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). 

Beyond Lecture: Techniques to Improve Student Proof-Writing Across the Curriculum

This book has some ideas on how to provide active learning experiences to our students.  The e-book version is available for free to MAA members. One of the articles, by Patrick Rault, focuses on Teaching Proofs via Inquiry-Based Learning.

Inquiry-Oriented course materials

"Teaching Abstract Algebra for Understanding" (now "Inquiry-Oriented Abstract Algebra"), "Inquiry-Oriented Differential Equations", and "Inquiry-Oriented Linear Algebra" are each sets of course materials based on extensive research build from Freudenthal's "Realistic Mathematics Education" paradigm. After requesting access, instructors can see polished course materials that includes discussion of goals and design concerns, examples of student work, and likely student conceptions along the way. Website: http://times.math.vt.edu/

(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.)

How College Works

Book by Chambliss and Takacs, How College Works, Harvard University Press: Cambridge MA, 2014.

A look at what makes college "successful" (or not) for students, based on many different notions of "success".  A major discovery is that early connections with a good professor and/or mentor make a bigger difference than we think.

(Shared by Annalisa Crannell.)

Make it Stick: The science of successful learning

Book by Brown, Roediger, and McDaniel, Make it Stick: the science of successful learning, The Belknap Press of Harvard University Press: London, England, 2014.

This book describes how to use quizzing, distributed practice, interleaving to increase student learning (or rather, to "interrupt forgetting"). Highly readable, both for teachers and for students.

(Shared by Annalisa Crannell.)