The Real Meaning of Pi

Chalkboard with Pi

Today is Pi Day. Because the 14th of March could be written as 3.14, the first three digits for the irrational number we all learned something about in elementary mathematics.

Of course, this little bit of trivia only works if you’re writing the date as we do in the US. The whole exercise falls apart in most of the rest of the world where they traditionally write the day before the month. 14.3 makes no sense.

Anyway, beyond the fluff of memorizing lots of the digits and serving actual pies to math teachers (which we do appreciate), pi is a core mathematical concept with a long history and many important applications.

In this New Yorker article from three years ago, a math professor at Cornell University briefly offers a few reasons Why Pi Matters.

So it’s fair to ask: Why do mathematicians care so much about pi? Is it some kind of weird circle fixation? Hardly. The beauty of pi, in part, is that it puts infinity within reach. Even young children get this. The digits of pi never end and never show a pattern. They go on forever, seemingly at random—except that they can’t possibly be random, because they embody the order inherent in a perfect circle. This tension between order and randomness is one of the most tantalizing aspects of pi.

A little knowledge makes for a better Pi Day.

The image is from the header of the New Yorker article.

The Mathematical Obstacle Course

In a Medium post, a “research mathematician turned educator” discusses how extremely talented students are often disillusioned by high powered mathematics competitions like the International Math Olympiad.

Of course, extremely few high school students will ever be involved in this kind of “cheap competition that brutalises the subject into a performance act”, and this piece is of very limited interest to even most math teachers.

However, this observation accurately describe the high school math experience for most students.

School maths is engineered as a relentless competition, where students are ranked and judged according to the narrowest measures of aptitude. The spoils go to those who can mercilessly commit facts and procedures to memory (irrespective, and often at the expense, of understanding), and recall them in the arbitrary confines of exams.

In most high schools, the math curriculum imposed on students is a complex obstacle course aimed directly at Calculus, a class few of them need or will ever use.

Ending Math Phobia

An engineering professor at Dartmouth College wants you to stop telling kids you’re bad at math. Excellent suggestion.

Why do smart people enjoy saying that they are bad at math? Few people would consider proudly announcing that they are bad at writing or reading. Our country’s communal math hatred may seem rather innocuous, but a more critical factor is at stake: we are passing on from generation to generation the phobia for mathematics and with that are priming our children for mathematical anxiety. As a result, too many of us have lost the ability to examine a real-world problem, translate it into numbers, solve the problem and interpret the solution. [my emphasis]

Of course, we don’t really teach math that way, so it’s not at all surprising that most people don’t leave school with that ability. They never learned her process in the first place.

Maybe if we taught math as a tool for problem solving, instead of asking students to memorize a long series of meaningless rules, we would wind up with fewer math phobic adults.

Just a thought.

The Weekend Collection

A small collection of good things to read, and hear (no watch) when time allows this week.

Read: This past Tuesday, March 14, was Pi day. 3/14 = 3.14, the approximation of this classic irrational number. From two years ago, a writer for the New Yorker goes beyond the trivia to briefly explain in relatively simple terms Why Pi Matters. A little math for all you non-mathematical types. (about 3 minutes)

Listen: If you’re not between the ages of 18 and 34, you’re not in the target demographic for SnapChat. You may not even know how the service works, or why so many young people check in and use it over, and over, and over every day. A recent episode of the Note to Self podcast tries to explain why this app is worth more than $10 billion, as well as “how far Silicon Valley will go to capture and control your eyeballs”. (18 minutes)

Read: Rolling Stone celebrates the 20th anniversary of Buffy, the Vampire Slayer with a nice essay that summarizes what made the series both fun and meaningful. I actually like the very flawed movie on which it was based and the series hooked me from episode 1. (about 6 minutes)

Listen: I’m late to Jenn Binis’ very informative podcast, Ed History 101, in which she discusses the background to our profession that you probably missed in college (or which they got wrong). A good starting point is the segment on summer vacation, a topic that generally falls into that got-it-wrong category. (23:11)

Read: Although I disagree with the central premise that Google is making us dumber, this interview with the author of a new book about how adults learn is still interesting. I do believe that many of the techniques we were taught in high school (and that are probably still taught) are not particularly effective. (about 6 minutes)

The “Right” Way to Learn Math

In a short essay for a Canadian newspaper, a high school math teacher reflects on his work and wonders if it’s pointless.

I also don’t feel the time I spent helping students (mostly freshmen and sophomores) understand math was “pointless”. I do disagree with with his idea of “math as a gym for the mind”, that doing math regularly “keeps the mind active” and improves abstract thinking.

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Certainly there are aspects of studying mathematics that can help students develop their analytical skills, but most of what we teach in K12 classes is largely focused on memorizing and recreating canned procedures.

However, the writer of this particular piece is exactly on target with this assessment of what math education should be.

The “right” way to do mathematics is not to learn many techniques, but to solve many problems using the learned techniques.

The problem must come first. Then we discover what tools, mathematical or otherwise, are needed to solve it.

That’s how math is really used, so why not help students learn that process? Instead of the very artificial one that embodies the math curriculum in most high schools.