I went on a brief rant on Facebook yesterday about an Op-Ed piece in the New York Times which I found remarkably bad. As with many rants, the author wished that it could have been longer… So, below you will find my thoughts a bit more fully expressed. Enjoy!
Aristotle wrote that “all men by nature desire to know.” And yet, too often, educators treat math students as if the pursuit of knowledge is irrelevant to them: truth is nice and all, but what we must give our students is economic benefit.
Sadly, just such an approach was advocated in an editorial in the New York Times this past Sunday. In “Who Says Math Has to Be Boring?”, the author advocates fixing math education in this country by implementing an approach known as STEM—which stands for Science, Technology, Engineering, and Mathematics—which treats these subjects as an integrated whole. The author would have math class be filled with technology and real-world examples, with the clear aim of preparing students for 21st century careers.
And yet, the reality is that math curricula in the United States have been geared towards this approach, or ones quite similar to it, for a very long time. Today, math education in this country continues to be as much of a failure as ever, despite our consistent push for the pragmatic and the relevant.
The problem is this: as long as we treat math as a tool, as a subject that should be pursued because of its practical, real-world benefits, we will fail at math education. We can only fix math education by showing students that math is first and foremost a pursuit of the true, the good, and the beautiful, through the use of logic and reason.
The STEM approach has a long pedigree in the American education system. We can properly trace it back to the Pragmatism of John Dewey, who said that an education is that “which increases ability to direct the course of subsequent experience”—as practical and career-oriented approach to education as ever you’ll find. This philosophy was infused into math and science classes with a vengeance in the wake of Sputnik: the Cold War made it so that Science, Technology, Engineering and Mathematics were the responsibility of every good American, and every math and science teacher’s duty was to prepare the next generation of Rocket Scientists who would defend us from Moscow.
Decades later, we still find ourselves belaboring the practical side of math, only now the menace we face is our economic competition with China. It is now the duty of every math teacher to prepare his students to increase GDP. Of course, this supposedly carries benefits for the math student as well: since, as the theory goes, a math student who is shown the practical benefits of math class will be more motivated to pursue a career in science or engineering, his likelihood of making a high wage will increase substantially. And so, it’s out with the abstract, in with the pragmatic: math education is only seen as being valuable as a loyal handmaiden of our technological enterprise.
But the reality is that the economic benefits of higher math studies are widely known by the general public, including children and teenagers. The fact that accountants and actuaries are well-compensated is so familiar to our students that to repeat it is to indulge in banality. Young people know that high achievement in math class can lead to a rewarding and remunerative career, and yet somehow, no matter how practical we make math class, no matter how subservient we make math to science, technology, and engineering, we cannot stifle the yawns of our students. Math achievement in this country has gone down in the decades since Sputnik; clearly the pragmatic approach is broken.
So in a world where math class is already supremely practical, and yet still overwhelmingly boring, what’s a math teacher to do?
I would have math class be less practical. As long as we treat math as simply another tool in the technological shed, students will find it as interesting as so many wrenches and screwdrivers. We must instead show our students that math is, first and foremost, a relentless pursuit of the true, the good, and the beautiful. We must orient math class around the use of logic and human reason.
Mathematics as a discipline has always been about using logic and reason to arrive at truth. The great mathematicians of history, from the days of Pythagoras and Euclid, found a supreme beauty in the pursuit of knowledge: they knew that they were proving timeless truths. Practical applications came along, of course, but math found its inspiration and its drive as a branch of philosophy, and as St. Thomas Aquinas said, philosophy arises from awe.
Today, we must give back to our students this beautiful pursuit of the truth. We must allow them to experience the joy of mathematical proof. We must help them train their minds in the use of logic and reason, to think abstractly, and to go after knowledge relentlessly. Anyone can look up a mathematical formula in a book and then punch it into a calculator; only a well-formed mind can find a good argument for why that formula works in the first place. It should be the priority of math teachers to make such well-formed minds.
So, enough with the real-world models and the overuse of technology. For too long, we have given students “real world scenarios” involving right triangles, and then asked them to plug numbers into the Pythagorean Theorem to have the length of the hypotenuse spat back out to them. I would rather spend my time training my students to make good arguments for why the Pythagorean Theorem is always true. Have them play with abstract arguments, have them fail and fail and then finally succeed, and have them always be encouraged to return to the logical pursuit of knowledge with greater vigor the next day. Let the science teachers and the engineering professors worry about the pragmatic side of things, and let the math teachers return to what math has always been about.
Ironically, the approach I am suggesting would actually have enormous practical benefits. Is it hard to imagine that a bridge or a building designed by an engineer who had been taught to love the truth and beauty of mathematics would be a superior product? Moreover, can it not be said that any democracy would be better off with a citizenry who had been immersed from childhood in Logic and Reason? We would have more economic utility from our math classes if we stopped treating math as a mere tool and instead saw it as truth.
The pragmatic side of mathematics will always be with us. But rather than following an instructional approach whose origins lie in a desire to aim missiles at the Soviet Union, let us craft classes designed to show our students how to pursue mathematical truth through Logic and Reason. We owe it to our students, because as Aristotle predicted, they desire to know.