You will not be surprised to learn that in the course of my work as a tutor, I have encountered a great many people who are not particularly skilled in mathematics*. Most of them are blasé about this: they will make some comment about how their little brains can’t handle it, (or even in one memorable instance**) how “girls and mathematics don’t mix***”), and then laugh dismissively and beg me to help them pass calculus and get into law school or whatever.

Now, first of all, let me say that some of them, in my opinion, have an actual disability when it comes to mathematics; just as dyslexia can make it inordinately difficult for some people to learn to read, I have absolutely no doubt that dyscalculia also exists. That said, in my estimation, the overwhelming majority of students with mathematical difficulties that I have encountered *do not have this condition. *So why then is innumeracy so shockingly wide-spread?

My answer is that the difficulty of mathematics is a social construct. Now, mathematics itself is the definitive example of a subject which is not a social construct and I do not dispute this, but the cultural attitudes which* surround* mathematics most certainly are. I can say from my own personal experience as a child North American society tells people from all sides that math is both difficult and boring, beginning at a very young age. It’s one thing for education students to tell me in a completely unapologetic manner that they are bad at math and expect me to just accept that; it’s quite another when these same people become Grade One teachers and convey the same message, whether consciously or unconsciously, to their students. And this is not even mentioning the messages coming from the media (a broad overview of which can be found here).

I should note that while innumeracy is a problem facing everyone, it is also a gendered problem: women and girls are particularly at risk, but the apparent gender gap in math scores has already been largely explained-away by socio-cultural factors. Indeed, studies have shown that girls who are told that they are naturally worse at math than boys will perform worse than those who are not told that. I would argue that such factors can probably be extended to include not just girls, but anyone: if you tell people that math is hard, what you are in essence telling them is that *people inherently are not good at math*: psychologists refer to such self-fulfilling prophecies about one’s own innate capabilities as a Human being as “entity theories.”

The question now becomes:* if the difficulty of mathematics is actually a social construct, then why does it exist?* I’m not precisely sure.* *One possible explanation is that most people’s brains, by their very nature, aren’t as well suited to learning mathematics as they are to learning, say, language: since mathematics is actually* is* harder for most people than other subjects that one learns in school, the message gets transmitted that it is *hard* and then gets reinforced through the psychological mechanisms mentioned above. There may be a grain of truth to this, but I’m fairly comfortable dismissing this hypothesis: in my experience, most people have absolutely no difficulty learning to think in ways for which the evolutionary history of the Human Race by no means prepared them; why, I myself just spent the last two days learning to conceptualize movement in a non-bijective Cartesian three-space****.

On the other hand, I have long noted that, given the extent to which our civilization depends on mathematics for everything from finance to ensuring that buildings remain standing, those of us who are literate in the ways of mathematics inherently belong to something of a privileged class. Perhaps the true reason that mathematics is considered “difficult” is simply because people who enjoy influence or prestige for their knowledge of mathematics have been asserting that it is for generations. Or even that others make use of the “Just World” hypothesis, and assume that it must be difficult or it wouldn’t pay so well.

Whatever the case though, given the fact that the subject basically undergirds all aspects of modern life, I think that everyone who *can* do so has a duty to themselves to shelve their assumptions and become literate in mathematics.

________________________________________

*As well as quite a few twitchy-eyed pre-medicine students who are perfectly good at mathematics and frankly have no business engaging my services in the first place, but who pay well.

**Back when I was still presenting as male.

****Blegh. *Internalized misogyny for the lose.

****This being an impressive way of admitting that I spent the weekend playing *Portal 2. *I’M A POTATO.

That last footnote–OH JAIME

It works on basically every level; easily the best footnote I’ve done, if I do say so myself.

“what pronouns are potato”

*literally what I thought*

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I’m inclined to believe (based also on tutoring) that some cases of apparent dyscalculia are due to math being a domain of answers that are not negotiable. If a truth is non-negotiable, anyone–anyone, at some time in their life, “doesn’t want to know.”

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Maths is one of those subjects where the teacher has more impact on students than most. I remember not understanding what on earth was going on for most of my school career except for one year when I had a fantastic teacher.

Later, back to the usual type of incomprehensible prof, I got my maths O’Level by the skin of my teeth and thanked the lord I’d never have to grapple with the fog again. Comparing that exam with what they do now, I was actually not bad at maths!

What does “non-bijective Cartesian three space” mean? I know that for a bijective function, f: X -> Y is one-to-one, so each unique element of X maps to a unique element of Y. For a space to be non-bijective, then, it follows that f: X -> Y is not one-to-one, so there exist some unique elements of X mapping to a single element of Y. I can visualize bijective and non-bijective functions. But what does it mean to have a bijective or non-bijective space?

I was meaning to describe a situation in which a single point in space can be described by two different sets of Cartesian coordinates on the same system. I was referring to the game Portal, where points at different parts of a room can be mapped on to one another.

I’m not sure whether the term “non-bijective Cartesian three-space” is actually the best one to use to describe the resulting geometry, but it seems accurate to me.

I’d say it works pretty well. I was just having trouble parsing, I suppose. If it makes you feel any better about spending your weekend playing Portal, I spent my weekend playing Minecraft when I probably should have been building an op-amp.

I think the “my knowledge is a number” mindset can affect confidence in unintuitive subjects. I know when I’ve had difficulty with something (nearly always in association with a poor grade), I tend to get it into my head that I just can’t do it. I see a lot of other students just give up on classes for similar reasons. But where I’ve taught myself to push through it, a lot of people just give up, because they’re still stuck in that sinkhole where a single grade says absolutely everything about their knowledge and potential for knowledge on a particular subject. When I discuss a difficult homework question with a classmate who tells me that “I’m lucky I’m so smart,” it gets frustrating. This question that’s giving them trouble very likely also gave me trouble, too. I very well may have spent hours getting absolutely nowhere before finally figuring it out. Sure, some things are intuitive. But most of what I do is just work. It’s hard and it can get tedious and it sucks sometimes, but it’s worth it because in the end I know more than I did before.

It makes me wonder if it’s not necessarily that math is “harder” to learn than other subjects, but if learning math or other subjects brings about the same kind of enthusiasm in everybody. People who aren’t as excited about math or the same kind of physics as I am might find it more difficult to learn simply because to them, these aren’t satisfying subjects. That doesn’t mean that the subject can’t be learned. But if I find circuits boring or less satisfying than gravitational lensing, I’d be more inclined to have trouble with circuits just because I wouldn’t feel like learning about them when I’d rather spend that time reading about gravitational lensing. I can still push myself to learn circuits, but that’s hard work, and it’s so much easier to give up and say I “just don’t get” circuits than to keep pushing myself to learn more.

That’s a good point, about interest. And, of course, there it’s even easier to see how broader cultural ideas about math — it’s hard, it’s boring, it’s for nerds, it’s for boys — would set up a self-fulfilling prophecy.

And maybe you’re right, maybe a lot of, or even

all, the reason math seemed intuitive to me is because I found it fun. Beautiful, even.Circuits I’m kind of blah on — I don’t dislike them, and when my dad* puts a diagram in front of me and says, “Hey, want to try reading this?”, I can get into it, but I don’t love them enough to pursue the subject on my own. The one STEMmy subject that just shuts my brain down with its dullness (to me) is computer programming. I don’t know why, but I just cannot see any appeal whatsoever in the field, despite having lots of friends and family members who like it. And to the naive observer (which I am), there’s no obvious difference in difficulty between learning to analyze circuits and learning to program; the only difference is in me, in how much I’m willing to invest in either pursuit.

*Electrical engineer, builds guitar amplifiers as a hobby

I wish there was a “LOVE” button in addition to the “Like” one — I like a lot of your posts, but this is probably one of my favorites. (I totally agree that “math is hard” is a social construction. I do know that for some people it’s more intuitive than for others — it seemed to come naturally* to me and to my brother, while my sister found it harder, though she’s also good at it.)

*Not as in, “I was born knowing how to do algebra and can accurately measure angles and calculate trig ratios on sight” — that would actually be a pretty awesome minor superpower — but as in, “when teachers write out how to solve a problem on the board, every step makes total sense and I can now solve similar problems,” no matter how well or poorly the teachers explain the process. I had to be taught, obviously, but my mind fit around it easily and readily, like a well-worn catcher’s mitt around a baseball.

I *do* think ways of thinking come into it — the thing that made my mind so baseball-glove-like when other, equally smart or smarter people’s minds were not like baseball gloves, and had to stretch more and take longer to adapt themselves to the concepts. But maybe part of it is the mismatch between the way of thinking that is most conducive to

doingmath and the way of thinking that is best suited to learning from classroom lectures. I don’t know that either is necessarily harder or more active — indeed, I remember listening to professors being a very active thing, sometimes too involved even for me to take notes — so much as they’re justdifferent. When I try and think about what each state of mind is like, what it does with the bits of information it has, the listening-in-class state is like taking them in the order they are received and stacking them, while the doing-math state is like fitting jigsaw-puzzle pieces together.So I guess I think there are lots of ways a person can have real, not-entirely-psychogenic difficulties with math; the person’s mind can just

not go that way, or not go that way very fluently (this is me with music — my dad hears all sorts of things I can’t hear in a piece of music), the person can have trouble juggling the different ways of thinking required to learn something, understand it and then apply it, and theteachercan have problems juggling the different ways of thinking required to know something and to explain it. If you are an intuitive Math Person, a lot of times writing out the steps you took to solve the problem is explanation enough. If you’re not, you want to know what happened to get from each line to the line following it, and if you are an intuitive Math Person trying to explain it to them, you might not know what else to say. I’d be interested to know if there’s a difference in how well people learn math from, say, an interactive computer game as opposed to a classroom environment. It’s more hands-on, and less verbal, so the awkward convert-words-into-math stage could be sidestepped, but at the same time there’s no professor to ask about what happens between line 4 and line 5.Oh look, I wrote a book.

” But maybe part of it is the mismatch between the way of thinking that is most conducive to doing math and the way of thinking that is best suited to learning from classroom lectures. ”

That’s actually a very good point, now that I think about it. Personally, when I’m taking Math (or math-intensive) courses, my strategy is usually just to write down whatever appears on the board without thinking too deeply about it, and then take it home to read and understand on my own terms. This is very different from how I approach virtually every other subject.

And:

Aww. That person should’ve been in my AP Calculus class in high school. Not only was the teacher a woman, but more than half the class was girls, including someone who was probably one of the two top scorers. None of them were shy about raising their hands, whether to volunteer an answer or to ask a question, and most of them were very conventionally feminine. (Probably all but two, or maybe even all but me, were members of the dance team.) No one could’ve been in that class all semester and retained the notion that something inherent to femaleness, or even

femininity, is incompatible with advanced math.Pingback: The World Needs More Humanists | voxcorvegis

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