Perhaps this is an unpopular idea during shopping period, when every required class seems deliberately placed at the same time as your favorite seminar, but Yale is absolutely right to include a quantitative reasoning requirement. Unfortunately, undergraduates and freshmen in particular have far too little information about which classes to pick. The math placement tests and the Blue Book emphasize MATH 112-115-118-120, the calculus progression, so for the unwary freshman, college math can seem like the same kind of conveyer belt sequence that was common in high school. But for many freshmen, these classes are the wrong choice.
If you don’t plan to take higher-level math classes after you’ve fulfilled your QR requirement, there is absolutely no reason that you should take courses in the calculus sequence. The MATH 112-115-118-120 sequence is a long introduction to the basic techniques you’ll use in higher level classes. If you never go on to take them, you’ve spent a lot of time doing the equivalent of assiduously studying lab safety and never running an experiment.
The current structure of the QR requirement implies that math is a technical skill that requires a certain minimum level of mastery, rather than a discipline as rich and varied as literature or history. Practically speaking, nearly everyone at Yale has already cleared the minimum bar of math knowledge required to function in the world. If the QR requirement is meant as a guide, not a burden, Yale should revise its recommendations to point students towards the classes and professors who will teach quantitative reasoning, not merely quantitative tools.
Yale should take its cue from people like Computer Science Professor Dana Angluin. Every year, Angluin begins Computer Science 201 with a quote from computer scientist Alan Perlis, “A programming language is not worth learning, if it doesn’t change the way you think.” Angluin lives up to this pronouncement for the rest of the semester, teaching problem solving and critical thinking as they apply to computer science.
After three years spent flirting with the math major, I’m convinced that, if Yale truly wants to teach reasoning, the QR requirement should place its emphasis on statistics, perhaps going so far as to make a statistics class required for all undergraduates. I should clarify that I mean a statistical theory class, not a quick primer on using computers to perform tests of significance.
It is useful for people in academia to learn how to analyze data and conduct significance tests, but it is not an essential part of a liberal arts education. Few of the numbers we encounter in the real world are presented with sample sizes and accompanying methodology. What we really need is a way to become familiar with the theory of statistics, to understand how make estimates and gauge our confidence in these estimates. A good statistics class is at least as good an introduction to the peculiarities and foibles of the human mind as any introductory psychology course.
And, luckily, such statistics classes are available at Yale. “Probability and Statistics” (STAT 238), taught by Joseph Chang, the chair of the statistics department, remains one of the best classes I have taken at Yale. The course begins at a basic level (though you should be comfortable multiplying matrices) and takes you through the theory that undergirds modern statistics. Unlike a class that depends primarily on formulas, the theory-based class has allowed me to look critically at all kinds of statistical problems and reports, even if I’m not yet familiar with the exact test used.
If the math component of Professor Chang’s class is a little daunting, keep your fingers crossed that Charles C. & Dorathea S. Dilley Professor of Political Science Alan Gerber ’86 and A. Whitney Griswold Professor of Political Science Donald Green will reprise their phenomenal seminar “Experimental Methods in Political Science” in the spring. By guiding classes through critical readings of political science papers, Gerber and Green provide a tour of the most common — and most embarrassing — weak points in human reasoning. Math classes done right force us to refine our work in other disciplines by making us aware of our own blind spots and, in classes like Professor Michael Frame’s “Fractal Geometry,” introduce us to new ideas of beauty and complexity. And when picked right, they have potential to make us better and more creative thinkers in every field.