In this study, we analyzed professors' performance of teaching in college of science and engineering from the perspective of the CHAT. Two professors volunteered to participate in this study. Their syllabi were collected before the lectures, and their lectures were observed and videotaped. Semi-structured interviews were conducted before and after their lectures. The CHAT components were classified into 'subjects', 'objects', 'rules', 'communities', 'division of labor', and 'tools'. We extracted the content of six CHAT components from the data and constructed the analysis framework based on the extracted contents. The analyses of the results revealed that both professors had difficulties due to the contradictions among the components of subject, object, rules, and community in the activity system. Both professors used various strategies to relieve the contradiction related to students' ability, such as inviting students to participate in their lecture. However the extent of providing opportunities to students to participate was different between two professors. Meanwhile, both professors preferred to continue their own strategies, because they observed positive changes in students' learning. In other words, the success experiences of two professors influenced their performances of teaching. We discussed some suggestions to improve the quality of the lecture in the college of science and engineering.