**Ruth Wroe, OCR Subject Advisor**

In this blog I’ll be outlining why biology students should be encouraged to take core maths and how it will support their studies. I’ll also highlight some useful cross-curricular resources and promotional materials.

I’ll be focusing on our AS/A Level in Biology specifications (H020/H420 and H022/H422), but core maths will support equivalent Level 3 qualifications in biology from other awarding organisations that you may be teaching at your centre.

### Why take core maths?

Students who achieve a grade 4 or better at GCSE Maths but don’t wish to continue studying maths at AS/A Level need a convincing argument to take a Level 3 maths course. The fact that it covers the kind of maths that they will need in their other Level 3 subjects, which should help them to do better, is a compelling argument though.

### What are the aims and content?

The aim of Core Maths A and B is to take students who have attained at least a grade 4 at GCSE and enable them to confidently tackle the kinds of mathematical problems which they are likely to encounter in their other subjects or in their future lives. It does not have the algebraic focus of AS Level Maths, but it is a Level 3 qualification which introduces some new Level 3 content, as well as reinforcing the required GCSE Maths content used in other A Level subjects and vocational qualifications. So, for many students, core maths is a much better option than AS Level.

### What will your students learn?

In core maths lessons students will practise applying their skills in different contexts so they become more confident at tackling problems set in a range of situations, and more adept at mathematical reasoning. As a result, they’ll become more competent at dealing with the maths in the context of biology – identifying the maths involved, carrying out the required steps, understanding how their answer relates to the problem asked and interpreting what their answer means in the context of biology.

Studying core maths alongside biology complements its key mathematical requirements of using calculations, graphs and tables; selecting appropriate statistical techniques; and interpreting and exploring data.

### Mathematical requirements of AS and A Level Biology

The A Level Biology specification states that:

“10% of the marks available within written examinations will be for assessment of mathematics (in the context of biology) at a Level 2 standard, or higher.

The following will be counted as Level 2 (or higher) mathematics:

- application and understanding requiring choice of data or equation to be used
- problem solving involving use of mathematics from different areas of maths and decisions about direction to proceed
- questions involving use of A Level mathematical content (as of 2012) for example, use of logarithmic equations.”

Studying Core Maths A or B will certainly help to address the first two statements. In fact, biology students will have met most of the required mathematical skills at GCSE Maths so the focus will be on revisiting and mastering their application in a biology context.

The third statement is highlighting that a few of the mathematical skills listed in section 5d of the specification (M0.5, M2.5 and M1.9, and to some extent M1.5 and M1.10) will not have been met at GCSE Maths and are in A Level Maths. Importantly, these skills are in our core maths qualifications too. ‘A Level’ has merely been referenced in the specification as a benchmark as this would be familiar to biology teachers.

Core maths qualifications are relatively new, and little would have been known about them at the time the specification was first published but as you’ll see they’re brilliant support qualifications for A Level biologists.

### What’s covered in Core Maths A and B?

These are the mathematical skills required in biology that are included in Core Maths A and B:

M0 Arithmetic and numerical computation (0.1 – 0.5)

M1 Handling data (1.1 – 1.4, 1.6 – 1.8, 1.10 – 1.11)*

M2 Algebra (2.2 – 2.5)

M3 Graphs (3.1 – 3.6)

M4 Geometry (4.1)

* Order of magnitude calculations (M1.8) are explored more fully in Core Maths A, while calculating standard deviation which falls under measures of dispersion (M1.10), is covered in Core Maths B.

Some topics will have only been met in higher tier GCSE, such as exponentials, their graphs and growth (M0.5), histograms (M1.3 and M3.2) and measuring the rate of change from a curve (M3.6). Their inclusion in core maths will really support your students that took foundation tier GCSE Maths.

In core maths the emphasis is on using and interpreting statistical diagrams so the requirement of constructing diagrams (M1.3) will need revisiting in biology lessons. Frequency tables, frequency diagrams, bar charts, line graphs and scatter diagrams will have been met at GCSE, but histograms will be new to some.

Several requirements are biology context specific so although the maths content has been met at GCSE Maths it will be further reinforced in core maths. For example, simple probability (M1.4) includes the probability associated with genetic inheritance. This builds on sample space work from GCSE Maths.

Order of magnitude calculations (M1.8) draws on the GCSE concepts of ratio, enlargement, and units of measure. In core maths similar problems involving several mathematical concepts will be encountered and there may be the opportunity to practise in this context. Likewise, students will have met percentage change in GCSE Maths but the work on percentage error calculations in core maths will help when handling uncertainties in measurements (M1.11).

Although core maths is not heavily focused on algebraic manipulation, students will work with formulae and will be able to rearrange simple formulae involving the four operations, powers and roots (M2.2).

Logarithms (M0.5, M2.5) will not have been met at GCSE Maths but they are introduced in core maths. Core maths students will be able to use and interpret a logarithmic scale, represent numbers as log values and solve problems involving exponential growth rates. With this being identified as one of the more challenging maths skills in A Level Biology, it is invaluable content in core maths.

There is a whole section dedicated to working with graphs and gradients which will support M3, and a geometry section to reinforce M4.

### What extra is covered in Core Maths B?

Sampling methods (M1.5), calculating standard deviation (M1.10) and using the chi-square test and Spearman’s rank correlation coefficient (M1.9) are covered in Core Maths B.

Students will have been introduced to sampling in GCSE Maths, but the rest is distinctly Level 3 content.

Standard deviation and sampling are introduced in the common component to Core Maths A and B. Core Maths A students will know that standard deviation is a measure of spread, but its calculation is covered in Core Maths B. Likewise, Core Maths A students will know the meaning of the terms **sample** and **population** and the idea of random sampling, but in Core Maths B students learn about using suitable sampling methods in appropriate contexts, so this supports the work on random and non-random sampling techniques in biology.

Some of the concepts met under M1.5 are specific to biology, such as Simpson’s index of diversity and the Hardy-Weinberg equation, but working with a variety of formulae in core maths will help.

Standard deviation, statistical hypothesis testing, and sampling are in AS Level Maths, but the chi-square test and Spearman’s rank correlation coefficient are only introduced in AS Level Further Maths. Core Maths B, on the other hand, covers them all.

### What’s not covered in Core Maths A or B?

Symbols used in order of magnitude calculations (M2.1), selecting statistical tests and using the student’s *t*-test (M1.9) are not covered in our core maths qualifications.

As core maths is more about the application of maths skills, less emphasis is placed on notations, but they will be familiar with:

less than <

greater than >

is proportional to ∝

and is approximately equal to ~

The symbols used in calculations for order of magnitude can be reinforced in biology lessons:

much less than «

much greater than »

and the use of ~ to mean of the same order of magnitude as

Criteria for selecting the most appropriate statistical test is not covered in our core maths qualifications. The focus is on using and interpreting statistical tests.

The two-sample *t*-test and the paired-sample *t*-test were in legacy A Level Further Maths, but they are no longer in either Further Maths A or B. It’s mathematical content specific to A Level Biology. However, Core Maths B students cover the background to the Normal distribution and hypothesis testing which will help with their understanding of the student’s *t*-test. They will have also worked with other tests, so they will be familiar with the testing process and the use of critical values.

### Formulae used in AS and A Level Biology

Core maths students are expected to recall and use the formulae required for GCSE Maths as well as some additional formulae detailed in the specification content and it’s a similar situation in AS and A Level Biology. The GCSE formulae (circumference, area, volume, mean and percentage change) that biology students will need to recall are all used in core maths. Taking core maths alongside biology will help instil these formulae which are too often forgotten after finishing GCSE Maths. Many of the biological formulae that need to be recalled will also be better understood from working on areas, volumes, ratio, and exponentials in core maths lessons.

### Core maths resources for biology

Our Maths for biology webpage has online resources for the five modules listed above. These were developed in partnership with the University of East Anglia. The Mathematical skills handbook provides contexts in Biology for the different mathematical skills and there is also a useful Mathematical skills statistics booklet.

MEI’s Integrating Mathematical Problem solving (IMPs) has a section on ‘The mathematics of biology’. There are currently three activities on:

- statistical testing in medicine (hypothesis testing, chi-squared test, association),
- the microscope (enlargements, ratio, converting between units and magnification calculations),
- exponential growth (logarithms and logarithmic scale).

Resources on Integral’s Core Maths Platform and the activities and exercises in the *OCR Core Maths A and B (MEI)* textbook can also be used for introducing the mathematical content in biology.

### Core maths takeaways for biology teachers

AMSP have produced a postcard and poster that you can display in classrooms and use at open events to promote core maths with your students. They also run a variety of free CPD events for both core maths and biology teachers to help in delivering the maths in their subject.

### Stay connected

If you have any questions, you can email us at maths@ocr.org.uk, call us on 01223 553998 or Tweet us @OCR_Maths. You can also sign up to subject updates and receive information about resources and support.

### About the author

Ruth supports the Level 3 maths qualifications and has chief responsibility for Core Maths A and B. She joined the maths team in 2014, working on the development of A Level Maths. Previously, Ruth taught maths in the UK, New Zealand, Kuwait, Oman and Qatar. Outside of work she cares for elderly parents but in her spare time she enjoys travelling, live music, real ale and dog walking.