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In this chapter, I consider the relative powers of cultural forms, how agency is frozen into and circulates through forms over historical time, and how these processes are relevant for design-oriented studies of classroom learning and teaching. I start with a question about the costs and timescale of invention, comparing innovation in the classical music business (the "power of inertia," as analyzed by Howard Becker) with processes underway in the classroom learning and teaching of statistics, which are offered by Rich Lehrer and Leona Schauble for secondary analysis in this volume. After a description of my own path through the corpus materials, I look across analyses in the target chapters that anchor this volume to build a synthetic account of the corpus as a case of what I call "the discovery of invention." In this account, not only are children asked to invent data displays, but also the entire apparatus of teaching statistics for conceptual understanding is in the midst of invention. Just as it would be difficult to invent a truly novel way of authoring, performing, and hearing classical music, it has proven difficult to invent a novel way of teaching and learning mathematics (in this case statistics) in US public school classrooms. Reviewing the substantive and (in my view) complementary contributions of each target chapter, I argue that the difficulties of inventing a new way to teach mathematics are instructive and worth continued, collective effort.

DOI: 10.1007/978-1-4419-7582-9_22

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