Engaging Students in a Deeper Understanding of Calculus Concepts: Oral Reviews

Abstract: This paper discusses how the discourse practices of oral reviews in Calculus courses can improve students’ understanding, grades and retention in STEM (Science, Technology, Engineering and Mathematics) majors, and influence the teaching of faculty and graduate students. Oral reviews are ungraded, optional small group sessions, based on a constructivist approach to learning. In the three days prior to a written exam, groups of five students meet with a facilitator who asks the students scripted conceptual questions and encourages the students to discuss important concepts to be covered on the up-coming written exam. Students learn to negotiate meaning with their peers and make mathematical connections. Facilitators gain insights into student thinking and acquire information about common student misconceptions. Observations reveal that after participating in oral reviews the facilitators´ recitations and office hours become more interactive and dynamic. Initially, these oral reviews were used for at-risk students in a special two-semester Calculus I course with algebra. We compared the treatment students to control students with comparable mathematical preparation, and found that the treatment students passed Calculus I at a better than 90% rate, while control students passed at a rate under 20%. The treatment students then reintegrated into regular Calculus II courses with an 80% pass rate. After the dramatic results with at-risk students, we began using oral reviews for all Calculus I and II students, Mechanical and Aerospace Engineering students, and high school algebra students. The data shows significant improvement in course pass rates, retention, attitudes, and understanding of the nature of science and mathematics