Are proofs necessary in Algebra I

[mommyoftwo]

I am comparing four Algebra I textbooks for my ds for this school year (Foerster's, Lial's, Prentice Hall, and McDougal Littell).  I was going down a CYT Mathematics Sequence Checklist that was suggested on this forum in another thread and I noticed that "proofs" are mentioned in a few places in this checklist. 

 

For instance:  "use number properties in proofs," "prove theorems related to slope, and "prove theorems involving multiplication and division."

 

I can't find the word "proof" in the index of Foerster's or Lial's.  Are proofs necessary?  Could it be listed as something else in the index?

 

Thanks,
Melissa

 

 

[kiana]

Did you find them in the other two indices? It'd be very rare for an Algebra 1 course to include much in the way of proofs (and frankly, I think that they should be at least demonstrated and problems assigned to the more able students), but Foerster's is an excellent course and Lial's is also very solid. Your child will not suffer in more advanced courses for having worked out of these.

[Gwen in VA]

Proofs can help students to really "get" the basic properties of numbers. While I wouldn't say algebra 1 proofs are essential, I would say that they can be VERY helpful for students, especially more able ones. The Houghton-Mifflin Algebra 1 texts by Dolciani incorporate proofs very effectively.

[mommyoftwo]

Kiana,

 

Out of the four texts I listed in the original post, the only one that I could find proofs in was the McDougal Littell Concepts and Skills book.

 

~Melissa

[Candid]

I've commented on this before: real proofs don't necessarily spring out and look like what moms expect them to look like. Singapore's NEM program endeavors to show students why things work the way they do in their math books. Never do they have two column proofs or even use the proof word. But the process is there. 

[Jann in TX]

Lial shows the 'proof' (rule used) next to each step in the text examples.  Students are NOT required to explain the proof.  Most Algebra 1 level students are just not there mentally--but they can still LEARN basic Algebra and they can see how it relates to arithemetic.

[letsplaymath]

Yes, proofs are necessary. But they don't look like what you are thinking.

• A "proof" answers the question, "How do you know?"

Therefore, when your student is working through a problem, periodically stop and ask about a step, or about the problem as a whole. "How do you know you can do that? How do you know that's what will happen? How do you know this is true?"

 

When he answers (or at least, when he gives any answer other than "Because that's what the book says"), he is giving an informal proof. Informal proofs are the best kind. Trying to be too formal tends to bypass a student's common sense.

 

 

[mommyoftwo]

Thank you so much for all the helpful replies.

 

Jann-- When you say that "Lial shows the 'proof' (rule used) next to each step in the text examples" are you referring to the words in blue next to each step of the examples? 

 

Thanks again,

Melissa