Calculus

SEE THE TEACHER NOTES FOR EACH PRESENTATION BY CLICKING THE STICKY NOTE BELOW THE PRESENTATION.

MORE RESEARCH ON WHY WE SHOULD LECTURE LESS:

A COMMON VISION FOR UNDERGRADUATE MATHEMATICAL SCIENCEs PROGRAMS IN 2025

-Karen Saxe and Linda Braddy for the Mathematical Association of America

"The status quo is unacceptable."

"We see a general call to move away from the use of traditional lecture as the sole instructional delivery method in undergraduate mathematics courses. The ASA (2005) asserted that, “[a]s a rule, teachers of statistics should rely much less on lecturing and much more on alternatives such as projects, lab exercises, group problem solving, and discussion activities” (p. 9). Even within the traditional lecture setting, we should seek to more actively engage students than we have in the past."

"Cooperative learning, problem-based learning, and the use of case studies and simulations are also approaches that actively engage students in the learning process (University of Michigan Center for Research on Learning and Teaching, n.d.). These types of pedagogies promote collaboration and provide opportunities to practice communicating ideas. A multifaceted approach to instruction is important for helping students develop flexibility in the ways they process information, and the use of diverse instructional approaches should be a strategic part of the curriculum."

WHAT DOES ACTIVE LEARNING MEAN FOR MATHEMATICIANS?

-Benjamin Braun, Priscilla Bremser, Art M. Duval, Elise Lockwood, and Diana White

"Active learning often has a particularly positive impact on student persistence and sense of belonging."

"For many faculty using active learning, these techniques inspire richer discussions with students and provide a window into the reality of students’ mathematical experiences. This allows faculty to be more responsive to students’ misunderstandings, which in turn causes students to feel more supported in the course, frequently leading to increased engagement."

"Active learning provides opportunities for faculty-student interaction not present in courses focused on direct instruction. Active learning methods can reach and excite some students who might not typically be vocal or engaged in class—students who are quiet and reserved by nature frequently demonstrate their full potential when provided with the right opportunity. On the other hand, active learning methods can uncover deep misconceptions about mathematics, even from straight-A students, that homework and exams do not reveal. Further, students often respond to active learning tasks with interesting observations and thought-provoking questions, infusing standard courses like calculus with fresh energy."

"Expect resistance from some students. For many reasons, it is common for some students to resist active learning methods, especially at the beginning of a course. Some students are not particularly interested in mathematics and do not want to engage at a deeper level. Other students have experienced significant success in traditional mathematics courses and feel threatened by an unfamiliar environment. With all students, instructors need to clearly articulate the value of the active learning methods they use and maintain high expectations for student participation and engagement. Often, students who are initially resistant find themselves surprised at the end of a course by how much they appreciate active learning."