There is loads of maths in science. We know that science involves loads of formulae as well as manipulations and practical applications of the maths we teach in maths lessons.
But I don’t really know what science teachers are doing with maths, or how they are doing it.
For students to make good progress in maths and science, it makes sense that maths teachers and science teachers should use methods and approaches that are familiar and similar, and consider together how and when they should do this.
The mathematician EH Moore was complaining about the water-tight separation of maths and science and the “unaccountably stupid way of teaching” that resulted from this as far back back as 1902.
Yet I’ve never spoken to the science department about algebra, or the issues our Year 7s have with understanding fractions. I’ve never really invited them into the fold to look at approaches to teaching algebra and fractions and I certainly don’t know which of my maths students are able to apply their algebraic manipulations in science.
That was until I reviewed my ITT trainee’s assignment on the teaching of algebra in science.
Here’s a particularly pertinent piece from her writing:
Despite science and mathematics having much in common, both being underpinned by ideas of “quantitative reasoning” (Thompson 1994; Isaacs et al 1997) and being related in their “aim to discover patterns and relationships” (AAAS 1989), the relationship between the two disciplines has not always been a productive one (Lenton and Stevens 1999; Orton and Roper 2000; Pietrocola 2008).
It is therefore important for me to reflect on the impact of my own practice on the positive relationship between science and mathematics, which, as teachers, we are so encouraged to develop (DfES 2001; Ross et al 2010).”
And it made me think that perhaps I really should do that too. Especially considering she had already done the groundwork.
Maths topics in science
My school also uses AQA for science and my ITT trainee identified 15 areas where algebraic manipulation was required in KS3:
- Cell biology
- The digestive system
- The heart
- Quantitative chemistry
- Rates of reaction
- Energy changes
- Specific heat capacity
Common issues in algebra in maths and science
To do algebra you need to be able to do two things: 1 recognise what symbols mean and substitute them for numerical values, and 2 rearrange equations.
There is lots of good material by the NCETM. One of its suggestions is that pupils write a list of the symbols they already know and explain their meanings before they learn new symbols. It also has some great activities to help pupils to grasp the ‘balance model’ of equations.
There are further studies showing many examples where mathematics in science is a purely procedural process. The use of formula triangles is, for me, a symptom of ‘outcome’ over ‘process’, fine detail over conceptual understanding.
Students are often offered shortcuts to how to get an answer. At best this is a wasted opportunity to apply their maths and to reinforce their understanding by working through the maths with a common approach. At worse it undermines the teaching in maths. In many schools, Year 7 pupils first meet an equation that needs rearranging in science.
So thanks to my ITT trainee, the next INSET day is now planned to be a joint maths, science and humanities day. We are going to look at how we teach these topics and the analogies and language that we use to do so and will be trying to find out which of our students can apply mathematical approaches to scientific contexts outside the maths classroom. This should provide some really useful, quick feedback for us, which should be useful at least 15 times over all of KS3!