I had completely forgotten how many "fun" math books we read to supplement what was happening in school. I was very worried that DS would think that math was *just* about calculation and not about the big fun ideas. One book we liked was called (I think) , The Adventures of Penrose the Mathematical Cat. We used it as a bedtime story and then would work the problems together.
Another thing that kept DS thinking was that the state standardized test auto-leveled, so when he got a question right, he would get a harder problem. The test was not timed. He was definitely getting algebra questions by 3rd grade (which resulted in his desire to learn algebra) and would take as much time as he wanted to try to figure out how to do the problems, usually problems he had never seen before. He'd be in the test room for hours and often missed recess. I thought it was cool that he liked to try to puzzle out things he did not know how to do. It seemed good to let him try to work on things he hadn't been taught; it gave him a chance to look for patterns and come up with novel approaches rather than just following the rules.
Based on this I wonder if it would work for other kids to present them with above level challenge questions and then give the kids time to work on them without giving them direction. In this case it seems right to then reward (however you want to define reward) them for their thinking and attempts, rather than correct solutions. It seems like this might foster creative mathematical thinking, which is not what the school is doing.
