名詞節のthatか関係代名詞のthatか
ビジュアル英文解釈P97より
Discover what your students do not know and then try to explain it to them in a way that everyone will understand.
このthatは、名詞節のthatかなと思うのですがどうでしょうか?伊藤和夫は、このthatは関係代名詞のthat「学生が何を知らないかを発見し、次にそれを誰にでも分かる方法で説明するようにつとめなさい」だと言っていますが、その場合、元となるのが、understand a wayとなり方法を理解するというのが基礎となってしまい、本文の趣旨とずれると思います。
すると、a wayの内容を説明する名詞節のthatととらえたほうが良いのかなと思います。
また、いちおう高校で教鞭をとっているので、初歩的な説明(完全文とか不完全文とか)は省略して頂いても構いません。手間になってしまうと思いますので。
There are a few general principles that apply to all the kinds of teaching. The first principle is that the teacher should be clear. Whatever you are teaching, teach clearly. Discover what your students do not know and then try to explain it to them in a way that everyone will understand. Use many examples and illustrations. Allow enough time for discussion. A good pupil is seldom silent.
Patience is the second principle. Nothing worth learning can be learned quickly. Real teaching is not just giving information. It involves a conversion, an actual change in the pupil's mind, and this does not happen quickly. Lessons should be carefully planned and plenty of time allowed for repetition and review. Emotion should be controlled. Whenever we become too emotional as teachers, we are forgetting that conscious reason is what makes us men and not animals.
The third principle is responsibility. Anyone who teaches should realize that it is a serious matter to guide another person's life.