Just Do the Math!
by David Albert
Photo Purchased From iStockphoto.com
Photographer: Dale Harris
David Albert's articles on mathematics always inspire and challenge me, and this one is no exception. The study described in this article underscores the fact that many difficulties with this subject stem from our efforts to teach it before a child is ready, when he is unwilling to learn it, and in a way that is stripped of relevance to our lives. Albert also offers ideas on involving your children in "real life" math experiences.
"Not possible," homeschool mom proclaimed glumly, shaking her head.
I had just explained how the Sudbury Valley School (www.sudval.org) – a democratically managed, child-directed learning environment that has been around for almost 40 years – has demonstrated repeatedly that a child could learn math – all of it grades K through 12 – in eight weeks. Average (if there is such a thing), normal (never met one), healthy children, scores of them, learned it all, leading to admissions to some of the leading colleges and universities in the nation.
“Must be some kind of trick,” she insisted dolefully, remembering her own dark days in the classroom slaving over the seemingly inscrutable, all joy wrung out as from a wet sponge, then as an elementary school teacher herself, and now finally fighting daily what she was convinced was a losing homeschooling war with her nine-year-old over the required workbook pages.
“Nope, no tricks, no special techniques, magic curriculum, or innovative teaching method,” I informed her. The secret, if there was one, was to wait until the child asked for it, indeed insisted upon it, and had a use for it, even if the use was just college admission.
I directed her to an article on the Sudbury Valley website “And ‘Rithmetic” (from the book Free at Last -- www.sudburyvalley.org/texts/freelsat.html#rithmatic). In it, the author and school co-founder Dan Greenberg writes of teaching a group of a dozen boys and girls, ages 9-12, the entire K-6 math portfolio in 20 contact hours. Greenberg, who admits sheepishly that in a past lifetime he was partially responsible in the ‘60s for the development of the “new math” and now had lived long enough to regret it, tried to dissuade them by suggesting that it would be a lot more fun to go out and play. But no use – they were obstinate and determined. He set only one rule: be on time, 11:00 A.M. sharp, twice a week, for a half an hour. If anyone was five minutes late, class was cancelled. If it happened twice, no more teaching.
Greenberg found an old math primer from 1898, with lots of exercises, and away they went. No shortcuts. They added the long columns and the short columns, the fat ones and skinny ones, “borrowed” and “carried” and memorized the times tables. Long division. Fractions. Decimals. Percentages. Square roots. (Square roots? They stopped teaching that in the ‘60s, I think, when we were – or least the more “gifted” among us – given sliderules.)
In 20 contact hours, every single one of the kids knew the material cold. No slackers. No failures. No one “left back”. No “math anxiety”. No boredom, frustration, embarrassment. No shame or humiliation. No competition, “achievement”, “failure”, or “success”. No prizes. Just ‘rithmetic. The students held a party to celebrate.
Walking around in a self-congratulatory haze, Greenberg contacted a friend, a leading elementary math specialist in the public schools, to gloat.
“Not surprising,” mused his friend.
“Why not,” asked Greenberg, having had the wind at least temporarily removed from his sails.
“Because everyone knows,” he replied, verbally stomping on Greenberg’s ego, “that the subject matter itself isn’t all that hard. What’s hard, virtually impossible, is beating it into the heads of youngsters who hate every step. The only we way we have a ghost of a chance is to hammer away at the stuff bit by bit everyday for years. Even then it does not work.” (Honesty is refreshing, isn’t it?) “Most of the sixth graders are mathematical illiterates. Give me a kid who wants to learn the stuff – well, 20 hours or so makes sense.”
I could see homeschool mom was becoming more disconsolate by the minute. She could begin to get her head around it, maybe, for the K-6 stuff, but what about all that algebra and geometry and trigonometry and pre-calculus? (whatever that is – when I was in school, it didn’t exist – is it some kind of holding pen?) I asked her if she remembered learning much at times when she herself was unmotivated, uncommitted, and uninspired. I felt like apologizing the moment I asked, for it was the wrong question, as all I had succeeded in doing was to make her feel uncomfortable.
“Try this,” I suggested, “Let’s do the math together. Let’s imagine you had one of those kids who, as a teen, was really motivated, ready to spend 30 hours a weeks on getting all the math down. (I used the 30-hour figure because it is about the number of hours per week the “average” high school kid spends in the classroom. I like the metaphorical “spending” as it begs the question “what is being given in return?”) And then, let’s compare what might happen if you were to learn the same stuff in school.”
Now studies have shown that in the standard U.S. school day at the average American public school, approximately one hour and fifteen minutes goes into actual instruction of new material. That’s right – 75 minutes. This is not as strange as it might initially sound. Consider what happens in a six-hour school day: movement from class-to-class and the required settling in and getting up, attendance-taking, pledge, bureaucratic busywork, lunch, recess, “physical education”, drug-taking (both of the prescribed and illicit variety), sexual harassment. Inside the classroom, review of stuff from the day before, last week, or last year; homework assignments collection and distribution; dealing with “behavior problems”; classroom organization; tests, including review time for the statewide ones – you get the picture. I’m ignoring the days the student is sick, or the teacher is sick, or the school is sick (lots of school buildings in my state get closed occasionally because of “Sick Building Syndrome” – I would have called schools “sick buildings” by definition, but let’s not go there.)
So 75 minutes of new instruction time. But wait! Since instruction is aimed at the “average” kid, 50 percent of the time the student already knows what is being taught, so the actual instruction time from the child’s perspective is closer to 40 minutes a day. Now let us imagine that 40 percent of that, or 15 minutes a day, is devoted to math. (But wait again! A good portion of that time while the child is being instructed, she would prefer to be somewhere – anywhere – else!)
Anyhow – do the math: 15 minutes a day, 75 minutes a week, for a 180-day school year comes to 2,700 minutes or 45 hours per school year (of which a portion is in time during which the child wasn’t paying attention, or just didn’t want to learn – so figure 30 hours a year.) But wait again! Some of that formal math in the early years was being taught at a time when it took twice or three times as long as it would have later. After all, Greenberg had already demonstrated that all of K-6 required only 20 contact hours.
So, do the math. If you figure the actual math time at 30 hours a year for 8 years (accounting for the wasted time in the early years), it totals 240 hours. Lo and behold – if, at age 15 or so, you wanted to learn all the math K-12, weren’t inhibited by math anxiety, and were willing to spend 30 hours a week at it, it would take you...8 weeks!
Nothing magic here, except that you might actually learn it.
If you never teach a stitch of math, in a mathematical culture your kids will learn heaps of it anyway. Whether it be from reckoning time/distance/velocity ratios so they can figure out how soon they’ll get home from looking at highway signs, to ascertaining how many Twinkies they can get with their allowance (Twinkies? Does that date me?), to helping dad bake the pies or mom replace the oil in the car (how many quarts is that? And why are engines measured in liters???), learning math along the journey is a difficult thing to avoid.
Want a place to start? If your son has a sweet tooth, play “The Cost is Right”. Go to the supermarket, and give him two bucks. Tell him he can buy as much candy as he can manage with $2 (no tax at this stage), but that if the total adds up to more than two smackers, he loses it all. You’ll be amazed at how swiftly the two-place, long-list, carrying addition falls into place, and the multiplication, and the borrowing subtraction. If you watch carefully, you’ll also discover something really interesting: the “correct” way to add a group of multi-place numbers is from left-to-right, not right-to-left, and anyone who has $2.50 in his pocket and needs to buy a can of cream-style corn ($.88) and a bag of kidney beans ($1.39) knows it. That’s why you had to spend all that time on those horrible worksheets, to train you in a method that goes against the grain of all human experience! Got two competitive kids? Really play “The Cost is Right”, and the winner gets an extra dollar for next time.
Have your daughter help you fill up the car with gas (and have her be the lookout for fluctuating prices in the neighborhood.) Let her make the change, and compute your gas mileage. On a long trip, have her count the number of trucks you pass on the highway (I’m assuming you speed like the rest of us), and figure out how many you pass per hour, or per 100 miles.
Daughter saving her allowance and birthday presents to purchase the poodle? Paste a picture of Mr. Poodle on top of a bar graph and make plotting out progress toward the goal part of the exercise. Get a special poodle-purchase bank account. (In better times, you might even get to explain interest, but currently there isn’t likely to be any.)
Petey the Poodle Puppy already arrived? Well, put some graph paper on the wall, and make weighing and measuring part of caring for said canine. (Speaking from experience, I can tell you it works for snakes as well.) Say, every two weeks. Height, length, maybe even girth, too! Think of it as future veterinarian training. Put two graphs on the wall, and measure the “child puppy” as well. (Most children love to see analogies to their own development.) You might decide to do the same with dad, but only if he’s on Atkins.
You get the idea. If you still feel your child MUST do the workbook thing, so be it. But remember that whether she succeeds with it or not will be more a function of motivation and inspiration than anything else. Give her a reason and a purpose that becomes her own and she will discover an education truly worthy of the name.
Might take even less than eight weeks.
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San Diego homeschooling mom Julie Brennan, a CPA who was formerly employed by two international public accounting and consulting firms, has created an awesome website called “Living Math!” She has been working to find ways to link math to real settings, and to the human drama – the history and literature – that created mathematics as we know it. Julie has developed a family math group, set up a discussion forum related to living math methods and materials (great archives!), and a ‘heart of mathematics’ study group. There are terrific book reviews, and an enormous number of resources and book recommendations and links. You can wallow in it for days! Check it out at www.livingmath.net
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Copyright David Albert. This article was previously published in Home Education Magazine, and is reprinted here with the author's permission.
David H. Albert is a homeschooling dad, writer, storyteller, and author of Homeschooling and the Voyage of Self-Discovery (Common Courage Press, 2003), And the Skylark Sings with Me: Adventures in Homeschooling and Community Based-Education (New Society Publishers, 1999), editor of a new book about his Indian parents The Color of Freedom (Common Courage Press, 2005), and two books about the uses of storytelling called The Healing Heart~Families and The Healing Heart~Communities (New Society Publishers, 2003). A new book Anti-Social Studies: A Father Wrestles with His Children’s Questions about Race and Inequality is forthcoming.
He holds degrees from Williams College, Oxford University, and the University of Chicago, but says “the best education I have received I get from my kids.” Residing in Olympia, Washington, David is the moderator of the Quaker Homeschooling Circle, and has given homeschooling talks and workshops across North America, and could come to yours! Visit his website at www.skylarksings.com. David also welcomes your comments – e-mail him at firstname.lastname@example.org
Growing Together Family Learning Newsletter, Vol. 1, No. 3, page 16