Parent Pulling Her Hair Out

Date: 03/03/2001 at 19:00:48
From: Carol Parent
Subject: Parent pulling her hair out!

I'm very sorry to bother you, and wouldn't, BUT am at my wits end.  I 
am helping my son with his homework and we have become stuck on a 
problem. We would very much like to solve this.  

This is the problem:

(x+3)^3 + 2(x+3)^2 - 8(x+3) = 0

I get as far as 

x^3 + 11x^2 + 21x + 21 = 0  

and get stuck. What am I missing here?

Any input would be greatly appreicated. I keep thinking I am doing 
or missing something in one of the earlier steps, possibly how I am 
working with the numbers in the ()'s that need to be squared or 
cubed. Thanks again.

Carol

Date: 03/03/2001 at 19:47:05
From: Doctor Mitteldorf
Subject: Re: Parent pulling her hair out!

Dear Carol

There are so many things I want to say to you, starting with 'Don't 
apologize!'  We're here to answer questions. We're doing it as 
volunteers because we enjoy it. I'm glad you wrote to Dr Math and gave 
me the opportunity to think about this with you. You needn't wait 
until you're at your wits' end.

Second: It's your son's homework, not yours. He comes to you for help, 
and what he really needs is support and encouragement. Get him to 
think out loud, try other things. You can do this even if you don't 
know the answer yourself.

I'll tell you a story. I used to work in a think tank with other 
physical scientists. People would come into my office when they were 
stuck, and I'd "help" them. All I did was to listen to them and nod as 
long as they sounded confident, and when they started to sound 
uncertain, I'd say "explain that to me again - I'm not sure I 
understand it."  Well, many a scientist solved his own problem at that 
point, and I was credited with being a "brilliant" resource.

Third - I'll take the same advice I've been giving you: you don't need 
an answer, just encouragement and a direction. They gave you an 
equation about (x+3). You turned it into an equation about x. But 
actually the original was much easier to solve. Think of (x+3) as an 
entity unto itself. If it helps you, rewrite the equation putting a y 
wherever there was an (x+3). Then solve for y and subtract 3.

You still have a cubic this way, not a quadratic (which would be old, 
familiar territory). But if you step away from the problem for a bit 
and come back to it, I'm sure there's something you'll notice that 
will let you simply turn it into a quadratic.

Solve it yourself, to be sure.  But don't then give the answer to your 
son - just encourage him to keep trying different things until he gets 
it. The name of the game is to have interesting experiences exploring 
mathematics, not to get to the one and only right answer as fast as 
possible. So we redefine success: success is an enjoyable challenge, 
with exploration, trying different ideas, and honing of mathematical 
skills.   

One more thing: Your hair is quite fine just the way it is. You don't 
want to teach your children anxiety. Teach them instead to enjoy their 
explorations.

Please don't hesitate to write back - tell me you got the answer, or 
tell me you need another hint, or just tell me how your son responded 
to this new attitude...

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/   

Date: 03/03/2001 at 20:22:56
From: Carol Parent
Subject: Re: Parent pulling her hair out!

It worked EXCELLENTLY!

It took 30 nano seconds to do a problem that I had literally been 
working at for 2+ hours. (Yes, I know it was a bit obsessive, BUT I 
HATE not solving puzzles. I spent much time going through the books 
trying to "see" what I was missing, when it turns out I just needed to 
"see" the problem in a different way.)  I had told my son we would go 
over it later, so no, he didn't "see" my frustration.

You totally made my evening!  I can put it to rest now and discuss it 
with my son in the morning (plus the neighbor girl who is also having
difficulty with factoring).  Have a very wonderful weekend!

Carol