I'm not sure if we're late to long division compared to other homeschoolers or even the local school kids but yesterday Catherine got her first exposure to it. It went...Okay. I let my husband do most of the work explaining and while he was at her side she did well. When he wasn't by her side she was unsure of what she had to do.
Today the husband's at work and Catherine and I were left to explore it on our own. First thing I did was prop up the big dry erase board and opened the new pack of dry erase markers. Math is much more fun done big and in a variety of colours. I wrote a problem down and Catherine picked a colour and began working. We went through four problems and she was still having problems remembering the steps. Then I started diagramming what she was doing as she did it.
Warning. This sounds daft.
She'd be faced with finding out how many times 4 went into 9. I'd draw and arrow to the right. She'd have to write 2 on top. I'd draw an up arrow. She'd multiply 2 by 4 and as we're working left, I'd draw and arrow going to the left. She's write 8 below the 9 and I'd draw a down arrow.
This didn't help her at all.
But when we both realized that the arrows roughly represented a circle and I blurted out that she simply had to work each step in a circle, cycling back to the same starting step and to begin again and then she got it. Long division went from a confusing and patternless process to simple cycles of just a few steps each. She was thrilled and starting drawing circles to cement the image in her head. After that, with that image of the circle, she declared long division was easy and fun.
Our process - "The Divine Circle of Division"
(Hokey name but we were reading about Pythagoras the night before)
I sometimes think the next best thing to having a teacher that knows a subject inside and out is having one who's almost as clueless as the student. That's certainly me. When encountering something like long division I'll approach with no ideas of how I need to teach it but rather come up with an idiotic-seeming idea like making a picture of the process that turn out to be just what my daughter needed.