Foerster Algebra and Trig: why are there proofs?

[pjssully]

We are beginning with Foerster Algebra 2 (Algebra and Trig. book) and I noticed that in chapter 1 there are proofs using algebraic concepts.  I have not seen this before and I am curious as to why some books have proofs and some do not.  What is the benefit to completing an Algebra 2 program with proofs-or is there a benefit?  After proofs in geometry, I kinda thought we were done with that! :)

 

Any thoughts/insights?

 

 

[regentrude]

 What is the benefit to completing an Algebra 2 program with proofs-or is there a benefit?  After proofs in geometry, I kinda thought we were done with that! :)

 

The benefit of proofs and derivations is that you know WHY something is the way it is and that formulas are not just randomly falling from the sky to be memorized.

I prefer math curriculum that derives/proves as many relationships as possible (with the tools available to the student; some proofs would require more advanced concepts and have to be omitted), because that makes math understandable and not a random assortment of theorems.

 

The reason proofs are introduced in geometry is because it is easiest for the students to begin proving these kinds of not so abstract relationships, before proving more abstract things in higher math courses. You are never "done".

 

ETA: many proofs are actually not proofs but derivations. Extremely valuable for long term retention. A student may forget the quadratic formula he had memorized, but a student who understands where it came from will forever be able to re-derive the formula.

Edited March 29, 2017 by regentrude

[amymeg]

Thanks, this makes sense and after I went through the lesson, I agree with you even stronger. While I was initially intimidated, I can truly see the benefits now,! Thanks for your timely response!