T: (Confused look)

MPPS: Yes, yes it can.

T: Okay, how many times can 3 go into 15? What's your guess?

MPPS: 20.

T: 20? (Head starting to hurt) 20? But that's bigger than 15.

MPPS: (Confused look) 30?

T: Thir...Ok, let's try to multiply. What's 3 times 30?

MPPS: I don't know.

T: Let's do it on your paper. Ok, 3 times 30 equals.

MPPS: I don't know.

T: Alright, what's 3 times 0?

MPPS: 3.

T: 3?

MPPS: Yes, 3! (exasperated)

T: Ok, then what's 3 times 1?

MPPS: 3.

T: So they're both 3?

MPPS: Yes. (Light bulb) No.

T: So what's 3 times 0?

MPPS: 0.

T: Ok, good. So where do we put the zero?

MPPS: (Puts zero behind a decimal point. Teacher is not quite sure where the decimal point came from, but realizes that the students have been learning about decimals, so the student has just decided to put them everywhere.)

T: Um, are you sure you want to put it behind the decimal? There's no decimal in the problem.

MPPS: Yes. (Studies paper) No.

T: Right, it has to go in front of the decimal. Actually, you don't even need a decimal in this one.

MPPS: Why not?

T: This time you don't, because there's no decimal in the problem. Ok, the zero goes there. So what's 3 times 3?

MPPS: (Looks quizically at paper)

T: Alright, let's count it up. What's 3 plus 3?

MPPS: 5. No, 6.

T: Yes, 6. And what's 3 plus 6?

MPPS: Why do we need to know 3 plus 6?

T: Because that's 3 times 3. We're doing 3 plus 3 plus 3, which is the same as 3 times 3.

MPPS: 3 plus 6 is 9.

T: Good, so what is 3 times 30?

MPPS: Nineteen.

T: Nineteen?

MPPS: Ninety.

T: Is ninety bigger than 15?

MPPS: Yes.

T: So can we put 90 into 15?

MPPS: No. Yes. I don't know. No.

T: (Mouth open)


T: Good. Okay, what you have to remember about division is that you can only use the numbers 0 through 9 for each part of the division. It can't be more than 9. So what do you guess? How many times does 3 go into 15? Remember, the most we can do is 9.

MPPS: 9!

T: No, I wasn't. ..I wasn't trying to tell you 9...

(This continues for twenty minutes. Eventually, the answer is determined, but the student doesn't understand why. It is at this point that the teacher seriously considers all of the great times he had at Mackubin Consolidated Widgets of Schenectady, New York. Since great is not an adjective that normally precedes times when referencing the Widgetorium, the teacher starts thinking about Battlestar Galactica, and how he should really finish up Season 3 as soon as possible.)


Samantha said...

i'm agreeing with you about the BSG.