About twenty years ago Mattel rolled out Teen Talk Barbie - a talking Barbie that had 270 phrases. One of them turned out to be controversial and the doll disappeared from the shelves to be replaced by one with 269:
The remake was warranted, but sadly many Americans agreed with what she was saying and helped instill the sentiment in their children. Americans tend to believe math is hard and that you need special gifts to do it well. They also see it as little more than a tool. An exceedingly unfriendly tool.
A few friends mentioned Andrew Hacker's book on math education was wrong to the point of being clueless. I had come across a few of his newspaper op-eds that were enough to keep me away, but last week Evelyn Lamb, a math postdoc at the U of Utah, published a great commentary in Slate.
I've only taught in universities and can't claim to be a professional teacher. Some of you are and have a much better sense of challenges and direction, so consider what I say nothing more than opinion from someone who went deep on the science and math track years ago. It may seen odd, but I worry that STEM education is gets too much attention and, in its current form, is poorly tuned to the needs of most students and society. I've commented on my belief that those who will go on into technical areas are already well served.1 Science and math courses need to be taught so as to engage and even inspire more of the students. We need to move from the pre-professional track that excludes most students to something that engages most students. We can't have people nodding their heads thinking Barbie was onto something.
Math is in particular need of re-work. There is too much repetition, memorization and mechanical effort. Math has a beauty of its own - a beauty that can be taught at many levels. Kids can worry about puzzles, knots, various types of infinity, probability, risk analysis, and dozens of other areas without touching on trains traveling from Cleveland at 47mph. Interdisciplinary work is obvious - probability fits in with sports, biology, history, science and many other subjects. Here's an example that might appeal to young bike riders - the math could easily be worked out by high school students. The fact it took a real mathematician to work on it is commentary on how many interesting questions there are rather than the problem being difficult.
Beyond the useful there is the beauty of the subject. It really needs to be considered on a level with art and music and not just a tool. There are simple ways that can bring flashes of insight .. You may have seen the construction attributed to Archimedes that seems to indicate the circumference of a circle is 4 rather than π. Of course this is wrong, but understanding why and gets you into a class of beautiful objects. I remember being enthralled with them when I discovered them in an article by Martin Gardner in Scientific American. Here Vi Hart encourages students to dip their toes in the subject:
Unfortunately a good deal of the STEM curriculum was written by technical types who work towards the preprofessional pipelines. One is reminded of buying parachutes designed by birds - maybe for those who will grind it through to become experts, but everyone else gets killed along the way. We've seen this type of panic over job relevant skills before.2 The notion of relevant STEM is fine, but it needs to engage and inspire most students on one hand and isn't watered down like Hacker suggests on the other. Students need to realize there are many dots to connect and having played with dot connection a bit first seems right and math is a big fundamental dot that has connections, both obvious and subtle, nearly everywhere.
Evelyn, the young mathematician who took on Andrew Hacker, came to her passion as an undergraduate and is fascinated by the mathematics of sewing (among other things). It turns out to be deep .. she notes:
When you get down to it, sewing is applied geometry. You are using flat pieces of fabric to approximate the curvature of a complicated surface. Seamstresses and other sewists don’t get much credit for their research in applied geometry, perhaps because traditionally "feminine” activities are not assumed to be very mathematical. Of course, those of us who sew or make crocheted hyperbolic planes or Klein quartic curves know better!
Barbie indeed
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1 There is a good deal of underemployment in many of the sciences - far too many Ph.D.s, often brilliant, for each position.
2 So many stories here. One of the funniest was a group of universities trying to mandate computer literacy by mandating APL classes for the entire freshman class. This was in the mid 70s and fortunately crashed and burned before the end of the first semester. A friend who happens to be one of the great computer scientists of the world has taught introductory CS courses and notes kids who had a high school background often come with bad habits that are difficult to unlearn. The kids who do best are those who had a bit of logic and probability in high school. Also music students did very well.
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Recipe corner
Spring has finally arrived! Here's a quick linquine
Spring Asparagus Linguine
Ingredients
° 12 oz linguine
° 1/3 c olive oil
° 1/4 cup of nuts - pine nuts are traditional, I used pecan bits
° 4 garlic cloves sliced
° 2 pounds of asparagus, trimmed and cut into inchish pieces
° salt and pepper
° 2-3 oz shaved parmesan (omit if vegan)
Technique
° cook the pasta according to directions on the box, drain and return to pot
° heat the olive oil in a skillet over medium heat. Add the nuts and garlic and cook for a minute or two - don't overcook. Add the asparagus and cook 'til tender .. 2 or 3 minutes.
° add the asparagus+nuts to the linguine with some salt and pepper and toss. Sprinkle with the cheese if you like and serve
Technique
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