### Thinking outside the parallelpiped

Jul. 16th, 2009 09:01 am**matthewdaly**

So I went and laid out my argument a few days ago that high school mathematics education in the United States is not what any rational person would choose to implement if she were solely responsible for rebuilding it from scratch. I hope it didn't come across as an indictment that the asylum is being run by the inmates, but rather that it is a case of collective action where a community of rational individuals cannot be fairly expected to seem rational when considered as a single entity. It requires a more delicate analysis to untangle where we're headed in such a hurry and how we got into the handbasket. I hope that I illuminated a few pieces of that puzzle in my previous post.

Still, I am reminded of my eighth grade social studies teacher. When you made an argument in his class, he would pepper you like a four year-old with a mantra of "So what?" until you either reached a conclusion worthy of your data or (more often) broke down in tears. So, let's move on in that spirit. High school math is FUBAR; so what? Who cares? What do we do about it? I say: not much. Let's slap a disclaimer on it, supplement the ways in which it does not meet our individual needs, and spend our lives focused on more pleasant things.

I mean, truly, what branch of the high school curriculum isn't FUBAR? Science promotes the same dead recitation of the experiments of the eighteenth and nineteenth centuries without teaching the pleasures of research (plus it's not like anyone is claiming that the Bible contradicts the Quadratic Formula). English class is about studying only six stories a year, all by dead white men two of whom are always Shakespeare and Dickens. History is a cobbling of complex stories into oversimplified narratives that overlooks anything that gets in the way of "the moral of the story". The treatment of math is starting to look more comfortable. The only reason pure mathematicians have a stick up our collective asses is that the Death March to Calculus is only a part of the beautiful story of the "true math". It would be like if you were a Jordanian who adored the courageous outreach of Queen Rania and had to endure a larger world in which people thought that she was pretty hot but no Carla Bruni-Sarkozy.

Also, it's not new, and it's not dire. If this were the death knell for math, math would have died thirty years ago. I'm not actually even convinced of the unstated assumption that it is the role of formal education to teach students to love a field of study. (If it were, would the students fail if they didn't care for the topic?) In point of fact, there are currently many more vectors for the math bug than there were fifty years ago, and more than there were when it bit me twenty-five years ago. Here are some of them:

- Books. Martin Gardner wrote an amazing survey of recreational mathematics for

- Programming. Computers are computational devices, and very usually one is brought to learn coding techniques with mathematical studies. I remember in high school that we were tasked with writing programs to estimate pi by a series of different algorithms and come to decisions about which were the fastest and most accurate. Project Euler is a much larger catalog of problems requiring a combination of mathematical investigation and algorithm design skills.

- Puzzles. Abstract logic puzzles of the sort that Nikoli produces on a commercial level and folks like the World Puzzle Championships craft at the OMGWTFBBQ difficulty level, and they existed to a lesser but still regular extent in my teenage days. Some of the puzzles are actually number-based to various degrees, but they're all mathematical. You're investigating an abstract environment that is unfamiliar to you and developing and refining heuristics to address the problems that you face there with increasing productivity. The specific tactics that you discover for each individual puzzle don't have much utility on their own, but the strategies for researching and formally codifying logical structures is a necessary skill for survival in our real world.

And there's more than this, of course, but it's certainly more than enough to pique the interest of someone who is earnestly searching for it. And there is so much injustice in the world that I simply can't get myself worked up over the issue that these avenues of research have to be found instead of spoon-fed from a licensed teacher and you don't get "credit" for doing it. It'd be nice if there were more respect and support for this sort of learning, but for all I know it's even more beautiful because it is done out of personal curiosity rather than that it was a homework assignment.

Still, I am reminded of my eighth grade social studies teacher. When you made an argument in his class, he would pepper you like a four year-old with a mantra of "So what?" until you either reached a conclusion worthy of your data or (more often) broke down in tears. So, let's move on in that spirit. High school math is FUBAR; so what? Who cares? What do we do about it? I say: not much. Let's slap a disclaimer on it, supplement the ways in which it does not meet our individual needs, and spend our lives focused on more pleasant things.

I mean, truly, what branch of the high school curriculum isn't FUBAR? Science promotes the same dead recitation of the experiments of the eighteenth and nineteenth centuries without teaching the pleasures of research (plus it's not like anyone is claiming that the Bible contradicts the Quadratic Formula). English class is about studying only six stories a year, all by dead white men two of whom are always Shakespeare and Dickens. History is a cobbling of complex stories into oversimplified narratives that overlooks anything that gets in the way of "the moral of the story". The treatment of math is starting to look more comfortable. The only reason pure mathematicians have a stick up our collective asses is that the Death March to Calculus is only a part of the beautiful story of the "true math". It would be like if you were a Jordanian who adored the courageous outreach of Queen Rania and had to endure a larger world in which people thought that she was pretty hot but no Carla Bruni-Sarkozy.

Also, it's not new, and it's not dire. If this were the death knell for math, math would have died thirty years ago. I'm not actually even convinced of the unstated assumption that it is the role of formal education to teach students to love a field of study. (If it were, would the students fail if they didn't care for the topic?) In point of fact, there are currently many more vectors for the math bug than there were fifty years ago, and more than there were when it bit me twenty-five years ago. Here are some of them:

- Books. Martin Gardner wrote an amazing survey of recreational mathematics for

*Scientific American*from 1956-81, and that has been collected into quite a few books that I greedily devoured in my formative years. Raymond Smullyan wrote fictional adventures that involved accessible but deep forays into non-elementary topics like combinatorial algebra and decidability. Kids today have access to these books (perhaps second-hand, admittedly) and a greater access to the layman-friendly works of John Conway and the fiction of Dennis Shasta.- Programming. Computers are computational devices, and very usually one is brought to learn coding techniques with mathematical studies. I remember in high school that we were tasked with writing programs to estimate pi by a series of different algorithms and come to decisions about which were the fastest and most accurate. Project Euler is a much larger catalog of problems requiring a combination of mathematical investigation and algorithm design skills.

- Puzzles. Abstract logic puzzles of the sort that Nikoli produces on a commercial level and folks like the World Puzzle Championships craft at the OMGWTFBBQ difficulty level, and they existed to a lesser but still regular extent in my teenage days. Some of the puzzles are actually number-based to various degrees, but they're all mathematical. You're investigating an abstract environment that is unfamiliar to you and developing and refining heuristics to address the problems that you face there with increasing productivity. The specific tactics that you discover for each individual puzzle don't have much utility on their own, but the strategies for researching and formally codifying logical structures is a necessary skill for survival in our real world.

And there's more than this, of course, but it's certainly more than enough to pique the interest of someone who is earnestly searching for it. And there is so much injustice in the world that I simply can't get myself worked up over the issue that these avenues of research have to be found instead of spoon-fed from a licensed teacher and you don't get "credit" for doing it. It'd be nice if there were more respect and support for this sort of learning, but for all I know it's even more beautiful because it is done out of personal curiosity rather than that it was a homework assignment.