Thursday, May 08, 2008

On the Teaching of Math

The world appears to be split into two types of people: symbolic thinkers who seem to be born with the "math gene" and concrete thinkers who more appreciate words. The language and word lovers are often left scratching their heads when a symbolic thinker makes a mathematical explanation, whether orally or in writing. Listen to what Jacques Barzun says about this:

"....from the very first grade one child "loves" math and another hates it. This is the beginning of the school's difficulty. (SNIP) What is seldom noticed is that the trait in students who favor math is also the cause of much poor teaching. For the mind that feels at home with math is likely to lack the qualities that make a good teacher. (gasp!!) SNIP

....the math or science teacher may fail, although well prepared and of course well intentioned. He or she, moving easily among abstractions and their symbols, has no idea how the "other mind" works---does not perceive how strange the square root of minus one seems to the concrete-minded (SNIP) It is a case of two minds out of tune with each other. And a proof that the disparity is not accidental or occasional is that the same fault is found again and again in math and science textbooks. The author assumes a kind of scientific common sense which will make things clear at once. Accurate with symbols, as writer or teacher he often uses words carelessly, failing to see that to the concrete-minded words have distinct connotations."

Barzun follows this with an example from a textbook, and shows methodically how the poor wording would befuddle any word lover.

Being myself a word lover and a recovering math-o-phobic, I've given serious consideration to this dilemma. As a student who was befuddled by murky explanations, I now sit in the seat of a teacher who wants to make math come alive for my students. My solution: DO NOT RELY SOLELY ON A TEXTBOOK.

Most people who know me know that I am allergic to textbooks :) I use them more in math than in any other subject, but try not to over- rely on them. Steve Demme has taught me that "teachers teach~textbooks drill." I think there is a lot of wisdom in those words.

So how do you wean yourself from dependence on a textbook? The first thing is to set apart one day a week to do math in a different way; no textbook allowed. Friday is that day at our house.

Here are some ways to use that time:

*Play games. Lots of games: dice games, strategy games, board games, card games. Remember that math is not just about numbers; it is the study of patterns. Games are invaluable in imparting the art of logical thinking. It's fun, too!

*Choose math stories to read together. Look at Julie's list of literature books that qualify as "math" here. Some of our favorites have included The Number Devil, Math Smart Junior, books by Greg Tang , and Sir Cumference series books.

*Keep a math journal. Write where and how you saw math being used in your everyday life.

*Narrate. Some people are surprised that you can use narration in a math lesson, but it is very effective. To have a child explain HOW he works a math problem brings it out of the realm of symbols and into the world of words. This can be done as either an oral or written narration. For very small children, you can switch roles. Pretend you are the student and ask them to be the teacher and explain their current math concept to you. They won't even know they are doing school! Today, one of my highschoolers explained very lucidly how to approach an algebra problem using the correct order of operations. Narration works for young or old.

*Play with math. My husband is a true symbolic thinker and it is second nature for him to pose math problems at the table as though he were thinking out loud. This week, he mentioned to us that he had determined that his car gets 2 more miles per gallon if he uses regular unleaded gasoline rather than ethanol. "Yes, Daddy, but doesn't it cost 10 cents per gallon more?" And then ensued a real brain teaser. What is the difference in price between a tank of ethanol vs. a tank of unleaded? How many miles can you drive on each tank? Which is the better value? Keeping alert to these kind of applications brings math down to earth.

*Build things. Buy bridge building kits. Make geodesic domes out of rolled newspapers (that is what you see in today's picture). Construct architectural models using marshmallows and toothpicks.

*Buy a few age appropriate math computer games. My kids enjoyed Cluefinders when they were younger. There are probably better ones now.

Next time....stimulating your own passion for the subject of math.

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