I think this phenomenon illustrates a very widespread misunderstanding of what math is and how ones becomes good at it. Consider the following two anecdotes:
1) Sammy walks into advanced Greek class on the first day of school, eager and ready to learn. He is crushed when, about 15 minutes after the class begins, he realizes he has no idea what the teacher is talking about. Despairing, he concludes that he is “terrible at Greek” and “just dumb”.
2) Sammy walks into advanced algebra on the first day of school, eager and ready to learn. He is crushed when, about 15 minutes after the class begins, he realizes that he has no idea what the teacher is talking about. Despairing, he concludes that he is “terrible at math” and “just dumb”.
Anecdote 1) just seems ridiculous. Of course if you walk into a language class that’s out of your depth, you’re going to be lost, everyone knows that. Every normal person can learn every natural language; there’s no such thing as someone who’s intrinsically “terrible at Greek”. The solution is just to swallow your pride and go back to an earlier class. But it seems like anecdote 2) is not only plausible but probably happens rather often. There is some irrational belief that skill at mathematics is some kind of unrefinable Gift: some people can do it and others just can’t. This idea seems absurd to me: there is no “math gene”; there are no other examples of skills that some people can get and others not.
It’s actually anecdote 1 that seems plausible to me and anecdote 2 that does not.
I happen to have been a language teacher, teaching adult hobbyists. It seemed to me that lots of my students had very unrealistic ideas about how easy it would be for them to learn a foreign language. They really did come to class expecting one thing and 15 minutes later finding out quite another thing. They typically brushed off their past bad experience with learning, say, Spanish back in school, on the theory that they’d never really been motivated to learn Spanish but they were really truly motivated to learn language X which I was teaching. Then they realized that learning language X involved a lot of the same boring grammar talk and memorization which they’d found so hard/boring when learning Spanish. (Of course it’s also possible that my classes just sucked.)
By contrast, no-one walks into advanced algebra classes having no idea what math is about. People who think they’re terrible at math usually infer this from having spent 10 years in a school system where they consistently had trouble with math assignments, performed poorly on math tests and had trouble understanding what math teachers were talking about. Most people who think they’re bad at math probably are actually bad at math. Sure, in some other universe they might have become good at math if some early stimulus had swung another way—maybe another teaching style would have helped, or a role model or whatever. But it also seems very reasonable to think that some people are born with more aptitude for math than others. General intelligence certainly has a large heritable component and I’m sure that holds for the special case of mathematical aptitude.
I spent many years operating under the assumption that everyone was about as smart and constructing elaborate explanations for why the reality I was confronted with seemed to be in so much conflict with that theory. Sure, if you add enough epicycles you can do it—but there’s a far simpler theory which has more explanatory power: Some people are “just dumb”. I personally find that a liberating theory to operate under. A lot of my “aha moments” seem to involve either the realization that “yes, people really are that stupid” or the realization that “yes, I really am that stupid”.
Unlike most other subjects, math is cumulative: students are taught one technique, they practice it for a while, and then they’re taught a second technique that builds on the previous. So there are two skills required:
The discipline to study and practice a technique until you understand it and can apply it easily.
The ability to close the inferential gap between one technique and the next.
The second is the source of trouble. I can (and have) sat in on a single day’s instruction of a language class and learned something about that language. But if a student misses just one jump in math class, the rest of the year will be incomprehensible. No wonder people become convinced they’re “terrible at math” after an experience like that!
Unlike most other subjects, math is cumulative: students are taught one technique, they practice it for a while, and then they’re taught a second technique that builds on the previous.
How is that unlike other subjects? Seems pretty universal.
I think this phenomenon illustrates a very widespread misunderstanding of what math is and how ones becomes good at it. Consider the following two anecdotes:
1) Sammy walks into advanced Greek class on the first day of school, eager and ready to learn. He is crushed when, about 15 minutes after the class begins, he realizes he has no idea what the teacher is talking about. Despairing, he concludes that he is “terrible at Greek” and “just dumb”.
2) Sammy walks into advanced algebra on the first day of school, eager and ready to learn. He is crushed when, about 15 minutes after the class begins, he realizes that he has no idea what the teacher is talking about. Despairing, he concludes that he is “terrible at math” and “just dumb”.
Anecdote 1) just seems ridiculous. Of course if you walk into a language class that’s out of your depth, you’re going to be lost, everyone knows that. Every normal person can learn every natural language; there’s no such thing as someone who’s intrinsically “terrible at Greek”. The solution is just to swallow your pride and go back to an earlier class. But it seems like anecdote 2) is not only plausible but probably happens rather often. There is some irrational belief that skill at mathematics is some kind of unrefinable Gift: some people can do it and others just can’t. This idea seems absurd to me: there is no “math gene”; there are no other examples of skills that some people can get and others not.
It’s actually anecdote 1 that seems plausible to me and anecdote 2 that does not.
I happen to have been a language teacher, teaching adult hobbyists. It seemed to me that lots of my students had very unrealistic ideas about how easy it would be for them to learn a foreign language. They really did come to class expecting one thing and 15 minutes later finding out quite another thing. They typically brushed off their past bad experience with learning, say, Spanish back in school, on the theory that they’d never really been motivated to learn Spanish but they were really truly motivated to learn language X which I was teaching. Then they realized that learning language X involved a lot of the same boring grammar talk and memorization which they’d found so hard/boring when learning Spanish. (Of course it’s also possible that my classes just sucked.)
By contrast, no-one walks into advanced algebra classes having no idea what math is about. People who think they’re terrible at math usually infer this from having spent 10 years in a school system where they consistently had trouble with math assignments, performed poorly on math tests and had trouble understanding what math teachers were talking about. Most people who think they’re bad at math probably are actually bad at math. Sure, in some other universe they might have become good at math if some early stimulus had swung another way—maybe another teaching style would have helped, or a role model or whatever. But it also seems very reasonable to think that some people are born with more aptitude for math than others. General intelligence certainly has a large heritable component and I’m sure that holds for the special case of mathematical aptitude.
I spent many years operating under the assumption that everyone was about as smart and constructing elaborate explanations for why the reality I was confronted with seemed to be in so much conflict with that theory. Sure, if you add enough epicycles you can do it—but there’s a far simpler theory which has more explanatory power: Some people are “just dumb”. I personally find that a liberating theory to operate under. A lot of my “aha moments” seem to involve either the realization that “yes, people really are that stupid” or the realization that “yes, I really am that stupid”.
Unlike most other subjects, math is cumulative: students are taught one technique, they practice it for a while, and then they’re taught a second technique that builds on the previous. So there are two skills required:
The discipline to study and practice a technique until you understand it and can apply it easily. The ability to close the inferential gap between one technique and the next.
The second is the source of trouble. I can (and have) sat in on a single day’s instruction of a language class and learned something about that language. But if a student misses just one jump in math class, the rest of the year will be incomprehensible. No wonder people become convinced they’re “terrible at math” after an experience like that!
How is that unlike other subjects? Seems pretty universal.