Wednesday, October 07, 2009
Children learn more rapidly than adults, though they are also very ignorant. In a way, they are idiot savants, good at one kind of thinking (acquisition), poor at another (facts, judgment). A friend of mine had a foreign exchange student from Germany last year, I think she was a junior (ie, about 17). The girl thought of it as a sexual vacation and remarked to the shocked mom that the African American boys were much better in bed than the white boys. The mom was rather horrified by the example set for her own little snowflake; however, I was wondering how to interpret this lapse in judgment. In one scenario, the German exchange student was making stereotypes based on a few people, and this is a bad habit. On the other hand, she might have had statistically valid sample sizes and been inferring correctly. Either way it wasn't a good example for her little American sister.
My daughter is two, so I figure I have a decade or so until I give the 'when a mommy and daddy love each other very, very much...' talk.
My 8 year old son has a different learning quandary. His math homework from our public schools is rather incoherent. He's just getting his addition and subtraction down, and his latest homework had many questions on geometry: identify the isosceles triangle, the right triangle. Before algebra or trig I don't see the point of going over geometry because you really can't use these things, instead, you define things like 'parallelogram', and that's it. He should learn the point of a concept, like a right triangle, is to solve problems. Until he can do more math, these geometrical problems don't help him solve anything, so it's just pointless memorization.
One question showed a square. It then asked, what is the length of a side such that the area is equal to 36. Now I'm sure Terrance Tao could solve this when he was 4, but I'm not holding him to that standard (see the Field Medal winner's test he aced when he was 8 here). This involves reverse engineering a square root, and his knowledge of math tables is sketchy right now. This is why I love Kumon. They drill math mastery systematically using proven methods. They only move forward when a concept (such as subtracting by 4 for single digit numbers) is mastered. Each week there's steady progress, and more complicated concepts are not addressed until students have mastered concepts necessary for their understanding. It's all about overlearning, tracking, and a thoughtful sequential presentation of ideas.
In contrast, the public schools show a bunch of concepts, never long enough for students to really learn them. Their efforts to make math 'relevant' makes it irrelevant, because the best way to teach relevance is to have what you learned last month essential for what you are learning this month, ad infinitum. Instead, we have bizarre little segues to topics like 'lines of symmetry' that are applied to blocks and butterflies, but then forgotten.
My niece is getting a Master's in education and wants to be a teacher for young children. Part of her degree involves designing an experiment to test a hypothesis about learning. One would think, given hundreds of thousands of education Master's students--and their pet ideas for improving teaching--there would be progress in pedagogy out of all this, at least for straightforward subjects like math and reading. Alas, I don't think it is much better than what was taught in the early twentieth century, in spite of probably a million people formally exposed to teaching as a discipline, and studying this systematically, writing theses, journal articles.
We seem in a bad equilibrium. I think Kumon has figured it out, but society has constraints that keep such practices from becoming popular, often based on patronizing ideas about developing creativity of both the teacher and the student. In pandering to parents and teacher's unions, saying "we have a rather rigid process to maximize your kid's learning" is not as popular as saying "tests don't measure anything. We should treat each child as if they were their own special kind of genius." One thing our society is not learning, is how to learn.