Mathematical Writing

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Prof Franco Vivaldi on developing a writing course in mathematics, using writing as a focus on conceptual understanding.

Transcript of Professor Franco Vivaldi (QMUL School of Mathematical Sciences), ‘Mathematical Writing’:

I started thinking about embedding elements of writing in mathematics courses in the mid-90s. Then I started implementing some fragments of this programme first of all in a small course that I was teaching then I started attempting, experimenting with other courses and then eventually that became a feature of all the courses I taught. I was asking the students to provide very brief descriptions, explanations, trying to avoid as much as possible the use of symbols. To bring attention onto the concept, to the attention of the meaning of words, also to avoid plagiarism from the web because it’s very difficult to find material that deals with, say, a mathematical topic without any symbols at all, so that worked rather well.

But these were sort of sporadic attempts and they taught me a great lesson: that when you, essentially exposition – of which writing is one form – brings the student’s mental pattern to centre stage. You can see exactly how accurate or inaccurate are their thoughts. It’s a bit brutal, like as a tool, but it offers you the opportunity to remedy the sort of model of learning that is based on automatic application of certain recipes.

And so I started developing this and in conversation with Wilfred Hodges, a logician within the department, who after a while started developing the idea of using writing as a learning tool for a logic course that he wanted to develop. And so the course, Logic 1, was introduced four or five years ago by Wilfred Hodges. It was the first course in this department that had writing as a essential element.

Eventually Wilfred retired and so I inherited that course, and I changed that course from a pilot scheme – it started off with only 6 students – into a – I won’t say a mainstream course, but a course for a large audience – and it changed its title, it’s now called Mathematical Writing, it’s a course for second-year students. Normally instructions about writing mathematics are not given to undergraduates, they are normally given to postgraduate students in order to prepare them to write research articles or a thesis but we found that this emphasis on writing particularly at the beginning of the second year is extremely useful to help the students develop a coherent approach to conceptualisation and also to prepare them to write a project in the third year.

Now this course has now been running for, this is the third year. It has been very useful for certain students but it also exposed great problems. Essentially the response of the students to this format has been very very bimolar. Because the course is irreducibly conceptual. You cannot write about things that you don’t understand and whereas we can sort of find ways of getting students who don’t understand completely things to learn enough to be able to produce material sufficient for a pass in the course, and so this, I think it’s been a useful lesson.

We are now thinking as a result of this, as a result of the problems that this course has actually exposed, the deficiencies in the student learning, to introduce a baby version of it in the first year which is now under consideration.

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