Pre-Calculus... Calculus- Must you understand proofs

[CathieC]

Ds is taking pre-calculus. He doesn't understand how to do the proofs.... they are so different each time. There doesn't seem to be much on proofs after next weeks lesson. Is this one of those things that he can move on, and not worry about, or is it something crucial to getting most of pre-calculus, and calculus? Normally, math is easy for him but this is bringing both of us to tears. I never took any calculus, and this has always been one of my fears as to homeschooling. We have used the curriculum support but each problem is so different that we're back to square one with each attempt. He's gotten a few correct but most are mind boggling... Need insight asap.

[creekland]

It will totally depend on his college profs. Some absolutely love proofs, others just show them to students and move on. IF he is looking at a math heavy major he is more likely to get the first type. If he isn't he's more likely to get the latter.

Proofs come in many different types - from Alg to Geometry to Trig Functions and more. They are simply a mathematical way of "proving" what is known to be true. Some are trickier than others. Since it's Pre Calc, are you in the Trig Functions proofs? If so, those tend to be less needed than some others... They are barely taught in our school nowadays... but keep in mind I'm homeschooling my own kids because our school falls behind the curve in math education...

[CathieC]

I homeschool mine for the academics too. This is the first time I've considered just not worrying about it. He didn't have issues with them in Geometry. Yes, it is trig functions. I'm clueless in the area. He is thinking about about Computer Science w/ a concentration in Info. Technology. Only the first two semesters of calculus are listed as being required at the school he plans to attend.

It will totally depend on his college profs. Some absolutely love proofs, others just show them to students and move on. IF he is looking at a math heavy major he is more likely to get the first type. If he isn't he's more likely to get the latter.

Proofs come in many different types - from Alg to Geometry to Trig Functions and more. They are simply a mathematical way of "proving" what is known to be true. Some are trickier than others. Since it's Pre Calc, are you in the Trig Functions proofs? If so, those tend to be less needed than some others... They are barely taught in our school nowadays... but keep in mind I'm homeschooling my own kids because our school falls behind the curve in math education...

[MomsintheGarden]

My son is double majoring in math and computer science in college. We did Chalkdust for his high school math (Geometry - Calc I). We didn't emphasize proofs in his math, except for geometry. He would do perhaps one proof per math section, if that. CD does have a lot of concept-testing problems, though, even if they aren't formal proofs. Right now he's doing his first proofs class in college, a junior level course. I was a bit nervous that he might not do so well in it, but he is getting an A so far.

I would try to do SOME proofs, but don't worry about them too much. Try for one per section if you can (and if it's a section that has proofs as problems). We have a 20 minute rule in our house. If one of my students has put 20 minutes of productive effort towards a problem and hasn't finished, he puts it aside. Later in the day, I check his work and we do the missed and troublesome problems. I then either coach the student through the problem or we look at the solutions manual together. If it's something I really think is important, I have him do a similar problem (easy with Chalkdust, because the evens mirror the odds). Otherwise, we're done.

It is VERY important for him to understand trig and memorize as MANY trig function relationships as possible. Ds did the AP Calculus AB test and got a 5; he also got an A in Calc II at college. The one thing he said he wished he had spent more time on in high school was memorizing his trig relationships. At the end of his first semester he said he really knew them because he had to:)!

ETA: He is in a scientific computing-type CS major, so it is very math-heavy, so much that he wouldn't have needed to take any more math courses to get a math minor. Other CS majors, such as those that focus on IT, may not require as much math. YMMV.

HTH,
GardenMom

[CathieC]

I would try to do SOME proofs, but don't worry about them too much. Try for one per section if you can (and if it's a section that has proofs as problems). We have a 20 minute rule in our house. If one of my students has put 20 minutes of productive effort towards a problem and hasn't finished, he puts it aside. Later in the day, I check his work and we do the missed and troublesome problems. I then either coach the student through the problem or we look at the solutions manual together. If it's something I really think is important, I have him do a similar problem (easy with Chalkdust, because the evens mirror the odds). Otherwise, we're done.


Thank you so much, what a helpful suggestion. A limit on time. The longer he works, the more frustrated he gets, and nothing gets accomplished. :)

[creekland]

Trig function proofs/identities are a bit like a puzzle - moreso than other types of proofs IMO. Some very talented math kids don't get them and some less talented math folks get them easily. I think it's more of a logic and pattern thing than typical math.

I like the suggestion made of a time limit - but do be sure you go over the answers. Most kids see them easily when you go over them. What gets some is the thinking outside the box to rearrange... but the more they see ones that work, the better they often get at figuring them out themselves.

[CathieC]

What is frustrating is trying to figure out the logic. It doesn't seem nearly as logical as algebra! We are starting the time limit thing today. Not to worry, we'll still go over the problems he doesn't finish. However, the only guidance we have is the solutions manual. We can do livechat (or call) with the curriculum provider but that seems harder to do with this type of problem.

Trig function proofs/identities are a bit like a puzzle - moreso than other types of proofs IMO. Some very talented math kids don't get them and some less talented math folks get them easily. I think it's more of a logic and pattern thing than typical math.

I like the suggestion made of a time limit - but do be sure you go over the answers. Most kids see them easily when you go over them. What gets some is the thinking outside the box to rearrange... but the more they see ones that work, the better they often get at figuring them out themselves.

[CathieC]

Thanks to all for their input. Yesterday went much better. I gave ds a time limit for each proof. He got 2 out of 4 correct on his first attempt. One we worked through using the solution manual. He re-worked one on his own since he was close, and had an ah-ha moment. I'm so much more relaxed about this area. I can't tell you how much I value the Hive's input with this one!:bigear:

[MomsintheGarden]

Thanks to all for their input. Yesterday went much better. I gave ds a time limit for each proof. He got 2 out of 4 correct on his first attempt. One we worked through using the solution manual. He re-worked one on his own since he was close, and had an ah-ha moment. I'm so much more relaxed about this area. I can't tell you how much I value the Hive's input with this one!:bigear:

2 out of 4 is fine! And those ah-ha moments are what make homeschooling worth it for me! It is so good that you are coaching him through this - he will learn so much, and you will find that you have to get fewer hints as time goes on.

Best wishes,
GardenMom