I am firm believer that in education, you must first start with where you want to get to, and then build a path to that goal. As I have lamented, there is a huge need for better and broader research to assist in knowing where we should go. (Although only part of this can be solved with research, as there are also inherently values and normative statements in this mix, which research cannot determine.)
But, with the research we do have, and my personal knowledge, I can see that in our technological environment, there is a need for different foundational skills and knowledge than the traditional. In fact many of these were part of “New Math”. But “New Math” was such a failure, that if I even mention it to someone, they nearly look at me in horror!
Here is what I see as the root cause of this and results:
- In our species deep past, only simple mathematical processing was generally required to survive.
- Therefore, through biological evolution, our brains are naturally wired in a way that can calculate these types of traditional problems.
- Our technological evolution has only recently needed different knowledge and skills as are contained in “New math”, and further only recently could we as a species even recognize that understanding the basis of ourselves (quantum physics, etc.) requires a different type of logical processing than the basic arithmetic of the past.
- Therefore, most people still have a past mental model of mathematical concepts, and democratically they can not see in sufficient mass the need for the different models.
- Because New Math was pushed onto the populous without them being able to understand it, and pushed onto children at a development cycle that was likely completely the wrong time for them to learn such concepts (or at least was presented in a way that did not match with their developmental stage), New Math was a failure.
- All of this makes bringing these concepts back again a challenge.