So I was watching a HK TV series describing a smart and nice guy. One day he was at a restaurant and saw a kid doing homework and asking his mom:
Kid: "Mom, what's the area of a trapezoid?"
Mom: "How is mom supposed to know?!"
The nice guy tells the kid immediately: "It is top base plus bottom base multiply by height divided by 2"
Do you remember that mouthful formula? How would YOU help the kid?
Do you ever have to use the formula? No, I never had to use it.
Students whine and whine about having to remember a lot of formulas in math. You don't have to remember this one!
Why? Because you can derive it on-the-fly. Instead of remembering the formula: KNOW what you are dealing with!
I would tell the kid like this:
me: "So, what is a trapezoid?"
kid: "Is is a 4 sided figure with 2 parallel sides"
me: "Here is an interesting thing you can do with a trapezoid, make a copy of it! Fit the two to make a parllelogram"
(If the kid ask why, I will tell him about parallel lines and a transversal)
kid: "What do I do next?"
me: "Now, what's the area of the parellelogram here?"
(If the kid know, we are getting closer, let's say the kid does not know)
kid: "I don't know"
me: "For any parallelogram, you can chop off the triangle, move to the other side and get a rectangle"
kid: "So?"
me: "What's the area of the rectangle?"
kid: "base x height"
me: "In this case, your base is top base + bottom base of that trapezoid"
kid: "but what's the area of that trapezoid?"
me: "Well you got this rectangle by doubling the trapezoid, divide that by 2. So this is where the formula come from."
Mom can watch you derive that formula, moms can also know some formula too!
We should teach kids problem solving approach, and not just make them remember formulas.
Give a man a fish; you have fed him for today. Teach a man to fish; and you have fed him for a lifetime.
Tell a kid a formula, he can apply it for a problem. Teach a kid where the formula come from, he will be able to apply it for a lifetime.
This trapezoid formula you can derive on-the-fly. However, things like the quadratic formula or the Pythagorean theorem are nothing obvious: those are the ones to remember.
Want an application of the trapezoid area? You may remember the Trapezoid Rule from calculus: to estimate the area under a curve by adding trapezoids.
3 comments:
Why are we not teachers? because there is no money in teaching.
(I spent 2 years of my life studying exactly that, math teaching; then I did the math and there is no way I can make a decent living as a teacher)
Why do kids memorize formulas? because they have to speed their way in the exams and race through math homework drills. There is no time to think.
You can proof PI R^2 as well. But it gets tedious, and sometimes formulas just get the job done.
Think of circle as a triangle with a round base. The height of the triangle is the radius and the base is just the circumference of the circle.
Tada. Pi R ^2
As for pytagoras, imagine 4 similar right triangle and rearrange them into a square with (a+b) as the side. Soon you'll get a derivation easily.
How to Learn Math
For that circle thingy..
it's .5 * height * base
=.5 * r * 2 pi r = pi r^2
I would need some drawing to show pythagoras derivation but you can find those on the net easily.
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