Show your work, or, how my math abilities started to decline

I
think it's problematic the way schools teach Algebra. Those meaningless
show-your-work approaches, without knowing what Algebra is truly about.
The overuse of calculators and the piecemeal way of teaching without
the unification of the math concepts are detrimental to our children's
ability to think critically and logically.

Of course
eventually, it would be beneficial to students if they show their work
with the much more challenging word problems (harder Mathcounts state
team round, counting and probability questions, etc...), but it's totally different from what some schools ask of our capable students.

How
do you improve problem solving skills with tons of worksheets by going
through 50 to 100 problems all look very much the same? It's called busy
work.

Quote from Einstein. "Insanity: doing the same thing over and over again and expecting different results."

Quotes from Richard Feynman, the famous late Nobel-laureate physicist. Feynman relates his cousin's unhappy experience with algebra:

My
cousin at that time—who was three years older—was in high school and
was having considerable difficulty with his algebra. I was allowed to
sit in the corner while the tutor tried to teach my cousin algebra. I
said to my cousin then, "What are you trying to do?" I hear him talking
about x, you know."Well, you know, 2x + 7 is equal to 15," he said, "and
I'm trying to figure out what x is," and I say, "You mean 4." He says,
"Yeah, but you did it by arithmetic. You have to do it by algebra."And
that's why my cousin was never able to do algebra, because he didn't
understand how he was supposed to do it. I learned
algebra, fortunately, by—not going to school—by knowing the whole idea
was to find out what x was and it didn't make any difference how you did
it. There's no such a thing as, you know, do it by arithmetic, or you do it by algebra. It was a false thing that they had invented in
school, so that the children who have to study algebra can all pass it.
They had invented a set of rules, which if you followed them without
thinking, could produce the answer. Subtract 7 from both sides. If you
have a multiplier, divide both sides by the multiplier. And so on. A
series of steps by which you could get the answer if you didn't
understand what you were trying to do.

So I was lucky. I always learnt things by myself.

## Wednesday, August 1, 2018

### Show Your Work, Or, How My Math Abilities Started to Decline

Labels:
algebra,
article on math education,
problem solving

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