I have chosen to discuss the roll of the community of inquiry framework in the most common learning activity in most university-level math classes: the lecture. This will be instructive for me as a thought-exercise to explore how the lecture affects learning for my own students, and I hope I will also be able to add insight from my own experience as a student who has sat in one too many lectures. To organize my thoughts, I will focus separately on each of the three branches of the community of inquiry we have learned about in this module. However, I will try to be mindful of where those branches overlap and how that may impact students experience in a learning community.
I begin with teaching presence. Lectures are in many cases dominated by teachers. A teacher who has mastered the lecture can lead a motivating class which lifts students up and fills their mind with new, exciting questions. On the flip side, a bad lecturer can make the clock the only interesting part of a classroom. Much of this is related to the learning climate and learning regulation. A positive lecturer frequently asks interesting questions, challenging students to predict or build on the material presented. In the best classes, this is a social interaction where students share their thoughts socially with the lecturer and others in the class, but this can also be effective as a student-self interaction where a lecturer’s questions help students to check understanding and organize thoughts internally. Learning regulation deals with how a teacher presents lecture materials to students. Materials should be introduced clearly at the proper pace. Too slow, students lose interest. Too fast, students get lost. Learning how to regulate the learning environment and classroom climate are two essential skills every graduate-student lecturer in mathematics has had to battle, yours truly included.
Next, I turn my focus to cognitive presence. In my own experience as a teacher, I have found this the difficult branch of the community to monitor in a lecture setting. It is often difficult to judge students individual and collective ability to synthesize information and learn. Obviously, these skills in lecture are tied with the presentation of the material by the teacher, but to me the link with social presence is also key. Most of my monitoring of the cognitive branch of the community of inquiry comes via social interactions in and out of class with students. For lectures, this occurs most commonly through questions exchanged in the lecture, but office hours outside of the lecture are crucial in determining which concepts are difficult to students and where learning needs further work. Evaluations are the worst case “social” interaction, where a bad score on a quiz or test leads to a group re-examination of the groups learning from both students and teachers.
The social branch of the community of inquiry is the most difficult branch to cultivate in a lecture setting. Even in the best lectures, question and answer techniques make it difficult to foster a community feeling among the class. In my previous classes, I have tried to bolster this by repeatedly using students names, particularly at the beginning of the course. As mentioned above, office hours are also crucial to developing teacher-student and student-student bonds. One of the most powerful learning techniques in mathematics is repetition of materials through re-teaching or re-explaining concepts to a teacher or classmate, and doing this in small group settings outside of class leads to better learning outcomes and a better sense of community in the class. One takeaway for future classes of mine will be how to introduce group projects and social-based learning activities more heavily into lecture-based courses.
In summary, the three pillars of the community of inquiry provide an interesting lens through which to examine the common lecture-based format of mathematics classes. Previously, I had focused on my role as a the teacher in the teaching presence pillar, and the university emphasis on learning outcomes has made me aware of the cognitive function of the class in my lectures, but writing this post has emphasized to me how inseparable these branches are from the social presence of the community. In the future, I hope to focus more on this branch and find new, creative ways to include social interactions both student-teacher and student-student within lectures.