The significance of rounding and significant figures

I now find myself chairing the production of two new Open University modules, so writing course materials ought to take priority over writing this blog. That’s a pity, because there’s so much assessment-related that I want to reflect on.

As a compromise, I’ve decided to report a few more of the things that I’m finding out from our analysis of student responses to  Maths for Science e-assessment questions (since it’s Maths for Science that I am deep in re-writing at the moment). Some of the findings reinforce what we already know, some are unexpected. However, in each case, if there are mistakes being made by a number of students then it behoves us to look carefully at our teaching in those areas.

As an example – our students seem to be really bad at rounding – they will truncate 1.465 to 1.4 rather than rounding it to 1.5. I still don’t really know why this is, or whether it’s a common problem with students at conventional universities. However, when I looked carefully I realised that so far Maths for Science was concerned, one of the problems was that we didn’t explicitly students how to round (though we did teach rounding in the context of orders of magnitude). Oops! Hopefully the new edition of the book will do better.

Our students are also really bad at quoting numbers to an appropriate number of significant figures. After more than 20 years of teaching OU students, this finding didn’t really surprise me – and it is reasonable that students will more readily quote an answer of 3.4 as being to two significant figures than they will 0.034 or 3.0. I’ve tried to improve our teaching of these points too, but I’m not optimistic as to my chances of success.