We have introduced the peer instruction well known in physics to coursework in mathematics. The peer instruction is a method to promote mutual learning by students, then it is aimed at essential understandings of learning contents. In the peer instruction in physics, it is an important process to discuss concept tests by students. Through the discussion, they notice differences between the exact meaning of physical contents and the intuitively understandings in real life. The learning contents in calculus course also include various aspects, such as exact definition, concept in calculation, geometric significance, sense in application, historical background, and so on. Japanese students often learn only one face of learning contents, usually how to solve problems. By showing the concept tests about learning contents, the students notice the various aspects of what they have used for solving problems. It is noteworthy that this will happen in the discussions between students, that is, peer instruction. In this conference, we report on class case introducing the peer instruction in calculus course. Indeed, such a class is active despite the mathematics class, discussions will begin as soon as the display of the concept test. Thus, it became a calculus course for training engineers, near CDIO principles. We have practiced over the course of a year and a half, revealed the difficult points and improved them. Then, we report on difficult and improving points in mathematics class and verification on whether they understand various aspects of mathematical contents.
