Algebraic proofs?

[Carol S]

Do you know of any algebra curricula that teach formal algebraic proofs? We did this in my honors algebra I class, but nobody else did, and doing them does not appear to be the norm. But I really think it was valuable training just for logical thinking, as well as mathematical thinking, and it make geometry pretty much of a snap.

I'd love to find one that includes this, or at least some way to guide me so that I could introduce it to them on my own.

[Linda]

Would that be classified as "Linear Algebra"?

I know my dh's aunt taught math at a prep school in St. Louis for many years. When she was visiting I asked her her thoughts about different algebra curriculums. She said the best one she ever saw, and taught, was one that incorporated Alg w/ Geom., it was called an integrated approach.

I know that Life of Fred combines Alg. 1, Geom. and Alg 2 all in one book. She didn't look at our LOF book in depth so had no comment specifically about LOF, but she said anything that can get all of those working together, so the kids see the connections from the beginning, is the best way to go.

I can ask her what the curriculum was that they used in her school. I know they dropped it after she was no longer teaching the course (she moved on to being the Dean of the school). It was so different, none of the other teachers were willing to learn how to do it, let alone how to teach it. She was disappointed that they dropped that class.

[Gitel in nj]

Would that be classified as "Linear Algebra"?

I don't know the answer to your question, however I am pretty certain that the answer is NOT Linear Algebra. My DS will be taking linear Algebra next year after having taken Honors Algebra 1, Honors Geometry, Honors, Algebra 2, and AP Calculus AB--only 2 or 3 other kids in his school are willing to even go near the class. The rest of the kids on his track have opted for AP Stats.

[Susan Seaman]

It's not Linear Algebra - Linear Algebra deals with matrices.

I remember doing Algebraic proofs back in high school - in a class that we called Algebra III back then. I particularly remember having to prove the Binomial Theorem.

That's the only time I did something like that even all through college where I had calculus, differential equations, math modeling, etc.

If I'm thinking right, proofs of this type are called inductive proofs (as opposed to deductive proofs normally done in geometry). You might do some google searches about what curriculum includes inductive proofs.

[Susan Seaman]

Or did you possibly mean the logic-type proofs that used to be done in math - the statements with the p's and q's. I remember doing those in Alg. II. I don't know of a curriculum that does these now except Bob Jones Geometry did a little. I know that the Saxon curriculum didn't cover them.

[Gitel in nj]

It's not Linear Algebra - Linear Algebra deals with matrices.

Thanks for explaining that Susan..no wonder he wants to do it, the kid is fascinated by matrices. He once tried to explain something about them to me and I didn't understand a word. Fortunately Architects don't really need to know much more than Geometry and Algebra 1.

Good luck Carol, finding what you are looking for!

[Susan Seaman]

I love matrices, too! With them as a tool, you basically learn the easy way to do most of the stuff you did in Alg. I and II. I can remember being really aggravated that we learned the hard way first.

Most curricula do teach matrices in Alg. II (and there is usually at least one question on the ACT involving them), but Linear Algebra is a whole class just on that subject.