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The study by Abrahamson, Shayan, Bakker, and van der Schaaf [this issue] makes important contributions to several aspects of research, including pedagogy, methodology, and theory. The use of tablet technology to implement new pedagogical practices was innovative. Further, the integration of eye-tracking, microgenetic, and clinical interview methods enabled the researchers to capture ecologically valid data with all the rigor of more quantitative procedures. In turn, such a rich data set provided a concrete explication for some of Piaget’s more abstract theoretical ideas. In our commentary, the focus will be on issues that are most directly related to theory. We are in general agreement with the underlying theoretical frameworks and many of the specific aspects of the model that are being advocated in the target article. Given this general convergence we offer areas in which we think the underlying framework could be extended or clarified. First, let us summarize what we take to be the theoretical core of the article. Abrahamson and colleagues provide a theoretically substantive answer to the following pedagogical question: “How does one steer conceptual construction?” In answering this question, Abrahamson and colleagues suggest that we revisit Piaget in order to better understand children’s development of new conceptual categories with a particular focus on the area of mathematics learning. The general Piagetian insight which their analysis is based on concerns the emergence of conceptual knowledge from within a sensorimotor ground. More specifically, reflective abstraction was the process through which Piaget modelled “conceptual schemata rising from sensorimotor operatory schemes” [Abrahamson et al., this issue]. In turn, Abrahamson and colleagues enlist the process of reflective abstraction in order to teach children in elementary school about mathematical concepts. Finally, Abrahamson and colleagues

Stepping Back: Reflections on a Pedagogical Demonstration of Reflective Abstraction