"Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.
Is my arithmetic approach algebra in disguise? (I thought I was adding numbers.)
This is still the arithmetic board, right?
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
Your arithmetic method is part trial and error, and part recognition of what can be thought of as finding a slope (algebra). I wouldn't say that it's literally true that everything other than trial and error is algebra in disguise, as I suggested, but things do tend to work that way for many problems.
But I'm still waiting to hear from the OP about what methods are really available. There are methods taught at the elementary level that are equivalent to algebra without using any algebraic notation.
Whether mmm's answer is algebra in disguise depends on how we define algebra. I don't think his answer depends on elementary algebra in its traditional sense. It is more a combination of trial and error and very basic number theory. In principle, it is always possible to solve a system of bounded Diophantine equations by trial and error without need for anything other than arithmetic. Does the teaching of arithmetic include the identification of bounded Diophantine equations nowadays?
Last edited by JeffM; 11-21-2017 at 11:34 AM. Reason: Fixed misspelling
Well, that's the way I always approached it when I was a child. Of course, I was pretty much a freak, as far as that goes.
"Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.
"Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.
My feelings exactly - and same goes for word problems.
I taught my children and grandchildren addition/subtraction. But all the problems were almost always posed as word problems:
"You have five crayons in a box and your brother ran away with two of those. How many crayons are left in the box right after that?"
Rarely did I ask them "How much is 5-2?"
“... mathematics is only the art of saying the same thing in different words” - B. Russell
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