Guided Inquiry into a Physics Equation

We present the theoretical argument that the use of mathematics in physics can be productively conceptualized as using a language and that learning to make sense of physics equations and appropriating them into novel scientific inquiry can be understood as a process of learning to read fluently with a high level of reading comprehension and to express one's thoughts in writing. The data are drawn from a longitudinal ethnographic account of a high school student's year-long research apprenticeship, in which a significant part of the work required the derivation and interpretation of an advanced physics equation (the phase velocity of waves in liquids). The analysis examines in different timescales the extended learning process as a complex activity system. The findings illustrate empirically how this type of learning can be productively analyzed by researchers and instructionally implemented by teachers or mentors as engagement in practices, a perspective that complements more standard cognitivist accounts of mathematical sensemaking. We highlight productive pedagogical and discursive instructional moves that facilitated this process and explicitly connect them to the learning they induced in terms of change in the student's participation. While constrained by the scope of this case study, the concrete, microanalytic account of the learning process concretizes some of what physicists do with equations and suggests pathways to teaching students to meaningfully participate in this practice.