The betrayal of math education
There are so many things I want to write about. I want to write about how I fell in love with mathematics. I want to write about some special gems of recreational math. (Yes, that’s a thing.) I want to write about the profundity of certain paradoxes. I want to write about whether God created the universe with logic, or if logic is a part of God’s very nature, or if God is the embodiment of logic itself. But I’m not going to write about any of those things this week. Because I read something on Friday. Something that made me incredibly angry. Really, really incredibly angry. Now, most people who know me know that I’m very passionate about many things, including various political issues. But there is a big difference between passion and anger, and many of my close friends will probably agree with me when I say that even though I’m passionate about different things, I seldom become angry at something.
It’s probably a good thing, therefore, that I gave up profanity for Lent. Otherwise this post would probably have some strong expletives.
What I read was a New York Times article published on Friday. The URL for the article is here:
The article features a video, posted below. The video was recorded secretly by an assistant teacher who remained anonymous. TRIGGER WARNING: this video includes the psychological abuse of a six-year-old child.
The article describes several other similar incidents at this school. In this case, this teacher—the abusive one in the video, not the one filming—had been lauded as an exemplar. She was the model that the school wanted all of their teachers to aspire to. What happened after? She was suspended for a week and a half, and then the school again held her up as the same aspirational model. Other teachers from the school, many of whom resigned, talk about incidents of ripping students’ work in front of them, destroying a child’s toy he was playing with during class, humiliating their students in front of their classmates, and honestly, the list goes on. I wish I could say that the Times just had an agenda against this school, but I have at least one friend who interviewed to work at Success Academy and told me that this seems pretty representative of their classroom environment. In one case, a principal at one of their schools had a list of students, dubbed the “Got to Go” list, of students whom the school wanted to leave because they were performing unsatisfactorily in class, and they didn’t want these students to bring down the school’s standardized test scores. This is a network of NYC charter schools. Those are public schools owned and managed by private corporations. You aren’t supposed to weed children out of a school sponsored by taxpayers. That’s not how the system is supposed to work.
I have no interest in beating a dead horse. The article does a fine job of criticizing Success Academy’s charter school network. Instead, I want to flag something that I see as a deeply rooted problem in the American educational system. Now, even though I’m an educator myself (I teach a 52-student class in college algebra to Penn State undergrads), I’m not an expert on educational theory. I can list a few problems with the educational system across the country, and I have ideas on how to solve each of them individually, but I don’t pretend to have a solution to everything that can be applied everywhere. Education is a monstrously complex issue, and the flaws in the American educational system have deep historical roots, especially in urban areas and low-income neighborhoods. But I want to raise awareness to one problem in particular, a significant problem that many adults carry with them throughout their lives. The problem is this:
It is cool to be bad at math.
Let me explain. Nine times out of ten, when I first meet someone and I tell them I’m a mathematics graduate student, their first response is a variant on one of the following:
“I could never do that.”
“I suck at math.”
“Why would you do that to yourself?”
“So are you, like, really smart or something?”
This gets older and older and older the more times I hear it. Meanwhile I almost never hear,
“Oh, you must really like math then.”
The emphasis is always the same: Math is hard. Math is not enjoyable. If you’re good at math, then you’re a genius. As I was writing this post, I did a Google search and begun typing "I'm bad at..." and lo and behold, the first thing Google filled in was, "I'm bad at math." As an undergrad, if I were an English major, or a history major, or a linguistics major, someone might annoyingly ask me what I would do with my degree. But no one would respond by saying,
“You’re an English major? I suck at reading.”
“You’re a history major? You actually enjoy studying other cultures?”
And if someone did respond in one of those ways, no one would take them seriously. This is what I mean when I say it’s “cool” to be bad at math. Within some social circles, friends will joke with each other and say “Yeah middle school math sucked, I was so bad at it” like they’re wearing a badge of honor. Or they'll wear it on a t-shirt, as in the image. As adults, even though this pride may disappear, very often the anxiety over simple mathematics remains. The perception that mathematics is an onerous and painful task is pervasive throughout much of our culture. Does that same perception exist about reading classical literature, fascination with history, multilingualism, and musical performance? If it does, I’ve never heard it.
Some friends of mine who were humanities majors as undergrads may howl at me (and in fact some have in the past) and say, “But Dom, everyone’s talking about STEM education right now in politics! Arts and humanities are being defunded in public schools. How can you say that people think it’s cool to be bad at math?”
Yes, arts and humanities and social sciences are being defunded in schools. Yes, that’s a problem. And I submit to you that this is causing the very same problem I have just described.
You read that correctly. I am a mathematician who is extremely critical of the political emphasis on STEM education in our country right now. Because our STEM education is floundering. No one denies that. But as a human society, we want solutions with immediately recognizable effects. As a consequence, politicians are quick to find “solutions” that we can measure. So they propose raising standards in school, and measuring it with standardized tests. Intuitively, this solution makes sense: if you raise your expectations for children’s learning, and set a high bar for them, they’ll learn more. And you can measure these results with standardized tests. If a school doesn’t meet those standards according to those tests, then threaten to shut them down; clearly their system isn’t working, so we’ll find a new school to replace that system. What could go wrong?
Here’s what goes wrong. A principal at one of these schools now puts pressure on their teachers to make their students do well on standardized tests; if not, their school may get shut down. So if you’re a teacher, and the principal is putting this pressure on you to make your students perform well, you now begin teaching your students to pass the test. Whether or not they learn the material is of secondary importance, and although those two things are correlated—skill in a subject area and skill in passing an exam in that subject area—they are not synonymous. The reason they are not synonymous is because you have to teach your students to answer questions correctly, but do nothing to develop their skills at synthesizing new material of their own. They know how to answer questions, but not how to ask the kinds of questions to help develop the material. And in mathematics, you learn primarily in two ways: by asking the right questions and connecting the dots from one idea to the next, and by doing practice problems.
If they get a problem wrong, they are penalized. This is natural. Mathematics is a subject where many students learn by making mistakes. Even I make mistakes in my work; I failed an exam last semester because I forgot one theorem, but now I will never forget that theorem again, and I know how to implement it.
So if your student makes a mistake, you have a choice. You can tell them the answer, or you can help them see where they went wrong and how to get it right. Probably you’ll do some combination of the two, and you usually only do the second significantly more if you feel passionately about the subject and about seeing your students grow and develop. But if you’re a teacher at one of these underperforming schools, it doesn’t matter if they understand the material; you only care if they know the answer to the question, so they do well on the test. More likely than not, you don’t really care about the material you’re teaching; you just want to drill it into their heads. Plus there’s lots of material to go through, and you’re beginning to fall behind on your lesson plans. So you give them the answer, without explaining how you got it, because you need to get through all of the material in the course. The child hasn’t learned the material though; it wasn’t explained in a way the child understood, and they’re not mature enough to go out and fill in the gaps outside of class. So days or weeks later, you ask them a similar question, and they get it wrong. Now the test is coming up, so you get frustrated with this child. You wonder why they haven’t learned the material. You express that this child has disappointed you. Meanwhile the child is horrified and ashamed that they’ve disappointed you, their authority figure. They’re scared of disappointing you again. So they shut themselves down. They are reluctant to speak up in class to answer questions, in case you get frustrated with them again. And this happens to this same child again, and again, and again, with different teachers, all in mathematics, because mathematics is one of the only school subjects where you can tell if your work is right or wrong. This might happen in some other subjects for this student as well, but it very often happens in lower-level math classes.
Congratulations. You’ve just taught this child that they’re bad at math. They will carry that with them through their entire lives. They will remember this more than anything else, and they will implement this lesson in all of their future math classes. They will implement the lesson that they are bad at math.
Now usually it’s not as extreme as it appears in the Success Academy article, but this betrayal of young students can happen in more subtle ways. Remember how I said that often you learn mathematics by making mistakes? Students need to feel that they can make mistakes with their teacher. They have to be able to trust their instructors with their mistakes. If they can’t do that, they will be paralyzed with fear of making math errors, and this paralysis will interfere with their learning for possibly the rest of their academic career. And so a student’s belief that they are bad at math is a vicious self-fulfilling prophecy that started with one teacher’s betrayal, one teacher who visibly didn’t care about their intellectual development.
Of course I know that it’s almost never 100% the instructor’s fault that this happens. But uncaring instructors often play a pretty big role, even if that role involves not caring about students who, as children, have a hard time sitting still and focusing in class.
This affects me personally, and not just because of those questions people ask me when they learn I’m a mathematician. I’m a math teacher for adults. Because I teach adults, I get to have higher expectations that they’ll spend time outside of class reviewing material that they don’t immediately understand. I get to hold them accountable for doing work outside of class to supplement their learning. I get to tell them, very honestly, that I want them to succeed in the course, that I’m committed to helping them do that, that I am more than happy to meet with them outside of class and outside of my regular office hours to discuss tricky topics, but I can’t do the work for them, and I need them to meet me halfway. But many of my students really do need a lot of help, and many of them were apprehensive at first about making an appointment with me to go over material because they didn’t want to sound like an idiot. Several of my students at the beginning of the semester told me, either to my face or via email, that they’re awful at math. I told every one of them the same thing:
No, you’re not awful at math. No one is good or bad at math. Everyone comes from different backgrounds, either in terms of the material they've seen or the way they've been taught it. Some students learn things better when it's explained in different ways. Some students need to think about something for a little while before it makes perfect sense. Mathematics doesn't come naturally to anyone. It's purely a function of how much time you spend thinking about it, how much time you spend practicing it, how willing you are to seek help and admit you don't understand something, and how comfortable you are with making mistakes.
What I don’t tell them is if you don't have good teachers, those last two factors are basically dead. I’m a teacher, not a psychologist. Damn it, Jim.
I think it’s pretty telling, by the way, that several of those same students who told me they were bad at math just got a perfect score of 20/20 on their last quiz. And it’s not because I’m an awesome teacher; I can’t evaluate that. It’s because they know that they can come to me for help. They know they don’t have to worry about making mistakes with me, because I want to help them learn through those mistakes. In some cases, this might be the first time they know they can seek help from their teacher.
The sad thing is, when people ask me if I’m a genius because I’m a mathematician, the truth is, no. I’m not. In fact of my fellow math grads at Penn State, I’m one of the least experienced. I’m asking my classmates for help constantly. The only reason I’ve gotten this far is because I was lucky enough to have teachers who inspired me at a young age, who were actively interested in seeing that I understood the material. I say this is sad because when people respond in one of those ways to me being a mathematician, deep down I wonder if they just had some bad experience at a young age. Through no fault of their own, mathematics was ruined for them.
Do I have a solution? Not one that I know how to implement across the board. But I think we need to start with having teachers for young students whose primary interest is seeing their students grow and develop, not so they can take a test, but so that they can become stronger thinkers. We don’t need mathematicians and specialists teaching elementary school arithmetic. We need teachers who are there because they love to teach and want to see their students’ faces light up when they understand a new concept. Ideally this should be a baseline requirement for being a teacher, but I think there’s a big lack of interest because teaching isn’t usually seen as an especially glamorous job. That paradigm needs to change, because the result is more teachers who either don’t care about their students, or are pressured to care more about their test performance than their intellectual development.
So if you think you’re bad at math, ask yourself: when did I start disliking math? Was it first grade? Third grade? Who was my teacher? And what could they have done differently?
EDIT: Several students of mine did come seek my help in advance of that quiz, but there's another reason many of them did so well (a lecturer at Penn State pointed this out to me). This quiz was on material that involved a very direct, executable procedure (graphing linear functions and solving systems of linear equations). Previous quizzes had been on problems that were more conceptual, and less procedural ones. It seems that many students in general are quick to execute a direct procedure without understanding the concept behind why they execute this procedure; this can be good, but this can also cause issues if the concept behind a problem doesn't match well with the logic behind a standard procedure to solve it.
The disconnect between mathematical concept and mathematical procedure... maybe an idea for a future post. I'm gonna tuck that one away.