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Classroom discussion has long been an important pedagogical tool in fields such as the social sciences and the humanities because it allows students to critically examine ideas about what it means to be a human living within communities of other humans. It allows students to formulate ideas and judgments and to reconsider these formulations as time passes and new information is revealed. Within the field of mathematics, however, professors typically rely on lectures to ensure coverage. While students are asked to think critically, they are likely asked to do so within the context of homework problems. The primary question we consider in this essay is whether class discussion enriches student thinking and problem-solving processes within the field of mathematics.
The University Honors Program at Southern Polytechnic State University has found itself engaged in answering questions concerning the benefit of discussion as a tool for critical thinking, creative thinking, and problem solving since its inception in 2003. At that time an honors committee, composed of seven people representing the four schools, honed the policies and procedures for the University Honors Program. This committee set curriculum guidelines designed to ensure that courses involve substantially more tangible content than typical courses at the same level in at least four of the following seven areas: creative thinking, critical thinking, problem solving, oral or written communication, collaborative work, experiential learning, and interdisciplinary components.
For the humanists and social scientists on the committee, the idea of discussion- based classes in which students actively engage in the exchange of ideas generated through creative thought, critical thought, and problem solving seemed a promising solution for meeting many of these guidelines. The scientists and mathematicians instead saw the use of mathematical problems and assigned laboratory experiments as an optimal way to engage students in creative thought, critical thought, and problem solving. These differences in pedagogy spurred quite a bit of discussion among the honors committee members about the different methods the various fields use to emphasize student engagement in learning.
No standard for the use of discussion was created. However, many of the reasons articulated for using discussion-based pedagogy are supported by research on discussion-based classes. Stephen D. Brookfield and Stephen Preskill list many benefits in Discussion as a Way of Teaching, such as:
1. Discussion helps students develop critical thinking skills as they scrutinize their own assumptions as well as the assumptions of others.
2. It helps to create intellectual agility since students must think on their feet and react to unanticipated comments.
3. Discussion helps students develop skills of synthesis and integration because they must listen and speak as they work to understand how information is related. (24–35).
Discussion-based pedagogy functions in a similar manner to the Saxon Math Pedagogy, which draws on research showing that continual practice and review help students to demonstrate more thorough understanding of the material being taught (Mayfield and Chase). Just as, in class discussion, students are continually engaged with ideas that are reviewed and refined as the semester progresses.
Not until the honors office received the evaluations for L. R. Ritter’s fall of 2007 Honors Calculus One class did members of the honors community reevaluate discussion-based pedagogy. Evaluations for Ritter’s class revealed not only that students in the Honors Calculus One class thought Ritter was one of the best mathematics instructors with whom they had ever worked but also that they felt the discussions were stimulating and contributed to the quality of the class.
The director decided to create a more formal study concerning the use of discussion as a tool for learning. In August 2008, the honors program hosted workshops and roundtables on the use of discussion, and these activities led William Griffiths also to implement discussion within the Honors Calculus One class. Ritter and Griffiths, along with Nancy Reichert, Director of the University Honors Program, have been involved in both initiating and documenting this process of implementation.
At the heart of our study is exploration of the following questions: What does it mean to run a “discussion-based” mathematics class? How is this discussion balanced with other techniques such as lecture or individual problem-solving? What pre-existing, cultural understandings about a field’s knowledge base and its pedagogy lead to the ways in which both teacher and students approach learning? Our answers are drawn from the multiple perspectives of the teachers, students, and honors director.