Have you ever said something to a class and felt something like a fog of non-understanding rolling towards you from the class? It has happened to me many times. Sometimes, especially if I am near the end of the session, I acknowledge the fog-of-non-comprehension but keep going; other times I pause and ask people to try to say to each other what they do comprehend of the topic. I might offer a couple of technical words from the topic and ask them to try to make a mathematically sensible sentence that connects the two words. I might, if we have established a suitably trusting atmosphere in the class, ask different people to read out their sentence and then ask people to consider what is appropriate and what if anything needs modifying.
The point is that learning involves, among other things, not only developing a personal narrative, but refining that narrative so that it is succinct and not likely to lead to confusions or errors in the future.
John Mason worked for the Open University Mathematics Department, where he designed two of the mathematics summer schools, contributed to numerous courses, and then helped form and run the Centre for Mathematics Education. He has written numerous books and booklets, as well as research articles and book chapters, the best known being ‘Thinking Mathematically’ (1982, 2010).