Out-of-field and in-field teachers’ professional learning gains on fostering understanding of multiplication: A randomized controlled trial

Abstract Many teachers seek to foster students’ conceptual understanding, e.g., for meanings of multiplication, but are only partially prepared to go beyond surface translations between multiple representations. This concerns out-of-field teachers as well as in-field teachers (i.e., with mathematics teaching certificate). The paper presents a professional development program in which teachers engage in PD inquiry activities (a) to specify what understanding multiplication entails and how deeper connections of representations are articulated, (b) to monitor students’ understanding and uncover surface translations, and (c) to enhance students’ understanding by engaging them in explicating unit structures in graphical and symbolic representations. The randomized controlled trial with n = 94 teachers investigates the extent to which out-of-field and in-field teachers’ approximated practices can change in a PD session, and whether their professional learning gains depend on an explicit summary in the PD systematization phase. The comparison of pre-vignettes and post-vignettes reveals significant professional learning gains for all three practices, slightly more strongly for out-of-field teachers. For out-of-field teachers, the explicit summary in the systematization phase has significant additional effects for specifying and enhancing, less for monitoring practices. The findings show that out-of-field teachers can undergo very promising changes, especially when including an explicit systematization phase on specifying the mathematical learning content.