Option #2: No, an observational study is not the best.
In this scenario, the teacher is actively implementing two different teaching methods and directly comparing their effectiveness on student learning. This setup is more aligned with an experimental study rather than an observational study. An experimental study allows for control over variables and can provide stronger evidence of causation between the teaching methods and student outcomes. In contrast, an observational study would merely observe the outcomes without manipulating the teaching methods, which would not provide clear insights into which method is more effective.