Numerical sensemaking in secondary calculus: Does it make sense?

In recent years, there has been a growing recognition of the diverse roles of calculus in STEM education, and of the limited success of calculus education to provide students with effective scaffolding throughout different academic pathways (Biza et al., 2022). For example, Jones’ (2015) findings indicate that many activities emphasized in the teaching and learning of calculus are
generally less relevant for physics students for investigating and making sense of various physics situations. One suggestion for better alignment of calculus education with the different needs of mathematics and physics students is to place greater emphasis on numerical approaches, and specifically on the notion of approximation (Sofronas et al., 2015). This notion can be a unifying thread in calculus curricula and provide powerful metaphors that support the conceptualization of mathematical objects, as well as powerful tools for calculating and applying these objects. So, how can the notion of approximation be used in secondary calculus lessons to promote numerical sensemaking and to connect calculus and physics? The premise of our study is that the promotion of
numerical sensemaking at secondary mathematics (SM) education requires multifaceted knowledge and expertise that does not lie within the confines of any sole stakeholder in mathematics education (Pinto & Cooper, 2022). Among other things, suggesting feasible and meaningful ways to engage students with numerical sensemaking in calculus lessons requires subtle understanding of numerical approaches and perspectives, as well as deep familiarly with the SM curriculum and with the professional obligations that underlie SM teaching (Herbst & Chazan, 2022). Accordingly, our research strategy relies on bringing together SM teachers, mathematicians, and physicists to jointly inquire into why, when and how SM students should be engaged in numerical sensemaking. Here,
we build on a two-year collaboration between the two authors in such a community of inquiry within the M-Cubed project (Pinto & Cooper, 2022). The first author has a PhD in Mathematics and is currently a full-time Mathematics Education researcher. The second author is a full-time Physics professor, who has been teaching physics in 10th -12th grades for the past eight years. In M-Cubed,
we have been watching videotaped SM lessons together with another physicist, two mathematicians and eight practicing SM teachers, and discussing mathematical and pedagogical issues recognized therein. Often, while discussing concrete instructional situations, we found ourselves also reflecting
on differences between how mathematics is taught and experienced at school, and how it is used and perceived in science, and specifically in physics. Here, we present two episodes featuring participant reflections on the notion of approximation.