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"given an existing problem, it may be better not to do something, or even to do nothing, than to risk causing more harm than good".I've been contemplating the phrase in relation to math--specifically the teaching of math. In my job I am privileged to work with a wide variety of ages, abilities, grade levels, and teaching situations. I'm alternately awestruck by some students' mathematical thinking and downhearted to see some students--still quite young--who have already had their little mathematical minds messed up. Some of these kiddos, only a few years into their school careers, have decided that math isn't supposed to make sense. Math is just a confusing, random, jumble of rules that they cannot remember...or rules that they can't apply to situations outside the 25 identical problems given on the daily assignment in their textbook. It's painful to watch a child pull numbers out of the air, as he assumes that a random guess has as much likelihood of being correct as anything else he might figure out. As an esteemed colleague said, "Nothing makes sense after you've had your thinking taken away." I worry about these kiddos. A lot. And they're found everywhere. In every grade. And in every school situation: home, private, and public.
A related section from the Hippocratic Oath has been translated asWhat if we applied it to the teaching of math?
I will follow that system of regimen which, according to my ability and judgment, I consider for the benefit of my patients, and abstain from whatever is deleterious and mischievous. I will give no deadly medicine to any one if asked, nor suggest any such counsel...
I will teach in a way which, according to all that is currently know about learning mathematics, I consider for the benefit of my students, and abstain from whatever will prevent them from becoming the best mathematicians they can be. I will do nothing to mess up any mathematical minds (even if a fellow teacher, homeschooler, administrator, or standardized test points me toward unhealthy teaching practices), nor will I suggest any mathematical teaching strategies that may harm someone else's child.In the homeschool world we hear a lot of debate about the practice of "unschooling"; I hesitate to even mention it because the concept means such different things to different people. But I will say this. It is far easier to introduce mathematics to a child who has never been taught formal math than it is to try to reintroduce a concept to a child who has had his thinking taken away.