Make Math Illegal

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!



Math is not linear on Prezi

Homeschooling and PDD: A Success Story

Matt Savage is described on the front cover of the Boston Globe Living Section (Feb. 9, 2010) with this headline: “The Improviser. Is this autistic 17-year-old from Sudbury the next great jazz pianist?”

Savage, who has a type of autism called Pervasive Developmental Disorder (PDD), displayed much musical promise by the time he was seven but his behavior was so erratic that even three years ago his parents didn’t think he could find the self-control to become a top-tier jazz pianist. The article notes, “Today, after years of specialized therapies and dietary changes, Savage navigates a daily maze of classes, practice sessions, homework assignments and dorm life at Berklee.” Berklee is a music college in Boston that focuses on jazz, an art form Matt Savage is mastering before he’s old enough to vote. Until this article came out very few of Matt’s teachers and fellow students were even aware that he is disabled by PDD.

I’m struck by the fact that his parents homeschooled him and continue to homeschool his sister. The Savage family took matters into their own hands at a time when other parents would throw in the towel and they were able to help their son flourish by homeschooling him. Speaking to the reporter, Matt “describes his autism now as “almost a gimmick” used to get his young talents noticed.

‘There’s still the issue of communicating with friends,” he says guardedly. “I really don’t have much of it anymore, though, thanks for the therapies my mom put me through.’”

Later in this article we learn that the Savages moved in 2002 from Massachusetts to a farm in New Hampshire. His mother mentions how music and travel helped her son a lot too, so there are a lot of factors at play in making Matt connect with the world in addition to his unique therapies and diets, which, unfortunately, we get no details of in the article.

One of my favorite La Leche League sayings is that the proper course of child development is for children to move from dependence on their parents for everything to independence from their parents: “Baby the baby so you won’t have to baby the man.” Of course, this isn’t easy, but the payoff is worth it. Diane Savage says, “…the more he’s shown he could solve problems on his own, the more we’ve been able to pull back. It’s really been harder for me than him, though, because Matt’s early years were so intense, his behavioral issues so extreme.” Now Matt is not only attending college, jam sessions and playing in bands, he is donating proceeds from his concerts and CD sales to groups that support autism research and outreach.

It is important to remember that sending such a child into the care of others is no guarantee they will come out whole; professionals struggle with these children too! In fact, as many homeschooling parents of special needs children have noted, sending such a child to school can be counterproductive to the child’s emotional and social development. But parents of special needs children are often so worn out by their responsibilities that the thought of homeschooling in addition to all else they do for their children seems impossible. However, there are stories like Matt Savage’s that let us know that parents can work with their children to seek and secure the help they need while homeschooling them, which is why having the homeschooling option, even if you don’t use it, is important.