Active Learning and Self-Awareness

One of the best "side effects" of active learning is that students develop metacognition - self-awareness of their own learning and problem-solving approaches. Metacognition supports mathematical problem-solving because students with good metacognitive skills can better analyze and adjust their own problem-solving approaches or abandon ones that are not fruitful. Thus metacognition transfers to other settings - it's a lifelong learning habit. A metacognitive classroom has a rich mathematical culture where students are behaving like mathematicians, examining claims and asking for justifications. Alan Schoenfeld demonstrates this link in his classic article on metacognition and problem solving and suggests four ways to foster metacognition in your own classroom. 

(Shared by Sandra Laursen, UC Boulder). 

Calculus Concept Inventory (Epstein)

While this paper and the tool it uses have been critiqued, this paper makes a compelling case that not all active learning classrooms are equal and that we need to strive for environments in which students articulate their thinking to get feedback in quick and meaningful cycles. While the paper is intended for educators, having students read it can be helpful for building student buy-in for active learning, especially if they feel that they would be learning more by listening.

(Shared by Brian Katz.)

PRIMUS (Problems, Resources, and Issues in Mathematics Undergraduate Studies)

PRIMUS is a pedagogically focused journal for mathematicians. The articles discuss math problems or teaching interventions, and they are written with the goal of allowing readers to adapt ideas for their own context. Many of the papers in PRIMUS can help mathematician readers apply research coming out of the Mathematics Education (especially RUME) community without having to develop the skills to read full research-level papers. Special issues on inquiry or active learning will be particularly fruitful, including the upcoming special issue on "Teaching Inquiry".

(Shared by Brian Katz.)

Ethnography Research and Inquiry Based Learning

There is much research showing that IBL is effective at teaching students mathematics. One of the most striking results is that the students' attitudes towards mathematics can change significantly after taking an IBL course, especially among students who are women. In the forefront of this research are the faculty of the Ethnography & Evaluation Research group at UC Boulder, led by Sandra Laursen.

Some of their articles on this topic are:

-Laursen, S., Hassi, M.-L., Kogan, M., Hunter, A.-B., & Weston, T. (2011) Evaluation of the IBL Mathematics Project: Student and Instructor Outcomes of Inquiry-Based Learning in College Mathematics. [Report prepared for the Educational Advancement Foundation and the IBL Mathematics Centers.] Boulder, CO: Ethnography & Evaluation Research, University of Colorado, Boulder.

-Laursen, S.L., Hassi, M., Kogan, M., & Weston, T. (2014), Benefits for Women and Men of Inquiry-Based Learning in College Mathematics: A Multi-Institution Study, Journal for Research in Mathematics Education, Vol. 45, No. 4 (July 2014), pp. 406-418.

-Kogan, M. & Laursen, S.L. (2014), Assessing Long-Term Effects of Inquiry-Based Learning: A Case Study from College Mathematics, Innovative Higher Education, Volume 39, Issue 3, pp. 183--199.

The complete set of their research can be found in http://www.colorado.edu/eer/research/steminquiry.html