If you are fortunate enough to get your hands on a copy of The Search for Solutions (no, you can't have mine – it's one of the few hardcover books that I have retained), you will find an interesting story of a young girl, aged eight, who, like my boys, was as yet unspoiled by an educational system that force feeds children with information and demands that they regurgitate it without thought. She “...had just stumbled onto the fact that some numbers are prime... She called them 'unfair numbers...' because there's no way to share them out evenly.” My boys, too, understood well the concept of unfairness.
Almost every class began with a demand that I give them a riddle to solve. They rarely had anything to do with piloting, seamanship, or small boat handling. For example, I once challenged them to figure out how many handshakes it would take for each of them to shake hands with every other boy in the room. They huddled up and decided to model the problem. They formed a line against one wall. The first boy shook hands with each of the others and wrote the total on the board. The next did the same, omitting the boy who had already gone ahead. When the last one had no one left to shake hands with, he added the numbers written down by the others. It was a fair and correct solution for a group who had never studied algebra and could not craft a formula to solve the problem.
What you probably are missing at this point is the fact that had the Deputy Probation Officer in the room and I smiling. Many of these boys were rival gang members and it was miraculous to see them shaking hands with each other. Ordinarily, they would be fighting tooth and nail, often with knives and firearms.
Now, some of you may wonder why I never became a real classroom teacher. The simple truth is that most teachers I have known have told me that the establishment would have destroyed me. I tend to agree with them.