While I was out of town, I left DD a division problem to convert to words, and she was not successful - every word problem she wrote was a multiplication problem.
When I got back, I gave her a sheet of paper with "Write the equation you need to solve the problem. A full set of blocks has 100 pieces. How many blocks does Alex have if she has" across the top, and a list in the form "x sets" down the side. She filled it in in no time at all. When x was a whole number or decimal, she correctly wrote a multiplication problem. When x was a fraction or percent, she wrote a division problem. Oh, dear, not good. And completely consistent with our observation that she was almost always fine with whole numbers and almost always wrong with fractions.
So I talked at her for a long time, while she sat with her fingers in her ears. "I'm bored!" "Nope, you're frustrated. Bored is when you already know the answer, not when you don't know it and really wish you did."
Finally, I said, "If this were a multiplication problem, do you have the two factors, or one factor and the product?" And she could answer that question for every problem I threw at her. And knowing the answer to that question, she could correctly identify whether the word problem called for multiplication or division, and could set the division problem up in the right order. Every single time, without hesitation.
OMG. That is not a gap that would have been remediated in the classroom. Time might have resolved it, but I don't think time alone would have been sufficient. I had a similar mental block years ago in my professional life, where I always arrived at the right answer in my workpapers, but wrote up the entry that changed the official records backwards. And I did that for years (like 10 years - long past the time my work was being reviewed routinely), making the change, checking the results, and reversing everything because it was backwards. Then one day I suddenly realized how the workpapers related to the change entries, and I never made that mistake again.
Kid-who-learns-by-epiphany is hard to teach. (And as an adult who learns by epiphany, I can attest that it is a frustrating way to learn, too, when the epiphany does not come quickly.)
