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Fostering independent math problem solving

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Background:  My 10th grader has always struggled with math(and other academics).  But we keep inching forward and her attitude is good.  She has trouble remembering things or even remembering that it is something that she has forgotten :)     I want her to be better at problem solving – the ability to take a concept she has been exposed to/learned and to apply it to a different looking problem.  I want her to become confident at tackling a new problem.  My goal this year is to finish the last third of the Geometry book by Jurgensen (new and major health issues kept us from finishing it last year) and she is also working slowly through the AoPS prealgebra.  She is only in the 2nd chapter of AoPS Prealgebra.  Before Geometry she did Foerster Algebra I and before that she did MEP through most of Year 6.  When she completes the Geometry text I will have her review through an Algebra I text and continue the AoPS Prealgebra.   We will do Foerster Algebra 2 the next year or may start it in April to give her a little more than a year to do it. I am quite comfortable with math and have taught my kids through AP Calculus AB. 


I think my main question regards how to work through AoPS with her or how to move her to more independence with tackling problems.  Often during the  problem sets in AoPS she needs near continuous help.  Is that just what I need to do or is there something I can do to foster independence and increase her ability to struggle with it herself for awhile?


I’m also open to other options that you think will meet my goals and am open to suggestions for refining my goals. 


Thanks in advance,



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I don't know if this will work for you, but here is what I've done, both by accident and on purpose.  We'd be working together with a white board.  But, suddenly I'm called away to help one of the other kids, I'll be right back, see how far you can get, oops let me get the laundry in the dryer, etc.  Little by little, make that time longer.


When my student asked what to do next, I'd ask a question.  Figuring out what question to ask without giving it away is the tricky part.  Getting to that point where your student feels the thrill of solving the puzzle herself and wants more - that's the goal.  For my dd, while she didn't want me to leave the room and frequently asked for help, she still wanted to do it herself ("help me!!!  no don't tell me!!!").


Chapter 2 in particular was a huge change in perspective - for me :)

Edited by wapiti
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We've been using AoPS for almost 3 years. I find myself always telling Dd to just do something with the problem. Don't just hold the pencil and stare at the problem. Write anything down and start tinkering with it.


It's a long process but she has improved a lot with problem solving this year. It doesn't mean she gets it right each time, but that's our mantra - just do something, anything.

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Mark - thanks for the suggestion.  Is this for review/supplementing?  I could use this for the algebra 1 review we do.


wapiti - thanks for the ideas and suggestions.  This is what I needed to hear!  I have felt that some of Chapter 2 was not review from the Algebra 1 we did.  My 7th grader is also finding this chapter hard, so I am glad to know that it may become more independent after Chapter 2, at least for awhile.  I will try what you suggested.  I also just realized that I need to directly share the goals with her.  She has been doing every challenge problem, so I think I will back off a bit on those for awhile.


We are doing Geometry 3 days and prealgebra 2 days, but when Geometry is finished we will do the prealgebra 3 days and Algebra I review 2 days or something like that.


I love what you said here, thank you -  â€œ and what I loved about the  Prealgebra book when I saw it - is that for a kid who has forgotten some earlier math, this approach will put that math into a bigger picture context that will hopefully be easier to remember.  (Not to mention that you may be opening a window on math that she hasn't seen before and might appreciate)â€


Crazyforlatin – you have reminded me that we have not been doing this long nor consistently, and we have only been schooling a week this year.  Maybe with some steady work and some altered tactics we will see progress.  I will get more insistent about just doing something.  I say it, but then I think I am helping too soon and not requiring that she write something that she knows. 

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