Turning 'C' students into mathematicians
Bill Handley, an Australia-based educator, has made a reputation for himself as something of a math liberator. His methods for quick mental calculation and his way of teaching young children to use them have transformed math skeptics into confident problem-solvers. He is author of "Teach Your Children Tables" (a bestseller in Australia), and the new "Speed Mathematics," which builds on the calculation strategies of his first text and also includes an easy method for calculating square roots.
He spends the bulk of his time teaching in a variety of Australian schools and helping other teachers improve their methods. On periodic visits to the United States and Canada, he helps schools interested in adopting his techniques. Following are excerpts from a recent interview with the Monitor's Stacy Teicher.
What's been the impact of your teaching methods in Australia and abroad?
When I give a class, students are excited about what they can do. It raises the expectation level. Students often have a very poor idea of what they are capable of, and all of a sudden they find that they can do far more than they ever dreamed. I had one student come up to me and say, "Do you really think I can be an Einstein?"
Teachers are excited because ... they have a motivated class, and the students are succeeding, which makes the teachers successful. Why people don't like math is because they've failed. The response [to my methods] has been almost universally positive.
I was working with one class in Melbourne, and the children were in real trouble; they didn't know any of the basics. I felt a bit frustrated - I wasn't sure if I had achieved much at all that was worthwhile. But the children used the strategies. [There was one child] I had almost given up on because he didn't seem to be accomplishing anything. But I'd given him the tools, and the school noticed an immediate improvement. For the first time, he was successful at mathematics.
How has math typically been taught in Australia?
There was a uniform way - children would chant their tables. Then there was a departure from tables because people had the idea that it wasn't good for children to learn by rote. But they had no alternative.
For a while, a lot of children suffered because they didn't know their basics. [The attitude was] why would we use our brains when God gave us
calculators? There's been a move back, but a lot of teachers and schools have been reluctant to go back to the traditional way of teaching tables, by chanting and reciting.
[My way is] a far more pleasant method of learning tables and the basic number facts, because you are achieving something - visible results, if you like - immediately, with each calculation.
Share some of your thoughts on the importance of the teacher's attitude toward his or her students.
Even if they haven't been taught a skill, people will work out a strategy. It is often a complicated strategy, and because it's so complicated they might make mistakes more often.
An observer just sees that they are slower and make more mistakes - so [they assume] they obviously are not as intelligent. So they treat them accordingly, and the tragedy is when people believe other people's assessment. Einstein did stupid things, but it didn't make him a stupid person.
I don't put children under pressure. I tell them it's easy, I'll show them how to do it.... If someone can't, we'll make sure that they can.
It's interesting, after the first five or 10 minutes, the children will believe that they can do almost anything, because they've already succeeded at things they say straight out at the beginning of class, "I can't do this."
What's the relationship between your method and the role of memorization?
I'm not opposed to memorization of the times tables. Some children like memorization. But if they don't know the tables from rote, they've got an easy method to calculate it.
There was a young boy in Canada, a Grade 9 student who seemed to have missed all information about math. He didn't know 3 x 3. When I went back a week and a half later - he had taken home a handbook and a practice cassette - he'd found he was able to do the calculations.
He suggested one of the strategies [that ended up in the book]. I said, "You're thinking like a mathematician."
When did you first take an interest in mathematics?
When I discovered you could find out things for yourself using mathematics. With some friends, we figured out how to measure the height of the lamp pole in the street. We used graph paper.
When I first learned algebra, I thought this was great because I enjoyed puzzles and logical reasoning, and here is logical reasoning and problem-solving made a science or an art. I still dislike people talking about rules of algebra. I like to understand - it makes sense if you do it this way.
When did you develop the methods you currently teach?
The basic formula came to me by reading a book by Martin Gardner on mathematical prodigies.... He had a formula for squaring numbers, and I wondered, could it be adapted to multiplying any numbers? And so I came up with a formula, and then discovered it's been known for centuries. My own touch to the method are the circles (see example, right), and using the strategies as teaching tools.
What responses have you had from students when you help bring everyone up to speed with new methods?
They say, "Well, why didn't someone tell me this years ago?" One boy was resentful when I taught a method he had figured out for himself. He said, "I've had a reputation for being better at math.... Now they can all do it. I deserve some recognition."
He's got a valid point. But it's the job of teachers to make it as simple as they possibly can for everyone, and you shouldn't need extra intelligence to be able to do these basic calculations easily. This should be the birthright of everyone who does mathematics in school.
*Handley can be reached at
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