Our research is quasi-experimental. There are two groups to be tested under different teaching approaches however we don't know how many participants should be in a group.
Without knowing more details about your research project, it is difficult to make meaningful statements here. Which research approaches in which domain do you want to test empirically? It cannot just be about the number of participants in the group. As a rule, certain preconditions and contextual conditions must be taken into account: What is the research question? What are the scientific objectives? Which specific teaching/ learning settings are to be evaluated: combined vs. shared, synchronous vs. asynchronous, individual or cooperative, etc.? Should it be a comparative study? Is a control group planned? These and other requirements must be clarified and defined. Then the research design can be precisely conceptualized.
The type of test, number of variables, and number of interactions need known. As a general rule of thumb, larger is better. Beware of p hacking. G*Power is free software to compute power. Review the literature for rules of thumb. Baseline equivalency is important.