I have discovered, or perhaps learned how to articulate, something fundamental: I like explaining things. Allow me to explain.

I do and have done a variety of different jobs. Mostly, of late, I am a lecturer in mathematics. I enjoy planning lectures, putting thought into the structure and how to make the content flow. I enjoy working with individual students who are stuck with problems, prompting them to come to the realisation about where they need to go rather than just giving them the answer. And I enjoy arranging group work activities, designing hoops and hurdles to develop students’ understanding of themselves and their skills.

Until last year, I worked to arrange teaching staff development activities and allocate funding for research and curriculum development projects. Besides this, I have spent time writing up educational research and teaching activities for a practitioner audience. I enjoyed planning and speaking at workshops and conferences, helping present teaching ideas and findings from our research to staff, and perhaps provoking people to think about the way they teach. I also enjoyed writing articles describing ‘what I did and why it was interesting’. Perhaps this latter even includes writing my PhD thesis, though it’s still a bit recent in the memory to fully appreciate this.

Alongside all this, I do bits of popular mathematics writing and speaking. I like writing, or more correctly I like ‘having written’, enormously. I feel these blog posts are at their best when I take some idea I have been mulling in the back of my mind and express it well to the reader, whether it is something strictly mathematical or not. (Whether this post counts remains to be seen!) I’ve also done a little work arranging and designing puzzles for outreach activities, which are most pleasing when they provide a staged development, with a simple version provoking thought and interest in a more advanced version.

To some, this all seems a hodge-podge of bits and pieces, like I can’t make up my mind about what I want to do, but I have been feeling that there is a common thread that I can’t quite express. A couple of months ago I picked up, and have now read, a copy of ‘Lecturing and Explaining’ by George Brown (1978). Brown has a “working definition” of ‘explaining’ as “giving understanding to someone else” (p. 7). Given this, Brown says that “explaining is at the heart of teaching in higher education just as its obverse, understanding, is at the heart of learning” (p. 39).

With this definition, I learn to detach explaining a little from the rest of the activity of teaching, and so to detach the ‘explaining’ elements of the other activities I have enjoyed. Writing an article about a mathematical concept for a non-mathematical audience? Explaining. Designing a series of activities or asking a set of questions to help someone come to understand something they have been struggling with? Explaining. Planning a talk so that each idea is broken down and progressed as part of a greater whole? Explaining.

Anyway, I’m entirely delighted to have come to this understanding (after Brown, through his book, explained it to me) and to know that so many of the aspects of my various jobs that I have most enjoyed are, in fact, the same.