My apologies! I got bounced off of the system. Assuming that the first protion went through, let me continue:
Now the point is that NOBODY can predict which of these ideas kids will pick up on, become excited about, and build on. NOBODY can. some people imagine that they can - but this is only because they have not tried lots of wlternatives with real live kids, or have not done so in appropriately-inventive ways. Any of these would have to be made user friendly - which definitely can be done.
When SMSG came along, they imagined that they did not need these zeroth-approximation preliminary trials. They could plan books, write them, and then try them out. Of course you can do this - but either your "new" program will not in fact be very different, or else you will be merely guessing at which things will work, which won't, and which need to be redesigned.
... which is just what SMSG did.
I worked with Page, with Beberman, had my own project (the Madison Project), with SMSG (as Begle's assistant, for one year, and as a writer for their books). I worked with ESS, with Zacharias, with Bob Karplus, with some of the programs in England, .... (and lots more, as a matter of fact).
SMSG was late on the scene, and was in many ways arrogant in their assumptions.
Look at part of what SMSG did for elementary school geometry: they lifte DEFINITIONS from traditional 10th grade Euclidean geometry, and had kids worrying about what what a "line" was, what a "ray" was, what a "segment" was, etc. -- in VERBAL terms! !
Now, we know that kids can be VERY interested in geometry, and can carry the study of geometry very far. But PRECISE VERBAL LANGUAGE is about the LEAST promising way to work with kids. You can reach all kinds of valuable goals - but we always made out better when we at least STARTED with tasks that kids cared about. (As one example: get kids arguing about how tall that flagpole is, and then challenge them to invent some method to find out. Kids CAN invent a great deal of trigonometry if they get interested in it. And I really DO mean that kids can INVENT it. In fact, our evidence seemed convincing that you cannot successfully TELL this math to kids, and you cannot successfully SHOW it to them - but kids CAN INVENT it themselves! We had to make films showing kids doing this, in an attempt to convince people that it really does work.
In large part, SMSG came along and swamped all of this very interesting work, because it was so huge (at one point it had 1,000 employees - not full time, obviously), and, in my view, because SMSG started out in the belief that they knew what ought to happen with children, and had no need to carry our elaborate exploratory preliminary trials before making key decisions.
Was it Leibnitz who said "Logic is the slow and tortuous method by which those who do not know the truth may arrive at it"?
I can do a LOT to substantiate my "facts".
The question is: Which of these was "the new math"? Not -- in my view -- SMSG.