Drama and Teaching Math by Mark Wahl

Drama and Teaching Math
by Mark Wahl

My use of the "personal" side of numbers for instruction goes all the way back to when I was working on my master's thesis in math. It required investigation of complex proofs in the University of Maryland library's musty math journals. Commonly, while picking through a baffling formula for hours, I would gradually descend into that early sleep stage known as hypnagogic, where strange dreamlike episodes often make people wake with a jerk.

In my dreams the mathematical entities I was studying would begin to animate, Alice-in-Wonderland style, becoming people with mathematical traits. That is, the negative numbers became negative, the powers did "power trips," and all were all trying to do complex "operations" on each other. There was some kind of major episode going on with characters trying to resolve a problematic situation. While getting emotionally involved in this drama I would pop awake, details rapidly fading, but with a fleeting sense of having observed a complex "soap opera."

Over my many years of math mentoring students of all ages I have noticed this "opera" reappear in pieces as I search for metaphors and connections that convey math concepts. For instance, when teaching addition and subtraction of negative integers, especially to preadolescents, I find that moods are the best metaphor. A -9 mood is pretty grumpy while a +20 is ecstatic.

The expression -7 - (-2) describes a person starting out with a -7 mood, receiving a compliment that removes (subtracts) -2 (two negatives) from his mood and now he is in a -5 mood. Later, students can use the mnemonic shortcut that two dashes together, i.e., a -(- ) can crisscross to form a +, making the expression become -7 + 2. Without conceptual development or the mood model, though, a student will retain no "gut feeling" as to why the answer to -7 - (-2) must be -5.

Continuing the personal approach, I speak of two different "lands," Multiplication Land and Addition Land. In multiplication land there are factors that multiply, but there are other things that go on there like division, powers and square roots. In Addition Land, only addition and subtraction happen. Zero is the "nobody" of Addition Land because it goes over to, and adds with, a number and the number doesn't even think anything happened. It just shrugs and walks away unchanged. But if zero takes a vacation and goes to Multiplication Land, look out! It feels very powerful as it annihilates anybody it comes into contact with! On the other hand, one is the "nobody" of Multiplication Land. Yet when it goes to Addition Land it can at least cause numbers to gently change.

The expression "5to the zero power" means that there are zero factors called 5. This happens in Multiplication Land, so the absence of any factors, when nothing is happening, gives us the nobody of Multiplication Land, one. When "nothing is happening" there we must signify it by 1.

Most new learners think "5to the zero power" should yield zero, the nobody of Addition Land, but "5to the zero power" has no taint of Addition Land in it. (Of course there are mathematical arguments for why "5to the zero power" should be 1, but "dramatic" talk like this helps a learner to expect the correct concept.)

A last example (among many possible) of the use of personal references and drama to make number concepts meaningful and memorable is the simple teaching of addition facts. I like to speak of ten as the "big shot" or "ruler" or "king" of our number system. Some kids don't believe it is the most important number in Numberland. I say, "How do you find out who is, or has been, very important in a country? You look at the coins and stamps." If you're in Numberland all you look carefully at the numbers. You'll find here's hardly a whole number that lacks the imprint of ten. There are numbers like six-teen (meaning six and ten) and six-ty meaning "six tens" and 6 (being one of exactly ten one-digit numbers) and one hundred (meaning ten tens).

Then how does 9 feel? (Almost important.) We could describe 9 as "Hungry for 1." So when it meets 7 it says "How would you like to hang around with a ten?" The 7 says "Wow! Of course!" The 9 says "You only have to make one sacrifice. You must give up one and be a 6." The 6 says "It's worth it!" and hands over 1, and together they are six-teen (six and ten). The moral of this story is that when 9 meets any number in Addition Land (even 47) it asks for one and becomes a ten.

The use of drama in communicating math is one way to tap the intrapersonal and interpersonal intelligences to teach math. There are eight known intelligences (using Howard Gardner's multiple intelligences model) that we can tap for training and communicating math. See my book Math for Humans: Teaching Math Through 8 Intelligences for many more ideas on this approach.

About the Author:
Mark Wahl is the author of Math for Humans: Teaching Math Through 8 Intelligences (LivnLern Press, 1999)., and Math Nuggets: 80 Thoughtful One-Page Activities for Pleasure, Insight, and Challenge (LivnLern Press, 1997). You can order either book by calling LivnLern Press at 1-360-221-8842.
You can reach Mark Wahl at mathman@markwahl.com, or visit his website at markwahl.com

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