Competing meanings, perturbation, and engendering shifts in (prospective) teacher meanings

Through building models of student thinking, researchers have identified quantitative reasoning as a foundation for students’ mathematical development. This has generated a need to support teachers’ capacity to teach for such reasoning. In this paper, we discuss a perspective on supporting prospective and practicing teachers in constructing meanings that foreground quantitative reasoning and research-based models of student thinking. We call this perspective competing meanings and describe it as a three-phase cognitive process. First is a perturbation of an extant meaning resulting from its enactment. Second is the construction of an alternative meaning to reconcile the perturbation. Third are acts of reflection to compare extant and alternative meanings. We introduce the competing meanings perspective and illustrate it with examples. We also discuss theoretical resources that inform this perspective, including Piagetian constructs, quantitative reasoning, and mathematical knowledge for teaching.