Applying Active Learning Strategies to Advanced Mathematics Courses

The passive teaching approach had been the only way in mathematics teaching because it is really difficult for students to understand by self-studying in a short time. Unlike other sciences, mathematics are not driven by hypotheses and experiments. We should always learn the correct definition, statements, and justifications. The teachers can make the learning process easier and faster for students. However, active learning strategies can be applied to mathematics teaching, particularly in advanced mathematics courses. For example, I am teaching Math 674, Computations in Linear Algebra. There are eight graduate students enrolled for this course, seven from Math Department and one from engineering. The class meets twice weekly with a computer lab biweekly. For most of lectures, I bring the definitions, motivations, and main statement as r the core materials for this course. In this class, students are not passively leaning from me only. I tried several complementary strategies as active learning process