Abstract

This research is a follow-up of Sierpinska, Bobos, and Pruncut’s 2011 study, which experimented with three teaching approaches to teaching absolute value inequalities (AVI), visual, procedural, and theoretical, presented over an audio lecture with slides. The study demonstrated that participants treated with the visual approach were more likely to engage in theoretical thinking than those treated with the other two approaches. In the present experiment, two groups of participants enrolled in prerequisite mathematics courses at a large, urban North American University were taught AVI with the visual approach using two different teaching styles: discursive (permitting and actively encouraging teacher-student interactions during the lecture) and non-discursive (not allowing teacher-student interactions during the lecture). In Sierpinska et al.’s study, the non-discursive style was used in all three approaches (the lectures were recorded and the teacher was not present in person). In the present study, a live teacher was lecturing in both treatments. Another difference was that in Sierpinska et al.’s study, lectures were delivered individually to each participant, while in the present study, all participants in a group were treated simultaneously. Therefore, in the discursive approach, not only teacher-student but also student-student interactions during the lecture were possible.
The aim of this research was to explore the conjecture that the discursive approach is more likely to promote theoretical thinking in students. The group exposed to the discursive approach was, therefore, my experimental group and the other played the role of the control group. The conjecture was not confirmed, but the two approaches seem to have provoked different aspects of theoretical thinking. The experimental group was found to be more reflective, while the control group tended to be more systemic in their thinking. Some striking results, not predicted by Sierpinska et al.’s study, were also found with respect to reflective thinking, definitional thinking, proving behavior, and analytic thinking.