Connected or compartmentalized knowledge use: Two views of MKT with implications

One common approach to assessing mathematical knowledge for teaching (MKT) is designing items to measure individual subdomains of MKT as specified by a theoretical framework, with factor analyses confirming, or disconfirming, hypothesized subdomains. We interpret this approach as adhering to a “compartmentalized” view of MKT, as opposed to a “connected” view of MKT. We argue in this paper that a compartmentalized view of MKT is embedded in the ways that frameworks are represented, discussed, and used in the field. However, a compartmentalized view of MKT may unintentionally undermine understanding of MKT, and in turn, how to measure and cultivate it in teachers. We support this argument with an empirical analysis of nine typical practice-based items designed to assess MKT at the secondary level, categorized according to dimensions of five prominent frameworks for MKT. A key finding is that all of the items capture multiple subdomains, suggesting they are not measuring compartmentalized knowledge well. This finding held across all five frameworks, suggesting that it is more a characteristic of practice-based item design than of the frameworks used. We suggest that viewing MKT from a connected view can open potential lines of research that can impact assessment, learning, and teacher education.