**Ruth Wroe, Maths Subject Advisor**

In this blog I’ll be outlining why psychology 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 A Level Psychology specification (H567), but core maths will support equivalent Level 3 qualifications in psychology from other awarding organisations that you may be teaching at your centre.

### Why take core maths?

Students that achieve a grade 4 or better at GCSE Maths but don’t wish to continue studying maths at AS or 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 that 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 maths skills in different contexts so that 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 psychology – 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 psychology.

Studying core maths alongside psychology helps to instil and reinforce the maths met in A Level Psychology. It complements its key mathematical requirements of selecting appropriate statistical techniques, interpreting and exploring data, and using diagrams and calculations.

### Mathematical skills requirements of A Level Psychology

The A Level Psychology specification states that:

“10% of the marks available within written examinations will be for assessment of mathematics (in the context of psychology) at a Level 2 standard, or higher. All assessment of these skills will be in the component 1 examination (Research Methods).

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).”

Studying Core Maths A or B will certainly help to address the first two statements. A Level Psychology students will have prior learning from GCSE Maths (9-1) and most, but not all, will have developed quantitative skills from GCSE Psychology. Maths skills developed at GCSE will be revisited and their application in a variety of contexts, including psychology, will be mastered.

The third statement is highlighting that a few of the mathematical skills listed in section 5c of the specification (D1.8, D.11, D1.12, D1.13, D1.16 and to some extent D1.5 and D1.14) will not have been met at GCSE Maths and are in A Level Maths. Importantly, most of 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 psychology 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 psychologists.

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

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

- D0 Arithmetic and numerical computation (0.1 – 0.3)
- D1 Handling data (1.1 – 1.4, 1.6, 1.7, 1.9, 1.11, 1.14 – 1.16)*
- D2 Algebra (2.2, 2.3)
- D3 Graphs (3.1, 3.2)

* Order of magnitude calculations (D1.9) are explored more fully in Core Maths A, while calculating standard deviation which falls under measures of dispersion (D1.14), is covered in Core Maths B.

Some topics will have only been met in higher tier GCSE, such as histograms (D1.3 and D3.2). 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 (D1.3) will need revisiting in psychology lessons. Frequency tables, frequency diagrams, bar charts, pie charts, line graphs and scatter diagrams will have been met at GCSE, but histograms will be new to some. Categorical and numerical data will have been met at GCSE, but different types of data and characteristics of normal and skewed distributions will be introduced in core maths.

Core maths students will work algebraically with formulae and equations which matches the requirements of D2. There is also a section dedicated to working with graphs which ties in with D3.

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

As the maths in psychology is essentially working with data, using statistical techniques and representations and interpreting findings, the B specification offers greater support in the required statistical techniques. The following are covered in Core Maths B:

- Using suitable sampling methods (simple random, opportunity and self-selected) (D1.5)
- Using Spearman’s rho and the chi-square test (D1.8)
- Using statistical tables to determine significance (D1.13)
- Calculating standard deviation (D1.14)

Students will have been introduced to the idea of random sampling and bias 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 the use of suitable sampling methods and identifying sources of sampling error are covered in Core Maths B.

Core Maths B students will be able to understand the process of hypothesis testing and use the associated language (null hypothesis H_{0}, alternative hypothesis H_{1}, significance level, *p*-value, 1-tail test, 2-tail test, critical value, critical region, acceptance region, rejection region). Two non-parametric tests are included in Core Maths B; Spearman’s rho and chi-square. The focus is on using and interpreting these statistical tests.

Standard deviation, statistical hypothesis testing, and sampling are in AS Level Maths, but the chi-square test and Spearman’s rho 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?

The following mathematical requirements are **not** covered in our core maths qualifications:

- Snowball sampling and control of extraneous variables (D1.5)
- Levels of measurement (nominal, ordinal and interval) (D1.10)
- Criteria for using a parametric test and a specific non-parametric inferential test (Mann-Whitney U test, Wilcoxon signed rank test, chi-square, Binomial sign test, and Spearman’s rho) (D1.12)
- Use of specific non-parametric inferential tests (Mann-Whitney U test, Wilcoxon signed rank test, and Binomial sign test) and type 1 and 2 errors (D1.8)
- Mathematical notation (much less than « and much greater than ») (D2.1)

Criteria for selecting the most appropriate statistical test is not included in our core maths qualifications. Of the five non-parametric tests used in A Level Psychology, Core Maths B covers using and interpreting Spearman’s rho and the chi-square test.

The Mann-Whitney U test (also known as the Wilcoxon rank-sum test) is in A Level Further Maths A and the Wilcoxon signed-rank test is in A Level Further Maths A and B. The Binomial sign test is not in A Level Further Maths, it’s mathematical content specific to A Level Psychology. Core Maths B students will have the benefit of transferable skills from working with other statistical tests though, so they will be familiar with using formulae, the testing process and the use of critical values.

As core maths is more about the application of maths skills, less emphasis is placed on notations, but they will be familiar with <, >, ∝ and ~. The symbols used in calculations for order of magnitude (« and ») can be reinforced in psychology lessons.

### Core maths resources for psychology

Our psychology qualification page offers teaching support in the form of statistical guides, workbooks and activities. These are located under Teaching activities for research methods in the planning and teaching section of A Level Psychology. The Quantitative skills guide and the Descriptive statistics workbook for GCSE Psychology also serve as useful preparatory resources for A Level students.

In addition, the Association for the Teaching of Psychology hosts maths resources for teachers of psychology and in collaboration with the Advanced Maths Support Programme (AMSP) have produced Desmos activities for Psychology to help deliver the mathematical requirements of psychology.

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

- correlation study (statistical hypothesis testing, product moment correlation)
- finding the way (statistical hypothesis testing, Mann-Whitney U test, choosing an appropriate statistical test)
- take your partners (statistical hypothesis testing, Spearman’s rank correlation coefficient, quality of data)
- music and maths (statistical hypothesis testing, Wilcoxon signed rank test for paired samples, choosing an appropriate statistical test).

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 psychology.

### Core maths takeaways for psychology teachers

AMSP have produced a postcard and poster that you can display in classrooms and use at open events to promote core maths with students. They also run free CPD events in conjunction with the Association for the Teaching of Psychology to help psychology teachers deliver 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.