Going deep could include working on physics and chemistry knowledge that is accessible with that level of math.
He is learning math because it is a tool for him, not a goal in itself.
Very good points. This is often the carrot that we choose to dangle under my "live and breathe science" kid. But my son would still prefer to race ahead to algebra, since that is where the cool and exciting ideas are. He sees calculus as something akin to Harry Potter's magic wand, and the faster he gets there (according to him), the better.
It is like DS8 is dreaming of running down the sidewalk to another place, when he is still learning to crawl in his own small yard. He can see down the street. He knows it is there, just waiting for him. And he doesn't understand why he can just get up and go. As a parent, you feel as if you are constantly trying to hold these kids back and slow them down. Yes, they have to master the finer details. But at what point do they just give up the dream of running free?
Just around his 8th birthday, DS was sitting and eating lunch, staring off into space. He then asked, out of the blue, "How do you calculate the volume of a cone?" And I responded, "Gee, I don't know. How do you calculate the volume of a cone?" He then preceded to tell me that if you know the area of a circle, which he does, then you could stack consecutively smaller circles upward to fill the volume. Or, he said, you could take a triangle and rotate it through a circle to fill in a cone. He is already doing the beginning steps of calculus, without any instruction at all. So much for the Calculus Trap! It is not determined by how fast the material is presented to them. It is determined by how quickly they invent the material all by themselves.
If you don't feed it along the way, it will die from neglect.
