I attended the HEA Developments in Mathematics Support for the Physical Sciences one day meeting at Liverpool University back in April. Various speakers described how maths was tackled in their subject at their university (I was one of them, describing Maths for Chemistry at Keele’s (r)evolution over the past 6 years, you can find the presentation on my slideshare), and a lot of good discussion was had.
So why did we need to have a maths meeting for the physical sciences and what is the problem? Most academics who spoke described the wide range of mathematics qualifications that their incoming first year students have. Keele is no exception and we require a C at GCSE. Having recently become aware of different papers sat by GCSE students, I now understand that this may not be an appropriate entry level of maths as it allows students to avoid some topics that are quite important for studying chemistry at university level. Our first year cohort has maths qualifications ranging from the C at GCSE through to acceptance on a course to study Chemistry and Mathematics. What does this mean for teaching chemistry or physics? It means that we can make few assumptions about the level of prior knowledge our students have. It also means that no matter what maths support we put in place, some students will find it straightforward, others will find it very challenging. This is for a variety of reasons.
At this point I’ll note that I’m aware a few of my students read this. I do take great care about the language I use to describe our students, and I try to make positive generalisations. I’m not keen on applying deficit models of any subset of students [I find the language of ‘women underachieving’ to be extremely annoying] so I’m trying very hard here to make general points without trying to single out any group.
Why will a group of students find maths challenging? Many don’t have confidence in their own ability to ‘do’ maths. Many have had past experiences of maths that may mean they think that they cannot ‘do’ maths, as if it is some fixed ability that they have in a fixed quantity. Many made different subject choices post-GCSE and maths wasn’t one of them so there is a little catching up to do. But I do know that I have never met a student who had a fundamental inability to ‘do’ maths. I’ve met students (both while teaching and as a student myself) who were extremely resistant to trying maths, I’ve met students who wouldn’t put time in to practice but never a student who, by virtue of some intrinsic trait, couldn’t do maths. If there’s one area of science where a defeatist attitude really holds students back, it’s maths.
I loved Peter Khan’s talk ‘Studying a physical science in the language of mathematics’ in which he described maths as a language. Like all languages he said, it is best to learn it young and it takes a lot of practice to gain fluency. I came back to his words later that day as I read a joke about differentiation by parts and my maths language skills kicked in to translate the symbols into words to explain why I was laughing to someone else (admittedly it took a fair bit of explaining…). I haven’t really used that maths skill for 3 years.
So where does that leave those of us who teach the more physical side of chemistry, or really anything that requires calculators? I think we have to split maths into two broad areas. One is scientific numeracy where students have or develop the confidence to perform tasks in the chemistry context that use maths. A yield calculation, determining the concentration of acid in a titration, working out the mass of reagent to add, the ability to put numbers into an equation and manipulate the equation to obtain the answer, drawing a straight line graph…I could go on. Sometimes I think we confuse students by pointing out the little tricks they can use to check they’ve got the right answer. As I teach spectroscopy, I often give them ‘typical values’ for spectroscopic quantities. Perhaps that muddles the issue for those who are focussing on getting an answer first. So there’s the scientific numeracy and then there is the other maths stuff, things like calculus and the like.
The only thing I’m sure of is that unless a student is willing to try when it comes to maths, and be smart enough to try at the first opportunity given, some topics will be unnecessarily difficult.