Unsettling facts and calls for change (site page | summary handout). Formal schooling is based on outdated beliefs about learning—with some really unfortunate consequences for students. This page includes some "unsettling" facts about those consequences, as well as calls for change in how we teach undergraduate mathematics from prominent organizations in the mathematical sciences. 

Engaging students in mathematical activity (site page | summary handout). If we take the position that mathematics is the human activity of structuring the world and the art of explanation, then our primary goal as instructors should be to engage students in mathematical activity. This page describes more about what mathematical activity is, and what it looks like in the classroom when we engage students in mathematical activity. In other words, take a thought experiment. While traditional schooling is based almost entirely on learning mathematical content, what if we focused instead on engaging in activity?

Active learning

Of course, as college math instructors, we all have content goals for our students. Active learning is a suite of techniques in which students are expected to learn mathematical content and engage in mathematical activity.

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.