July-August 2011 Selected Content
Math Lessons - Cheryl Trzasko
Gazing over the deep blue Indian Ocean, I felt the breeze in my hair and the sun on my face. Then I bent back down to the papers in my lap. I had a math lesson to do.
My parents did the opposite of many homeschooling parents. Mom bought correspondence school curriculum for every subject except math. Dad said second grade math didn't require a book, and he saw no point in paying for one. Instead, he would be in charge of math lessons. He mapped out a simple plan. I'd already learned to add and subtract, back in the school I went to before we started our voyage. So, the next step would be to master multiplication. That would be the whole of second grade math, he declared.
Dad's methods would have horrified professional educators. They were irregular and unplanned. Whenever he had spare time from his sailing duties, and he happened to think of it, he'd call me over for a math lesson. Sometimes days, or more than a week, would pass between math lessons. The lessons were not lively or entertaining; there was no variety in them. He'd write a list of multiplication problems and tell me to go copy them one hundred times each. Yes, one hundred times. After I'd finished the tedious copying, he'd quiz me. His oral quizzes were always the same. He'd say a multiplication problem such as "four times five" and snap his fingers. If I didn't say the correct answer before he snapped, I had to copy the problem another hundred times and face another quiz. And the quizzes included not only that day's problems; any problems he'd given previously were fair game.
His lessons weren't meant to be fun. He explained, "Learning to use a hammer properly is rather boring. But you have to know how to use it well if you want to build great things. The excitement comes after mastering the basics." That explanation worked for me because I'd seen him build a lot of wonderful things, including the beautiful cement yacht we were sailing the world in. So, I did his math lessons and learned my multiplication facts very well.
But more important, I think, were the math lessons that he didn't realize he was teaching.
When we docked at a new port, one of the first chores would be to trade some of our money for the local currency. Simple multiplication or division would be used to figure out how much of their money we could get for our dollars. At the market or store, he'd carefully add up how much he could spend with the local money.
Out at sea, every day, at precisely noon, Dad took out an old-fashioned sextant--a black instrument shaped like a triangle with a curved bottom--and peered through its eyepiece. Pointing the eyepiece at the horizon, he moved the bottom of the device until the sun was reflected in its mirror. Then he wrote down the number the device's pointer indicated. Down below deck, he'd pull out a huge book, several inches thick, of trigonometric tables. Hundreds of pages full of numbers. With his slide rule, a ruler with a sliding part in the middle that was used for calculations before the invention of pocket calculators, he'd figure out our latitude and longitude and mark them on a large map. It was amazing to see him figure out exactly where we were when there were no landmarks around us, only the endless blue of the sea.
Using a pair of calipers, he'd study his chart and determine which direction we should head. He'd measure how far to our next destination and set a course based on the direction of the current and the wind. Using math, he could figure out if there was an island we could reach by nightfall or whether we'd be at sea for some time yet.
A rope with a weight on one end and knots tied every foot would be thrown into the water when we sailed through shallow waters. Pulling the rope out and seeing how much of it was wet, he could measure the depth of the sea and know whether it was safe to continue on.
Math was everywhere. With little privacy on a boat, I had a clear view of these daily calculations. I was willing to learn the tedious multiplication tables because I witnessed the power of math regularly.
Today, I homeschool my own children, and I try to remember the lessons my dad taught. Teaching math means making sure that the children see me using math in action. Tempting as it is to balance my checkbook, calculate the changes I need to make in a knitting pattern, double a recipe, or even just count something quietly, out of sight of the children, those sorts of simple things should be a basic part of their math education. I may not be calculating my way around the world, but I do use maps to plan trips, or compare prices of items in the store, or a hundred other things. Making sure the children are a part of these activities is a major part of our math lessons.
The math lessons I received from my father during our two year journey gave me a wonderful foundation in math--one that led to me eventually graduating with a degree in mathematics from one of the top universities in our country. Dad's methods were highly unconventional, but he taught much more math than the multiplication tables. He showed me the value of math and its great power.
© 2011, Cheryl Trzasko