ABSTRACT
I begin a commentary on the foregoing chapters by assuming the uncomfortable role of academic curmudgeon and engaging in a little critical hyperbole. Specifically, I will voice three brief (and somewhat heretical) reactions to this book as a whole, then return to each in order to clarify and to fine-tune the criticism. https://www.niso.org/standards/z39-96/ns/oasis-exchange/table">
Heresy 1.
Research, as represented in the body of this book, is being driven by available and promised technologies; it seems, if anything, too sanguine about the role that technology might play in classrooms. Having caught a vision of what we can do, we too often uncritically assume not only that it should be done, but that it will in fact solve long-standing problems.
Heresy 2.
Research has failed to deal effectively with what I will call the content domain of the graphical representation of functions. Specifically, we as researchers have failed to provide a comprehensive analysis of the subject matter with an eye toward informing research on learning or teaching.
Heresy 3.
Research has also failed to deal effectively with understanding the graphical representation of functions. Specifically, we have failed to engage in the sort of careful analysis of tasks and structures that would allow for modeling the understanding, learning, and teaching of graphs and functions.
