Geometry Proofs What do you really need to do

[Karin]

Dd is doing both LoF and Dressler. The LoF because she prefers it, and the Dressler because I want her to learn it from 2 different books for various reasons.

In LoF, she's allowed to use the word Algebra as a reason for a step in the proof. (do I have the right word? In the column where you write Given, etc). In Dressler, she actually has to name specific Algebra postulates. As some of you may be able to imagine, my 14 yo not only prefers to say Algebra over naming specific Algebra postulates, she was, with all the intensity an intense 14 yo dd can muster, telling me why she shouldn't have to name the Algebra postulates. (she thinks it's a waste of time, mere busy work, etc.)

IRL and on things such as the SAT, etc, will she actually need to know the various Algebra postulates? Am I making her do needless steps? Will she learn the logic well enough doing it the LoF way?

[EKS]

I don't think she'll ever need to know and be able to apply the various algebra properties either IRL or on the SAT unless she becomes a mathematician. However, I think that being able to say "algebra" as a substitute for "addition property" or whatever is fairly nonstandard. Having to write the property instead of "algebra" doesn't qualify as busywork (IMHO) because there is thought and understanding involved in figuring out which property to name (and it's as easy to write "addition" as it is to write "algebra", or it should be for a 14yo).

[LizzyBee]

I don't think she'll ever need to know and be able to apply the various algebra properties either IRL or on the SAT unless she becomes a mathematician. However, I think that being able to say "algebra" as a substitute for "addition property" or whatever is fairly nonstandard. Having to write the property instead of "algebra" doesn't qualify as busywork (IMHO) because there is thought and understanding involved in figuring out which property to name (and it's as easy to write "addition" as it is to write "algebra", or it should be for a 14yo).

:iagree:

But depending on her college major, she may do proofs in college and be glad that you forced her to use standard, more precise language. My oldest niece (an Economics major) took a 1-credit proof class in college that took more time than any of her 3-4 credit classes that semester. She now teaches honors algebra and geometry classes, and she spends a good bit of time on proofs with her students.

[Sharon in MD]

I know proofs are a pain....but you could theoretically say Algebra, Algebra, Algebra for several lines and then therefore...

The point of proofs is to make a student show logical processing and understanding of how to get from A to P depending on the complexity of the problem. It is easy to say...well algebra works...it is harder to show the step by step process that makes it so.

I know it is extremely laborious to do proofs, but I think there is huge cognitive value for the student in working through them. Not just for math, but logical thinking in general...these are important brain connections to form and I, unfortunately, think it is really worth the effort.
I'll be interested to see what others have to say.

[FloridaLisa]

I know it is extremely laborious to do proofs, but I think there is huge cognitive value for the student in working through them. Not just for math, but logical thinking in general...these are important brain connections to form and I, unfortunately, think it is really worth the effort.

I agree with EKS and Sharon. We're also working through LOF and, as much as I like it, I mutinied at his suggestion to simply list Algebra as a reason. My tried to counter-revolt, but I laid down the law on that one! Ugh. I was imagining a lazy mind using Algebra as a catch-all, rather than really thinking through what math properties/rules were required to prove the theorem.

I had my dc write the math properties/rules in their notebooks (associative property of multiplication, etc.) so that they could refer to them along with the other rules/definitions/postulates they are developing through the text.

Lisa

[Karin]

Thanks!:D This is what I was thinking, and now, armed with four replies that all agree, I'm going to stick to this. However, I might let her do each book their way since I'm making her do two books and have to choose my battles carefully. But learn to do them with Dressler for sure, she will.

Of course, I semi secertly hope for a math major someday, even though none of my dc think they want to do that.;). It will be up to them, of course, but they'll be equiped just in case they discover a love of math down the road.

[Karin]

(and it's as easy to write "addition" as it is to write "algebra", or it should be for a 14yo).


Writing it is easy, but she claims it's too much memorization and that her brain doesn't work that way. Not that I buy that, but it's true that she had to learn her math facts by doing and not by rote. However, she did memorize those and has memorized many other things that need to be memorized in math.