Saturday, May 2, 2009

Math and pigs

Some unschooling life as it's happening today.

Last night Serenity was invited to stay overnight with her friend Isabel. Serenity met Isabel at some SFBUNie events and we've been meeting her family and several others at parks in Livermore most every week recently. Isabel and Serenity get along great.

When I was dropping Serenity off at Isabel's yurt, yes, they live in a yurt up on a hill outside of town, I got to talking to Cindy, Isabel's mom, about math and how it's taught in schools. She told me about this article "A Mathematician’s Lament" by Paul Lockhart. What a great read! I encourage anyone who had the love of math pounded out of them by schools the way I did to read this. It's pretty long at 25 pages but well worth the read, it's funny and sad at the same time. I saw myself in it all over the place.

Here are some of my favorite parts:

“…if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”

“…if you can’t be real, then you have no right to inflict yourself upon innocent children.”

“This is intimately connected to what I call the “ladder myth”— the idea that mathematics can be arranged as a sequence of “subjects” each being in some way more advanced, or “higher” than the previous. The effect is to make school mathematics into a race— some students are “ahead” of others, and parents worry that their child is “falling behind.” And where exactly does this race lead? What is waiting at the finish line? It’s a sad race to nowhere. In the end you’ve been cheated out of a mathematical education, and you don’t even know it.”

(Larry) The preceding goes for most every subject I can think of, not just math.

“So not only are most kids utterly confused by this pedantry— nothing is more mystifying than a proof of the obvious— but even those few whose intuition remains intact must then retranslate their excellent, beautiful ideas back into this absurd hieroglyphic framework in order for their teacher to call it “correct.” The teacher then flatters himself that he is somehow sharpening his students’ minds.”

(Larry) This is why they kept saying show your work?

“SIMPLICIO: So we’re supposed to just set off on some free-form mathematical excursion, and the students will learn whatever they happen to learn?

SALVIATI: Precisely. Problems will lead to other problems, technique will be developed as it becomes necessary, and new topics will arise naturally. And if some issue never happens to come up in thirteen years of schooling, how interesting or important could it be?”

“SALVIATI: …There should be no standards, and no curriculum. Just individuals doing what they think best for their students.

SIMPLICIO: But then how can schools guarantee that their students will all have the same basic knowledge? How will we accurately measure their relative worth?

SALVIATI: They can’t, and we won’t. Just like in real life. Ultimately you have to face the fact that people are all different, and that’s just fine. In any case, there’s no urgency. So a person graduates from high school not knowing the half-angle formulas (as if they do now!) So what? At least that person would come away with some sort of an idea of what the subject is really about, and would get to see something beautiful.”

“And there you have it. A complete prescription for permanently disabling young minds— a proven cure for curiosity. What have they done to mathematics! There is such breathtaking depth and heartbreaking beauty in this ancient art form. How ironic that people dismiss mathematics as the antithesis of creativity. They are missing out on an art form older than any book, more profound than any poem, and more abstract than any abstract. And it is school that has done this! What a sad endless cycle of innocent teachers inflicting damage upon innocent students. We could all be having so much more fun.”

Oh yeah, the pig part of the title to this post. I sent an email to Cindy this morning asking how things went with the overnighter and thanking her for the article and she replied:

(Cindy) "Glad you're enjoying the article! We did have a fun and peaceful-in-a-very-loud-way evening! The girls went to bed at about 11:30 and Serenity was the first to wake up just after 7... She said "That NEVER Happens!" :-) So, just forewarning you that she may be a bit short on sleep... They are all up and around drinking hot chocolate now.

Oh boy! Our neighbors' pig just arrived for a visit and Serenity and Addison (another unschooling kid who spent the night) are going out to introduce themselves, this should be fun!"

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