diSessa and Cobb (2004, JLS) mention metarepresentational competence and sociomathematical norms. Mor and Winters (2007) mention design patterns, Sandoval (2004) gives a brief example. But what are the exact criteria for a theoretical construct to be justifiably called an ontological innovation?
First, there are no 'exact criteria' for anything in mathematics education. All constructs are interpreted and re-interpreted by colleagues. This mirrors the way a new word is added to a person's vocabulary: first the word is used rather too broadly, then its use shrinks to match the use by those in the surrounding community. The latter aspect seems to take a very long time in education circles.
Second, all 'constructs' are constructed by an observer (resonance with Maturana: "everything that is said is aid by an observer"). Constructs are labels for events discerned by an observer, and may become phenomena if the label is applied to more than one 'instance'.
For example, ZPD is a good case in point because it has been largely mis-interpreted by authors alighting on a single paragraph in one translation of one book by Vygotsky.
So the ontological question depends on the world you inhabit. ZPD, Enactive-Iconic-Symbolic modes of (re)presentation, instrumental and relational understanding, etc etc all exist in the mind of the researcher, but not in the material world.
JohnM
Thank you, John. I agree that 'exact criteria' is exaggerated, and I agree with your philosophical note. However, it would still be nice to know more examples of what design researchers consider ontological innovations. If there are still only a handful of examples, the concept becomes less interesting to me.
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