On Jun 3, 2013, at 7:32 PM, kirby urner <firstname.lastname@example.org> wrote:
> Basic finding an unknown, rules of equality, we can call those "algebra skills" and we can keep weaving in that same material.
That isn't algebra. That is the dumbed down version that it became after decades of mass trying. That is algebra after you strip it of its art and sense. Algebra is making sense of one or more mathematical relationships and using that sense as the means to some mathematical end. It isn't any particular result or some finite set of instructions like the recipe for banana bread. That is why I don't care how many computers you have. Without that sense and art you can't apply those computers to "algebra" any more than a chimpanzee can write Shakespeare using a typewriter.
This happens to many teachers. Day in and day out they are going through the motions of teaching mathematics to brand new faces and they forget the point of the process. They forget the pedagogy and development or they never understood it in the first place. Or I suppose they are charged with really difficult cases. They moan "Why am I teaching kids to add numbers? A calculator can add numbers!" And I tell them "You are not teaching them just to add numbers. You are teaching them the sense of ADDITION, and if you don't use numbers what the hell are you going to use?" We don't need to teach children that calculators can add numbers. We need to teach children what "add numbers" means. There is no other way to do that with sufficient payback (acquisition of senses) than to have children add numbers. The same applies to algebra. You cannot show students how to solve with tools (computers) before they have developed the personal sense of what "solve" means. They have to experience it and the nuances of it. Mentally.
You are in a state of euphoria about all the things a middle aged Princeton educated man can talk about but your chief problem is that you seem to have no recollection or sense of how you got to where you are. You want to start these kids at the end of that journey, rather than at the beginning. Yet, in previous discussions you are quick to defend older texts like Dolciani. If I were you, I would get a copy of a textbook you studied as a child and go through it start to finish and try to put yourself back in that time. Try to remember the discussions and exercises and your transition from not knowing to knowing.
There is no easy button to all of this. There are more computers in this world and they are more powerful than you or I would have ever imagined as children. And everyone has one. There has been no math revolution because it has nothing to do with computers. It has to do with thinking and being smart and the technology of thinking and being smart hasn't changed in the last 50,000 years and will not change in the next 50,000 years.