**Ruth Wroe, Maths Subject Advisor**

In this blog I’ll be outlining why geography 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 Geography specifications (H481), but core maths will support equivalent Level 3 qualifications in geography 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 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 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 geography – 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 geography.

A Level Geography students will have prior learning from GCSE Maths (9-1) and most, but not all, will have acquired geographical skills from GCSE Geography. However, taking core maths alongside geography helps to instill and reinforce the maths met in A Level Geography. 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 Geography

The bulk of the required mathematical skills are listed under the geographical skills section, but there are also some in topic-specific skills.

The geography specification states that ‘Geographical and fieldwork skills are fundamental to the study, practice and discipline of geography. They are integrated into all aspects of the subject.’ In fact, geographical skills are assessed in all three component exams and in the independent investigation.

The assessment objective AO3 is specifically dedicated to assessing the use of **quantitative**, qualitative and fieldwork skills. Across all components, AO3 makes up 28% of the A Level with 20 of the 28% in the independent investigation (see section 3b of the specification).

With such a sizable contribution to the overall assessment, it is clear that geography students need to get to grips with the quantitative skills required in their subject.

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

#### Subject content

The quantitative nature of geography means the A Level subject content covers a wide variety of data in different forms. For example, A Level students will work with wind speeds, tidal ranges, average sea level, the Human Development Index, global mean energy balance, climate modelling, areas and volumes of the world’s oceans, the Global Food Security Index, seafloor spreading rates and thermal heat gradient of the earth’s crust amongst others. This will involve working with index numbers, percentage change, ratios, rates of change, averages, range, the modelling cycle and areas and volumes; all of which are covered in both specifications.

#### Topic-specific skills

The mathematics in the five main topic-specific skills are also covered in both specifications:

- Mass balance (work with formulae; convert units of mass and time; work with rates)
- Sediment budget calculation (work with formulae, units of volume and mass, scales; evaluate data displays)
- Climate graphs (interpret compound graphs – bar and line graphs)
- Rates of flow (calculate and convert between rates of change, with time or distance)
- Unit conversions (work with and convert between units of measure for distance, area, volume, density, mass, time, temperature, angle; use standard form for very small and large numbers)

#### Geographical skills

The geographical skills fall under four headings: geographical information, geo-located data, qualitative skills and quantitative skills. Core maths offers the greatest support for geographical information and quantitative skills. The following are covered to some extent by both specifications, but the italicised skills are covered in more depth in Core Maths B:

- understand the ethical implications of collecting and representing geographical data
- understand the nature of and use different types of geographical information:
- qualitative, quantitative, primary, secondary, numerical and spatial data
- images, maps, diagrams and graphical representations

*collect, analyse and interpret such information, and demonstrate the ability to understand and apply suitable analytical approaches for the different information types**undertake informed and critical questioning of data sources, analytical methodologies, data reporting and presentation, including the ability to identify sources of error in data and to identify the misuse of data**communicate and evaluate findings*- understand the purposes and difference between the following and be able to use them in appropriate contexts:
- mean, median, mode,
- range, interquartile range and
*standard deviation* - lines of best fit and correlation on graphical representations
- measurement,
*measurement errors, and sampling*

Some of the above will have been met in GCSE Maths, but some topics will have only been in higher tier. Coverage of histograms, cumulative frequency graphs, box plots, measures of central tendency and interquartile range from graphical representations of grouped data will really support your students that have foundation tier GCSE Maths.

It is also worth noting that in core maths the emphasis is on using and interpreting statistical diagrams. Constructing statistical diagrams is taught at GCSE and diagrams for grouped data such as cumulative frequency graphs and histograms are in higher tier GCSE Maths so these will need revisiting in geography lessons.

The geo-located data section is geography context specific so although the maths content has been met at GCSE Maths it can be further reinforced using real-life contexts in core maths. For example, geo-spatial mapping skills includes bar charts, pie charts, proportional symbols and flow lines which draws on statistical techniques and the concepts of ratio and proportionality from foundation tier GCSE Maths.

Students will have met categorical and numerical data and the concept of outliers at GCSE but different types of data and methods for determining outliers will be introduced in core maths.

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

As the maths in geography 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 geographical skills are covered in Core Maths B:

- understand the purposes and difference between the following and be able to use them in appropriate contexts:
- standard deviation
- tests of association and significance tests, such as chi-squared and Spearman’s rank correlation
- measurement, measurement errors, and sampling.

Apart from an introduction to sampling in GCSE Maths, these geographical skills are 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.

Coverage of chi-square and Spearman’s rank correlation focuses on applying and interpreting these statistical tests. Criteria for selecting an appropriate statistical test and the conditions required are not included.

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?

The two-sample *t*-test and the Mann-Whitney U test are **not** covered in our core maths qualifications.

The two-sample *t*-test used to be in legacy A Level Further Maths, but it is no longer in either A Level Further Maths A or Further Maths B, so it is mathematical content specific to A Level Geography. 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 using formulae, the testing process and the use of critical values.

The Mann-Whitney U test (also known as the Wilcoxon rank-sum test) is in A Level Further Maths A but Core Maths B students will have the benefit of transferable skills from working with other statistical tests.

Some graphs used in geography, such as dispersion graphs, radial graphs, cross-sections, population pyramids and rose charts, are not explicitly listed in the core maths specifications but the skills developed from working with other statistical diagrams will assist with understanding of these.

### Core maths resources for geography

Our geography qualification page offers teaching support in geographical data skills in the form of a teacher guide, a set of PowerPoints and a student workbook. In addition, the Royal Geographical Society (with IBG) hosts core maths resources for geography and the data skills in geography project resources.

MEI’s Integrating Mathematical Problem solving (IMPs) has a section on The mathematics of geography. It currently has an activity on hydraulic radius (maths content: area, perimeter, Spearman’s rank correlation coefficient, statistical hypothesis testing).

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 geography.

### Core maths takeaways for geography 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 Royal Geographical Society (with IBG) to help geography 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.