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A Sufficient Mathematical Background

A couple of weeks ago, the Washington Post ran an op-ed written by G. V. Ramanathan, emeritus Professor in mathematics, statistics, and computer science, entitled “How much math do we really need?” As the title suggests, Ramanathan uses his space in the paper to argue against the grain of conventional wisdom when it comes to mathematics education; his point is that American students are actually receiving too MUCH math, rather than not enough. It’s an appealing thesis, especially for those looking for an excuse to embrace their own math phobia, but ultimately I find it to be less than responsible.

Consider, for example, the following passage:

How much math do you really need in everyday life? Ask yourself that — and also the next 10 people you meet, say, your plumber, your lawyer, your grocer, your mechanic, your physician or even a math teacher.

Unlike literature, history, politics and music, . . . → Read More: A Sufficient Mathematical Background

Happy Tau Day?

In the past, I’ve used this blog as a platform to make clear my mixed feelings about Pi Day, a math themed holiday celebrated every year on March 14th (3/14, har har) in honor of the beloved mathematical constant . My thoughts on the subject can be found here.

It would seem that I am not alone in my frustration. Michael Hartl, an educator and entrepreneur (as well as a Ph.D. graduate from Caltech), has just today launched a website in favor of Tau Day as a replacement for Pi Day. However, his argument (based on a 2001 paper by Bob Palais) goes a step farther – he argues that day shouldn’t be celebrated because isn’t the fundamental constant we should be considering! Rather, he argues that the true fundamental constant is , which is approximately 6.283185… . Hartl argues that this should be the fundamental constant of interest, and . . . → Read More: Happy Tau Day?

Patient Problem Solving

Last year, I remarked on a TED talk from mathemagician Arthur Benjamin, who argued for the displacement of Calculus by Statistics in the hierarchy of high school mathematics. This year, TED has sponsored a talk by high school math teacher Dan Meyer, who discusses what, in his view, are the major problems with the way mathematics is currently taught to kids, and what can be done to fix things.

His opening is spot on: “I teach high school math. I sell a product to a market that doesn’t want it, but is forced by law to buy it.” He goes on to argue that the problem with math education, a problem exacerbated by most textbooks, is that it discourages what he terms patient problem solving. Problems in textbooks rarely reflect the types of problems one encounters in real life: textbook problems usually supply you with just . . . → Read More: Patient Problem Solving

Read a Mathematician’s Lament

I recently had the pleasure of stumbling across Paul Lockhart’s essay, A Mathematician’s Lament. Lockhart, a former research mathematician in analytic number theory who received his Ph.D. from Columbia in 1990, decided to leave academia in 2000 in order to concentrate on K-12 math education, which he hass been doing at Saint Ann’s School in Brooklyn.

Lockhart’s article lambasts the current state of mathematics education in this country. Some of his main points are the following: Mathematics is an art form, but unlike other art forms like music or painting, is not understood as such by the general population. As a result, students are not exposed to the beauty of mathematics, and are instead taught through drill and memorization, which effectively kills any natural curiosity the student may have. The most important part of mathematics lies not in the facts or theorems that students memorize, but in the arguments that . . . → Read More: Read a Mathematician’s Lament

Restructuring the Math Pyramid?

A friend recently shared with me the following video from TED (see below). In it, mathematician (or, in this case, mathemagician) Arthur Benjamin gives a brief argument for eliminating calculus as the top of the “mathematical pyramid” in high school education, and replacing it probability and statistics. The main reason for this shift is that unless you are planning to have a career in a technical field, it’s unlikely you’ll find a use for calculus in your everyday life, but an understanding of statistics can benefit you no matter what you do. For example, it can help you to build an intuition about day to day decision making when risk and uncertainty are involved. Here’s the video (it’s short, only a couple of minutes):

A noble goal, to be sure, and it’s certainly a solution that wouldn’t cost a whole lot. There is an argument to be made for such . . . → Read More: Restructuring the Math Pyramid?