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What is active learning?

Active learning is difficult to define. We defined active learning as:

Learning situations where students have at least some opportunity to engage in mathematical activity, and where the instructor and class activities are at least somewhat responsive to that activity. 

Teaching techniques exist on a continuum. At one end is a traditional lecture that only focuses on mathematical content, all content comes from the teacher, and which is not responsive to students. At the other end is a Lockhard/Schoenfeld-style classroom where the only focus is engaging students in mathematical activity, without specific content goals. At this end, all content for from students' activities. "Active learning" is a spectrum of techniques that are to the right of the "traditional lecture" end of the continuum. 


We focused on three techniques in this continuum. 
  • Toward the right is "inquiry-based learning," in which the teacher has content goals, but the primary mode of engagement in class is mathematical activity, and the activities are designed so that mathematical content will emerge from students' activity. 
  • Classroom voting ("clickers") and flipped classrooms are "hybrid techniques" that combine lecture and activity. Some content comes from the teacher and some content from students' activity. Class is somewhat rigid, and somewhat responsive to students.