This is the thread that inspired this thread, but I’m not trying to single anyone out. It’s just worthwhile background reading.
It’s been my experience that there’s no social stigma attached to being bad at math. This comes largely from being a math major at a large university (the University of Virginia, just in case that’s relevant), and also from just paying attention as the days go by.
Now I’m not saying that it’s perceived as OK to be bad at other subjects, say English, but if someone’s bad at English, people will suspect how hard they’re working, or how much they want to succeed. Not so with math–if you’re bad at it, it must just be because you’re not cut out for it.
I think a lot of this has to do with bad teaching at the primary and secondary levels. Additionally, someone here (sorry, can’t remember the name) mentioned a culture of failure–basically, parents tell their kids that they were bad at math, and the kids get the message that it’s OK to be bad at math.
Those are both interesting theories, but I wonder if that’s all it is. And so I put it forth to the inhabitants of GD: why is it OK to be bad at math?
The way math is taught tends to bore people. “1 times one equals one, one times two equals two”. The more enterprising students greatly expand on what they learned, and make up and solve more complex math problems, rediscover some algebraic associations, Euclidian theorums and number theory on their own (I did, before an unfortunate accident), without consulting books. Those are the ones that become mathmeticians.
A calculator doesn’t help you figure out the sequence of keys you need to press to get the right answer. I’m not talking about arithmetic ability, the type that a calculator can help you with. Rather, I’m talking about the sort of ability that allows you to solve complex problems.
Perhaps it’s because a LOT of people find math hard, so they sort of band together into a mutually reinforcing “math sucks” viewpoint? In other words, it’s socially acceptable because it’s common (a variant on the “culture of failure” idea that you mentioned in the OP).
It really depends on what you mean by “bad at math”. It is not “okay” for someone to be unable to make change for a ten. But beyond that many people’s contact with using math is limited. They see math skills beyond fifth grade level as something used in school only or by very particular professions, not as a skill that they use, or a way of thinking that is familiar to them. Day in, day out, I do not use calculus, or trig, or even algebra.
I’ve heard the comparison made that the math that most of us learn, up to perhaps calculus, is like learning grammar and spelling but never reading any real literature or poetry, or learning the scales but never playing any real music. With reading we all have at least read some literature so we know that it is a learnable skill for the masses. With math, the really good stuff is beyond the reach of most of us (myself included, I just know that it is there) BTW, I am bad at music and that is “okay” too. Artistic talent is also considered the same way. As is an affinity for learning foreign languages.
Well, it depends on how bad. Not being able to rapidly calculate a waittress’s tip is a little different than not being able to add one digit numbers together. I’m betting there’s a huge stigma attached to the latter.
Depending on the situation, I’m willing to cut people slack. If I’m teaching college-level students majoring in science, I expect them to be able to do more than basic mathematics. If I have 50 ml of water and I want to make a salt solution of 15 parts per thousand, I would expect anyone seeking a BS to know exactly how much salt to add. And if they don’t, there will be a stigma attached to them. Not a societal one, but a classroom one.
But if I’m dealing with an everyday person, I don’t see why I have to give them a hard time just because they don’t know what episilon delta means. Math is important, but it’s not essential for the commonman who knows how to operate a calculator.
English is used for communication while math–in an everyday sense–is not. I would argue that’s why there’s a greater stigma attached to English illiteracy over math illiteracy.
I think a major problem is that many math texts and math teachers approach the subject as if everyone has that special innate math ability. Just as some people can easily learn other languages or have an innate ability for musical talent, some people have a natural understanding of the language of math while others do not.
This may not be the case today, but when I was in school math texts were basically a bunch of equations with little if any explanation. I don’t think they even used complete sentences.
Some of my math teachers approached teaching the same way. This works fine for people that “get” math intuitively, but is useless for those who don’t. I wouldn’t expect to go to Music 101 and be expected to pick up a random instrument and start jamming. But I think that some math teachers approach math that way.
I find it interesting that I can read papers about quantum physics and often can make sense of them because many physicists include much more explanatory text than math. Of course, with math you have to have the formulas as that is the point, but some explanation leading up to the actual math would make a world of difference.
I’m not particularly “in tune” with math, but when I read something like the wonderful book The Language of Mathematics, I can understand and appreciate all sorts of advanced math concepts.
So I guess my answer to the OP is “why is it OK to teach math as if it comes naturally to everyone?”
I honestly think that the only thing that kept me from dropping Heinlein like a hot potato the first time I read that quote was that I only came across it after having already delved fairly deeply into his writing. Even then, it lit my fuse for days.
I’m innumerate. That doesn’t mean I’m lazy, or stupid, or not willing to try to learn. It means that I did try, for years, to understand mathematics other than arithmetic and very basic geometry and algebra. I don’t get it!
It was suggested that a better term than innumeracy for people like me would be dysnumeria, since it’s more akin to dyslexia than general illiteracy. It’s not really how it was taught, it’s how I perceive numbers. All of that elegant, dignified, “dance of numbers” crap is lost on me. All I see is a bunch of digits with a lot of symbols that I don’t understand and probably wouldn’t know what to do with.
I also believe that the lack of a social stigmata comes from the continued misconception about how one will never need to use math in their lives. As long as a significant amount of people hold that belief, they will write math off as something that only a few people need to be good at, and if you can’t do it, hey, it’s worthless anyway.
This reminds me of my daughter’s fifth grade teacher’s comments. When I expressed worry over my daughter’s complete lack of math understanding this lady told me that very few students are actually good with math! She told me my daughter would eventually catch on.
The next year I expressed the same concern with the sixth grade teacher. She said my daughter was lazy with math. She said most kids don’t want to do the extra work involved with learning math.
I kept pushing for testing until she was diagnosed with dyscalculia, or dyslexia primarily with numbers. Since there was no assistance for this problem here, I decided to homeschool.
Instead of trying in vain to catch her up, we went back to the beginning, shapes, tracing numbers…kindergarten stuff. Slowly we worked through whole numbers, fractions, measurements. I think she’s finally in the groove. It seems to me she must have missed something valuable at some point and spent the next few years trying to catch up. She could sound off multiplication tables, but she just never understood concepts.
When I look at textbooks I see half pages of explanations and thirty problems, two of which might be story problems. Real life applications just don’t exist in these textbooks. Ask a kid what it means when you say “three times five”. Many times I bet they have absolutely no idea.
I know you are talking about more advanced maths, but I believe this dislike and misunderstanding starts in the early years. If a child doesn’t understand “three times five” how can he or she get to the point of enjoying real applications or understanding advanced maths?
I think a major difference between how people perceive a person’s being poor at math vs. English is that one is exposed to English from their first day of life (if they’re at native speaker) so others assume that they should have a fairly decent grasp of it. Math on the other hand doesn’t (usually) go beyond counting to ten or thirty until one starts first grade. Language is far more intuitive and something most people just “pick up” from constant immersion without the hours of instruction that math requires.
I’m poor at math. I could write you a sestina that would make sense if you gave me a half hour, but I’d require the same amount of time, at least, to add up a string of four or five digit numbers without a calculator; my brain just doesn’t seem capable of performing math functions easily. While I did have a teacher for pre-algebra and algebra that was written off as a terrible instructor by the rest of the faculty, I don’t think it made that much of a difference; even the best teacher wouldn’t have helped me much, I think. I don’t understand numbers on a very basic level: for example, I know that any number times zero is zero, but it seems entirely irrational to me, because I can’t understand why the original number disappears. While people who love math more than English laud math as being concrete(and, oddly enough, English being abstract,) I can’t help but find it abstract to the extreme. The only time math makes perfect sense to me is it’s in the form of a word problem, because there’s a reason for doing the calculation. That’s the only reason I was able to get a B+ in college-prep chemistry, and A in physics in high school…while earning Ds in my math classes at the same time.
Math in school proved to be a humbling experience, because it was the one thing that, no matter that I worked harder and longer at it, I couldn’t master. By the time I had to take my one math gen ed I no longer put extreme effort into it, because I knew that I was going to barely pass it no matter what I did.
It isn’t ok to be bad at math, but I feel a lot more sympathy for those who are because I find it so difficult myself. However, I think it’s human nature for people to feel disdain for those who can’t adequately master things that come easy to themselves. People who find outrage in others lack of math skills are more likely to be those who find it easy than those who are only marginally skilled at it, and the same goes for any subject.
I liken mathematical ability to a skill aquired in any other circumstance. I can manipulate numbers because it is useful in my everyday life. I wouldn’t expect a welder to have to know higher level math anymore than I would expect myself to understand the many aspects of welding. People choose to learn skills based on whether or not they are enjoyable and their usefullness.
Suppose there’s a whole bunch of little boxes sitting in a warehouse. Each one of these boxes contains 10 M&M’s.
Pick up 5 boxes. How many M&M’s do you have? Well, since each box contains 10 M&M’s, you now have 50 M&M’s. Right? That’s 10 times 5.
Now, put down those 5 boxes. You now have zero boxes. How many M&M’s do you have? You have 0 M&M’s, right? Ah! But the boxes still have 10 M&M’s in them each, even though you don’t have any boxes! That’s 10 times 0.