Having spent my share of time trying to teach mathematics, I’m very familiar with innumeracy. What I’m not sure about is so-called “math anxiety”. Is there really such a condition specific to mathematics? Are there people who become gibbering, neurotic heaps when asked to solve a quadratic equation? I’m inclined to believe that there are people who (understandably, given the way it’s often taught) just don’t like math, but that there are also people who just don’t like history, and our society justifies the one by giving it a name. Then again, I never did care that much for psychology class.
Edit: “care that much for psychology class, so I could be wrong.”
As you go through college you are asked 800 times a day “What’s your major” it was always interesting to see someones reaction when I say “math.” Anyways, yes there are people who just don’t like math, and who just don’t like history etc… But I think there are a lot of people that are beyone, just don’t like math, more like, just can’t do math. If you’re a math person, you know that once you get past basic algebra, it get’s hard fast. If someone doesn’t like math, they’re going to have a hell of a time grasping trig, and calc is pretty much out of the question. With things like history and english, it CAN be done just by memorizing everything, but that just isn’t the case with math. If you don’t understand things as you go along, you’ll only make it so far. I guess I’m rambling here, but what I’m trying to get across here, is that I think there are people that just don’t get math, above and beyond not liking it. It just doesn’t work for them.
Well, there is that cumulative aspect to mathematics. I tend to hear something described anecdotally as almost pathological, almost like a panic attack.
I guess I could streamline like this: a) Do people really develop full-blown phobias of math, panicking when confronted with it and everything, in more than isolated cases (“off a set of measure zero”)? b) Do people not develop similar phobias for other subjects?
Yep.
I think it’s related to some classic nightmares. The one where no one can hear/understand you [talking to no effect] or you can’t catch up with a goal [running to no effect] and the one where you are publicly humiliated [caught with no pants].
In math, you can (and frequently do) get caught in an indisputable mistake; not a difference of opinion, not looking at something from a different point of view, but a flat just plain wrong. To move forward from this you must first admit your error; disguising or hiding it with more words or actions or distractions doesn’t work as well as with gaffs in other fields. If you can’t accept such situations with humor or perspective, then you feel humiliated.
Fear of more humiliation, of course, lowers your I.Q. twenty or thirty points and self-fullfills its prophecy. This leads to a nasty cycle terminating in panic and idiocy. Only by steadfastly avoiding the whole area (“I’m just not a math person”) can some people maintain their dignity and feelings of self-worth. Then, when they can’t avoid it, panic is even more magnified.
In our society it is getting harder and harder to avoid math related subjects, which only makes it more important and thus scarier yet.
Not so much.
Blowing it in other areas, while not fun, is not as unforgivingly humiliating as it is in math. For one thing, people forgive ‘awkward’ or ‘forgetful’ or ‘ignorant’ more than they do ‘stupid’ and errors in math come across more ‘stupid’ than missing a shot or forgetting a name or other errors found in other subjects. For another, errors in other areas are easier to hide or disguise. One can generally B.S. his way out of problems in fuzzier subjects.
Case in point - I am so mentally deficient (in memory) that geography, physiology, history, liturature, spelling, organic chemistry and other areas requiring memory are forever beyond me. And yet many in our school consider me brilliant because I can figure out problems using a few mathematical principles. This is nice for me, but things are tougher for those whose mental abilities are the complement of mine. I get regarded as ‘a bit eccentric’ or ‘absent minded’; others are marked as 'stupid."
I know an intelligent woman who graduated 2nd in her high school class, who, at the time of her H.S. graduation could not make change for a dollar. When she was very young (5 or so) and didn’t know how to make change, her mother demanded to know why not - was she stupid or something? Asking the question made it so.
The existance of repressed memories (related to trauma) are the subject of much current speculation, debate, and interesting research. Repressed intelligence (related to fear) needs no such research 'cause we have all experienced it. Math Phobia? Even mathematicians experience it sometimes.
What I can’t decide, though, is whether they don’t like math because it was never taught to them properly, or if they just don’t like it. Most people I know who don’t like or are actually anxious about math look at it like a series of formulaic manipulations… very much like a formalist. Rules to be followed, steps to memorize. Somewhat like high school biology or history. Whereas, by contrast, people who “get” math don’t really remember formulas or steps per se, but know how to derive them as the need arises. I’m excluding here people who pursue advanced mathematics; obviously we can’t “simply” derive the Navier Stokes equation or something just because we understand math. But for things like area, or solving algebra equations, or turning an everyday situation into a math problem they can solve…these things are something that never comes with memorizing formulas. This style of learning defies generality, from my admittedly anecdotal experience.
Ehhh… I think you trivialize history and English if you think so. Understanding how a language evolves isn’t something you “just” memorize like so many genus and species. Understanding microevolution isn’t a matter of mere facts. Historical trends emerge for the historian.
While this is true, I still think it has everything to do with how it was presented to them. I’ve never met a person I couldn’t explain the fundamentals of calculus to. Of course, the point wasn’t to be able to do calculus, but I feel anyone can see what’s going on with it. People perform simple algebra all the time in their daily activities, so the problem with them doing algebra on a piece of paper doesn’t come from not getting it. The proper level of abstraction has just never been presented.
I often find myself wide awake in the middle of the night, racked by my own maths questions like: “can you prove that |x^(1/x)| (x is a member of (0,infinity)) tends to 1 as x tend to infinity and x tends to zero?” (incidently can anyone prove this? as I have been wondering a while), which surely must count as a form of maths anxiety.
As has been said, math involves deductions based on precise rules and premises. Figuring out new and unique relations may be an art, but ultimately they have to defended deductively and rigorously. I think most people are aware of this at some level. So, deficiency in math exhibits a more concrete (& humiliating) message than deficiency in most other subjects.
Surely you didn’t mean for x to approach infinity and zero at the same time. The case where x tends to infinity is easily handled with L’Hospital’s rule, after taking logs to convert the indeterminate form infinity^0 into the fractional indeterminate form infinity/infinity. Assuming that you’ve already proved L’Hospital’s rule and the continuity of the logarithm function to your satisfaction, this method is just as rigorous, and perhaps easier, than a first-principles proof using an epsilon-N argument.
I think it has to do with bad early math teaching more than anything else. The accusations of stupidity for failing to grasp basic math are part of it but there are also very few math teachers at early levels who can convey how interesting and wonderful math can be. Combine this with very little in the way of works on popular mathematics and you get people dividing themselves into “math people” and “non-math people”. There just isn’t a good middle ground provided.
On a related note I don’t think the "fuzzy’ fields are really easier. These fields have more people in them and more middle ground because these fields are based on language and interpersonal relationships, which everybody has to deal with and many people have an opinion about.
Here’s a thread I started called Math Anxiety. It is real, and I have it. I like my math class, and I am very happy when I can solve the problems. Sometimes it just doesn’t make any sense, that is when I run into problems. I can’t really pin down why I struggle. Some of the stuff makes perfect sense, but then I will run up against a brick wall and everything comes to a halt. I can’t see the relationships between the numbers correctly. It is like traveling to a foreign country and getting really hungry, then going to a restaurant and the menu is printed in a totally unfamiliar language. I panic, and I don’t know where to begin.