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A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form Paperback – April 1, 2009
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Lockhart believes (and I agree) that the current focus on rote memorization, "skillz drillz," and repetitive exercises causes students to falsely believe math is a heap of formulae in a vacuum. He expertly dismantles how math is taught while demonstrating the discipline's true, dynamic nature. To Lockhart, mathematics should foster inquiry and a curious, question-driven mindset that then pursues answers. Math teaches how to face challenges without road maps.
But on page 40, Lockhart asks: "What other subject shuns its primary sources--beautiful works of art by some of the most creative minds in history--in favor of third-rate textbook bastardizations?" Would Lockhart like me to start a list? I could do it alphabetically. Historian James Loewen and literature professor Gerald Graff have voiced the same complaints in their fields. Discouragement of inquiry is endemic throughout education today.
Reading Lockhart's demonstrations of popular mathematical concepts, I was struck by how seemingly complex concepts suddenly appeared both clear and welcoming. I remembered the difference between my undergraduate education, which favored memorization and regurgitation, and graduate school, which encouraged individual discovery and growth. But why must I or anyone wait for grad school before unlocking the truth for ourselves?
Some of Lockhart's critics say that math should focus on memorized formulae, because knowledge is cumulative, and few students can savvy higher math without a comprehensive foundation. But how many want or need higher math? As a student of mine said, she'll never need to factor polynomials in real life. No, we don't study math for its perceived utility. But that's not to say that math isn't useful.
Lockhart's eloquent, graceful proofs demonstrate a mind which faces questions that lack explicit answers, and then pursues those answers. This process of investigation is necessary in a world where clear-cut options are few on the ground. Too many graduates, facing adult life, stumble when they find that work and family aren't closed cases. These habits of investigation and inquiry are useful inasmuch as life offers more questions than answers.
Math is useful and desirable because it opens doors of thought. Too much of school appears closed to debate, but real life forces us to ask questions that don't have answers. People who aren't equipped to face such questions take on adult roles without their most valuable tools. Whether it's math or science or art or business, we must learn to face questions, weigh possibilities, and seek that "Eureka" moment.
Often, people who would dominate us seek to create the false impression that sophisticated questions can be solved as simply as textbook exercises. Appropriate education, including an introduction to math, should teach us not to plug memorized answers into dynamic, changing questions. Math teaches us that each question opens new answers, and, like all disciplines should, invites us to learn how to ask and investigate for ourselves.
In my experience as an elementary teacher, I have always wanted my students to love the exploration aspect of solving problems. He hit the nail on the head when he spoke about encouraging play, for it is through play that children learn.
I also find it interesting that the back cover says that the author has now dedicated himself to teaching K-12 students... at an exclusive private school in New York. The reality in a regular public school in America will be much different than what goes on in that environment.
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Here I was thinking this book was going to be some boring math book. Boy, was I wrong!Read more