Math! Part 1
by David Albert
This homeschooling father and author of Homeschooling and the Voyage of SelfDiscovery, And the Skylark Sings with Me, and other books shares ideas for homeschooling parents on teaching math. His ideas emphasize illuminating the beauty and order of math..
A group of homeschooling mothers gathered together in a circle to discuss unschooling approaches to their children’s education.
“I can’t get mine to do any math,” moaned one, and heads began to nod.
“Mine neither,” whined another. “ She never wants to.”
The heads rolled and shook more vigorously, and soon I found myself sitting— metaphorically, of course, and with no offense intended— amidst a Greek chorus of heartrending laments, sighs, and whimpers, perhaps something like a modern homeschooling rendition of Euripedes’ The Trojan Women.
“I’ve tried to convince her that math is a skill she’ll really use later in life, but she isn’t buying it.”
I’ve pondered this for some time now. Perhaps the kids have a sixth sense about them. They somehow know it is a lie. Most of the math I learned in school I have never used. Not once. Nary a differential equation, nor a logarithm, nor the area of a scalene triangle has wriggled or waddled across my path in more than 30 years, and I use a significant amount of quantitative analysis in my day job. My carpenter friend Bill, who flunked geometry and dropped out of high school, makes use of angles and sides all the time; I have yet to encounter a colleague who still uses a slide rule.
Consider the dukes and duchesses, counts and countesses, marquis and marquises, earls and earlesses of earlier times. They didn’t learn math so they could balance their checkbooks (there were no checkbooks!), or so they could become accountants—they hired people to do that for them. They didn’t use math in shopping; they had stewards for such mundane activities, who paid the grocer’s and haberdasher’s bills. And unless they were real misers (or getting ready to flee), they didn’t spend a lot of time counting money. They didn’t study their Euclid so they could become architects. They did so because it added meaning and beauty to their existence, rather like the required “continental tour”, only this one a travel excursion of the mind.
Preaching future utility is futility—it is a wrong—headed approach. It’s not only based on a lie, one of many my teachers told me (they may have believed them, too, for all I know), but an ineffective one to boot. The young child comes into the world as a princess. The whole world is there, and is hers, waiting to be discovered, fully explored, and finally occupied. She is a “stout Cortez when with eagle eye/He star’d at the Pacific— /Silent, upon a peak in Darien.” What use worrying about some wholly inscrutable future time, when this glittering oyster of a world lay opening before you!
Don’t attempt to brainwash your kids into contemplating something that is ultimately unknowable. All that can be known with certainty about the future is that it will be unlike today (and checkbooks will probably have gone the way of sliderules.) Teach them (yes, unschoolers, I’m using the forbidden “ T” word) that mathematics is one of the most beautiful creations of the human spirit. String necklaces of colored beads in varying mathematical patterns, and wear them with pride. Provide allowances in wampum (convertible to hard currency, of course). Get out the old magnifying glass and count centipede legs (are there really 100?) Give your child a set of pattern blocks (as soon as you are sure she won’t swallow them)—chances are that if you provide them at 3, she’ll still be playing with them when she’s 12. Count the sections of oranges and tangelos, plot them on a graph, and see if the distribution falls in any particular pattern. Read books about Archimedes and see how a lever, properly placed, can move the world (don’t let the kids try this without adult supervision.)
When they are ready, show them the Fibonacci numbers, and where they can be found throughout the natural order: in the spirals of shells, branching plants and leaf arrangements, flower petals and seed heads, pineapples and pine cones. To me, these are God’s handprints upon the world, which we are all but children learning to read. (Check out the book Fascinating Fibonaccis: Mystery and Magic in Numbers by Trudi Hammel Garland, and her wonderful posters). Make beaded bracelets in the pattern of the Fibonacci— related Golden String (1011010110101101…you can have fun for hours on the best Fibonnaci website) If you know the Fibonnaci series, you may be able to sit in a field of daisies and figure out whether “she loves you, or loves you not” without picking a single petal!
Go to the library and get a copy of the extraordinary Arthur C. Clarke video “Fractals: The Colors of Infinity” on the Mandelbrot sets, those extraordinary patterns of fractal geometry to be found in nature that may remind you of the wall projections during an ‘60s Grateful Dead concert (my age is showing, but the soundtrack really is by Pink Floyd!)
Find a set of Zometools, sophisticated tinkertoys updated for use by architects, research biochemists, and hobbyists, and which are just plain fun! (Your daughter or son may end up making “ truncated icosahedrons”, also known as “ Buckyballs” after Buckminster Fuller, or “ clustering Kepler solids”—whatever they are!) Be forewarned, however: Zometools are outrageously addictive, and will quickly supplant all other forms of youthful human activity.
Okay—sold on beauty but still want to ensure that the usefulness of mathematics seems like a plausible hypothesis? Well, you probably learned that one in Unschooling 101. But to review: bake cakes. Go to the supermarket and figure out the per ounce costs of all the breakfast cereals; convert the ounces to grams, too. Compare distances to various friends’ houses using the odometer, and compute how much the gas costs to get there and back. Does your son want to purchase something with his savings? Construct bar charts with the goal, and calculate and plot the percentages of how much has been socked away thus far. Have your daughter balance the checkbook as one of her chores (she might learn to do a better job than you would anyway, and she’ll have learned a vanishing art.) Figure out how many jars (by volume) it’s going to take to can all the peaches from the tree in the backyard. Concerned about your weight? Have your son manage the calorie counter—he’ll keep you honest!
Do your kids surf the Internet? Help them explore the Boolean logic operators behind their searches (AND, NOT, OR), and use them to solve some of the marvelous puzzles by Charles Dodgson, otherwise known as the author of Alice in Wonderland. (For a primer, try here.) Choose a neighborhood tree and try to find three ways to figure out its height without climbing or employing the aid of a helicopter. Sort potatoes—see if you can come up with a volume rule for Mr., Mrs., and Baby PotatoHead. Measure absolutely everything—from the size of the living room rug that needs replacing to the relative girth of olives, from small to super colossal (that’s the kind with St. Louis stuffed inside it.) Use this one as an introduction to “ fuzzy set theory” (ever see a fuzzy olive?)
Oh, I know. You still want them to understand that the math they learn today might be of use later in life. Mrs. Blum, the 9th grade algebra teacher with the voice of one of the Harpies, has infected your bloodstream and there’s no known cure. Well, don’t preach—visit! If your child seems interested, meet with an architect, an air traffic controller, a computer software designer, an epidemiologist, an astronomer, a baseball statistician, a physicist, my mother’s stockbroker Larry, anyone who uses math as part of her daily work—anyone, that is, but Mrs. Blum! Don’t know any? That’s okay, that’s what phone books are for. Work with your child to develop a list of questions she might actually like to ask. If you’re still stuck, go visit my friend Bill the carpenter.
Whenever we are stuck in our homeschooling routines, whether it be around math or anything else, I am learning not to be frustrated with my children, but to step back and ask myself three questions: Have I provided what is necessary so that my kids can discover the beauty in what they learning? Have I given them opportunities in the present to use it? Do they have models in front of them to which they can aspire if they put in the necessary learning effort? And, my experience has shown me that when I can answer these questions affirmatively, there’s not an awful lot left to worry about. My kids, bless them, can take care of the rest.
Except maybe for the centipede legs…
Math! Part 2
copyright 2002 David Albert
Growing Together Family Learning Newsletter, Vol. 1, No. 1, page 14
