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I don't think that my daughter does not KNOW the material...I think she's just really, really good at convincing herself she doesn't.Â

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If you think she knows the material, then insisting on going over the same ground in the same pencil-and-paper way day after day is quite pointless, I think. It's just an exercise in whining and resistance, entrenching those behavioural patterns and negative associations. Your instincts that she knows the material and has the skills are likely correct, and I doubt she's really "convincing herself she doesn't." Instead I'm guessing that she's feeling something else about the math work that she doesn't know how to articulate, and it's coming out as a sort of indiscriminate whining. The real message beneath the resistance is likely something like "this isn't how I learn." I think I would really really start thinking outside the box for ways that aren't pencil-and-paper to carry her math learning forward. At least in the medium-term, to try to get a better handle on her learning style and to try to break the negative association with math.

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I agree with SweetSilver that the approach of having a child do assigned work and then checking it for correctness can be very toxic to some children. They feel like it's all about judgement, and every error is a failure. For my kids it helped to do the work on a white-board, rather than on paper, and to have me help them with any problems they began to go astray with. With prompts and redirection they were always able to get the correct answer. Then we'd wipe the board and go onto the next problem. Using the white board got rid of a lot of that implication that they were creating a tangible record of their lack of perfection, and also the implication that doing math was about completing worksheets. I wanted them to know that doing math was about learning. At the end of a session, there was no record of work done, only the knowledge we both had that they were able to solve certain types of mathematical problems logically and accurately.

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I could tell the extent of their mastery by how much help they needed to get to the correct answer. If they wanted to work entirely independently I'd give them an answer key. They could work the question, and check that their solution matched the answer. If they couldn't figure out how to arrive at the given solution, they could come to me for help. Again, we both knew that it was about learning, about understanding, not completing problems.Â

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If I could tell they were struggling with something, I would address that area at the beginning of the next session, not as a correction or remediation after the current session. The message was therefore "I have an idea that I think might help you move forward" rather than "You did this wrong today and we need to fix it."Â

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My whiteboard example is still very much about working problems with written symbols. For the time being I think it would be worth discarding that model with your daughter and taking a much more wide-ranging, playful, experimental approach to math. Play guessing games: Ask her "how old were you five years ago?" And "How long ago was 2008?" And "Here's a really tricky one: What's a number between twenty and thirty, and when you subtract the one digit from the other, the answer is six?" Or play Snakes and Ladders, but allow her to move forward or backwards (adding or subtracting) to get the most advantageous move. Teach her how to use an abacus counting frame to add and subtract. Play "store" with pennies and dimes, selling each other pencils for 5 cents each and pens for 7 cents. Make change for the dimes you pay each other with. Learn cribbage. Build a spinner from a paper plate and create a board game together with adding and subtracting along a number-line gameboard. Build a 20-minute "math lab" into your day in the same way that you currently have worksheets or whatever. Use those activities and experiences to build your understanding of what your dd understands about math, and of what grabs her interest and gets past her resistance most easily.Â

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Am I correct in understanding that she has a younger brother who is almost as adept, or perhaps more adept, at the worksheet type stuff? That can be very very difficult for an older siblings. Her resistance may be her way of saying "I am afraid I am stupid, and therefore unloveable, because my little brother learns better than me. If I finish this work, that provides more fodder for comparison, and I'm afraid I will be the loser." If you suspect any of that sort of emotional overlay, your main priority will need to be making her feel smart. Tell her that there are snatches of absolute brilliance that you see in her mathematical reasoning, and you haven't yet discovered how to really turn all that brilliance on, but you know it is possible because you've seen that it's there. So you're going to mix things up a bit and figure out how to help her learn math *her way*.

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John Mighton, author of a fabulous book called "The Myth of Ability" and founder of the charitable tutoring organization called JUMP (Junior Undiscovered Math Prodigies) has some amazing advice about unlocking belief in the sense of math, and belief in one's ability to understand that sense, and the absolutely transformative results on children. The secret is to give the child success, and encourage her to believe that she is brilliant because of that success. And by success, Mighton means steps as small as finger-counting. He starts out by moving ahead into new skills well ahead of where the child is, and teaches them the smallest step at a time. For instance, you could teach your dd division by showing her how to count up groups on her fingers. Divide 12 by 3? Every time you hold up a finger, count up three numbers. Stop when you get to twelve. "1-2-3 ... 4-5-6... 7-8-9.... 10-11-12." Four fingers standing, so 12 Ă· 3 = 4. Have her do this. Is she successful? Did she get four fingers standing up? She can do division! She's brilliant. Try 12 divided by 2. That means saying two numbers every time you hold up a finger. Whoa! Six fingers!Â

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I would do this independently with her, without her brother around. Let her feel smarter than him in that she is learning division, and he is not. Give her something that she can do mathematically that makes her feel brilliant, and then begin to build on that.

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Good luck!

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Miranda

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