# Thread: Never too Soon for Algebra

1. ## Never too Soon for Algebra

Originally Posted by Dr.Peterson
If you can't use algebra ... anything other than trial and error will ultimately be algebra in disguise.
Well-stated!

Q: "Why do I need algebra? I'll never use it!"
A: Yes, you will. Granted, you may not recognize it.

Better to learn the abstraction sooner and let the notation help you.

2. Is my arithmetic approach algebra in disguise? (I thought I was adding numbers.)

This is still the arithmetic board, right?

3. Originally Posted by mmm4444bot
Is my arithmetic approach algebra in disguise? (I thought I was adding numbers.)

This is still the arithmetic board, right?
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.

4. 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?

5. 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.

6. Originally Posted by tkhunny
Well-stated!

Q: "Why do I need algebra? I'll never use it!"
A: Yes, you will. Granted, you may not recognize it.

Better to learn the abstraction sooner and let the notation help you.
Except that this was posted to "Arithmetic", not "algebra", so it is reasonable (perhaps ever required) to assume that the poster has no knowledge of variables or algebraic equations.

7. Originally Posted by stapel
Except that this was posted to "Arithmetic", not "algebra", so it is reasonable (perhaps ever required) to assume that the poster has no knowledge of variables or algebraic equations.
Because our students NEVER post in the wrong forum!

8. Originally Posted by Dr.Peterson
… and part recognition of what can be thought of as finding a slope (algebra).
Aha. I was doing something algebrish. I didn't see it. Thanks!

9. Originally Posted by stapel
Except that this was posted to "Arithmetic", not "algebra", so it is reasonable (perhaps ever required) to assume that the poster has no knowledge of variables or algebraic equations.
I don't disagree with your assessment.

I do disagree with the pedagogical approach. Always have. Algebra sooner. No need to hide it until later.

My views. I welcome others'.

10. Originally Posted by tkhunny
I don't disagree with your assessment.

I do disagree with the pedagogical approach. Always have. Algebra sooner. No need to hide it until later.

My views. I welcome others'.
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?"

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