I just finished a PhD in statistics, but my program was actually not in a mathematics or statistics department, and I was surrounded by social-science doctoral students who would talk about how much they disliked math and were glad to be getting their degrees in a “softer science.” Sure, business research requires mathematics in the form of basic design of experiments and analysis of results, but it’s not nearly what is required of mathematics or statistics research. I was a graduate assistant for many doctoral level classes and many of them had great difficulty with Calculus I topics (e.g., integrating x^2).
I always told them that they were lucky. They will never have to read the sentences in their journals that start with “It is trivial to show that…” or “By an easy calculation, we have…”, or the dreaded, “Obviously, …”, followed by some mathematics that is anything but “easy.” I used to tell them–facetiously, of course-- “Mathematics is the only subject that actively makes you feel stupid for reading it!”
As for the reason why people hate math, I’d say it’s mostly bad teaching. I only came to love mathematics through my statistics classes as a junior in college. Only then did I have someone who actually cared about teaching.
This, plus what Broomstick said, plus (in my personal experience) abuse by no fewer than three math teachers. And that’s including my first grade teacher who shamed me in front of the entire class, and a college professor who, when I asked him for some pointers because I was having trouble and seriously behind, said “people like you, who don’t understand math, are psychologically sick, psychologically DAMAGED” and berated me for several minutes, until a fellow student showed up and unknowingly rescued me. (thank goodness he didn’t hear it).
Not everyone has the skill to do every academic thing on the planet. Some are good at math, some are good at other things. It doesn’t mean a person is stupid or lazy if that’s not something enjoyable or easy for them.
But the huge difference is, if you know even a little bit about the question on a history test (and particularly IF you have read the historians reasons…and particularly IF even historians can’t agree on the “real” answer), you can write several paragraphs about that little bit you know, and still get the answer right on the test. NOT so in math. As several others have said, the answer is either right, or wrong, and when you have 50 questions that all look like this
b2/xm*z=mp3no blah blah blah…
And you have to not only memorize all equations but innately know in which situations to apply them? That IS harder.
Knowing math is a toggle switch, it’s either on, or off. Most other subjects are like that cute picture of the control panel for a woman. Many different answers can be “right”.
My experience in math was opposite, and more in line with Chronos’s point that math is, in at least some senses, markedly free of difficulties which are present in other subjects:
If you don’t remember something in history or biology or literature (or were too lazy to pay attention or study it in the first place), you’re not going to be able to conjure it up out of thin air. You can’t just sit down and figure out what the Boxer Rebellion or the stages of meiosis or the plot of The Great Gatsby are merely by reasoning it out from scratch in your head.
But in math, that’s exactly what you can do; so long as you at least understand enough what the questions are asking for, you can always try to re-derive the solutions for yourself. For me, as a rather lazy person, this was very appealing about mathematics as opposed to other subjects.
Now, I’m not saying everyone is going to be just as good at this sort of thing, but probably, to some extent, the teaching style of “Here’s a formula. Memorize it. Use it when you see a problem that looks like this” plays a role in this learned helplessness. (It’s also not clear to me what the value of teaching students to memorize and recall formulas is anyway [in the real world, no one forces you to solve problems without access to your textbook], so if the goal is not to learn how to think them up, then one might as well just spend time on more useful things…)
As other’s have alluded to, math sucks because it’s tedious. Math is either “right” or it is “not right”. There is no in between. It’s also why nearly everyone I know who works in information technology ( a closely related) fucking hates it. It becomes a never-ending nightmare of digging into equations that just don’t work because you forgot to carry a one somewhere.
And I have a degree in engineering so I’m no slouch when it comes to math and I still fucking hate it.
I’m not sure if you’re answering me, or just the thread in general. The thing with history, biology, or oh..ANYTHING with actual text is (and my point, and I do have one :D) is that you don’t have to remember all of it. Just some of it, and the rest can be BS’d through and you’ll still get the answer right. Especially if you can glean part of the answer from the questions themselves.
Nononoooo, you see…in math that’s what YOU can do. Others of us see a bunch of innocent letters mixed up in an eastside gang of math symbols and X’s and we just get brain freeze, brain freeze and “OH MY GOD, a MAMMOTH, a MAMMOTH is going to trample me! GAAAAAAAAAAAAAAH help me oh Lord!” out of it.
But see? Calling it things like “learned helplessness” just plays into the idea that “well math really IS easy and people who don’t think it is are causing the issues themselves, it’s THEM, they must have something wrong with them, because math is easy”.
I (and I think most people) agree that math is useful, and I believe most of we mathphobes would LOVE it if we could “get it”. Like another doper said upthread, she did her due diligence, she took every bit of help she could get and she just didn’t get it. Yes, most of us could do a little better if we studied it and/or had decent teachers (as opposed to the sadistic nazis that make up a large percentage of math teachers), but that doesn’t then equal “math is easy”.
I’m sorry. I did not mean to imply that. Perhaps a different phrase would have made my point better. In that particular instance, I was meaning to stress the problem that a large part of what you may have found difficult, and which actually is difficult, is tasks which there was no point teaching and testing in the first place; memorizing formulas and so on. If the teachers had instead focused on teaching something else of more value in mathematics (perhaps other approaches to thinking about the same problems or other kinds of mathematics altogether), you may have found that to be something you had an easier time with. (You may still have had difficulties, but they at least would not have been the particular difficulties of the pointless task of memorizing and applying formulas). My blame here lies with the teachers’ selection of what to teach and test; perhaps I should have called this “taught helplessness” instead.
I do not mean to engage in the mistake of assuming that math would be uniformly easy for everyone if only [whatever]; no subject is like this. I just think there are particular difficulties in math which are the fault of how it is taught. (More to come in another post, perhaps)
No offense taken. My point was that people to whom it comes easily often aren’t aware of how they’re viewing it. Which ties nicely into your point really… that is, that it’s how it’s taught. I think that’s a huge part of the problem.
I taught dance and aerobics at a local university before I left Anchorage last fall. A few semesters into teaching the dance class I remember one of the students said something to the effect of “don’t say a move is ‘tricky’ or anything, that makes people scared and think they won’t be able to get it”.
I thought about it, and my take was “I’ll try to hit a happy medium on my descriptions of moves, because if I say a move is ‘easy’ that’s going to make the people who don’t get it right away feel like they are cursed with two left feet and incurable klutziness”.
Oddly enough, my job requires a certain amount of college algebra, and my little blonde brain works such that, usually, as long as the math directly applies to something real (flow/velocity in a fuel system etc), I can do it. It’s the letters that always drove me to murderous thoughts.
(Not in direct reply to the above post; I started typing it a while ago)
I would say that, intrinsically, math would be like any other subject: some people will be more interested in it, and some will find it less appealing; some people will have an easier time with it, and some will find it more difficult.
But what has distinguished math as a subject is, I think, the degree to which what is drilled and tested in math classes is distinct from what is actually of significance and interest in math. [Not that other subjects don’t have elements of this as well (e.g., history as memorization of dates and battle names, or all the stupid grammar myths that get taught in English class alongside the actually valuable business of practicing composition and analysis)], but I think the disconnect between what math teachers teach and what mathematicians care about is particularly marked.
Before we had computers, it was maybe actually important to get people trained in memorizing and carrying out all these tedious “When a problem looks like this, shuffle symbols like this” calculational heuristics and algorithms, and if perhaps the time spent on that was to the detriment of other aspects of mathematics, that was a reasonable trade-off. It was never really the essence of mathematics, just a small part of it, but it was a chore which it was often necessary to work through to put the rest of mathematics to any practical use, so we as a society put a correspondingly large emphasis upon training for it.
Now, we have computers to do all that stuff for us; machines invented specifically to relieve us of this burden. We should not be wasting anyone’s time training them to do by hand something they’d be better off having computers do for them. That’s just time better spent on other things, possibly in math, or even possibly freed up for other subjects of more value to the student.
But cultural inertia means that, for the most part, we still erroneously identify all that “Learn how to be a computer” bullshit as the important core of what math is, so nothing in the curriculum changes; any attempt to get away from this is considered an attempt to water down intellectual integrity (the New Math fiasco didn’t help, lending its taint to the very idea of curricular reform in mathematics…). So kids go on being tortured with drills on material they don’t care about and consider quite rightly unimportant, and it’s no wonder they grow up to hate it (instead of what ought to be a worst case of merely not being particularly interested in it).
Can you imagine if driving instruction consisted largely of lectures on the mechanics of an internal combustion engine, or if we considered fluency in C++ prerequisite to learning to use Photoshop? We’d have a lot fewer people remaining interested in driving or digital art, and quite a lot more people saying “Me and cars just never got along” and bristling at mentions of JPEGs. This is the kind of attitude we take towards general mathematics education.
Not only this, but I think that the whole idea of putting math into that particular box, the one which supposedly emphasizes rule-following and getting from point A to point B and which has little tolerance for esthetism or emotion; specifically at odds with artistic pursuits and “fuzzier” subjects, is an error, and as you point out one that is sustained by the way math is taught. Lockhart does mention this as well in his essay.
Just look at how the people who’ve posted to this thread, right up to those who’ve actually gotten a degree in mathematics, view the subject. WhyNot rightly points out that an elementary school child thinks math is fiddling with numbers, and doesn’t really understand how it’s possible to have math without doing a set of predetermined operations on them. (By the way, WhyNot, math is vast and numbers are one of a large set of useful mathematical objects. Some branches of math work with them, others don’t.) Most people have done math up to the high school level, and have more experience than elementary school children. To then math is really solving equations, or perhaps differentiating and integrating formulas. Count how many times the word “equation” has come up in this thread, and how many people started hating math because they just didn’t know what to do with those equations with so many symbols in them. I’m sure some people think that as a Ph.D. student in math, my work consists in solving a really long equation, with thousands of symbols in it and which takes four years to solve; kind of an initiation into the Brotherhood of Symbol Manipulators. (Somehow I’m reminded of Asimov, which I guess is appropriate since Hari Seldon has posted to this thread. And lo! he in fact is a mathematician!)
amanset of course is more sophisticated; he’s got a degree in math so he knows what math is all about. He never did proofs before starting university, and that’s all he’s done ever since. So that is what it’s all about, right? But he still apparently views maths as a predetermined process. You have to prove theorem X, which means going from point A to point B by mathematical reasoning and referring to other theorems seen in class. The whole process is totally robotic and bequeathed to you down from above. Given this way of thinking about math, it’s not surprising that some people would think that it’s a subject more appropriate for computers than humans, and that given that they are artistically or emotionally-minded, they stand no chance of understanding it, unlike you or I who are basically androids or something.
But the way mathematicians actually work is yet again different, and something I’ve only recently really started to do. It’s not arithmetic, or solving equations, or even doing proofs, even though all of those are skills you may have to use in the process of doing math. Mathematics is creating objects, studying their properties, comparing them with other objects, generalizing them, or as Little Nemo says deducing facts, establishing patterns and considering the possibilities. It’s not predetermined, it’s an entirely human endeavour where we don’t necessarily know where we’re going, but fueled by inspiration. We have to determine what we want to do, whether it’s worth doing and if it’s feasible, and it’s entirely possible to backtrack or get sidetracked. (And despite the mutual disdain that there seems to be between pure and applied mathematics, both disciplines fall under this description. Pure mathematicians get their inspiration in other mathematics, while applied mathematicians get their inspiration in other fields.)
For someone who thinks that there is no maybe in math, that it’s only true or false and you get from A to B, a totally rigid field of study, it may be funny to hear mathematicians actually talk about their work. “I’ve been meaning to study this and this.” “Well, maybe you’re right, but personally I think it should be approached through this other way.” “But can this really be done? I know it’s more similar to this other well-known thing, but because of this difference, I think it can be a much harder problem.” And so on.
On the other hand, some of the math haters in this thread seem to hate more than just math itself, but mathematicians as well, as if we were responsible for your difficulties in high school and for your teachers. In the other thread aruqvan is alluding to (and claiming mistreatment), she ended up telling us that all what we do is basically pointless and doesn’t bring any societal value, and “some of us have to work!” So you may be angry at being called psychologically damaged for having trouble with math, but I also take exception to being told that no normal person could want to do math, and that it’s all worthless anyway.
For the record - and it appears although I thought I had been clear on this, I haven’t - my views in this thread have been directed for the most part, especially regarding the maths vs music and languages discussion, towards secondary school/high school mathematics as by the time you get to University level there’s a pretty low chance of you actually hating it. Let’s face it, you’ve just agreed to study nothing but it for three years …
But regarding proofs and predetermined processes, I don’t think I ever said that. My point is for school mathematics there is a definite answer and most marks come from working out that answer. When dealing with proofs there, generally speaking, isn’t a specific answer that one needs to get to. The process and the ability to justify every single step of the process is what is important. If one single step can’t be justified then the whole proof falls apart. There can be many routes through the proof, but there is no specific “answer”.
Certainly there is a difference between math as it is taught at the high school level and, say, music as it is taught at the same level. But the argument that math and music aren’t such different disciplines has some validity. The question is why math is taught that way in high school, and I think Indistinguishable has part of the answer: knowing arithmetic and calculatory heuristics used to be a useful skill, and through inertia and the fear of lowering standards, we’ve kept that as the main part of the math curriculum. Leading to students hating math and pointing out that they just won’t need it in real life, since they’ll have calculators. Which is true. (The fact that math teachers tend not to be confortable with math, or to not like it either, is also part of the answer, and makes it a vicious circle.)
Fair enough, although many propositions cannot be proved in a thousand different ways either. And the proofs we get to do in math class, even at the university level, are often basically going from A to B using known theorems. It doesn’t necessarily require so much originality.
Actually, that’s sort of exactly what “stupid” or “lazy” means. Not good at or not wanting to do something difficult that requires the use of their brain.
What do we mean by “not good at math” anyway? I get that integrals and diferential equations are difficult. But if you are a full grown adult and can’t do fractions or basic algebra, that’s pretty dumb.
I think that learning to think algorithmically, in terms of program and process, (and learning to be creative with this, being able to play around with and design algorithms for tasks,) is an important life-and-well-being skill that applies beyond fiddling with numbers. I also think that fiddling-with-numbers style math classes are the primary source of education into this way of thinking in public schools right now. To that extent, I think there’s something that should be preserved from such classes.
But it’s certainly true that when it comes to calculating with numbers, we’ve definitely got computers to do that for us now and we’re handicapping our kids if we don’t educate them in a way that acknowledges this.
My view is that in school, kids should be encouraged to play around with:
Means of communication
Algorithms and patterns
Color
Sound
Tactility and athleticism
Measurement and explanation
Story
(yes I just made that list up–I’m sure I’m missing things here)
Perhaps a shift of focus away from numbers and more to a kind of “programming” class would both cover the Algorithms and Patterns component and be of more service to students (and society through them) than a fiddling-with-numbers class.
(A “programming” class? I mean an environment in which students play around with figuring out how to construct rulesets or computational machines designed to solve various problems. Whether this is literally through writing programs or not would depend on the context. I think that this is an importantly different skill from machine building in general, but I am not certain of that.)
I’ll just point out that I’m terrible at math. Flat out awful. I can only work with positive integers between 0 and 1. But I don’t hate math. I’m jealous of those who don’t have trouble with it. I’d think in general that math is hard to absorb for many people. It involves a different language, complex procedures that have to be memorized, and it’s not very interesting to most. What people probably hate is math class.
I used to tell them–facetiously, of course-- “Mathematics is the only subject that actively makes you feel stupid for reading it!”
