David, thank you for your gracious and thoughtful reply, and your kind words about Rob MacDuff's work.
I don't think I have ever publicly acknowledged my debt to you, your writings and the part that you, your colleague Jane Jackson and the many others who have come together around your outstanding Modeling Methods project have played in my development. Your framework for understanding conceptual models and your approach to teaching Newton's physics helped foster a revolution in my own thinking and teaching, one which I could not retreat from if I tried as it has become inextricably a part of how I see the world.
I will grant that some may experience Rob's passionate advocacy for his views and positions as abrasive. However I suspect the deeper reason for the difficulty he's encountering with mathematicians and math educators does indeed lie in an essential philosophical shift embedded in his ideas, one which they perhaps understandably find deeply disturbing.
Galileo, in the title of A Dialogue Concerning the Two Chief World Systems, was of course referring to the Ptolemaic and Copernican systems, but Albert Einstein, in his preface to the Modern Science Library edition, puts his finger on the true essence of the two World Systems: "The leitmotif which I recognize in Galileo's work is the passionate fight against any kind of dogma based on authority."
In our time, the natural sciences have at least nominally abandoned appeals to authority as illegitimate. Mathematics however has over recent centuries gone the other way. Euclidian geometry at least had as its referent the observable properties of phenomena. In my efforts to apply the Modeling Method to helping students construct an understanding of arithmetic and algebra I came to see that math itself stands on the far side of Galileo's Divide, as a "dogma based on authority".
The power that mathematicians have granted themselves to play with the terms of the dogma does not fundamentally alter its condition.
MacDuff's distinction of number as representing a ratio between quantities - an idea which it turns out was clearly stated by Isaac Newton (p. 2, 1st paragraph) but has since been abandoned - is the fulcrum for a fundamental relocation of at least the "scientists' math" to the Science side of Galileo's Divide, as a system where every statement and symbol has as its ultimate referent some observable property or "empirically-familiar regularity" in the realm of real phenomena.
It is not surprising that this proposed paradigm shift sprouted in the soil you and your colleagues prepared. While all of natural science has long been on the Science side of the divide, science education is still largely dominated by a dogmatic, authority-based paradigm. The shift to the model-based paradigm of teaching, learning and constructing knowledge pioneered and supported by your work has brought science education over from the other bank, resulting in a learning experience that is philosophically harmonious with the subject being studied.
The task of designing a Modeling Math is more challenging because not just the pedagogy but the subject matter itself has to be transposed into the Galilean paradigm. I believe that the appropriate pedagogy for this shift is Rob's CIMM program. The newly-christened "structural algebra" on which it now rests owes a huge debt to your work in geometric algebra. Their divergence traces back to that philosophical shift at its heart, which I would invite you to reexamine with an open mind.