Parent Pulling Her Hair OutDate: 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 |
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