Are proofs necessary for algebra 2 and higher?

[Michelle in AL]

I hope I can get some help from any math moms out there. Dd wants to go into the sciences probably and will take through calculus in high school. we are using Foerster's Algebra & Trig this yr. We are on lesson 1.7 and I'm stuck (she hasn't done the lesson yet). Foerster is asking you to prove different axioms. I can not do this on my own to save my life. When I look at the solutions manual I sometimes don't even see how they thought of that step. Are proofs a necessary part of upper math? Must she be able to do them competently or can we skip this?

[Jane in NC]

Are proofs a necessary part of upper math?

A good Calculus course will have students do epsilon/delta proofs of limits early on in the course. Instructors in good Calculus courses prove things in class and expect their students to follow the proofs, but students would never be expected to come up with their own proof of the Fundamental Theorem of the Integral Calculus. Students in good Calculus courses will prove corallaries and demonstate that certain statements are true for all reals, problems that require students to know the basics of how proofs work and how to deal with abstractions.

Some students only learn how to apply Calculus to certain situations like optimization problems in business. This may be fine for them but I would not call the course a solid Calc course.

Engineers may weigh in to say that the proofs are unnecessary, that the tool of Calculus is all that matters. That may be true for them, but so much of math and physics relies on proof. I just cannot see skipping them.

Did you student learn to how to prove things in her geometry course? By the way, those proofs won't go away. Foerster has a significant number of proofs in the trig section of the book. Again, I don't know a good trig book that does not have proofs!

Jane

[8FillTheHeart]

I'm trying to separate different math courses out in my brain, but I am pretty sure that Foerster's alg 1 book has the kids working simple proofs near the beginning of the book. I know that there is an entire chapter devoted to axioms and postulates in his alg 1.

[Michelle in AL]

Hi Jane, yes she did do proofs in Geometry and did well. She used Chalkdust Geometry. Hopefully, she will do better than I on these proofs as it certainly sounds like it is necessary. I think I'll spend some more time today trying to wrap my head around this.

[Michelle in AL]

Thanks for both of your help. I studied the lesson again and got out the solutions manual which helped tremendously. I was just using the teacher's manual at first. The solutions manual sets up the proof, where it looks like the teacher's manual skips the first set up line which was confusing me. I needed to see how they set it up first.
I think I can waddle through it, but I think I may need to get Math without Borders to avoid problems in the future.

[Laura K (NC)]

My son just finished lesson 7 on Friday... he spent three days on it That book started out strangely, imo. That first chapter is unlike any of the others in the book, thank goodness. I was panicking because I'm doing this book along with my son and I didn't remember any proofs in Algebra 2 from way back when, and didn't remember any proofs in college trigonometry. I went ahead a little and worked through some of the lessons in chapter 2 and I was so relieved that it seemed much more reasonable.

As I looked through the book, I noticed that it seemed occasionally to refer back to this chapter. I decided for my son to have him work through the proofs (which are more difficult than his geometry proofs) with the answer guide open, because that's the only way I could do them, and I asked him to work to understand the reasons for each step of the proof, even if he couldn't write out the proof himself. The theorems and such draw upon not only the body of the lesson, but the previous exercises, so you can't skip around and do just the evens or just the odds... you would need to do both. I found it maddening that I couldn't see a summary of the theorems and definitions that I would need, and I thought it was unnecessarily vague. It freaked me out, since last year Foerster's alg. 1 was nothing like this.

(I'm long-winded on this... it's only just recently driven me crazy so I have a lot to say!)

I'm going to use the review as a test. If you have noticed the test in the book, it seems like an honors-level type application scenario, and I'm not prepared to call my son's year an honors class. Having gone through this chapter, though, I do think my son will be better prepared to handle the rest of the book. It was heartening to me to see that no further proofs seem to be necessary in this text... or if there were, I couldn't find them when I was skimming through, looking for them.

Is your son working with a syllabus of any kind? I'm trying to decide whether I should buy one (Kolbe has three different ones for this book: one for alg. 2, alg. 2 trig, or just trig.), or just plow on through and allow extra time for the lessons as we need to with 1.7. We're planning to do just algebra 2 and if we get to any trig. chapters it will only make things easier when he does trig/pre-cal. next year, but I'm aiming mainly for mastery, not speed.

[Michelle in AL]

Hi Laura, I'm glad to hear I'm not the only one who had problems with this. I'm glad to know it gets better too. I don't have a syllabus, but I do have the teacher's edition & the solution's manual. The teacher's edition suggests 4 days for this lesson, so you were on track doing it in 3. The teacher's edition included all the steps to the proofs in the exercises except the first line to set it up. Once I saw the first set up line in the solution's manual I understood it a lot better.
I'm using the reviews as a test too.
Hopefully, the rest of the yr will go better!