Every morning before school I help Garnisham, one of the older kids, do his math homework. He needs someone to help him one-on-one for two reasons. Firstly, he needs someone to explain every question to him. Secondly, he cannot sit down and concentrate for long enough to do a math problem unless someone is constantly encouraging him. After a couple of weeks of helping him for an hour every morning, he now has more trust in what I tell him than whatever is written down in his math book.
I have been trying to teach him about math concepts instead of sheer memorization, and it has been very challenging based on his schooling. Yesterday we were working with graphs, specifically rotating points and shapes 90 degrees about the origin. In his book it said that if you rotate (x, y) 90 degrees clockwise, the point becomes (y, -x). He had no idea what the formula meant, confused the negative signs, and could never keep straight the formulas for clockwise and counterclockwise.
The problem was that he did not understand what rotation was. So I physically rotated his math book 90 degrees clockwise and started to explain the concept of rotation. I drew a graph with some shapes on it and physically rotated the piece of paper 90, 180, and 360 degrees clockwise and counterclockwise. We began solving problems by rotating the graphs instead of using the formulas. After a half an hour, he finally understood what rotation was. In the end, I was even able to show him how the formulas were derived.
We'll see what he remembers tomorrow, but today it seemed like he finally understood the homework he was doing.