We as mathematicians seem practically hell-bent on removing the phrase “I’m just not a math person” from students’ vocabularies. Maybe that’s why they scream it so loudly and defiantly?

Math has so many tactical advantages over sports and the arts. Math is cheaper—you don’t really need special equipment or a whole lot of space or, unless a pandemic necessitates it, technology in the classroom. And politicians and administrators alike are convinced we need more STEM—our programs, unlike sports and arts, will not get cut any time soon. Yet while getting students to want to continue in math is like pulling teeth, they all would love to play a sport or dance.

It makes you wonder what they’re doing that we’re not.

I have some ideas.

Consider the following two scenarios:

(1) A child is put by its parents into Little League. In the course of being on this team, the child realizes they will never be a professional, not even professional enough to get a college scholarship. It doesn’t really matter how the realization comes. It could be due to teammates shouting hurtful if possibly accurate truths, or because the team always loses to [insert rival] at regionals. It could be from listening to an actual professional getting interviewed on ESPN and hearing how much work it takes. Maybe the child decides exactly what *kind* of professional they want to be—maybe they don’t want to end up in the majors but back in their home town as the current coach’s replacement? Maybe other subjects and extracurriculars are more interesting.

They quit the team.

You may expect the child when they’re grown to say, “I just didn’t have what it took to be an athlete.” But would you expect them to hate all sports, or the specific sport they quit? Would you expect them to not want their child involved in sports? Do you expect the coaches to be hypersensitive to how/that/when these children realize they’re probably not going to be a professional? That the coaches are afraid that if children don’t feel better about their athletic abilities whether they are actually present or not then their numbers will become so small that athletics in schools will cease to exist? [Athletics in school are shrinking, but not because of this.]

The answer to all of these questions, I think, is “probably not.” A kid who played Little League for one season, during which time his team positioned him further and further into the outfield, twenty years later is highly likely to be sitting on a couch in his living room in front of a big screen television rooting for his favorite professional team in the pennant.

That’s not to say you expect every child to grow up unscathed. But the kids who “get out early” and who are told “it’s OK to quit” or “it’s OK you’re not athletically inclined”, **the kids who are taught they can still enjoy and appreciate the sport without having to excel in it** are the ones who are generally more OK. It’s the kids who are told by an elder “You need to do this, no matter what” or “You need to do this because I wanted to and never could” …THEY are the ones who will grow up to have mid life crises. It’s the kids who thought they could be a professional but due to some injury had to “retire” that are going to end up blaming someone else for all of their problems and drinking themselves to death in a sports bar watching the team they thought they could make on a big screen television win the pennant.

(2) A child is put by its parents into “the arts”: a musical instrument (private, band, orchestra), or a chorus/choir. Maybe a theater group or some kind of dance. Eventually, the child realizes they probably will not be a professional. The reasons again could run the gamut. Others in the dance troupe/music studio/orchestra/chorale/theater guild could razz the child for their (lack of) ability. It could be because after a certain level of competition they always seem to lose. It could be because of hearing their favorite artist talk about the life of a starving artist and paying dues. Maybe they decide they want to run the town’s local ballet studio, or become their church’s pianist and they don’t really need to “go pro” to do either of those. Maybe other academics lure them away.

They quit.

This child again may say, “I just didn’t have what it took to be a professional [insert artist type]” and as a society we’re OK with that. And the instructors aren’t worried about a narrower flow of children coming through—there will always be kids in music, ballet, and theater lessons even if art and music programs in schools are “scaled” (hah!) back. But back to the child who quits. Do you think they won’t grow up to be that parent who takes their little girl to the Nutcracker at Christmas, or who puts their son in the childrens’ choir at church? Of course they will be that parent, because for the most part, they’ll still love music and going to plays and watching dance exhibitions. They will still have an appreciation for the arts—they may even be the arts’ biggest fans (especially in terms of money if they chose a different career).

Again, some kids will have issues. There could be those who had to quit ballet as part of their treatment for anorexia. There could be those who had a “dance mom,” someone so obsessed with the training that there’s a sometimes permanent period of cooling off where the child never dances or even goes to a dance performance. But these cases are fairly rare.

So now let’s talk about math and math competitions and encouraging students to participate in math. That is treated differently than these other two situations, and I’m not entirely sure why. Moreover, I not convinced treating math differently is really doing the mathematical community a whole lot of good.

As I’ve mentioned before in my post about competitions “we” as test/competition writers want to make sure x% of students taking the exam (where x is nontrivial) earn “some” points. The real reason has to be financial because philosophically zero equals the amount of sense it makes. It’s the equivalent of ensuring each kid with an at-bat gets a hit, or that each kid in orchestra gets a day as first-chair. It’s unrealistic. There’s this unspoken fear, though, with math competitions and exams and classes that if students don’t perform well then they’ll get discouraged about learning math, and if they become discouraged that will turn very quickly into a hatred for math, and THEN you might as well write students off as future English majors.

Another BIG difference, though: the notion that it all has to be “fun.” We try even to make our syllabi interactive. Increasingly, every single part of a student’s math experience must be stimulating, exciting, attention-grabbing and interesting. Why? If you’ve ever been to a sports practice, you know it’s not fun. There are drills, warm-ups, and no one cares about the entertainment level. Do you think ballerinas or pianists enjoy even half of the **hours every day** they spend going through their five positions, their spot turns, scales, and trills? They don’t. But they do it because if collectively they aren’t good at the “boring” drilled bits, they are NEVER going to make much progress with the more advanced “fun” parts.

Why is math so different? Why don’t we treat, say, multiplication tables or laws of exponents or even derivative computations in the same warm-up way that the athletes and artists do? Those are our etudes. Why not, just like them, build (however “fun” it is) a common fluency in the basics before moving on to the new and riveting?

There’s also the “not quite pro” options of Little League coach or church pianist. Students inherently know what the middle ground is between complete noob and pro in most realms. But what real occupations do we advertise to students who maybe don’t want to “go pro” in math? I remember having a discussion with someone about my REU alums. They immediately asked how many went on to math graduate school. Because that’s how many in our community measure the success of such programs. I argued the alum I probably was proudest of was the one who became a high-school math teacher. She loved math, wanted to understand it to the point she could contribute something new to one of the oldest branches of human thought, but saw her limitations in research and her strengths in education. She decided she wanted to spend her life (as someone who is, I must say, exceptionally well trained) encouraging others from her area of the country to continue in math. But many in the math community would write her off as a “loss.” They care more or only about those who go on to get a math Ph.D. **We need to realize there are plenty of intermediate possibilities between “not a math person”/English-major and Ph.D. in math and we need to push those intermediates with students as much, if not more, than the Ph.D. We need to quit writing off as a loss anyone who doesn’t get a Ph.D.**

When you think about all this, it’s really no surprise that once a student declares they’re “just not a math person” that they don’t become a sidelines fan and instead transform into an “anti-math” person. Students who aren’t math people can’t still appreciate it because they are given zero outlets, opportunities, or exposure to such middle grounds. No offense to blogs and podcasts but there aren’t even any really good mass-media outlets about math, let alone outlets accessible to those under the age of 18. Sports has ESPN. The arts have PBS and A&E. Politics has C-SPAN. Biological science has Discovery and Animal Planet. Even the Scripps Spelling Bee gets prime air time once a year. But math? Not so much. We keep saying “math is everywhere” as a way of getting people on board our mothership, but where is it exactly?

Consequently, a lot of people think of math as this Mensa-esque intellectually elitist cult. If only we could videotape a bunch of people at a conference trying to split a check and calculate tip—that’d probably do wonders for our society. So again, **maybe we should allow people to say they’re just not a math person, and maybe we should find ways they can still support and appreciate math without feeling like they need a Ph.D. **

Just a thought. What do we have to lose?

Thank you, kthompson, for another insightful read.

The situation of the math educator is interesting. I would imagine her family and friends have a very different definition of her success than the “math community.” Had she gone on to earn a math PhD (assuming she was capable, intellectually), her employment prospects would have been…well, from what I’ve heard about the supply of PhDs versus the number of tenure-track positions…perhaps not as plentiful (and very unlikely within a preferred geographic region) as those of a K12 math educator. Seeing her salary, time off, retirement, purpose, and influence, I wonder if her community sees her as more successful than they would have seen her had she joined the “math community” in its entirety.

Perhaps the high (and sometimes, unrealistic) standards of the math community balance those of “normal people” communities, which might view immediate influence, secure income/other economic factors, and control over one’s location as holistic factors of success.

My best coaches in athletics have always had standards I couldn’t meet, because I had other coaches/mentors/people who, in turn, also had standards I couldn’t meet. Because of time and effort constraints, I could not be the athlete my coaches wanted me to be, the students my teachers wanted me to be, and the helpful person my closest others wanted me to be. Nevertheless, I’ve still seen myself as a success, as have the people who love me the most.

As part of the math community, I think you’re allowed to see someone who didn’t make it to the PhD level as a “loss,” but as a person, you can see them as a success. Many of those “losses” to the math community have greater financial and Darwinian success than those in it or than the people they would have become had they joined it. Because success can be defined in so many ways, I don’t think it’s wrong, within your role, to have high standards for mathematical success. You don’t need to make that teacher a “winner” when she’s already winning in so many other ways. I myself am a “loss” to the math community in that same way, but on the other hand, I get dozens of adult students, mostly women, to go from hating math/”I’m not a math person” to actually enjoying some parts of it/”I am kind of a math person” each year. So every year, I help to reduce the animosity to the math community and the likelihood that someday, all those angry I-hate-math people are going to burn stuff down.

What I would like to put forth, however, is that there need to be other ways for people to advance in mathematics beyond a traditional PhD. I speak from experience. I studied economics and computer science in college, the most employable combination of studies in today’s market. I took math-intensive economics classes, honors physics, and even a class dedicated to solving Putnam problems. However, I am eight, upper-division math courses short of pursuing any kind of graduate education, and to be considered for even a master’s in math, I would need to pay, out-of-pocket, for eight classes that cannot be taken at community college. Believe it or not, I actually tried to audit all these classes at three different universities in my city, and the logistics and the fact that I’m working and paying my own expenses killed that plan.

What I realized, after this experience, is that for someone to make it in math, they have to know, when they are within their first year of college, that they want to study math. Most of us enter college right out of high school. It took me four years of engineering to realize I liked math better than programming. But, by then, the money was spent, the other degrees earned, and economic considerations took hold.

These are interesting considerations, and I concur on most points, but there is one crucial aspect that may be a bit forgotten in the discussion. In our society, arts or sports are easy to access, explore, or enjoy freely in many interesting ways outside of a school context. Compared to these subjects, exposure to mathematics is most often perceived as something that is only done in a school setting.

Also too many still believe that school math is something that is not really relevant in real life. The typical example is that of people that easily give the wrong answer to a school math calculation, but never fail to give the right answer to the same calculation if one adds a dollar sign in front of it.

For sure, our community knows well that math is exciting and present all over in our culture, in deep and interesting ways. However, it is a bit harder to make it as entertaining as books, music, movies or baseball games are for the general public. This may be one of the big differences.

Thus, on one hand, it is likely that someone will stay a fan of a subject, even after failing to become a specialist of a subject that is generally considered as entertaining. On the other, this is much less likely for a school subject that most consider that it only has to be studied because it is required by the curriculum, albeit with the usual insistence on its importance in the abstract.

We should look for ways to profoundly change this ingrained cultural bias.