It was a tough week tutoring the 11 year old in math. When she gets frustrated or confused, she shuts down and stops thinking. We hit a massive wall on Wednesday and it took days (and threats of finding her a different tutor!) to coax her out of it.
We've been doing proportions and ratios, which, now that I think of it, is actually one of the hardest subjects she needs to master before the ISEE. She has had a little exposure to everything else, but this comes out of the blue. It includes algebraic manipulation and a whole lot of reasoning.
But our problem wasn't even with ratios and proportions; it was with fairly simple fraction problems, sometimes with a variable, that she's been doing for months. She is able to do the hard problems, but got stumped on the easy ones. For example, here's a simple unit conversion problem. She couldn't get that you put the mile on the bottom of the second part, so that cancels the mile in the first part:
(Yes, I know that should have been 5280.) That is nothing but reducing fractions with words instead of numbers. She knows how to reduce a fraction! She kept trying to do it the opposite way, and got too frustrated to get it straightened out. This went on for two days in similar forms.
She also was adamant that I had told her, when you had one fraction equal to another with a variable running around, she needed to get the variable to the opposite of where it started. So, if the variable is in the denominator, you have to get it to the numerator (correct); and if it is in the numerator, you had to get it into the denominator (very incorrect!) Take this extremely easy problem:
All you have to do is multiply by 12 and you're done. Except she kept insisting that she had to divide by X! She couldn't accept that that was wrong, and switch to doing it the right way. She kept insisting and insisting that this is what I had told her to do!!! Finally, on the third day, the veil was lifted and she saw the light.
After several very frustrating days for both of us, we got through it. She'll need more time to let it all sink in, but she'll get it.