Abstract:

Effectuating student engagement and mathematical thinking in undergraduate mathematics courses can be challenging, particularly in university environments where normative practices permit students to engage in primarily passive learning. Learning opportunities for students in first and second year North American postsecondary mathematics courses typically consist of attending three lectures weekly and, if needed, drop-in consulting centers or workshops where teaching assistants and instructors hold their office hours over the course of a term. During the lecture, a professor delivers content to hundreds of students, and attendance in workshops is often low with spikes before tests. This structure provides few opportunities for students to move beyond a passive level of engagement in the course and does not provide students with enriched learning opportunities. Research on the teaching and learning of mathematics has shown that active engagement leads to improved outcomes for students.

In this study, we look at a university’s experimental implementation of a new system in one of its calculus courses that has four lectures per week and is designed for students who did not score high in pre-calculus courses. In this system, all students in the class attend three regular lectures per week together, and in the fourth class, the review seminar, they are split into groups of 25 students that meet at different times. During the review seminar, students work in groups on previously supplied problems under the supervision of the instructor and peer-tutors, collaborating at vertical whiteboards. As students work, the instructor and peer-tutors move throughout the room, providing support as necessary. The collaborative and public nature of the student work allows students to receive support from their group, from other students around the room, and from the instructor and peer tutors. In this qualitative study, we consider the observations of the instructor and peer-tutors, discuss the challenges and successes with respect to implementation, and interpret the results of a 13-question survey completed by the students at the end of their term. Results of this study indicate improved engagement during seminar time, a more positive disposition towards mathematics in the participating students, and an overall increase in student activity and performance. Our analysis of the collected data indicates that the seminars provided students with a new quality of studying, which was particularly reflected in students' feedback that the “learning by doing” aspect of whiteboard seminars provided them with an enjoyable experience learning mathematics.

Keywords:

Vertical whiteboards, student engagement.