I've 'fairly carefully' *read through* the two articles referred (but I've not *studied* them by any means, by which I mean I've not constructed 'system models' the better to elucidate to myself the 'structure' of what is being discussed): +++++ 1. Ma, Liping, A Critique of the Structure of the U.S. Elementary School Mathematics, NAMS, 60(2013), 1282-1296, <http://www.ams.org/notices/201310/rnoti-p1282.pdf>
Together, these articles make clear how astonishingly complex is what every child is expected to learn in school math - and that is without at all considering just how math is to be *integrated* with everything else that the child has to learn!
The complexity the child confronts in his/her school life is in fact 'immeasurable' by any mathematics we have at our disposal - and yet the child by and large does quite successfully accomplish much of the learning that is demanded. Of course, we generally ignore the uncomfortable fact that, by the time he/she graduates from school, the child by and large 'loathes and/or fears' maths. Recall that even President Obama confessed (somewhat shame-faced) that he was rather poor at math during his schooldays!
As to the child's general attitude to school and appreciation of what he/she learns, I guess the 'school system' in general should be given at least a 'passing grade' if not an A+ or 'Excellent'. For whatever may be their 'success' or lack of it, schools still do continue, through primary, secondary and high school and even beyond through college and university levels.
True enough, there are critics aplenty who claim that most students are unfit for anything beyond school and should be bundled off to 'vocational training courses' instead of drowning their parents/ themselves/ society in vast debts to pay for an education that doesn't suit their abilities or interests.
What strikes the interested observer (specifically, the undersigned) is that the 'experts' - Liping Ma; Mark Saul; AND the critics who want to pack 'the unfit' off to vocational school - they have not really thought *in any depth* about applying the powerful tools of 'systems science' to seek to design an effective educational system that would, at least over time, meet the perceived needs or aims the system is expected to serve.
I observe that Mark Saul has rightly suggested that "a conscious effort to fit together (the disparate views of the stakeholders in the debate) would effect a synthesis of the two views". However, he hasn't shown us any practical means of just HOW to fit together these disparate views, HOW to create the needed 'synthesis' (in a systematic way).
The critics who want to pack all the 'unfit' off to vocational school have chosen not to think about how the educational system (as an integral part of the 'whole system') should seek to satisfy the needs and desires of the citizens of the 'democratic system'. Labelling the great majority of students as 'unfit' and bundling them off to a 2nd class vocational career is scarcely democratic, though probably it is 'convenient' for them (the critics).
Remarkably enough, a US scientist, the late John N. Warfield, has through his seminal contributions to 'systems science' has developed practical tools for 'idea management' that could help resolve all such issues in very practical ways. In brief, Warfield's systems modeling tools enable stakeholders in any complex system to construct graphical models showing just how the disparate 'elements' in the system are inter-related. Quite easily, models describing systems can be developed into 'normative models' that enable us to develop the system as a whole to help us achieve the goals we desire the system to accomplish for us.
Quite simply, Warfield's work enables the stakeholders in any system to ensure that "the system is designed for the stakeholders - not that the stakeholders should resign themselves to fit the system that exists". More information about Warfield's approach to 'systems' is available at http://www.jnwarfield.com and from the "John N. Warfield Collection" held at the library of George Mason University, where Warfield was Professor Emeritus - see http://ead.lib.virginia.edu/vivaxtf/view?docId=gmu/vifgm00008.xml.
A simple aid to problem solving and decision making b ased on the Warfield approach to systems which I call the 'One Page Management System' (OPMS), now enables the stakeholders in any system to choose any (fundamentally feasible) 'Mission' and then to put together (i.e. to *integrate*) their available good ideas to help them accomplish that Mission.
It turns out that *integrating* available good ideas will demand that we learn how to get rid of the 'bad ideas' we have, which are always floating around our mindspace. This is sometimes quite astonishingly difficult to do, as we're often - for one reason or another - inordinately attached to our bad ideas. For instance, it may be quite difficult - perhaps even impossible - to convince those holding power in society that those they've designated as 'unfit' are in fact no less 'fit' than those already designated as 'fit'. How to ensure that the supposedly unfit do actually obtain their democratic rights in the society? This is the question on which many 'nominally democratic' systems founder.