Below, we describe a few references for instructors who are interested in learning more about active learning.
Braun, B., Bremser, P., Duval, A. M., Lockwood, E., & White, D. (2017). What Does Active Learning Mean For Mathematicians? Notices of the AMS, 64.
In response to the call above to use active learning, these authors provide some common active learning exercises in mathematics and detail the benefits that students and instructors can receive from using such techniques. Common concerns are mentioned along with solutions. There are active learning exercises for a mathematics classroom and these authors provide insightful responses to concerns that instructors may have with initiating the use of active learning. It short and succinct! Here, you can find a pdf version of this article (web link).
Conference Board of the Mathematical Sciences. Active Learning in Post-Secondary Mathematics Education. Washington DC, 2016.
This is a statement affirming the use of active learning in post-secondary mathematics education, issued by the Conference Board of the Mathematical Sciences, which houses seventeen national professional societies.These seventeen organizations all “call on institutions of higher education, mathematics departments and the mathematics faculty, public policy-makers, and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms.” This statement also provides a brief overview of the reasons to use active learning, benefits of active learning, and ways to implement active learning. Here, you can find a pdf version of this document (web link).
Cooper, M. M. (1995). Cooperative learning: An approach for large enrollment courses. J. Chem. Educ, 72(2), 162.
Cooper provides a detailed overview of activities, benefits, concerns and suggestions in employing collaboration between students via group work at the college level to enhance learning. The overlap between collaborative and active learning highlights the importance of using group work when possible to facilitate active learning in a classroom. This paper provides an in-depth overview of the aspects of group work that instructors should keep in mind along with tips on what instructors can do to prepare for the use of group work. For example, it is suggested that groups include 2 to 4 students and to have students work difficult multi-step problems that students typically have trouble with. Here, you can find an abstract of this article (web link).
Faust, J. L., & Paulson, D. R. (1998). Active learning in the college classroom. Journal on Excellence in College Teaching, 9(2), 3-24.
These authors describe a variety of active learning exercises that can be used in conjunction with lecture. Although these activities are not specific to mathematics, some of them can be adapted to a math lesson. The authors also address some common initial concerns that instructors may have along with a brief overview of the benefits of employing active learning based on their own research. There are various categories of exercises geared towards individual student work, paired work, and group work as well as questioning and feedback techniques that instructors can employ during class time. All these exercises are nicely organized within each category of exercises making it easier for instructors to select an appropriate activity. Here, you can find a pdf version of this article (web link).