When this question arises, I have a habit of immediately replying “because it is absolutely essential in the oil industry.” Then I watch their face fall. I am convinced that rarely are learners actually asking where the topic of the ideas or the procedures are going to be useful, even when it comes out that way. Rather, they are saying “I am lost” or “I can’t seem to do this.”
My evidence is two-fold. I have used this response, or ones like it, for many years with teachers when studying mathematics courses at the Open University, and I have noticed that it is only when I feel I am lost, when I lose confidence, when I feel as though I have reached my limits, that I find myself asking “why am I doing this?”
So an effective reply could be along the lines of “what are you struggling with?” or “what can you make sense of in this topic so far?” in order to find some common ground to which to return.
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).