The purpose of this study is to compare the two different kinds of mathematics lessons; traditional lessons in a typical junior high school and progressive lessons from a so-called alternative school. Typical school(school H) adopted one of the textbooks approved by MOE based on the national curriculum while alternative school(school E) adopted the translated textbooks of MIC(Mathematics in Context) which stressed the application of mathematics in the context of real-life problems. Mathematics lessons in school H were led and dominated by the teacher. Most of the time, the teacher explained mathematical concepts and how to solve the problems in front of the whole class. In general, the lessons were conducted in an orderly manner and the students were very well disciplined. The mathematics lessons of school E were substantially different from the mathematics lessons of ordinary schools. The teacher tried to provoke students\' interest by addressing relevant questions to them and suggesting some contexts in which mathematics was embedded in, and students actively participated in the lesson. After analyzing the 10 lessons in each school, mathematics lessons in these two contrasting schools were characterized along the two perspectives: product vs. process, and literal language vs. metaphorical language. The two contrasting lessons have strengths and drawbacks at the same time, and the characteristics of \"good\" lesson might be elicited from complementary considerations of these two lessons. On the other hand, based on the result of the TIMSS-R video study, traditional lessons partially share the features with two Asian countries(Japan and Hong Kong), and progressive lessons have the partial commonalities with five Western countries(Australia, Czech Republic, Netherlands, U.S., and Swiss). As a further research, it is recommended to investigate whether this tentative connection is valid for general instructional practices in these two Korean schools.