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Approaches and techniques

Inquiry-based learning (site page | summary handout). In "Inquiry-Based Learning," the primary mode of engagement in the classroom is student activity. Activities are designed so that the mathematical content comes from students' activity. There is some lecture, but this comes at the end of the activity, not before. The goal of the lecture is to summarize the mathematical content and help students build relational understanding. Still, the instructor plays a very active role in designing activity, facilitating group work, and selecting and sequencing student presentations.

Classroom questioning and voting (site page | summary handout). This is a hybrid methods that combines traditional lecture with student  engagement in activity. The content generally comes from a lecture, but students engage in deep questions throughout the lecture, and the lecture is responsive to students' responses. 

Flipped classroom (site page | summary handout). This is a hybrid method that combines traditional lecture with student engagement in activity. The idea is that "lectures" are delivered outside of the class meetings, and the class meetings are devoted to student engagement in activity. 

Making group work productive (site page | summary handout). Regardless of how one implements active learning, chance are it will involve students working together in groups. There are a lot of ways that group work can "go wrong"—and we're all very familiar with them. But group work can also be very productive, and can lead students to engage in high-level work than they could individually. This page contains resources to help make group work productive.