Toward a New Model for Research on Ambitious Mathematics Teaching

We propose a model for investigating the quality of mathematics teaching using learning opportunities as an alternative dependent variable to student learning outcomes. We define learning opportunities as opportunities intended by the teacher and engaged by students. We use a general learning goal—conceptual understanding—to show that sufficient empirical evidence exists to identify features of learning opportunities that reliably connect with commonly desired learning outcomes. If accepted, our model would allow teaching researchers to reallocate scarce resources to study, in more detail, the nature of teaching that yields learning opportunities with desired features engaged by students. We believe the model could clarify the criteria for justifying appropriate dependent variable selection in research designs, grant proposals, and manuscript drafts.