I recently came across Kalid Azad’s Better Explained, and recommend that you check it out. It’s a fantastic resource in itself, and has lots of helpful thoughts about teaching and learning.
His main point is that most of us have been taught maths (and lots of other things!) badly* and that we should spend a lot more time developing intuitive understandings of how things work before we move into technical definitions.
His ADEPT method works like this:
Analogy: start by telling me what its like with reference to something I already understand well;
Diagram: Draw me a picture to help me visualise it, allowing me to engage one of the most powerful parts of my brain;
Example: Allow me to experience the thing you’re talking about – let me see it happen, play with it and watch what happens if I change things;
Plain English: Describe the thing in every day words;
Technical Definition: Only then discuss the formal details: “It’s like sharing a song you’ve made up: you can hum it to yourself, but you need sheet music for other people to use.”
“BE ADEPT” adds two more elements
Brevity is beautiful
Empathy is important – use your natural style, relate to common experience, anticipate questions in your explanation.
I like this a lot. Recommended.