Connected or Compartmentalized Knowledge Use: Two Views of MKT with Implications

Heather Howell^1*Yvonne Lai²HeeJoo Suh³

• ¹Educational Testing Service, Princeton, New Jersey, United States
• ²University of Nebraska-Lincoln, Lincoln, Nebraska, United States
• ³College of Education, Sungkyunkwan University, Jongno-gu, Seoul, Republic of Korea

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 provide a review of five frameworks for MKT. Then, usingsupport this argument with an empirical analysis of response patterns to nine typical practice-based items designed to assess MKT at the secondary level, we illustrate categorized according to dimensions of five prominent frameworks for MKT. A key finding is that all of the tendency for practice-based items to capture multiple subdomains is a common issue, suggesting they are not measuring compartmentalized knowledge well. This finding held across all five frameworks, and perhaps onesuggesting that it is more a necessary resultcharacteristic of theirpractice-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.