# Making Maths Relevant to A level Biology

The majority of the skills were hidden away, often in the centre-assessed units of the older specifications which meant that students rarely had to go beyond **Simpson’s Index of Diversity** or the **Hardy-Weinberg Equation** in the examinations.

Fortunately, the content has dropped away giving us plenty of time to practise these skills with our students, oh wait, that’s not A level Biology.

It would be great if students were able to work through hundreds of similar problems to build fluency as in a Maths lesson, but the priority will always be given to the conceptual learning in Biology. So for me it is about giving students the opportunity to practise their skills in relevant scenarios that enhance the conceptual learning.

Certain mathematical formulae fit in to A level Biology without any additional thought such as RQs, Hardy-Weinberg, SA:V, etc, however others are much harder for students to see the relevance of, or indeed the application, for example logarithmic values.

My ethos with these mathematical functions is to increase exposure to build confidence first and hopefully fluency with the majority of students. This might mean using spreadsheets to calculate the standard deviation of a class set of enzyme data but plotting the error bars by hand, before going on to calculate standard deviation themselves at a later date.

Taking logarithmic functions for example, introducing these when carrying out serial dilutions adds another layer to the process. I still enjoy the caffeine-Daphnia investigation as the students can delve a little deeper into the control of heart rate, but it is also a great practical for students using semi-logarithmic graph paper to plot their dose-response curve.

Flipping the maths to exponential, the go to is **bacterial growth** but there are also the opportunities for PCR estimates or my favourite, genetic probability. This latter one is about putting independent assortment into context whilst improving numeracy. Students often come in with pre- (or indeed mis-) conceptions regarding chromosome number, for some reason it’s either n=2 (textbook diagrams) or n=23. I like to introduce a few different numbers, e.g.

Myrmecia pilosula n=1;

Arabidopsis thaliana n=5;

Lampetra fluviatilis n=86

to get students really engaging with the likelihood of identical gametes without even considering crossing-over.

Whilst on the cell division topic, it is a good opportunity to practise chi-squared and compare the frequency of cells in each part of the cell cycle of cancerous tissue to the expected non-cancerous tissue.

There is scope to have students predict the numbers by providing percentage of the cell cycle spent in each stage, and if you are keen have the students complete their own counts from images of HeLa cell cultures, although this needs a little more care to find appropriate numbers.

Using the same statistical analysis with meiotic cell division would highlight that prophase I is far too long when compared with mitotic cell division. Using maths in this fashion opens up the idea of what events are happening in prophase 1 that are not happening in mitotic prophase or indeed prophase II.

I might be a little too enthusiastic about the cell cycle now, solely the fault of the STEM Insight placement at the University of Birmingham.

So you want a different context, I can do that!

Student t-test, paired or unpaired, that is the question. With respect to the OCR A specification, it’s all about the exercise and heart rate, leading students to struggle to understand when it’s paired or unpaired as they see changing the population as just a validity issue. However, counting stomata opens up a raft of possibilities.

I like the imprints, both aesthetically and the ease of collection across a range of families.

Would your students be able to answer *“is there a significant difference in stomatal density between the upper and lower surface of a leaf?” *

What would they think was a reasonable sample size? What area should they count the stomata in? How will they work out this area? Does the entire leaf share the same density? How will they compile their data from the class?

Once the class has a full set of data, it gives the opportunity to discuss the spread of data around the mean and review standard deviation again before eliciting the components of the paired Student t-test. Then it’s simply a task of comparing different species to introduce the unpaired Student t-test.

Spearman’s rank again is frequently overlooked as tedious by students.

In Year 12 we drop it in to challenge preconceptions, for example does resting pulse rate correlate to height? This ties into that exercise investigation again, however we delve a little deeper into significant correlations when we study succession.

We are fortunate that we have access to a sizeable dune complex within a 20 minute drive. So taking soil samples every 100m and drying them out in an oven, students get 18 opportunities to calculate percentage changes to work out how much water was present. Then we can burn it (use a fume cupboard) and calculate the percentage of biomass in the soil. Is there a correlation? Or even better do calculated Simpson’s Index of Diversity for each site correlate with either percentage water or percentage biomass?

When I was teaching AQA, comparing Simpson’s Index with Mann-Whitney U was my go to, be it comparing two ponds, or sweep netting a playing field or verge.

The ASAB have produced a really good sequence of lessons that centre around the behaviour of meerkats that could be developed into a homework task that goes beyond simply plugging numbers into a calculator.

The Biozone resources in the Year 2 workbook are excellent for fitting in statistics into relevant contexts.