February 22, 2012

It's a Sickness

I'm tutoring the little girl down the street in PreCalc and they're on the Trig section.

They've had a teacher problem, as in something happened to their PreCalc teacher in November, and suddenly an Alg II teacher was told, "OK, you're teaching this now."

PreCalc is just Alg II on steroids, but she didn't have the luxury of having the summer to know the book and develop her own lesson plan with her own examples, so she's literally one step ahead of the class.

The good thing about having taught a class before is you know what problems to assign and what problems... not to.

So Monday she assigned the homework, the girl is totally lost, I went over and helped explain, but the VERY FIRST problem assigned (which was actually #26)... was something weird and immediately I knew... it was bad.

I said to her, "Look, we're going to skip this one. I can tell this one is ugly. Let's skip this, I'll go over it at home, and when I know what the answer is, I'll have you do it and I'll keep you on track."

So last night I came home and spent a good hour working on this one problem, catching various Alg mistakes because it was late and it was... a long problem.

She went to class today and her teacher apologized and said she had no idea it was so nasty, she promised nothing would be on the test like that, and she held up the piece of paper full of her calculations.

A paper that probably looked very much like this:

Trig.jpg

I give the teacher BIG credit for doing all the homework. My issue is with the textbook company.

Really? I don't know one Junior in HS that could pull this out of their hat. OK, maybe ONE, but that's one kid out of a lot of kids I know.

This is nuts...

But really, what does it say about me, that I had no qualms sitting there doing it until I knew I had it right? My eldest shook his head and said, "Mom, I can't believe it..."

However, I sent it to reader Peggy U, and she COMPLETELY gets it.

We're both sick...

Posted by Boudicca at February 22, 2012 10:14 PM
Comments

Forgive me, but what the heck does any of that have to do with surviving in the real world. How does knowing how to do that help you in running a business or getting a job in corporate America?

We have computers now. I'm not sure that this even has much to do with programming.

Even wayyy back in my day, I didn't understand the point of it. Back when all we had was calculators (and we had to sneak them in!)

Can somebody tell me the point of all this hieroglyphic math?

Posted by: DogsDontPurr at February 23, 2012 01:31 AM

You got to be kidding. That is just crazy. But looks like fun. Yaa... I miss math. Well, the math that actually makes you think, not the timed subtraction stuff my kids are doing. Ugh. I can understand learning how to do advanced math, it shows you can figure out a puzzle... but timing it? Really? Why do it fast?

Posted by: vwbug at February 23, 2012 05:52 AM

DDP- Actually, it's thought processes and thinking. Problem solving. Logic. When you sit down and logically think through something, it's teaching your brain that. Even my student said something to me about it after we were finished. She said, "I know I will absolutely never use this, but I just feel like I'm thinking deeper."

VW- I don't miss the 'I'm a Master Regrouper' days! I'm really enjoying moving into the higher math with them. I already told T that we'll take Calculus together. I'm kind of excited about that. I haven't had Calculus since... 1983?

Posted by: Bou at February 23, 2012 06:30 AM

You are sick! I shouldn't laugh because my kids need you at times and you always come to the rescue!

Posted by: JD at February 23, 2012 07:52 AM

I LOVE this stuff! (Then again, I am a maths teacher, and I regularly give up my prep hour to help kids with Pre-Calc, Trig, and Calculus, so I have it coming...)

Posted by: amelie /rae at February 23, 2012 08:33 AM

cos^6(x) = [cos^2(x)]^3 = [1+cos(2x)]^3/8
= 1/8 + 3/8 cos(2x) + 3/8 cos^2(2x) + 1/8 cos^3(2x)
= 1/8 + 3/8 cos(2x) + 3/16 + 3/16 cos(4x)
+ 1/16cos(2x) + 1/16 cos(2x) cos(4x)
= 5/16 + 7/16 cos(2x) + 3/16 cos(4x)
+ 1/32 cos(2x) + 1/32 cos(6x)
= 10/32 + 15/32 cos(2x) + 6/32 cos(4x) + 1/32 cos(6x).

So your answer is wrong by 2/32 cos(2x).

To verify I did it right, try putting cos(x) = 1.

Posted by: Carl Brannen at February 23, 2012 11:25 AM

Crap. I need to find my math error. I broke it down very basic for her. I should b able to find it. Dang it

Posted by: bou at February 23, 2012 02:20 PM

Here's a fun test for those old brain cells. Try to write down the 12x12 times table in 5 minutes. (I did it first time in under 2 minutes with zero errors.)

http://vixra.org/osky/thetimestables.html

Posted by: Carl Brannen at February 23, 2012 07:17 PM

Bou - I think there was a cos(x) = cos(-x) error, since the sign on that should be + rather than -. At least that is where I think the discrepancy came from.

Posted by: PeggyU at February 24, 2012 01:27 PM

The sign on the cos(-2x) I mean. That should become a + cos(2x).

Posted by: PeggyU at February 24, 2012 01:29 PM

I was trying to think why anyone would want to do this as well, and then I thought maybe if you had to take the integral of that cos^6(x), that it would be easier to do if it were rewritten in an equivalent form. OTOH, I would think there might be easier integration methods as well, but I haven't sat down to try it.

Posted by: PeggyU at February 24, 2012 01:31 PM

BTW, that is such a Peggy-type error, it made me laugh. :D

Posted by: PeggyU at February 24, 2012 01:34 PM