Access Maths

I enjoy David Colquhoun's blog. As someone who often thinks too long before speaking up, I enjoy forthright people and I often - not quite always - agree with what he has to say. I started to look at his book, Lectures on Biostatistics; statistical ideas and methods, much of which I'm at least aware of, but deployed in different contexts for quite different purposes so I was curious to see how he'd present and discuss them. Even if there was nothing else useful in it, this book would be interesting for its discussion of the experimental estimation of Purity in Heart index.

Almost immediately I came across these words: "...most of us find arithmetic easier than thinking." This is so true! I'm going to stick these words under the noses of my Access Maths students. Mostly Access Maths is about mastering standard techniques: how to find the solutions of a quadratic equation, how to find unknown sides or angles in arbitrary triangles, how to calculate the area lying under the graph of a curve (well, not any curve, those defined by functions we've learned how to integrate). These are not "arithmetic" but the same point applies: one can learn how to carry out these exercises without really understanding the ideas behind them; without really thinking. In fact they can be systematised so completely that there is software to carry them out (try Wolfram Alpha for instance).

There is an irresistible pull of gravity towards the calculations you can do without thinking. You're learning something new for the first time, you're not quite sure why other people think you should learn it, you know you need to pass the exam to continue next year/get a job/avoid getting a job.... "Thinking" is hard so let's look for "arithmetic" ways through the course. So every now and again I stick the occasional non-standard question in, and over the year I try to encourage people to develop the general habits of thought that will help with these previously unseen kinds of problem. But there are always people who want to know "how do you do that problem?"

How interesting, then, to also come across another blog post about a book I haven't read which seems to be all about avoiding that pull of gravity right at the start of education; about making Maths interesting by emphasising concepts and ideas rather than memorising techniques and for standard sorts of problems. When I meet people they bring grown-up motivations. They meet me, and Maths, in the course of a greater project of making their way through life and they're looking for strategies to get them through the course. If involvement in what we might call the internal life of the subject turns out to be the best way to deal with the course, well, that's a pleasant surprise. As children they don't yet have those motivations; mere "arithmetic" holds no interest for them. But ideas, thinking, well, that'll drag you in every time,