Department of Mathematics and Statistics
The Department of Mathematics and Statistics at Sonoma State is committed to active learning in all its classes. Active learning engages students in the process of learning during class—through writing, talking, problem-solving, and reflecting—in contrast, to passively "receiving" knowledge from an expert. It emphasizes higher-order thinking and often involves group work. The research evidence is overwhelming that “active learning increases student performance in science, engineering, and mathematics.” From a risk perspective, “on average, students in traditional lecture courses are 1.5 times more likely to fail than students in courses with active learning”. (Freeman et al., Proceedings of the National Academy of Sciences, 2014).
Active learning pedagogies provide greater opportunities for success in learning by students from all backgrounds. Particularly students historically shut out of mathematically-based majors and careers (including Native American, Latinx, African-American students, and women). This conclusion is endorsed by a 2016 joint statement of all major mathematics, statistics, and mathematics education professional organizations in the United States, which calls the mathematical sciences community to a community-wide effort to transform teaching at the postsecondary level.
The Freeman study explains the significance of the difference made by active learning pedagogy:
If the experiments analyzed here had been conducted as randomized controlled trials of medical interventions, they may have been stopped for benefit—meaning that enrolling patients in the control condition might be discontinued because the treatment being tested was clearly more beneficial.
The Department recognizes that changing teaching practice is difficult to work, and is committed to supporting new and continuing faculty in this change. Such support will include access to books and materials, professional development opportunities, and co-teaching opportunities.
Active learning methods span a wide range of pedagogical approaches, all designed for students to engage in mathematics in and out of the classroom; and for students to try difficult things, receive feedback, and improve their practice. Examples include:
- Think-Pair-Share (TPS), which can be implemented many times in every class. The instructor poses a brief task (conceptual question, calculation, explanation), asks students to try to complete the task independently (perhaps writing down their solution for themselves), then discuss it with a partner, then share some solutions with nearby groups or with the class. This classic technique was recently shown to have high efficacy in a randomized experiment; see Bernstein et al.
- Collaborative learning in which learners engage in a common task where each individual depends on and is accountable. This is often done in small groups with a shared end product. For a fuller description, see the department resources on Small Group Instruction.
- One-minute paper or exit ticket: Strategically-placed brief reflective writing exercises, which help students reflect on significant concepts and instructors gain quick insight into their students' current understanding.
- Paired board work: In pairs, students solve problems or explore patterns on the board. One student is assigned to scribe; the other is a quality controller.
Many more pedagogical tools and more detail are in the Mathematical Association of America's Instructional Practices Guide, including more intensive active learning pedagogies such as Flipped classrooms and Inquiry-based learning.