I agree that Mark Saul's attempt to fit Berlin's framework of 'hedgehogs and foxes' is not highly successful. It really doesn't matter to me at all that Saul feels that US thinking on elementary math curricula is more 'foxlike' and China's on the same subject is 'hedgehoglike'. (In his famous book "Fly and Fly Bottle" [which I believe had earlier appeared in several parts in the New Yorker], Ved Mehta was indeed highly successful in bringing to the general public's attention the celebrated framework; Saul's thought of using the acclaim that Ved Mehta/Isaiah Berlin received for that 'framework' does not seem to work).
Liping Ma has sugggested her opinion that the US thinking on elementary math education is organised by way of 'disconnected strands' while she feels the Chinese 'system of elementary math education (pre-2001 reorganisation)' has a well-defined 'core subject structure' composed of arithmetic with "four other components of elementary mathematics, (namely) measurement (M); elementary geometry, simple equations (E); and simple statistics (S)".
Professor Ma's suggested 'structures' for Chinese and US elementary education in math may well be accurate - I've not made any study of these contrasting 'instructional scenarios/structures', and I do not plan to do that - but she has not told us where she obtained these contrasting structures from or how she has developed them if they are hers. In her figure 2, she gives us a picture of the "pre-2001 organization of school mathematics in China" - again, I make no judgement about whether this is a factual description or not. I don't believe that is the issue at all.
Professor Ma states:
"The (Chinese) series of textbooks for six years has twelve small books, one book for each semester. All their content is considered essential rather than optional. On average, each book in the series has 113 pages, with page dimensions of 8 inches by 6 inches. Of all these books, only the first uses color and that occurs on only two pages. Each student gets his or her own set of textbooks.
"In contrast, in the U.S. an elementary mathematics textbook for one year often has about six hundred pages, frequently uses color,at and has pages approximately twice the size of the Chinese textbook pages. In general, the textbooks are the property of the school district rather than the student, and students are not able to bring the textbooks home".
(To my mind - and very much 'off-the=cuff', without having looked at either Chinese or US texts - it appears that the Chinese have rightly taken to heart Domenico Rosa's strictures about 'door-stopper texts' [without of course having seen them] and they ARE on the right track. (I emphasise that I'm not really highly knowledgeable on this - but the educational system's expectation that 6-year olds should master a 600-page text is one very good reason for the 'fear and loathing' of math that is so very wide-spread). And yes, I'm only kidding that the Chinese authorities have taken Dom Rosa's strictures to heart - though I entirely agree with his thesis).
To reach that point in Professor Ma's extremely complex exposition consumed more or less all the strength that I had and I'm afraid I had just skimmed through the rest of it.
However, I must state that it was Professor Ma's article that in fact gave me the proper understanding of just how very complex and demanding is the task we adults impose on all children (Chinese; US; Indian; other) of 'learning needed math' - and how very inadequate are our systems for accomplishing that.
To my mind, it is more or less a miracle that children wherever do generally pass out of their schools having learned 'some math' - though as I understand most of them appear to have a quite intense 'fear and loathing' of the subject by the time they get out of school.
I must qualify my remarks on Professor Ma's thesis in her article with the following:
If Chinese children have less of a fear and loathing of math than do US or Indian children when they pass out of school then to that extent Chinese elementary math education is more successful: that would be about the only judgement I can make. I don't believe either Liping Ma or Mark Saul have made a notable contribution to 'elementary math education'
However, Mark Saul's suggestion that the educational system should learn to *integrate* what is worthwhile in the respective Chinese and US systems is, I believe, entirely sound - though as I had observed earlier he does not suggest a practical means to accomplish any such end.
I do suggest a practical means - the 'One Page Management System' (OPMS) that can help accomplish such an end within just a couple of years of any such Mission being formally undertaken. By such a process, the stakeholders (&&) in the respective systems would see their good ideas integrated in what is actually done on the ground.
[&&: By 'Stakeholders' I mean: teachers (who must 'deliver' the knowledge); students (who have to learn the knowledge delivered by the system); parents; educators (including Liping Ma, Mark Saul and others); administrators; politicians; others interested in the issue, including Haim, Wayne Bishop, Robert Hansen who seem already to have delivered their ideas by way of slogans: they'd be invited to contribute those and any other fresh ideas they may wish to put forth].