I have always strongly believed in active learning. A large body of scientific evidence asserts that retention is improved significantly if learning is active, i.e. the student experiences the topic and uses a fuller range of cognitive functions.
While I have always incorporated various strategies into my teaching to accomplish student engagement, in recent years I have explored a variety of novel pedagogical techniques such as, peer instruction, blended learning, flipped classrooms, online teaching and MOOCs.
Below are some examples of my recent work:
- Discrete Mathematics Class (Fall 2012): This was my first fully flipped class. I recorded lectures using a Livescribe Smartpen. Students watched these lectures before class, interspersed with formative online quizzes. In class students worked in groups on problems, learned to write proofs and learned to present solutions to each other.
- Multivariable Calculus Class (Fall 2013): Students worked through content before class by reading PDF documents and annotating these, posting questions and responding to others’ questions. Pre-class online quizzes ensured adequate preparation for class. Annotations served to prepare and engage students, enable students to ask content questions immediately and help me gauge what concepts needed clarifications. These concepts guided my short in-class presentations. The remainder of class time was used for group-based activities.
- Complex Numbers (Spring 2014): This class had both physically present as well as virtually present students. I used video lectures and online quizzes (which I had previously produced for my MOOC “Analysis of a Complex Kind”, see below) to prepare students for our class meetings. In class we worked through problems in groups: the groups used tablets to communicate with group members who were not in the same location. We worked both as a whole class as well as in small groups.
- Introduction to Probability (Fall 2014): I am currently teaching from this book:
The authors, D. Bertsekas and J. Tsitsiklis, recently taught a class on EdX, based on their book:
I am incorporating a portion of their video lectures into my course: Students watch short videos before class, then answer quiz questions to ensure preparedness, and annotate lecture slides with questions they might have on the course material. In a Wiki, students also jointly work on problem solutions. In class we clarify difficult material and do group-based project work.
- Analysis of a Complex Kind (MOOC on Coursera): In the Fall of 2013, I taught a MOOC! See my page on Open Online Mathematics for details.