I'm doing math again and my head hurts

Miscellaneous and Personal Stuff I Must Share
1

I am…ahem…shall we say, expanding my horizons. I have some irons in the fire, but to be prepared to turn those irons into something, I need to brush up on my math.

Ivylad had some algebra, geometry, and calculus computer CDs, so I’ve been working my way through basic algebra to start. I am absolutely horrified at how much I’ve forgotten. :eek:

I admit, I’ve gotten rather lazy in the math department, relying on a calculator. I work in a business where you have to know how to calculate time (2 hours and 15 minutes plus 3 hours and 55 minutes equals 6 hours and 10 minutes, that sort of thing) and again, I’ve gotten reliant on my trusty time calculator.

I’d forgotten how to divide fractions. I got some of the questions wrong on doing basic equations. I’d forgotten that reducing while multiplying fractions makes things a lot easier (for instance, although I just refreshed my memory (1/2 x 5/8 x 4/15)/(3/8 divided by 3/40) knocked me for a loop)* I remembered my old maxim in high school that explained a lot of math errors, where A x B = A + B (meaning, a student doing higher math could add 2+3 and get 6, or multiply 4x4 and get 8).

My brain feels like mush. But, there is a bit of a thrill when I get an answer right. It’s not like English or history, where the answer can be subjective. In math, there’s one way to do it to get the right answer. There’s some sort of security in that…if you get the answer wrong, you can backtrack and see where you went off the rails. Plus it’s fun to know how well I remember my multiplication tables.

So, I would appreciate any good math voodoo you can shoot my way, as, after nearly 20 years, I start kicking and prodding that part of my brain back into shape.

At work, I plan to noodle out some stuff on paper and then check it with my calculator. Use it or lose it people!

*answer

1/60

2

No wisdom here, but lots of sympathy. I hate math with a passion. And I just found out I’m teaching a class in physics and chemistry this year. Equations? Um…yeah. I think I’m going to have to do some homework really quickly.

3

I never understood how people can dislike or fear math. It’s just a set of rules. If you follow the rules, you’ll never go wrong. There’s no guessing involved, no judgment. You just do what you’re supposed to do. How is that hard?

4

Maybe because I’m not good at following rules??:smiley:

5

Somebody should record a parody song and call it “Rebel Math”

6

ATTENTION CLASS! Memorize this rule:

x = ( -b ± sqrt(b[sup]2[/sup] -4ac)) / 2a

Now use it to find the roots of all your favorite quadratic equations. Easy, right? Just stick in the numbers. But that’s hardly doing math, it’s just executing an algorithm. Blindly following steps that were dictated to you. That’s a useful skill, but it’s not math. How many people who have memorized the quadratic formula can actually explain how it’s derived? How many people who have solved quadratic equations actually understand why the same formula always gives the roots?

Not me. But I got A’s in algebra and stuff. I hardly think I am a qualified algebrist, though.

In calculus, they teach you the rules to do simple derivatives. “It’s easy, just take the exponent and move it over here and make it a coefficient!” The hardest part is learning to do it recursively, but that was easy for me because I was a computer geek and already knew about recursive functions. Still, I did not know then (and still don’t know) why executing the chain rule produces a derivative function, only that it does.

I think there’s a big line to be drawn between “just follow the rules!” and actual mathematical knowledge or skill. There’s also the often troubling aspect that it’s all cumulative; you have to know arithmetic to solve a linear equation, and you have to know algebra to graph functions in calculus, etc. If your previous teachers were ineffective (or if you were lazy) you’re toast. I went into trigonometry and calculus without any idea how to “factor things out” of functions, and I still don’t really get it. I’m not sure how I even managed to get as far as I did with all the holes in my knowledge.

7

BTW, about a year and a half ago I started a project to relearn everything I had forgotten about differential and integral calculus (and learn various stuff that I was supposed to but never did, like the above-mentioned factoring). I wrote a few blog posts but then my job became insane and I had to shelve the project. Maybe now that I am working fewer hours I will finally take it up again.

8

The same way writing is just a matter of following all the rules of grammar, punctuation, etc.?

9

That’s pretty much only true for the parts of math that you can learn by rote. There are many areas that require a significant amount of math insight and intuition.

10

To divide fractions you just multiply by the reciprocal.

(a/b)/(c/d) = (a/b)*(d/c) = ad/bc
I use to have a fear of math. It was my worst subject in elementary school. A lot of kids made fun of me because I always had to stay in class during recess to work on extra problems. Then sometime in high school it just clicked. It’s like a light went on inside my head. It made sense and it was beautiful. I eventually got my degree in mathematics.

11

I think part of it has to do with the teacher. When Mrs. J taught vectors in math analysis (post trig, I think it was a pre-calc type course) I understood it perfectly. I get to Mr. D’s physics class and he might have been talking in Swahili for all the sense the vectors made to me.

I have this mental block, for as long as I can remember, where math and chemistry is concerned. Oh, I got B’s, but ask me to do it six months later and I couldn’t do it. It’s like a long series of numbers and letters make me go squiggle-eyed, and I can’t make heads or tails of it.

But hey, it gives my 20-year-old son a chance to show me what do to. He’s a very patient and good teacher. (That math problem in my OP he broke down for me so I could see what I did wrong.) The A x B = A + B maxim I mentioned above, he calls “bad driving.” or not reading the signs.

Danica McKellar (Winnie of Wonder Years fame) has written a couple of books called “Math Doesn’t Suck.” I think I’ve got the review covered with these computer CDs, but I’ll keep her books in mind just in case.

12

I’m also a math dunce, and sucked at it in high school. It always bugged me, however, that I couldn’t master simple algebra, so now and then I click up some remedial/beginner’s algebra website and try to study it once again. By about rule four, my eyes start to cross and I feel panicky and lost all over again, just like in high school, and I give up.

13

Okay, can someone explain this to me?

I get that x[sup]2[/sup] equals x times x, and x[sup]3[/sup] equals x times x times x. So 2[sup]2[/sup] equals 4 and 3[sup]3[/sup] equals 27, but how the heck does x[sup]0[/sup] always equal one? I can’t wrap my math-atrophied head around that.

14

That’s one of those things I take on faith.

Here is an explanation you might like, though:

15

Actually, the explanation has a glitch in it.

It should read
for all n <> 0, x, and y.

16

Take a look at this pattern:

2[sup]5[/sup] = 32
2[sup]4[/sup] = 16
2[sup]3[/sup] = 8
2[sup]2[/sup] = 4
2[sup]1[/sup] = 2
2[sup]0[/sup] = 1
2[sup]–1[/sup] = 1/2 (or 0.5)
2[sup]–2[/sup] = 1/4 (or 0.25)
2[sup]–3[/sup] = 1/8 (or 0.125)

Each time the exponent goes up by 1, you multiply by another factor of 2 (so 22 = 4, 42 = 8, 8*2 = 16, etc.). Or if you go in the other direction, each time the exponent goes down, you divide by another factor of 2 (so 8/2 = 4, 4/2 = 2, 2/2 = 1, 1/2 = 0.5, etc.).

To be consistent with this pattern, the only thing 2[sup]0[/sup] could be is 1. The pattern also explains why negative exponents work the way they do.

I just used 2 as an example; the same sort of thing would work with any other number. (As one of my math profs used to say, “Let 2 be an arbitrary integer…”)

17

Agreed. I admit I didn’t read it that closely. It also goes through the same thing as Thudlow Boink’s post, using “3” in the example.

18

Thanks, guys, that makes sense.

I aced graphing, so as soon as Ivylad can figure out why the disc stopped working, I’ll be moving on.

19

:frowning: My head hurts. I truly dislike math and suck at it. It intimidates me because it just doesn’t make sense.

Now, I’m no dummy, high school honor grad; one of those kids who NEVER had to study for a test in history, english, etc; but I could not wrap my head around math. I gave up after algebra and geometry. I couldn’t complete a simple algebra calculation to save my life now.

Every once in awhile, I think about taking a course; just for shits and grins, but then I remember how much I hated it. The worst thing was, it made me feel like a complete and utter failure.

Good on you, OP, for taking it up. Best of luck with it.

20

I was always good at math and loved it.

When you find yourself getting stuck, try reframing the question. As posted upthread, dividing fractions makes many people curl up into the fetal position, but use the inverse operation, invert the fraction, then multiply the fractions…easy.

Likewise, when people have to subtract with negative numbers. Change operation to +, reverse the sign on the number.

I think what helped me was that I could always visualize.

A) If you had a 10’ x 10’ room and needed carpet…well, when you draw that on a piece of paper, putting hash marks and all, you can count the squares and see it’s 100. Basic.

B) Now take that same piece of paper, show the .5’ marks. 1/2 x 1/2 will cover 1/4 only.

C) 1 divided by 1/2…if you’re going to divide the square into halves, there will be two. If you divide 3 pies into sixths, there will be 18 pieces. If you have half of a cake and divide it into quarters (of the original), you’ll have 2 pieces.

I was always able to visualize it, internalize it, and move on to the next. Physics buried me because I couldn’t visualize foot-lbs of torque etc.

A girl once asked me for help with permutations and combinations. So we took a red pencil, a blue pencil, and a yellow pencil. We grouped them physically in twos. She picked up red-blue and I wrote that; red-yellow, blue-yellow, same thing. “That’s all,” she said.

Those are the combinations. “What about blue-red, yellow-red, and yellow-blue? Add those and you have the permutations.” She said that really helped, doing it instead of just trying to manipulate it in her brain. She had already guessed that it would become pretty tedious if the number of items and groupings started getting large, like the lottery. How many ways can you pick six numbers out of fifty? 123456, 123457, 123458…

The formulas etc. are just mathematical shorthand and a lot of concepts they represent can be demonstrated in mundane ways.