A Case of Flipped Classroom for the Undergraduate Mathematics Education —— Analysis ——
To undergraduate mathematics classes, flipped classrooms were performed. The theme is an application for the Taylor expansion to find the approximate probabilities for a normal distribution. There is a critical issue in applying the Taylor expansion in some cases. For example, even though the exponential function can be expressed by an infinite polynomial series for all real numbers, to find the approximate numbers using a Taylor series with finite terms, we have to know in advance the relation between the degree of the polynomial and the accuracy of approximation. An intriguing problem to find the approximate probabilities for a normal distribution provides many educational lessons for beginners and practitioners of undergraduate mathematical courses.
The flipped classrooms were successful. Students felt stimulating and had fun in classrooms. To avoid boring mathematics classes using stereotype exercises, we have found that the flipped classrooms are useful in undergraduate mathematics education. Above all, the students did understand the significance of the mathematical reasoning.