I really couldn’t do better than this. It is a MUST_READ
Here’s a short extract, and the whole is an indictment of the present system.
For students across the country, there’s clearly an engagement deficit in the subject. Paul Lockhart, a math teacher in New York, writes in A Mathematician’s Lament [PDF] that if he had to design a system for the express purpose of destroying a child’s natural curiosity and love of pattern-making, he couldn’t possible do a better job than is currently being done. He explains that he simply wouldn’t have the “imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”
So, you want to do a fraction subtraction. Here’s how, as a geometrical construction. You will need a piece of paper and a ruler.
Draw three number lines through a common point, which is the zero. Pick a nice point on the middle line to be the 1, say 6 inches away from the zero. Label the other two number lines 1,2,3,4,5,6,7 at equally spaced points, scale completely immaterial.
Now do what is shown in the picture below. (the pairs of lines are parallel)
Now measure the distance with the ruler, and divide by 6 (if you put the 1 at the 6 inch point).
A simpler version of this (2 number lines) can be used to locate the point on the number line corresponding to any (relatively simple) fraction.
And I’m sure she’s not the only one !
Eve M. Cooper Blog
(A little commentary I wrote about math. Take this tongue in cheek!)
I don’t like math. I haven’t liked it for as long as I can remember but my mother said there was a time that I did like it and was good at it. Whatever. If it was so long ago that I can’t remember that I was once good, then it won’t help my self-esteem in the moment at hand.
There isn’t anything logical about math. Why anyone would want to spend their time doing something as illogical as math is beyond me, but hey, if it’s your cup of tea then have at it. Just don’t come near me with it. I remember distinctly my first day of algebra class. The teacher wrote on the board 2 + x = 4 then asked everyone, collectively, what’s x? I thought, what kind of question is that?…
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Polynomial division is a completely unnecessary procedure. It is not needed for partial fractions. It is not needed for finding factors, etcetera…
The same result can be obtained in a more logical and meaningful way, by considering the structure of polynomial and rational expressions.
Check this out :
They tell you that conic sections are exactly what the words describe : Slice a double cone, the edge of the slice is a conic section, parabola, hyperbola, ellipse.
Then they tell you that y = x^2 is a parabola, or that all second degree equations in x and y are conic sections, or worst of all, they come up with the focus/directrix definition.
NOBODY shows you how to get the equation from the sliced cone !!!!!!!!!!!!
Well, here goes – (the math is after the picture, and it is so simple)
From the previous post (it is now the next one !) it can be seen that projection of the unit circle from the double cone vertex onto the slicing plane will give a second degree equation. What a nice lead in to these equations, and also projective geometry, and to 3D xyz stuff.
The focus/directrix definition is so “rabbit out of a hat” that it’s time for its retirement. In any case, what use is the focus except for a parabola. And the directrix ? Surely “Directrix” is a female director !!!!!!!!!!!!
This is a simple test question for grade 1 math:
6. Choose the equation which answers the question:
What number added to 7 is equal to 9?
Well, I’ve been involved with math for too long, obviously, as I genuinely thought that the only number equal to 9 was 9 itself.
If you got the answer (c), you didn’t read the question!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
For more, see http://www.testprepreview.com/math-grade-1.htm
Here’s another one, from a grade 8 test, same source:
9. What is the decimal notation of 7×10-4? ( they mean 10 to the power 4)
Answer and EXPLANATION!!!!!!!!!!!!!!!!!!!!
9. D: Because the exponent of 10 is -4, the decimal which is located behind the 7 will move 4 spaces to the left, and any of the empty spaces will fill with 0’s. so 7x 10? -4=0.0007
I hope that the computer system used to present these tests can cope better with “strange” symbols. I looked as well behind the 7 and could not see a decimal.
I borrowed the picture from http://wordsonalimb.com/2014/05/13/self-destruct/comment-page-1/#comment-151
Would it be any better if they were calculators (graphing ones, of course)?
Why, oh why, are we burdening the youth of today with the associative law of addition?
It is OBVIOUS !!!!!
Adding three numbers corresponds in a one-many way to putting three bundles of things in a bag, mixing them up (optional) and counting them. It would be a sad day if the count depended on the mixing.
This is an example of how far you have to go in abstract algebra to find a non-associative operation (and a fairly useless one at that)
No further comment from me !