The Dimensionality of the Multiplicative Conceptual Field

• In Event: Measuring Teachers' Mathematical Knowledge and Behaviors

Abstract

The multiplicative conceptual field (MCF) is a heavily cited theoretical framework for understanding the relationship between numerous mathematical topics. However, the MCF lacks empirical evidence substantiating the proposed relationships among topics. Using confirmatory factor analysis, we analyzed data from 224 teachers to determine the relationship between two MCF components (fractions and ratios/proportional reasoning). We find that these concepts belong to a single construct, which provides empirical support for the MCF by substantiating its claims about the relationship between topics. We assessed which teacher background characteristics are associated with higher content knowledge of these MCF components and found that being traditionally certified and having a credential in mathematics are positively associated with teacher content knowledge.

Authors

• John Ezaki, University of Southern California

• Jingxian Li, University of Southern California

• Yasemin Copur-Gencturk, University of Southern California