The mathematical points are correct. But miss the key educational fact that the ability to learn abstraction seems to be tied to puberty in most children. Therefore drawing a "gentler slope" of slowly increasing abstraction pre-algebra will cause problems for many children due to developmental limitations.
By all means lay as correct a foundation as feasible. But be aware of the limits that children have, and do not set them up for failure by ignoring those limits. (This was one of the failings of the "new math" movement.)
BTW none of this is to say that I'm remotely happy about the disaster that is math education. I just don't think that this is the right solution to it.
key educational fact that the ability to learn abstraction seems to be tied to puberty in most children
What is the evidence for this, in view of the fact that children in several other countries around the world learn the same things the author suggests that American children learn at much earlier ages?
For evidence of the age at which children improve on abstraction, look at Piaget's work. The onset of puberty is when children usually move from Piaget's concrete phase to formal operations. Before that age you need to keep things concrete.
The links you provide don't contradict this in any way, shape or form. My complaint about the proposed curriculum change is that it attempts to teach arithmetic proceeding from definition to result. That goes over kids heads. Children learn better by repeatedly doing concrete operations that exercise the underlying concepts. The examples of Chinese teachers demonstrate good ways of doing that.
In short I'm complaining about pedagogy, not content.
Re-read http://www.cbmsweb.org/NationalSummit/Plenary_Speakers/ma.ht... with this in mind. I don't see children being challenged with abstraction. Instead I see concrete steps that are ignored in the USA being broken out and done repeatedly. Children may not be able to describe composing a mathematical expression in abstract terms, but they can learn to do it. And having that skill makes word problems a lot easier.
And, of course, the concrete skills and connected concepts give them a better foundation to build abstractions on when they are old enough to do that.
A random incidental note. Your links lead me to http://nces.ed.gov/timss/results07_math07.asp which suggests that the USA is not as bad in international comparisons as is often claimed. That said, the USA clearly could improve, and Taipei would seem to be a particularly good country to learn from.
Abstract thinking is sadly lacking from our school curriculums.
I've seen students even at university level who are bewildered
by equations like w^2-2w+4=0 or d/dm(m^3-m^2+m) just because the they haven't been taught that the variable x is just an abstraction.
By all means lay as correct a foundation as feasible. But be aware of the limits that children have, and do not set them up for failure by ignoring those limits. (This was one of the failings of the "new math" movement.)
BTW none of this is to say that I'm remotely happy about the disaster that is math education. I just don't think that this is the right solution to it.