Video 05: An active math class

Do proven (i.e. evidence-based) active learning strategies work well in mathematics classrooms? Most certainly! This 6-minute video clip illustrates how active learning strategies effectively remove old-fashioned lecturing from the classroom. As a result, the interactions between experts and novices (i.e. instructor and students) are enhanced, and the power of peer instruction is enabled.

In this class, the instructor uses Socratic lecturing as follow up to pre-readings, clicker questions are use thoroughly with solo, paired and whole-class discussions, and groups work on “challenge questions” (with on-demand guidance from the circulating instructor) which are then carefully followed up using an instructor-guided whole class discussion. See additional information using the “+” icons in the menu to the left.

WHEN WATCHING THIS 6:12 min. VIDEO, look for…

Students: how they WORK

  1. All students know what to expect and how to make use of this opportunity to practice new skills and apply new knowledge under the guidance of experts.
  2. Notice that students feel “safe” to speak out and try suggesting ideas that they are not sure about. This is a “comfortable” learning setting where respect and exploratory thinking are encouraged.
  3. During Socratic lecturing, the instructor elicits interactions with individuals by presenting by questioning rather than by “telling”. He ensures that not only one or two students are involved.
  4. Ad-hoc groups of four students work efficiently without needing instructions because this is a “normal” aspect of the course. Building “team working” skills is not a major objective in the course. The use of groups simply enables the benefits of peer-assisted feedback and distributed reasoning.
  5. All students have “clickers” and know they are expected to use them every day.

Aspects of instructional practice to notice include:

  1. The instructor’s words during the video outline his perspectives, reasons for particular strategies and their order, and some of the benefits (and challenges) of teaching this way.
  2. All these strategies can usually be managed by one instructor with a class of up to roughly 50 students (although some instructors can work in this manner with more).
  3. The expert is circulating and observing the thinking of as many groups as possible. Efficient tutoring depends on seeing/hearing thinking so that difficulties can be detected and feedback provided where and when needed.
  4. Commonly seen difficulties are addressed by interrupting student work.
  5. When offering support to groups or the whole class, student thinking is guided. These instructors do not just tell an individual, a group or the whole class.
  6. Lecturing (i.e. “telling”) is strategic. It serves to amplify or elaborate or provide expert perspectives on aspects that students have already started thinking about. There is rarely any simple delivery of new facts and figures. An element of story-telling is also included during lectures.


  1. Prepared worksheets are NOT needed for many of these “challenge activities”. However, they can provide some structure to the thinking for certain types of tasks.
  2. The instructor refers to “pre-readings”. Students have encountered basic new content before coming to class. Therefore, the instructor can spend time in class contributing expertise that helps students think rather than simply delivering facts and figures.
  3. See other videos at this site ( for examples of active learning in other settings (geoscience, physics, climate science, 1st and 3rd year service courses and 2nd year core courses, etc.)

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