John Holt wrote, “I suspect that many children would learn arithmetic, and learn it better, if it were illegal.” As an adult who has come to enjoy math after a youth filled with hatred and shame about the subject, I see the wisdom in Holt’s words. I probably would have arrived at this place sooner in my life if I hadn’t had to spend so much time pretending to comprehend math for my classes, so much time memorizing “math facts” that were meaningless to me, and so much time avoiding math during my years after high school because I thought I couldn’t do it. In my twenties I was fine with basic arithmetic and double-entry bookkeeping, but anything beyond that, such as number lines and exponents, and I would run away as quickly as possible from them.
Now I enjoy math, because I see how it works in things that interest me. This is not something a teacher in school showed me but something I realized as I grew older and learned more about math through my interests in literature, science, puzzles and magic. However, the long, non-linear path to learning I took for math does not fit in the curricular model of conventional schooling, and so we force our children into the same curricular charade of learning I, and many others, endured. Somehow I managed to pass my courses with, I think, only one bout of summer school for math during my school years, but I promptly forgot about all mathematics since I had no reason to remember or use any of it other than the threat of failure. Once that threat passed, all the algebra, geometry and other math I studied passed out of my head too. This is a pretty common occurrence among schooled people, but society is in complete denial about it. Instead we reason, “If we teach it, they will learn it, and passing a test proves they learned it and we’re good teachers.” We hold onto this belief despite evidence in all our lives to the contrary. All one has to do is look at the large numbers of high school and college graduates in the United States who have successfully completed three or more mandatory years of a foreign language and compare them to those who well-remember or use any of the languages they studied once they’ve graduated school.
While thinking about unshooling math, I was pleased to read Peter Gray’s recent Freedom to Learn blog about math, When Less is More: The Case for Teaching Less Math in Schools. In it, in addition to some good resources, he tells the story of L. P. Benezet, a superintendent of schools in Manchester, New Hampshire. In1929 Benezet dropped teaching arithmetic until after fifth grade. According to Gray, “Benezet went on to argue that the time spent on arithmetic in the early grades was wasted effort, or worse. In fact, he wrote: "For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child's reasoning facilities." All that drill, he claimed, had divorced the whole realm of numbers and arithmetic, in the children's minds, from common sense, with the result that they could do the calculations as taught to them, but didn't understand what they were doing and couldn't apply the calculations to real life problems. He believed that if arithmetic were not taught until later on—preferably not until seventh grade—the kids would learn it with far less effort and greater understanding…. In sum, Benezet showed that kids who received just one year of arithmetic, in sixth grade, performed at least as well on standard calculations and much better on story problems than kids who had received several years of arithmetic training. This was all the more remarkable because of the fact that those who received just one year of training were from the poorest neighborhoods—the neighborhoods that had previously produced the poorest test results.”
Unschoolers have long noted that having a longer scope for learning, even years, as this case demonstrates, is not a hindrance to children and actually confers many benefits. I think it is interesting that the children who were not taught math had teachers who were directed to spend time on “recitation,” a practice many parents use without knowing this label. According to Gray, this meant “The children would be asked to talk about topics that interested them—experiences they had had, movies they had seen, or anything that would lead to genuine, lively communication and discussion. This, he [Benezet] thought, would improve their abilities to reason and communicate logically. He also asked the teachers to give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers.”
There are many ways to approach learning math, we do not have to all use the standard drill. As the above shows, you can even more or less ignore math for years and not harm a child’s ability to calculate or learn higher math concepts. But, for some reason, many unschoolers worry about whether or not their children will learn math properly. There is some idea that the math curriculum is so logical, so necessarily step-by-step, and so demanding that it must be approached piece by piece in the most carefully orchestrated manner or the student will become helplessly lost. This is conventional wisdom that just isn’t true.
A teacher, Alison Blank, has created a neat type of online presentation called a prezi, posted below. Her prezi is entitled Math is not linear and I hope it will give you inspiration to consider other ways to think and learn about math. Blank writes from the perspective of a conventional school teacher (“To be clear, I am not advocating that students get to choose what they study any more than I would let five year olds [sic] choose what they eat. You still direct the class, but when possible, do it from behind the scenes by providing strategic problems.”) but her ideas can easily be adapted for use by homeschoolers, unschoolers, alternative schoolers, or autodidacts everywhere.
There are many scopes and sequences for learning math, many different entryways, and I look forward to sharing more in my next blog. I hope you’ll share some of your stories with me too!
Tuesday, September 13, 2011 at 10:04AM