Abstract
The purpose of this study is to improve the quality of non-face-to-face classes by introducing cases of non-face-to-face online calculus classes for college students and calculus classes for high school students. To this end, we collected data such as texts, videos, and student outcomes related to online math classes conducted over 2020 and 2021 for analyis and interpretation as part of a case study.
 As a result, the discrete mathematics lectures for university students were mainly conducted as real-time video classes, showing the characteristics of using C and Mathematica programming tools in order to cultivate the ability to solve problems by performing tasks and demonstrating presentations. The calculus class for 3rd grade high school students adopted a mixed form of providing real-time video classes using Google Meet and OBS Studio. The high school teacher mostly dealt with problem-solving step-by-step explanations to prepare for college entrance exams, and provided video recordings of blackboard classes as a supplementary. By comparing and examining the two class cases, we identified several stumbling blocks that would be resolved and suggested future direction for improving the upcoming online math classes.
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