Dr. Arthur Benjamin is a Harvey Mudd College math professor who moonlights as a magician – a mathemagician. What sort of tricks does a mathemagician do? Well, Dr. Benjamin can tell you what day of the week you were born simply by hearing your birthdate, for example, or calculate the square root of a three-digit number faster than a calculator. We asked him five questions about his mathematical magic.
1. Why did you begin performing as a mathemagician?
I have always had a love for mathematics and the performing arts. As a kid, I enjoyed finding new ways to solve math problems that were easy to do in your head. In high school, I did magic shows for children's birthday parties as The Great Benjamini. As I started getting requests to do shows for older audiences, my father suggested that I put some of my math tricks into my show. To my surprise, it got a great reaction, and I have been performing it ever since. My goal is to use my mathemagics to get more people excited about math.
2. Can you break the magician's code and explain to us how you do your magic?
Although I won't reveal the secrets to magic tricks, I'm happy to explain how I do my fast mental calculations and other mathematical tricks. (In fact, they are explained in my book, Secrets of Mental Math and in my DVD course produced by The Great Courses Series.) Using just a handful of techniques, involving addition, subtraction, multiplication and factoring, you can get quick mental estimates to almost any arithmetical problem. The most crucial tip is that mental math should be done from left to right, as this allows you to get a quick mental estimate of your answer. It's more important to know that your answer is a little over three million than to know that your answer ends in seven.
To illustrate, here's an easy way to square any two-digit number that ends in 5. Let's do 35 times itself. We take the first number (3) and multiply it by the next higher number (4) to get 12. Then we attach the number 25 (5 squared) to get the final answer of 1225. Similarly, the square of 65 is 4225. (The reason this works is based on algebra.)3. When did you first get interested in math and what got you into it?
I've enjoyed playing with numbers for as long as I can remember. I loved the fact that you could take a math problem, do it lots of different ways, and yet always arrive at the same answer. I found the consistency of mathematics to be absolutely beautiful and I still do today. In middle school and high school, I enjoyed playing games like backgammon, poker and bridge. To get really good at these games requires an appreciation of mathematics, especially algebra, discrete mathematics, and probability.
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4. What can teachers and parents do to get kids interested in math?
Make it a game. Have fun with it. Here's a fun trick that I want you to try. Think of a number from 1 to 10. Now double it. Then add 10. Now divide this number by 2. Then subtract the number you started with. Are you thinking of the number 5? I thought so! Why does this work? Algebra. If you start with the number N, then by doubling it, you get 2N. Adding 10 gives us 2N + 10. Dividing it by 2 gives us N + 5. Finally, when we subtract the original number, which was N, we are forced to get the number 5. If I taught an algebra class, I would do this on the very first day. It evokes a reaction of "How did you do that?" which is exactly what a math teacher wants to hear.
5. The scores for the 2009 National Assessment of Educational Progress showed that only 26 percent of high school seniors were proficient in math. There's been a lot of talk recently about improving the country's STEM education. Is it important for American students to improve at math, and if so, why?
It is very important for students to be proficient at math. No subject opens more doors to high-paying careers than mathematics. We are living in an age of information and we need mathematical tools, including statistics and cost/benefit analysis to really understand the data that surrounds us.
In my opinion, we need to elevate the mathematical training of teachers. I'll bet that if the NAEP test were given to math teachers, the number of proficient teachers would be well below 100 percent. This would not be the case in other countries like Canada, South Korea or Singapore. They recruit their teachers from the highest achieving students and pay their teachers a great deal of money and, more importantly, respect. If most of our elementary school teachers are nervous about their math ability, then we can't expect much more from our students. We need to find ways to attract our best and brightest students, those that have a real passion for mathematics, to enter the teaching profession.
Dr. Arthur Benjamin is a professor of mathematics at Harvey Mudd College in Claremont, Calif. He is also a professional magician, performing as a "mathemagician" to audiences throughout the world.
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