Student-Generated Connections in Learning about Compound Probability and Their Emergence during Instruction

In this report, we analyze students' learning of compound probability by describing connections they generated while engaged with tasks involving two independent events. Several of their connections were compatible with the development of expertise, such as recognizing the need to determine sample spaces across a variety of situations and noting structural similarities among tasks, even when their task solutions were incomplete from a normative standpoint. Students reasoned about dimensions of context, variation, mathematical structure, sample space, and probability quantification. We describe the extent to which they coordinated these dimensions. We also describe teaching moves, such as posing idealized situations and shifting to structurally similar tasks, that prompted students to attend to multiple relevant task dimensions.