The best teacher I ever had was my computer science teacher from grades 11-12, and it seems he used many of the same improvements that are shown here.As soon as we had the learned the basic syntax we needed to write a program, he started giving us problems that are well beyond what any of us would expect ourselves to solve, things that may already have been finished in the programming community, but we were learning it as if we were the ones creating the algorithms. There is a thrill to looking at an impossible problem, with almost no help, except the assistance of your classmates, and trying to figure it out before an imminent deadline. Strangely, we always made it in time. :) You never forget the answer, because your mind was changed in the process of coming up with it, and with each breakthrough the next next one seems easier.
However, there is a problem, my class had a pretty high dropout rate, even of those who were eager to program in the first place, so I am guessing that most people really cannot cope with an environment like that unless they are brought into it at an early age. What would it be like if we took a page out of one of your stories (the title escapes me), brought preschoolers out into the mountains with a herd of sheep, and put them in a situation where they needed to invent addition? After that, a few nudges would put them on the track to invent every other facet of the mathematical system, and eventually they might be strong enough that they could catch up with the more advanced stuff our way.
There is a series of textbooks for grade/high school math called Art of Problem Solving that focus heavily on deriving one’s own solution to the problem given evidence and maybe a hint or two. Not useful for those of us who are already out of school but could be used to train young’uns.
The best teacher I ever had was my computer science teacher from grades 11-12, and it seems he used many of the same improvements that are shown here.As soon as we had the learned the basic syntax we needed to write a program, he started giving us problems that are well beyond what any of us would expect ourselves to solve, things that may already have been finished in the programming community, but we were learning it as if we were the ones creating the algorithms. There is a thrill to looking at an impossible problem, with almost no help, except the assistance of your classmates, and trying to figure it out before an imminent deadline. Strangely, we always made it in time. :) You never forget the answer, because your mind was changed in the process of coming up with it, and with each breakthrough the next next one seems easier.
However, there is a problem, my class had a pretty high dropout rate, even of those who were eager to program in the first place, so I am guessing that most people really cannot cope with an environment like that unless they are brought into it at an early age. What would it be like if we took a page out of one of your stories (the title escapes me), brought preschoolers out into the mountains with a herd of sheep, and put them in a situation where they needed to invent addition? After that, a few nudges would put them on the track to invent every other facet of the mathematical system, and eventually they might be strong enough that they could catch up with the more advanced stuff our way.
There is a series of textbooks for grade/high school math called Art of Problem Solving that focus heavily on deriving one’s own solution to the problem given evidence and maybe a hint or two. Not useful for those of us who are already out of school but could be used to train young’uns.
The story you refer to is The Simple Truth.
Thanks