A place to discuss schools, kids, parents, and teaching as well as the changing world of 21st century education.
NYT: Is Algebra Necessary?
I found this to be a very interesting read. For the past two days, I have come back to the author's thesis, thought about how we design schools in the 21st Century, and wondered why we keep doing what we do in schools today. Well worth a look.
Take a look at this article (PDF on linked paged): http://www.maa.org/devlin/devlin_03_08.htmlToward the end of the NYT article, the author suggests incorporating math in art, music, "even poetry." I agree, but I think that the author is underestimating the level of mathematical understanding that addressing these subjects requires.The math behind music is intriguing---but it requires algebra to understand. Requiring algebra is not a bad thing; the trick is to motivate that algebra. I make musical math one of the focuses in my teaching of exponential and power functions in my classes. One activity is to have the students build a stringed instrument. Placing the frets requires understanding the math.In fact, one can go as deep as one wants with music and math. To understand the electronic recording, manipulation, and production of music requires understanding basic complex analysis (Euler's formula, discrete Fourier transform)---or put another way, it motivates one to learn complex analysis. At a secondary level, music directly motivates an understanding of complex numbers. Complex numbers aren't there just to provide roots to all polynomials, as many students leave school thinking. That music is produced through vibrations means that the mathematics of periodic functions (think trig, or even better, Euler's formula, which relates cos, sin, and i in one stunning equation) is essential.The same goes for art. A friend of mine applies modern signal processing techniques to find correlations between pieces and artists, e.g., to understand an artist's development or to spot forgeries.Poetry, too, can be analyzed mathematically; see the field of "natural language processing." Analysis goals might include, as with art, understanding an author's development or associating an unattributed work to an author. Generating poems might be fun, too---same for art. But anything even mildly sophisticated requires a basic understanding of math. And like it or not, algebra is about as basic as one can get.Still, I agree with your wonderment: why do we "keep doing what we do?" I think one fundamental reason is that many math teachers don't actually apply what they teach and thus lack sufficient expertise beyond the apparent level of the material that they teach. I say "apparent" because, in fact, mathematics is a beautiful subject in which big ideas and patterns thread their way throughout---from arithmetic all the way up. Therefore, mathematics can only be taught well---at any level---by a teacher who has a pretty deep understanding and long practical experience with the subject. In all subjects, but perhaps most emphatically so in mathematics, subject expertise ought to be valued above teaching credentials or experience.I'd love to see a new wave of secondary math teachers who spend half their time teaching and half their time as engineers, scientists, or pure mathematicians.
Brilliant response, Aaron. I tend to agree with your points about teachers who are experts in their field, but far too many schools don't have these experts. How do schools find them? I love your commentary here. Thanks for responding.
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