I never cared for math, but I forced myself to get decent grades. Lack of use means I’ve forgotten a lot of it, but it’s easy enough to look stuff up if I need it.
Yeah… Fractions… My problem is that I’m lazy. We weren’t allowed to use calculators, so it was easy to make silly math errors doing the multiplications and divisions to get rid of them. I always hated it when the answer came out to 69/43 or something.
My biggest mistakes were forgetting a sign, forgetting to write down a variable or writing down the wrong one forgetting to multiply an element, and stupid stuff like that.
This is something I have no trouble with. I’d rather write down minus-negative (or plus-negative) than plus (or minus), because it make what’s happening more visual.
I was never a natural in math, but a few years ago I bought an algebra and trig textbook out of the blue and started teaching it to myself on and off. Lo and behold, it finally made sense! I got through both algebra and trig and even very basic calculus. A couple of years after that, I found myself taking my GRE’s, and that knowledge came in pretty handy.
My humble opinion? It’s easier to teach yourself basic algebra and trig than to sit in a dull classroom listening to a boring teacher prattling on at bored students. Once I started teaching myself at my own pace (very important), the rules and methods started making sense. I still remember the thrill I got once I figured out those train problems.
OK, a couple of hints.
First off, you’ll need to buy or borrow a regular textbook so you can read the explanations and do the problems. For the record, I used Sullivan, and I would absolutely recommend it if you can afford it. If you can’t, no big deal. Pretty much any basic textbook that’s halfway legible will do. The important part is working through the problems.
There are also a couple of other works worth finding. I would recommend How To Solve Word Problems in Algebra, which is pretty much the best book out there to help you through word problems–vital if you want to really understand how math works rather than just the rules. Another book that helped me out was Isaac Asimov’s Realm of Algebra. It’s a short theoretical treatise on the foundations of algebra for the layman, and I managed to read it before starting the whole math thing. It’s kind of expensive to buy, but if you can score a copy through your library, it’s well worth the read. It’s even worth a nominal Interlibrary Loan fee.
You will not master math by reading about it. True mastery will come through hours and hours of practice problems. There simply isn’t any other way. Unless you possess an extreme natural gift for math, your best bet is to master the practice first and then go back to figure out the theory. By doing a wide variety of problems, you will learn how not to make careless errors (Don’t worry, you will absolutely make hundreds of them at first, but sooner or later, you will learn to avoid them.), and how to recognize certain problems and set up methods to solve them. You’ll learn to spot familiar patterns that will cut down on time and brain power needed to work through the problems. Here is where real mastery is achieved and nowhere else.
Don’t neglect the Internet, particularly message boards. My favorite one is–well, was, because I haven’t posted in years-- freemathhelp.com. They helped me through a few difficulties.
So I went from sucking at math to being OK at it (Got a 790 on my math score on the GRE, which while not great was at least enough to beat the mean), and that’s pretty much how I did it. Good luck! I went from hating math to actually learning to like it, although I’ve since gone back to languages. Good luck!
My math teacher never ever let us refer to a negative number as “minus.” I think that helped drum into our heads that negative 2 = -2, so six minus negative 2 equals eight. It helped to separate the function from what the number was.
Ivyboy thinks the algebra disc is corrupted, but I’ll ask him to take a closer look at it later. Meantime, I’ve popped in the geometry CD. I did three lessons and the congruency of triangles is making me dizzy. I’m going to go knit some i-cords and clear my head.
My trig teacher insisted that we refer to these as “the opposite of.” -x, if x = -6, is 6. I’m sure he wanted us to avoid the mindset that -x would have to be a negative number when we solved it.
@Johnny: right, if you’re dropping signs and making careless mistakes, you don’t meet with success and it would just get frustrating.
The most ironic thing to me is that people say, “Math…what’s it good for?” Every story problem you’ve ever read is its justification. There really are carpet layers who need to calculate how much to buy and engineers who want to make sure walls are straight and plumb, average citizens can’t figure out why they don’t have more equity in their homes, etc.
That’s why I had to work so hard to make the grades. I had to be conscious at every step of what I was writing down. That’s why I like my job. I just write the equations, and the computer does the work.
A couple of years ago I renovated the smallest bedroom in my house. There was a closet, and the water heater was in it. So after getting rid of the closet (actually, a friend did this while I was away) I built an enclosure for the water heater, leaving space on the top for a TV. (The closet was replaced with a wardrobe.) A little simple arithmetic, a few pencil lines, and Bob was my auntie’s live-in lover! The enclosure came out square and level, and the drywall fit perfectly.
Since I have a long commute I amuse myself by looking for mile markers and calculating what time I’ll get to my exit. On long trips I calculate how far I can go with the fuel remaining. (The miles-'til-empty computer is too pessimistic.) I like to cook, so I’m always calculating different quantities when I’m scaling down recipes.
From estimating how many planks you need for a floor, to estimating how long it will take you to drive from Point A to Point B, to making pancakes, people use math every day and often don’t realise it.
Had it been me, I would have made exquisite calculations, then totally mucked up the execution of it. I’d be proud if I managed what you did!
Yeah, that’s the first tragedy. So many tense up when the word “math” arises that they don’t see a lot of it describes ideas they already know and use.
The second tragedy is all the “math taxes” out there, like Rent-to-Own, exorbitant credit card rates, and so on.
Generally right. There was a program on TV one day about a syndicate that wanted to beat the lottery. IIRC it was Powerball. They had calculated the odds and waited until the payoff was greater, say, double or triple. Then they set in motion an army of people, using computer printers to make slips to cover every possible combination.
The program acknowledged some things. First, printer ink and time and gas etc. spent aren’t free (although I think the slips were). However, there are smaller prizes for matching 3 of 6 or whatever, so those costs would be covered.
Second, and more worrisome, was that if there were multiple winners, they’d have to share the payout. You could buy 100M combinations, hit the 200M jackpot, but if you share it with two other winners, you’d lose money.
So they printed out boxes and boxes (and boxes and boxes) of slips, sent armies to thousands (?) of various places to get the tickets. Sure takes a looooong time to print that many and they had a short window (like once Wednesday’s drawing didn’t produce a winner, they had to have the tickets in hand by Saturday).
And then…the lottery’s computer system went down. AAAARGHHHH! What if they couldn’t buy all the combinations before the drawing? Had they bought the winner yet?
It was total disarray and I think they came to the end of the program making frantic calls to their people and not knowing. A google doesn’t reveal what I’m looking for.
Ahem. Still, they needed luck or they’d be sharing the jackpot, which would trash the mathematical rationale for it.
In Virginia this month, one investment group came tantalizingly close to cornering the market on all possible combinations of six numbers from 1 to 44. State lottery officials say that the group bought tickets for 5 million of a possible 7 million combinations, at $1 each, in a lottery with a $27 million jackpot. Only a lack of time prevented the group from buying tickets for the remaining 2 million combinations.
But the thing is, math does make sense. Unlike other subjects, everything in math is stuff you could figure out for yourself, if you were clever enough and thought about it long and hard enough. There’s nothing arbitrary: the way things work is the way they have to work in order to be consistent with everything else. Well that’s not entirely true: there are some arbitrary things you just have to learn, especially in the realm of notation, like the symbols 1, 2, 3, 4, etc. But mostly, math is just what’s logical. Euclid’s Elements, the most famous math text of all time, starts with just a handful of assumptions and logically deduces a vast amount of mathematics from them, in ways so that anyone who understands pretty much has to say, Yes, it has to be that way.
Sometimes, alas, math is taught in such a way that it doesn’t make sense, whether because the teacher doesn’t really understand it or doesn’t care or doesn’t think he can afford the time to explain. In a book I recently read, I was intrigued to read that girls more often than boys find it important to understand why math works.
Linty Fresh, I liked your post (#22). I think that’s very good advice for anyone who wants to learn math on their own.
Thanks. I only wish I’d figured it out 20 years ago, back when I could have learned to actually make a living using it, but such is life. Meh, I’m doing OK with my languages.
Where we will force them to turn around and count, name, and memorize the features of every single brick in that wall, which will actually be slightly more interesting than what our teachers made us do in high school analytic geometry class.
I’ve read this before, and I think that Lockhart really goes off the deep end with his belief that mathematics ought to be useless. Near as I can tell this opinion is less than a century old, and started with G. H. Hardy, who’s mathematical work has actually found a number of uses.
I do try to think of physical reasons for the facts of math as much as I can. It’s crazy to say that math should be application-less when, say, the “negative time negative equals positive” rule exists because it makes calculations in the real world work.
I’d say it exists because it’s mathematically simplest… it preserves the distributive property of multiplication over addition, and such things. That this “makes calculations in the real world work” is a secondary consideration that simply follows from that. Any other system would be all the uglier and more ad hoc for destroying such a nice pattern, and thus have less natural applications or interest, real world or otherwise.
When I did maths in school, we had to solve quadratics by completing the square before we got to the standard formula. As a result, there was no mystery about the general formula when we reached it.
“Completing the square” is something that sounds vaguely familiar, but I must admit I have no idea what it means, and couldn’t follow any of the explanations upon a cursory Google search.
