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26 February 2010

Rawr! Algebra is hard! [More:]I have to take an intermediate algebra class and it's kicking my butt! I hate being 35 and not knowing the basics. If only I'd dealt with this when I was 13. Bah.
For me in my life, this fact has remained steadfast and true: I have never ever used anything beyond simple arithmetic once I finished high school. I did AP math, placed out of any college courses, then went on to obtain my BA and then an MA. I had statistics, which sucked balls, but I have successfully avoided math in all years ensuing. I intend to dodge math for the rest of my life. I am sorry you got smacked by the math ball at 35, serazin.
posted by msali 26 February | 23:24
I'd be happy to help if I can.
posted by Eideteker 26 February | 23:27
Man, I wish I could even ask for help. But I think I know what rules I'm supposed to be following and I guess I just have to practice each type of problems a million times till I get it.

And yeah, there's no way I'm going to have to really use this - it's just a pre-req I need. Grrr.
posted by serazin 26 February | 23:30
If I may overshare a bit here... as a 36 year old, one of the reasons I've been hesitant to reproduce is that I worry I won't be able to help my kids with their algebra homework as effectively as my engineering professor father helped me with mine.

For me, math has been mountain climbing with a heavy pack. Years of unrelenting hellish slog, capped off by an unexpected glimpse of the glory. The glimpse was linear algebra. It was worth the slog. Keep after it.

Also - At 35, there are no rules for obtaining help, beyond "don't copy outright". Every teacher teaches differently, and if B can part the clouds that A cannot, and that gets you through A's course... take it the help that B offers.
posted by Triode 26 February | 23:56
If I may overshare a bit here... as a 36 year old, one of the reasons I've been hesitant to reproduce is that I worry I won't be able to help my kids with their algebra homework as effectively as my engineering professor father helped me with mine.

I worry that we're going to end up with the stereotypical male/female split, where ikkyu2 can help with the math/science stuff and I'm stuck with the English. Which is fine, except I feel like a bad feminist not to have more math training. (And I took AP Calculus, it just made no sense to me. (And it double-sucks that ikkyu2 is actually extremely articulate and a good writer, since that actually gives me no upper hand here.... except, I guess, for the upper hand that does not involve helping kids with homework.... hmmmmmm........))
posted by occhiblu 27 February | 01:21
Ugh. I have a ridiculously hard time with anything mathy. I've gotten better in recent years in that I don't just freak out and hide under a desk anymore (I wish I was kidding) and that I can actually stand in a store and figure out prices and discounts (with a calculator on my phone) instead of fleeing like a little bitch.

Just take your time. There's no need to rush. (For me, rushing makes it even worse.)
posted by sperose 27 February | 01:57
Also, I'm a huge fan of putting mathematics in context. Popular science books like The Math Gene help with that. Big revelation: Math is the Science of Patterns. Sure, leaning the grammar is a PITA, but once you have that down, it is a language to talk about patterns. Cool, right?
posted by Triode 27 February | 02:53
I sometimes use higher-math-related concepts in real life, but I work with folks who do so nearly every day. My impression, based on talking to them and on my own ventures into realms I'm barely capable of navigating, is that algebra is REALLY FUCKING TEDIOUS and that's pretty much why everyone hates it and can't get past it.

It's the mathematical equivalent of a musician playing scales, over and over.

The bright side is that higher math seems a little bit like skilled musical improv -- once you have the scales down, you can start to use them in new and interesting ways.
posted by treepour 27 February | 03:07
Oof, Triode, linear? Really? I kind of liked math before then, up through AP Calc, but linear is where I hit my math wall. I barely got a B-, and I still have no idea what happened in that class.

I totally respect people who get higher math, because wow, I clearly do not.

On the flip side, today I had to explain to someone in college how to calculate 10% of 11, which made me despair for the state of high school math education.

Serazin - algebra is toooootally all about repetition. I'd be happy to help if I can as well. :)
posted by unsurprising 27 February | 03:37
Actually, as a software engineer I seldom use any higher math other than a little discrete math on occasion.
posted by octothorpe 27 February | 08:27
I have never ever used anything beyond simple arithmetic once I finished high school.

Here's some other shit I have never 'used':

Visual art
English Literature
Music History

...and yet I enjoyed all the classes I had in those subjects and feel richer for having them and having been challenged by some of them. I think that "What's the point, you'll never use this" is at best a cheap justification for letting yourself off the hook, and at worst it's like a compass needle pointing directly toward intellectual sterility. Not meaning to sound like a self-help book, but "As long as I have to do this, I wonder if there's any way to make it interesting?" is usually a healthier direction to consider.

Also: repetition can be important for fluency in some mechanical respects, but the human mind typically just won't tolerate too much of it without variations. There's something numbing - and often counterproductive in several ways - about going through a list of 20 or even half a dozen almost-identical problems. Here's a tip you can try; it doesn't work for everybody, but it can make a difference. If you have a section of similar-looking problems, copy one of them out and make sure you can solve it. The put the book away and try to make, say, a half-dozen of your own variations on the problem and see if you can solve those. You can learn a shitload by doing this if you take it seriously. You learn a lot about the scope of whatever technique it is you're looking it - "Oh, if I change this from a 3 to a 5, I can still do just the same thing. Oh, I guess I could really change that to a 7 or 1/2 or whatever and it would still work out ok. What if I make it negative? OK? Hm. What if I put a zero there? Hang on... now I can't solve it any more. Does that mean there isn't a solution? Or just that I need a different way of finding it in that case? Maybe I should make a note to ask about that."

The more you make a habit (or, 'one makes a habit') of doing this kind of theme-and-variation process, the less likely are to get caught off-guard by a problem your teacher makes up that isn't exactly like one you've already been assigned. Plus, if you get the knack of it, it's creative. I mean, my little imaginary dialogue there might sound a little dry, but figuring out ways to change one problem to another similar problem can bring out a lot of inventiveness and occasionally even the feeling of discovery.
posted by Wolfdog 27 February | 09:06
I'm teaching algebra this term at CUNY and the syllabus and the text have turned it into a cook book filled with recipes that no one wants to eat, but are described as tasty. The accompanying prose tries to be all upbeat and "relevant" but just makes matters worse. I try and convey some context but I more often feel like I'm a guard at Gitmo who manages to interrogate without actually waterboarding anyone, but my prisoners are still mostly innocent.

Just last week I tried to explain how the ancient Greeks freaked out when they discovered that there could be 2 lengths (I drew 2 straight lines on the board) such that, no matter how small a unit measure you chose, you could not get it to fit an exact number of times into both lengths. I was the only one in the class to find this interesting.
posted by Obscure Reference 27 February | 09:36
Thanks for the great encouragements and interesting comments guys. It helps to feel like I"m not alone in the sea of exponents here.

I had to take algebra for the first time a couple years ago, and I actually found it refreshing to realize that all those scary letters weren't that scary after all - and satisfying to figure out the rules and systems. This time though I'll do a problem 6 or 7 times and it still doesn't come out right! I re-read the explanation, have the online book show me similar, sample problems etc, and it doesn't work out. Grrr!!

Partially I guess I'm used to school stuff being easy (You know, when I actually try to do it) and so I'm coming up against what a lot of people have to do all the time - keep trying even when I don't get it at first.

I guess I should go to the school tutoring center.

Obscure Reference, do you know of a particularly good text for intermediate algebra that I could buy an old edition online for cheap? I'm only using an online based system and I guess I need more sample problems.
posted by serazin 27 February | 09:59
Hey, serazin, what kind of problems are you working on at the moment? Can you share one?
posted by Wolfdog 27 February | 10:21
I'm doing systems of equations. Here's a recent example:

4a + 7b = 27
8a + 2c = 34
6b + 2c = 0

So I guess I need to solve it using elimination and substitution. I follow the steps to do so (multiplying the whole equation by a figure that will allow me to eliminate one variable when adding the equation to another equation) but it just keeps coming out wrong again and again ):
posted by serazin 27 February | 10:57
I just worked that, and made an arithmetic error the first time through which I only realized once I'd finished it and checked the answer. I went back and started it again and got up to a point where I realized I must be making the same mistake again and had to stare at it for a minute before I noticed I'd made a plus/minus sign mistake.

There's not much way around the fact that solving a system of even three equations by hand by elimination and substitution is prone to arithmetic errors. If your brain allows to just grind through a lot of examples, you will get better at it, but it's not a super rewarding end in itself. If you asked a lot of people who think of themselves as "mathy types", I bet they would all tell you they still make frequent arithmetic errors like that, and I don't think any of them would tell you they enjoy solving systems of equations by hand. Unfortunately what's easier to test, and to score quantitatively, is whether or not you can walk through the arithmetic minefield without making any missteps - so I have a pretty good idea what your next test or quiz is going to be like. That's an unfortunate situation that we - like, everybody, for thousands of years - are still trying to learn how to deal with.

Here's a question or two for you, if you feel like tinker a bit. I assume you have the answer to that problem available to you (or you've worked it out by now).

Can you write a different set of three equations (make them up yourself) that has the same solution as this one?

If you can do that, could you write a still different set of equations that has the same solution? How many different ways could you cook up a set of three equations that are satisfied by a=5, b=1, and c=-3?

I don't like 5, 1, and -3. Could you make your own set of equations that has a=7, b=8, and c=9 as a solution instead?

Could you make a set of three equations for which a=7, b=8, c=9 is a solution, but a=5, b=1, and c=-3 is also a solution? (Say, is that even possible? I swear, that phrase, along with its close relative, "Is that really true?", is the key indicator of mathematical thinking occurring.)

If I asked you to solve {4a+7b=27, 8a+2c=34, 6b+2c=0} and you looked ahead and problem 2 was {4a+7b=27, 8a+2c=34, 6b+2c=0} and problem 3 was {4a+7b=50, 8a+2c=-12, 6b+2c=13} and problem 4 was {4a+7b=18, 8a+2c=9, 6b+2c=0} -- all of the problems having the same coefficients on the left hand side -- would there be any real difference in how you solved them? Would there always be a solution, or is there any set of values you could put on the right which would make it impossible to solve? Is there anyway you could use your work on the first one to make solving all the rest of them a lot faster?

If you had a dimwitted assistant - too dull to learn the process of substitution - that needed to solve a lot of systems for you that all looked like "4a+7b=THIS, 8a+2c=THAT, and 6b+2c=OTHER", could you come up with an easy way for them to calculate a, b, and c?

Could you make your own word problem (even a silly one - in fact, the sillier the better) that would lead to setting up these three equations?

Is there any way you could know 'just by looking' that the solution to this set of three equations was going to have nice, whole number answers instead of rotten fractions like 13/947 or extremely peculiar numbers like square root of 2, or pi?

Those are important sorts of questions to ask and you've probably been equipped with enough tools to answer them, but the kind of course you're taking will probably not give you the chance to discover that fact. If you come to the end and you've got better at arithmetic but never posed your own questions or tested the boundaries and limitations of the techniques you're learning, then - well - you should feel a little cheated; that's why people do come away from math classes feeling that what they got was useless.

posted by Wolfdog 27 February | 11:52
I make silly arithmetic errors on the board in front of my entire class. I use those moments to teach how not to freak out when you get things wrong, and how to recover from errors.

For those 3 equations, I'd first divide the last 2 of them by 2.
Then come up with a general strategy so you don't go around in circles:
e.g. solve the second for a in terms of c, and the third for b in terms of c. Then substitute for the a and b in the first one and you'll have only 1 variable, c.
posted by Obscure Reference 27 February | 12:53
I took Algebra when I was 27. Two things that helped, have a homework partner so you can talk through problems and having a really engaging teacher.
posted by doctor_negative 27 February | 13:38
You guys are awesome, and wolfdog, I will totally do these exercises tonight (after I put the kiddo to bed). I like the idea of "getting it" on a deeper level this way.

I came to just vent, but this has been a very reassuring and helpful thread!
posted by serazin 27 February | 18:47
Late to the math party, but I recently had to look at some floor plans to see if the measurements that a broker came up with added up mathematically, so I broke out all the geometry I remembered from high school, did research on how to calculate the are of a triangle, wrote down lots of equations, and came up with an answer. To double-check, I had my sales manager look it over and he had a formula at hand that was totally better than what I had, and was just as correct.

Which goes to show, even when you want to escape math, it will follow you in the end.
posted by TrishaLynn 28 February | 09:05
I love hearing stories of math being used in the wild. It helps me feel that I'm not totally wasting my time!
posted by serazin 28 February | 14:11
The Pitfalls Of Fiction || I just recently turned 38.