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I am approaching this all wrong, can someone guide me?


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I keep asking for advice on specific math (algebra) programs, and I think I should be asking for help on what methodology or technique I should use for my daughter. Her brain works differently than most. She does not do well with introductions to a problem, or lengthy instructions on how to do something prior to the problem.

 

Her method is to look at a problem and then attempt it without any introduction whatsoever, just jumping right in. She then backtracks to see where she has gone wrong. She pieces the steps together on her own and tries to recognize a pattern. Of course after a few problems she has figured out how to do them (she sees a pattern) t but she has never fully grasped why. She is impatient and moves on to the next problem, which, unfortunately, she will solve in a few short moments (through induction) and again, plow on.

 

If you try to explain it to her in terms of rules of Algebra it's like talking Greek, the words mean nothing, they actually confuse her. She likes to know what to do with the numbers/variables, why, and see it all in action. After a few seconds she understands it--the pattern--and can solve the problem. But she has never understood why her method works.

 

She is a whiz at decoding patterns--CryptoQuip, Cryptograms--and her precociousness with this kind of stuff has unfortunately gotten her into a jam.

 

Anyone who has been there, done that who have an idea on what type of method would work best?

Edited by distancia
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Have you looked at Art of Problem Solving? The way the books are set up seems like it would be a great fit for your daughter. It throws several tough problems at you to figure out, then explains the solutions to each of them after the student has worked them out, then gives you a bunch of similar problems to solve. It does explain the "why," but only after the student has tried to work through the concept on their own, and a lot of the teaching is along the lines of "don't make this mistake" or "be sure to remember [whatever]" rather than telling the student exactly what to think or how to solve the problem. They also have online classes, if that's something your dd would be interested in.

 

Jackie

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Life of Fred, may help. Although there is teaching in the story, students are often given problems to work before a full explanation is given; explanations are then supplied in the answers. Also, he is brilliant at taking complicated instructions and explaining them simply. This is one reason many think it's too easy. The drawback is that there may not be enough practice problems for your dd, but that's easy enough to rectify if you do Key to Algebra or another text along with it.

 

One thing I do suggest is that even if she figures out how to do a problem she then learns the explanation, as people have said you do in Art of Problem Solving. I have a dd who was very similar to this, and I took an entire year before starting Algebra so that she could learn the linguistic aspects of math. It's important for developing logical thinking skills. There isn't only one way to do everything in Algebra (you'll see this if you look at enough Algebra texts), but it is important to learn logical thinking skills.

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I did fine with my own style of 'learning' through Algebra 1 and 2 (self paced independent study). I had my own 'quirky' methods that worked for me--but I really could not explain HOW or WHY my methods worked (most of the time).

 

When I got to college level maths I realized that I had done myself a disservice! I had to go back and LEARN the traditional steps to basic Algebra... my unique mental ones were not enough.

 

I guess I'm trying to say that you should keep fostering your dd's unique logical prograssion--but she also needs to see/learn the reasoning behind more traditional methods--because in higher Maths she will need to PROVE how she got her answers...

 

I think she should enjoy the challenge of the AOPS materials--but she should also be exposed to more traditional problems.

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I did fine with my own style of 'learning' through Algebra 1 and 2 (self paced independent study). I had my own 'quirky' methods that worked for me--but I really could not explain HOW or WHY my methods worked (most of the time).

 

When I got to college level maths I realized that I had done myself a disservice! I had to go back and LEARN the traditional steps to basic Algebra... my unique mental ones were not enough.

 

I guess I'm trying to say that you should keep fostering your dd's unique logical prograssion--but she also needs to see/learn the reasoning behind more traditional methods--because in higher Maths she will need to PROVE how she got her answers...

 

I think she should enjoy the challenge of the AOPS materials--but she should also be exposed to more traditional problems.

 

 

So AOPS doesn't have traditional problems? Also, Jann, do you have any suggestions for convincing 12 year olds who plan to go into art or history even though they are mathy of why they should do this? Even though dd is showing me steps, she is doing it reluctantly. I used to do Algebra my way, too, but I could show some of it & had the ability to do it the textbook way even if I thought it slow & boring. Dd can do it their way now, but hates it. This isn't my extremely stubborn dc, though. She's the one I plan to have take Geometry with you eventually.

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