Guest Post: Ladders Go Both Ways

This guest post by Mr Kartik Chandra first appeared here on White Group Mathematics on 18 November 2017

Earlier this month, Frederick Koh, a Singaporean math tutor, invited me to write a guest post for this website of his. Of course I accepted --- blogging is, after all, a conversation.

But what could I write about?

I spent the month of November on the lookout for an idea worth sharing, and last week I found one. I follow a lot of math-educator blogs (blogging is, after all, a conversation!), and one of my favorites is that of Dan Meyers. Recently, Dan posted a rather provocatively-titled piece, "Dismantling the Privilege of the Mathematical 1%". He makes the case that those with a mathematical education --- those who are mathematically privileged --- those who make up the mathematical 1% --- they are the ones with the responsibility to define what mathematics is. Dan says, eloquently as always, that "through our action or inaction we create systems that preserve our status as the knowers and doers of mathematics."

Dan's post made me think deeply about where I myself fit into his spectrum: I'm hardly one of the 1% --- and certainly won't graduate with a math degree --- but at the same time, I love math, both as an activity and as a set of truths.

And I realized that this gives me a privileged position, one where I can comment on mathematical topics from a somewhat neutral perspective. I am neither the person who barely scraped through high school calculus, nor the person who skipped high school calculus because it was too easy. So, trapped between "math people" and "not a math person people", I wish to use this post to explore what exactly creates this divide --- or, rather, explore it in a way slightly different from what you have probably heard a dozen times already.

It is almost universally acknowledged that "education is good." More education, says society, will lead to a happier, more prosperous world. Educate everyone, says society.

I agree, of course.

And yet, paradoxically, we are so attached to the notion that education --- college, in my case, grad school or high school for others --- is a means to distinguish oneself from one's peers. A degree, we argue, makes us stand out in both the workplace and in society. The more competitive the institution, the more valuable the degree.

Less enthusiastically, I agree with this as well: reality forces me to concede the point. Why else would college admissions be so competitive? Why else would classes be graded on curves? Why else would we even have grades in the first place? As disturbed as I am by it, society cares very much about my academic performance, especially in relation to others.

And therein lies the rub. Reader, are these not contradictory notions? If the purpose of an education for an individual is to separate him or her from the general populace, then what follows is the absurd notion that universal education is self-defeating: that the more people we educate, the less an education is worth to the individual.

How does one reconcile this? Can education in the limit benefit both the individual and the society? As an optimist, I wish it could. And in fact I believe it can, but only if we rethink what education means to the individual.

Here is what I think. I believe that too often, we conceive education to be a ladder that lifts us --- above others, if we're fast enough --- rung by rung. The more you climb, the higher you get.

But too often, we forget that you can also climb down a ladder. That an education can also lower the arrogant to humility and place them alongside the less privileged, on common ground. That education builds capacity for empathy and communication, empowering the individual but also society at large to have a dialogue. That this view resolves the paradox of the previous section, because both individuals and society benefit from the capacity for having that dialogue.

What do I mean by this? Let's return to mathematics for a moment.

If you are reading my blog, you most likely have been at a gathering of mathematicians at some point in your lives. It is quite a marvellous thing to behold: a congregation of brilliant minds sharing ideas. Mathematics as a community has its own folklore, its own in-jokes, and its own language. You need only to glance at sites like The Art of Problem Solving or to see this community in all its glory.

I love it. There is charm to the way mathematicians celebrate their field, unlike any other profession I have come across.

And yet, imagine being an outsider for a moment. Imagine being part of the mathematical 99%. How would you feel if someone responded to a question of yours with a grin, saying "left as an exercise to the reader"? Or if someone made you use this weird software package with lots of backslashes to write up your homework? Or if someone went off on a tangent about why their coffee mug said "donut" on it? Or if someone makes an arithmetic mistake and then says "it's true in base 12" before you even notice the error? Or if someone claimed a very unobvious-to-you solution was "trivial"?

These phrases aren't meant to be exclusionary. Some are common inside jokes. Others are part of the mathematical vocabulary. The word "trivial," after all, has a very specific mathematical meaning --- think of the "trivial group" with one element, for example. I use it all the time.

Yet to an outsider, they make the mathematical community seem simply impenetrable. How am I ever going to understand all this? I can't think that fast!

"Math people" tend to be remarkably self-selecting, and I believe this is one of the reasons why: there is a divide between the initiated and the uninitiated, and far too few resources for the latter.

Education, I believe, should be tasked with bridging this divide --- rather than exacerbating it as it does now. Education should give the 99% the opportunity to join the magical world of mathematics, but education should also show the 1% how to open up the world to new members. It should teach students to write about mathematics, finding a middle ground between dense manuscripts weighed down by Greek-letter jargon, and airy puff-pieces that contain nothing of substance. Where will future Ian Stewarts, Martin Gardners, and Brian Hayes come from? I myself would almost certainly be very firmly a "not a math person" person were it not for an Ian Stewart book in my dad's bookshelf that taught me about Fermat's Last Theorem and the Mandelbrot Set when I was very young.

Education should also encourage the next generation of professors to move away from lessons that consist of the copying of lecture notes onto a chalkboard, and provide them with the tools they need to create engaging, interactive lessons that appeal not only to those whom we believe are preordained to be mathematicians, but to artists, musicians, writers, and athletes. It should teach students about the bigger picture of where their mathematics fits into society, about who produces and who consumes mathematics, and why.

At the same time, it should explain to the mathematical 99% what exactly those math people are on about all the time. It should teach them the mathematical canon, help them learn the language, and help them discover the beauty that the 1% have already found.

Yes, such an education will produce a more diverse generation of mathematicians, not only in terms of demographics, but also in terms of ways of thinking. It will produce a generation that writes not only more effective grant proposals, but also clearer papers. That's what the individuals get out of it.

But it will also inspire the mathematical community to rise up against the tyranny of Alice-gives-Bob-three-bananas standardized tests, to use their passion for mathematics and their perception of its beauty to guide the development of curricula and lesson plans. Not to reject non-math-people as heretics who refuse to see the light, but rather to see them as evidence of a broken education system that failed to convey the beauty of mathematics.

To redefine mathematics to be the way they see it, because, whether or not they realize it, the way the mathematical 1% sees mathematics --- as the pursuit of beautiful truth --- is far from what the mathematical 99% sees it as --- the painfully rushed manipulation of symbols on a midterm. To care.

That's what society gets out of it.

About The Author

Kartik is a student who studies and writes about mathematics. He cares deeply about education and the communication of powerful ideas. You can learn more about him at his personal blog, Comfortably Numbered.