Single Status Update
Why do math teachers suck at teaching math? In my book it's not an issue of not paying attention and then complaining/blaming everything on the teacher. Ever since the start of high school, I've had a consistent habit of failing at math until someone explained a concept to me in understandable terms, and then acing everything for the rest of the unit.
For example, I was taught that the definition of a linear equation is as follows:
1) F(a*X)=a*F(X) for every real number a
2) F(X+Y) = F(X)+F(Y) for every X and Y which can be taken as an argument of the function or the operator. These two conditions can be sinthesized in the following single one: CONDITION FOR LINEARITY: F(a*X+b*Y) = a*F(X) + b*F(Y)" etc etc etc
I couldn't understand a thing.
Then a trustworthy friend of mine explained that a linear equation simply doesn't contain exponents and doesn't curve on a graph. Aced the rest of the unit.
The definition of a linear equation is:
F(x) = Ax + B
Where A and B are constants. They can be anything (0, 1 , 0.564, ...), except A which can't be 0 (so that x doesn't fly away. You need a variable at least).
x is variable. x is raised to the power 1, in other words: x ^ 1.
A linear equation requires x ^ 1, if 1 is replaced by any number, the equation is not linear anymore.
F(x) = 2x is linear.
F(x) = 9x + 9 is linear.
F(x) = 5 is NOT linear. (because A is 0, so x isn't there) (not sure about constant-only equations, correct me if I'm wrong)
F(x) = x ^ 2 is NOT linear.
F(x) = 1/x is NOT linear. (1/x also equals x ^ -1)
And a graph of linear equation is always -from its name- a straight line.
I don't... that's a weird way to explain linear equations. I have no clue why anyone would teach it like that, and I've worked as a high school teaching assistant in math classes. I will say, there are times when your equations are gonna be weird like that, and when you'd need to do equations in forms other than the standard Y = Ax + B. For instance, if you're trying to figure out where two lines intersect, well then you have two equations, Y = Ax + B for Line 1, and Y2 = A2x + B2 for Line 2, so you'd set them equivalent in the form Ax + B = A2x + B2. That gets a little more messy, then you've gotta solve for x from there.
But that's more advanced stuff, for the basics, yeah, all you really need to know is y = Ax + B (or as C30N9 put it, f(x) = Ax + B, but for practical purposes, it's the same thing).
BTW, if you continue to have issues with math, feel free to post your questions here in the blogs section, I'm sure us fellow Doomers will be more than happy to lend a hand. I'm personally always up for it, it was basically my life until illness forced me to move home, so I'm glad to help if you ever wanna pm me or something.
- Show next comments 3 more