I'm big into helping students understand their maths at a deeper level to let them to tackle the most difficultly worded questions

I don't teach for the sake of answering a question. We all can answer question after question following a method, but I want my students to understand the process. An understanding of the foundation lets us freely think through the problem especially those confusingly worded ones. Methods break once the questions deviate, but understanding can let you see through it.