Practice, Practice, Practice

My son has always loved science.

In preschool and kindergarten, he used to binge-watch Magic School Bus, comparing the TV versions to the books. He knew some episodes so well he could lip-sync them.

But arithmetic did not come easily to him. In early grades I helped him learn addition and subtraction through many hours of simple math games like "addition war", a variant of the original game that requires each player to play two cards and add them together. We would play for hours. Astonishingly, improbably, hilariously -- he always somehow managed to come back from behind and win. ("Again?!? Unbelieveable!" Yeah, I was a crooked dealer.)

When it was time to learn multiplication, the rest of the class sped ahead and he didn't. What was going on?

We sought professional advice. A psychologist talked with him, administered diagnostic tests, and returned with a very interesting set of insights. She affirmed that he showed a strong affinity for logic and reasoning, the basic skills for math and science. He could explain addition and multiplication just fine. He could figure out the answers to multiplication problems, given time. He just wasn't committing those answers to memory.

Math Facts are Names

She explained that, for most people, remembering math facts is different from doing math. You don't calculate basic math facts, you just find ways to remember them, like the names of your classmates, or the names of the states on a map. "Six times six" is named 36. "Seven times eight" is named 56. She pointed out that our son had a hard time remembering names, too.

No matter, she said. For kids like him, a calculator is going to be his best friend. "He might never learn the multiplication table," she said.

Not on my watch, I thought. He was going to need more practice.

Selling the Practice

I sat down with my son to talk about it. He said that he thought memorizing math facts was boring and unnecessary, and he preferred to just use a calculator. I said that I agreed that calculators are great, but you don't always have one -- and anyway they are actually slow. I challenged him to a race: him with a calculator against me without one.

He agreed.

I prepared two copies of a worksheet of 100 simple, single-digit multiplication problems, presented in a random sequence. We sat down mano-a-mano. I finished first by a long shot, without a calculator. Yeah, he said, but did you get them right? I invited him to check my answers. Using the calculator it took him a few minutes.

Sorry, Son, but...

I would love to be able to say that he immediately bought into the idea of learning the math facts at that point, but that's not quite how it went down. He still wasn't interested in committing the facts to memory. He sensed that it would be hard. Not worth it.

I pulled rank. Sorry, son, but being fluent in the basic math facts wasn't going to be optional. For him to get where he was going in math and science, he would need to know them by heart. But I promised that I would be his partner in learning them. Here was the plan: We would sit down together with a sheet like this one every day. Whenever he could complete the whole sheet quickly and accurately without a calculator, we would stop.

Each Fact Stands Alone

My son learned a lot over the weeks that followed. I did, too.

I started taking very careful notes about how much time he spent on each problem.

On the first day it made sense to get a baseline. I set a stopwatch and watched him work at a copy of the worksheet for 30 minutes. He couldn't complete the whole thing, and made several errors. We talked about them, and I suggested some tricks to remember them. The next day he had fewer errors, and completed a little more more of the worksheet, but he wasn't getting much faster.

We kept at it, each day making slow progress. He was learning math, and I was learning how to help. The beginning of a breakthrough came when I started taking very careful notes about how much time he spent on each problem. For example, I remember he was succeeding readily at 3x4, but if the order was reversed to 4x3 it stumped him. "Those are almost the same, right? If you can see 4x3 as 3x4, you'll save 140 seconds! Want to try just focusing on that one?"

Feeling the Progress

He started to see results. He didn't love doing worksheets, but gradually he became invested in the idea. I started thinking differently about how to help.

Learning the multiplication table is a task of many parts. Knowing one math fact doesn't necessarily mean that you know the next one. The old Schoolhouse Rock songs are lovely, but even if you learn to skip-count by threes, do you necessarily know 3x7?

I scoured the internet for ways to help make each multiplication fact memorable, one by one. The square numbers appealed to him first. For example, he liked knowing that there were 64 squares on an 8x8 chessboard. I don't quite remember how the Beatles song "When I'm 64" fit in, but it was definitely part of it. It was easy for him to remember that 10x10 is 100 -- and isn't it weird that 5x5 is only 25? Four 5x5 squares can fit inside a 10x10. Meanwhile, isn't it strange that the square that's closest to being half of 100 is 7x7?

We examined the near-squares, one by one. Squash a 7x7 square to make it a little shorter and wider, and it becomes a 6x8 rectangle, but it spits out a spare one-by-one square in the process. All the near-squares do it. With practice, it was enough.

Learning 6x7 provided an opportunity to talk about the meaning of life, at least according to Douglas Adams. Seven times eight was one of the last stumpers. He finally got there with a rhyme we made up: "five, six, seven, eight, 56 is 7x8. Isn't that great?"

Look, it's not inspired poetry, but it was what he needed.

It Worked

As he progressed, joy became part of the experience.

Sometimes, especially at first, he resented the extra homework. It was difficult. There were some emotional moments, especially as I figured out what he needed and how I could help him. But as he progressed, joy became part of the experience. Each time he set a new speed record, he was proud of himself and I was proud of him.

Looking back on it, it didn't really take that long. Maybe five or six weeks. I suggested that he set a speed target for himself using a scrambled edition of the worksheet we started with, and when he hit his target we stopped the daily practice sessions. Is it weird that I don't even remember what target he set?

Last year, my son graduated from high school, passing Calculus BC along the way. He has been admitted to Northeastern University, where he will study computer science and digital art.

A Wonderful Story?

There are plenty of things to wonder about this experience. Without early professional evaluation and advice, I wonder when or if we would have figured out the kind of help he needed. If I hadn't insisted that he learn the math facts at that early point, I wonder if he would have come to think of himself as "not a math kid".

My son allowed me to help him using nothing but a paper quiz, a timer and talk. That's usually called "drill and kill." Our relationship survived the experience -- but I wonder how much of a risk I took by insisting.

Most of all, I wonder about all the other kids like my son. I feel really lucky that I had the time to tutor him. Most parents couldn't do that. Most schools aren't set up to intervene like this, either. California's classrooms are overstuffed, and learning specialists are scarce. I imagine how easy it would be for an unprepared or overburdened teacher to misinterpret his slow start in math as lack of interest, or lack of potential, or willfulness. I wonder how many kids are like my son, but without the advantages that give this story its happy ending.