John Easter on the Beauty and Practicality of Math

John Easter on the Beauty and Practicality of Math

As my attempt at retaking the Math SAT recently demonstrated, I’ve always had a shaky relationship with the subject. But just as I think a key to helping students engage with my field (writing), requires students to understand what’s so meaningful about writing outside of the context of school, I figured the same must be true with math.

So to better understand what’s underneath my frustrating relationship with math, I talked to one of EE’s tutors, John Easter, who has managed to excel in both math and literature, and has some interesting thoughts on how we could get students more engaged with the subject.

John Easter, a math tutor at Educational Endeavors, studied comparative literature and mathematics as an undergrad. He returned to school intent on getting a PhD in comparative literature, but ended up auditing math classes for fun and, eventually, teaching for the math department at Indiana University. He’s been teaching math ever since. In his spare time he endeavors to keep a handle on his chess addiction by riding his bike for long distances as often as possible. He’s circumnavigated Lake Michigan twice and has even pedaled his way from Chicago to New Orleans.

John Warner, EE Staff Writer: So let me get this straight. You like math? What is there to like about math?

John Easter: Like many people, I like doing things I’m good at. At least, it started that way. I made my way through the 1st, 2nd, and 3rd grade math curriculum at my elementary school during my 1st grade year. My love for math continued unabated until I got halfway through high school. At that point my interest shifted to literature and philosophy — math was getting more and more boring and didn’t offer any answers to the BIG questions. The best it could do was to help my understanding of physics and cosmology where one encounters many BIG-adjacent questions. In college, I was encouraged to continue doing math and I played along for a year. I nearly stopped there, but I decided to check out the first few classes of an Abstract Algebra class I was sure I would promptly drop in favor of a second semester of literary theory. On day one, the professor started with a famous proof that there are an infinite number of prime numbers. It was beautiful. I was hooked again. I’ve since learned several other proofs that there are an infinite number of primes. In fact, I have a favorite and a second favorite. Once you begin down this road, you quickly realize that math is an art, and who doesn’t like great art?

 

JW: I think I went through a progression of confusion, to frustration, to anxiety, to full disengagement, where I took great pains to avoid any math at all in college. In your experience, how common is this alienation from math? Do you see it often in your work with students? What are the roots of it?

JE: Instead of trying to convince students that there’s nothing to fear, I take a totally different tack that often surprises the student enough to get their full and undivided attention. I remind them that homo sapiens didn’t evolve mathematically, so to speak. We’re all bad at math. In fact, our evolution interferes with learning math. Research shows that an 18-month-old baby can tell the difference between 10 and 100, but not 10 and 11. In other words,  we’re born to count logarithmically, which is not a skill prioritized in our current culture. There’s an obvious advantage to this if you’re a primate competing for resources with other primates. My group has ten members, their group has 100 — let’s look for another source of water. But teachers spend a considerable amount of time beating this out of kids and trying to beat the base-ten way of counting into them. It’s so difficult to work against our nature, that success is very limited. As a result,many people learn to do basic computations by following algorithms with no understanding of how they actually work. It seems that the moment a student does begin to see the method behind the madness — and might be ready to take advantage of the structure of base-ten numbers to come up with their own more efficient algorithms — someone hands them a TI-84. 

We come factory-equipped to learn language, but everything you know about math was taught to you. We are all at the mercy of our teachers when it comes to math. And if I haven’t been clear to this point — I have little faith in our math teachers.

This doesn’t mean that there aren’t great math teachers out there. I work with many of them, but it seems like for every great math teacher, there’s a baseball coach who’s assigned an algebra class that administrators can’t find a teacher for. The class is an avalanche of worksheets with little explanation/teaching. This isn’t hypothetical — it’s happening at a selective enrollment school in a major city and I’m tutoring one of the students. That’s a systemic problem.

Another systemic problem is how math teachers are educated — and of course how they’re valued in general — but that’s a whole interview in and of itself. 

 

JW: What could we do to prevent student frustration with or alienation from math? Are there math-specific changes we could or should make, or is it a bigger thing around schooling in general? Both?

JE: Probably both. But, with respect to math, there are a few basics we could start with.

  1. Teachers of math should have math degrees, not math teaching degrees — there is a huge difference. 
  2. Administrators should leave math teachers alone. There’s nothing more likely to cause a serious math teacher to leave the profession than an administrator with a background in music education criticizing their lesson plans.
  3. More stats, more programming, no calculators — anything a TI-84 can do, an object-oriented language, like Python or Excel can do better. Stats is the basis of most of the AI that we encounter in our everyday lives, and learning how statistics work would be a great way to help students better understand the world. 

 

JW: When you tutor, particularly for something like the SAT, I assume you don’t have the time to do a ground-up rebuilding around a student’s attitudes and knowledge about math, so what’s your approach to helping them with that test? Or, am I wrong, and the best bet is to lay a better foundation before you train them for the test?

JE: I take a strategic approach to all standardized tests. No self-respecting math teacher gives multiple choice exams. That’s not a math test, it’s a matching game. I teach kids to play this game with clever strategies designed to outsmart the test writers. I do the same with adult students taking the GMAT or the GRE. I didn’t always use this strategic approach, but after working for a company that designed and produced such tests, I eventually realized this is the most effective and efficient approach.

 

JW: Lastly, who should take calculus?

JE: I’m conflicted about this.  Calculus used to be a required subject for undergrads at University of Chicago because it was the premier intellectual achievement of the 17th century. That’s the only good reason I’ve ever heard for everyone to take calculus. Regardless, it’s a bit extreme. Many say no one should be taking calculus in high school. That’s also a bit extreme. Here are a few things we need to consider:

  • The Greeks could find the slopes of tangent lines (a fundamental application of derivatives) and find the area of arbitrary shapes (it was called “The Method of Exhaustion,” and it’s basically an integral). Newton and Leibniz get the credit because they realized the two ideas are related, which is the fundamental theorem of calculus. Only a little bit of trig is required to apply the method of exhaustion to derive a good approximation for pi and find the area of a circle. There are other areas where we could integrate the basic ideas behind calculus without getting into the nitty gritty — without even mentioning “calculus.”
  • In the race to get to calculus we skip over a huge amount of important and interesting mathematics: combinatorics, graph theory, probability, non-Euclidean geometry, algorithmic thinking, linear algebra, complex numbers, and number theory to name a few.
  • If you’re going to teach calculus, you need to have a math degree and you should ideally have taken at least one semester of real analysis. Very few high school teachers would meet that requirement.I suppose some serious professional development work could turn a competent math teacher into a competent calculus teacher. I think Northwestern offers a summer course for just that purpose.
  • If you’re going to teach calculus in high school, go slowly and prove everything. Do limits in a formal way, derive all the basic derivative rules. You might not get very far, but it would be a nice reality check for all the kids that are “good at math.” They would get to see what real mathematics looks like before they go to college, start as math majors, switch to math teaching when they discover what math really is (proofs), and become the underqualified teachers causing many of our problems.

In sum, very few high school students should take the formal subject, and everybody should be introduced to the basic ideas. We should dump the AP test (an insidious source of inequity). If you really want to major in math, the honors calculus class you’ll take as a college freshman will make AP calculus look like basic arithmetic. 

Besides, if you’re going to continue math at the college level, many math departments will insist on it regardless of your AP score. 

 

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