*‘In an age of ‘big data’, geography and geography teachers have a key role in educating students to become critical consumers of the information they are presented with, both inside and outside school.’*

Mark Jones, 2017

#### Topics on this page:

- Thinking about numeracy in geography teaching
- Number in geography
- Discussion with a mathematics teacher
- Data-handling in geography
- Teaching numeracy for maps, charts and graphs in geography
- Teaching statistics and numeracy for geography examinations
- Reading

Numerical data is important for geography and numeracy is an essential skill for learning geography. Geography teachers must help students to develop and apply numeracy skills to extend their geographical thinking and help them to progress in the subject. However, *numeracy* involves more than merely working with data and requires a student to have an ability to use numbers and mathematical concepts.

Numeracy in geography is essentially mathematical thinking; this is not just the use of numbers, but more how the use of mathematics can help us improve our understanding of how the world works. Geography lessons provide many opportunities for developing students’ mathematical understanding and applying it to real-world situations.

In the UK in general, there are national concerns about students’ standards of numerical literacy. The English National Curriculum places the responsibility on teachers to concern themselves with developing their students numeracy. It expects that:

‘*Teachers should develop students’ numeracy in all subjects so that they understand and appreciate the importance of mathematics. Students should be taught to apply arithmetic fluently to problems, understand and use measures, make estimates and sense check their work. Students should apply their geometric and algebraic understanding, and relate their understanding of probability to the notions of risk and uncertainty. They should also understand the cycle of collecting, presenting and analysing data. They should be taught to apply their mathematics to both routine and non-routine problems, including breaking down more complex problems into a series of simpler steps.’ (2014 National Curriculum: Para 5.2)*

The reform of geography examinations since 2014 has increased the range and level of numeracy that students are expected to demonstrate in post-14 geography. All geography students need to be able to use numbers and mathematical concepts. This is an important element to include in planning GCSE and A level curricula and should be part of many geography lessons.

Harris (2018) explains the importance of data skills in the development of geographical knowledge and reminds us that geography teaching must not be diverted by teaching data ‘techniques’ when he writes, ‘*The simple point is that quantitative geography is not about teaching methods, but about teaching geography’.*

##### Key reading

- Jones, M. (2017) ‘Numeracy’ in Jones, M. (ed)
*Secondary Geography Handbook*. Sheffield: Geographical Association, Chapter 16. - Read about the importance of data skills in the development of geographical knowledge in Harris (2018).

#### Thinking about numeracy in geography teaching

As a new teacher you have three challenges to tackle:

- To make sure you have the necessary numerical knowledge and skills
- To find ways to integrate numeracy and data handling skills effectively into your geography lessons
- To gain the confidence and competence to use data and the technology that handles it in the geography classroom.

- Study carefully the
*Glossary of numeracy terms*in Jones (2017) p 216 and check you fully understand the meaning of each of these. You need to be precise and accurate in how you use these terms in your teaching if you are not to confuse students.

Numeracy for geographers | |

Category | Examples |

Numbers for measurement | temperatures, percentages, distances, river flows |

Numbers as coordinates | grid references and latitude/longitude |

Comparative data | ratios such as population density or GNP |

Contextual numeric data | to give a sense of scale and importance e.g. rainfall totals; value of trade; population numbers |

Visual quantitative data | tables, charts, graphs, choropleth maps, isolines |

Data for solving problems/ undertaking enquires | decision making activities, fieldwork data, statistical techniques |

- See Brooks (2006) ‘Cracking the code – numeracy and geography
*‘*. - See
*The Language of Mathematics in Science – a Guide for Teachers of 11-16 Science*from the Association for Science and Education. Geographers have much in common with science teachers when working with mathematical ideas. You might find this booklet useful for finding about any calculations or uses of mathematics of which you are unsure. - See the GA webpage on Conducting statistical tests for fieldwork
*.*

- When you observe other teachers’ geography lessons focus on
*how*and*why*numerical data, including graphs, tables and charts, are used to support geographical learning. - Ask the mathematics department if you can observe some of their lessons and think about how you could use some of their teaching approaches in geography.
- If there is a new mathematics teacher in your school you could also discuss this with them and perhaps co-teach some lessons.

#### Number in geography

In geography lessons we are constantly asking students to use numbers and manipulate them in calculations, for example to work out a ratio or percentage. If you are not confident as to how to break down the steps to help students with a calculation, discuss this with mathematics teachers. Some of the mathematical language and methods your students have been taught may be different to when you were at school, so it is always a good idea to check.

Students are often asked in geography lessons to use very large and very small numbers, positives and negatives, fractions and decimals. Some students may need help to make sense of these numbers, particularly handling fractions or decimals.

Roberts (2023) p 55 identifies some difficulties students have with number and quantitative units and you need to take this into account when you are asking students to use numbers. Consider whether the units of measurement you are using might be unfamiliar to students. It is helpful to use comparisons and analogies that are part of the students’ experience when you refer to numeric values.

Refer to these readings for more information about key stage 3 numeracy:

- Roberts (2023), especially Chapters 6 [Using Geographical Resources]; 15 [Intelligent Guesswork]; 16 [Five Key Points]. These provide good insights about teaching aspects of numeracy and graphicacy.
- Brooks (2006) pp 134-8.
- Davidson et al (1998) explains some common numerical problems affecting geographical learning.

Read these two examples of collaboration between the mathematics and geography departments at key stage 3:

- Jones and Nankivell (2016) which explores river fieldwork and includes a useful table linking the geography activities to the mathematics curriculum.
*ICT to support numeracy development in geography for year 7.*

Look at these simple ideas for using numbers in geography:

- Rogers (2017) ideas 9, 13, 15, 16.
- A from a GA Conference presentation in 2014. Can you create a similar numeric starter to use?

There are some numeracy skills that we often want to use in geography lessons before students are formally taught these techniques in the mathematics curriculum, e.g. for example, pie charts and scatter graphs. It would be beneficial to discuss with the mathematics department in your school when they teach students these skills in their curriculum.

Arrange to meet the numeracy coordinator in your school, or a mathematics teacher, to discuss strategies to improve students’ numeracy. Some points to discuss are:

- What aspects of the mathematics curriculum overlap with geography content?
- Are there any terms/methods of calculation that geography and mathematics approach differently?
- What aspects of numeracy give students most difficulties?
- What strategies to use to support students who are having difficulties?
- Which types of graphs do students find easiest to interpret?
- What ideas can they suggest to integrate numeracy in the geography topic you are currently teaching?

#### Data handling in geography

Data handling is an important component of geography teaching particularly in geographical enquiry. Look at this diagram of the framework for learning through enquiry with the focus on numeracy*. *

Data, particularly in the form of tables and abstract statistics, can be difficult for students to understand. Visual representations, such as shown on graphs or maps, are often easier for them. Data that they have experienced, because it is a topic they know something about or because they collected it during fieldwork, is also likely to be more meaningful.

Handling data and representing it in graphs and maps can be done more quickly and easily with technology and this can speed up access for students. But the *selection* of the appropriate techniques is important and results can be misleading if this is not done correctly.

- Refer to
*The data handling cycle and associated questions*(see Brooks (2006) pp 138-141, Jones (2017) p 221, and Biddulph et al (2021) p114). This shows the stages of data processing that students will need to engage with if they are to have some geographical understanding of data.

In today’s world ‘big data’ is a hot topic. This is data that is collected in large quantities across the world in real time; it results in huge data sets. This data can be only be processed software. Websites such as Gapminder and Worldmapper draw on big data and are very useful in geography to make big data accessible to students. ‘Big data’ can be volatile and difficult to verify and is open to manipulation to promote particular ideas. You should always use such data from sources that are reliable.

#### Teaching numeracy for maps, charts and graphs in geography

Basic map-skills involve several aspects of numeracy, such as co-ordinates and scale. Students must also be taught how to interpret map keys accurately so they understand the way in which quantitative data has been categorised may bias the story it tells. Many students find this challenging, as they do reading the axes of graphs and interpreting the measurements.

The interpretation of what graphs and tables are telling us geographically can be numerically challenging for students. Jones (2017) discusses the importance of ‘reading for meaning’ and identifies three stages that students need to be aware of:

- What does the data tell us?
- Reading between the data
- Reading beyond the data: what can we infer from the data?

- Read Jones (2017) pp 221-4 and study Figure 9 which provides an excellent description of the errors and misconceptions that students can make when interpreting data.
- Refer to Atherton, R. (2006) ‘Grappling with climate graphs’,
*Teaching Geography,*Climate graphs do not use the usual mathematical conventions, and this article has practical advice for helping students who struggle with climate graphs. - Read Harris, M. (2017) pp 107 – 110 for practical advice on handling graphs. He points out that it is important to spend some time investigating the data set, rather than just arriving at the end product.
- Refer to the guidance from the Field Studies council on data presentation.

Geography teachers have adopted different strategies to assist students to get to grips with interpreting graphs. One is using a ‘human graph’ which is often adopted ‘in the field’ (See Charlton et al (2012) to help students get to grips with the data they have collected. Another is the Living graphs strategy).

- Carry out Task 4.4 on page 117 in Biddulph et al (2021). This involves looking at the examination specifications for your school and noting the numeracy requirements and the range of skills. Then reviewing the key stage 3 and 4 curriculum to find out where and how numeracy skills are developed.
- Discuss your findings with your geography mentor. How are students’ numeracy skills progressively developed? Does the key stage 3 use of numeracy in geography provide sufficient foundation for GCSE and A level?

#### Teaching statistics and numeracy for geography examinations

The above paper lists the numeracy requirements for GCSE and A level geography which include cartographic, graphic, numeric and statistical skills. Numeracy accounts for 10% of the final examination at GCSE.

At AS and A level students are required to understand and critically apply quantitative data techniques. These are more demanding requirements than for previous geography examinations but the priority is to develop students’ geographical understanding and not just to teach the mathematical techniques. When teaching data skills in geography, it is important that the focus is not purely on the mechanics of statistical calculations.

- Read Jones (2017) pp 224–5.
- Refer to
*Data Skills in Geography*from the Royal Geographical Society. This webpage has many useful links, including the guidance written by the examination boards.

Harris (2018) explains why the four data skills of numeracy, visualisation, statistics and data handling must be seen alongside thinking geographically to enable students to explore geographical ideas and go beyond the calculation and presentation of data to interpretation and reflection. He argues strongly that teaching data skills in geography requires the embedding of data in the teaching of core geographical topics.

- Read Harris (2018) and (2020) for a thorough analysis of quantitative methods at AL and the implications for geography teachers.

While Harris’s review (2020) found that while the amount and difficulty of the mathematics at A level had not changed, the reintroduction of the independent study provides an enhanced opportunity for data skills and there is also considerable scope for the use of data to be embedded into the teaching of the geographical themes.

He also identified that the cognitive/intellectual demands made of students in relation to maths and data skills was greater than the level of maths alone suggests. Students are now required to undertake deeper reasoning and have more understanding beyond that of applying a statistical test. Harris adds:

*‘Some students find it really hard to transfer their maths skills into geography perhaps because real life data is messy. It is the need to understand, interpret and make linkages between data in a geographical context that takes the quantitative component (e.g. the doing of a statistical test) beyond rote learning and adds to the challenge of it.’*

- Refer to Conducting statistical tests for fieldwork on the GA website where statistical calculations and presentations are illustrated and demonstrated.

#### Reading

- Biddulph, M., Lambert, D. and Balderstone, D. (2021)
*Learning to Teach Geography in the Secondary School: A Companion to School Experience, 4rd edition*. London: Routledge, pp 113-7. - Brooks, C. (2006) ‘Cracking the code – numeracy and geography‘, Chapter 12 in Balderstone, D. (ed.),
*Secondary Geography Handbook*, Sheffield: The Geographical Association, pp. 134–38. - Charlton. M., Lapthorn, N., Moncrieff, D. and Turney, A. (2012) ‘Changing coastal fieldwork’,
*Teaching Geography*, Autumn. - Davidson, G., Stevens, B. and Williams, A. (1998) ‘Developing numeracy through geography’,
*Teaching Geography,*October. - Harris, M. (2017)
*Becoming an Outstanding Geography Teacher*, Routledge. Chapter 9: Numeracy in geography. - Harris, R. (2018) ‘From data to knowledge teaching data skills in geography’,
*Geography*, Spring. - Harris, R. (2020) ‘An independent review of quantitative methods in A level geography
*‘*, Royal Geographical Society. - Jones, M. (2017) ‘Numeracy’ in Jones, M. (ed)
*Secondary Geography Handbook*. Sheffield: Geographical Association, Chapter 16. - Jones, R. and Noncivil, J. (2016) ‘Developing numeracy skills through fieldwork’,
*Teaching Geography*, Autumn. - Roberts, M. (2003)
*Learning through enquiry: Making sense of geography in the key stage 3 classroom*. Sheffield: Geographical Association, Chapter 8: Focus on Numeracy. - Roberts, M. (2023)
*Geography through Enquiry: An approach to teaching and learning in the secondary schoo*l, Second edition. Sheffield: Geographical Association. - Rogers, D. (2017)
*100 ideas for Secondary Teachers: Outstanding Geography Lessons*, Bloomsbury Education. - St John, P. and Richardson, D. (1996)
*Methods of Statistical Analysis of Fieldwork Data.*Sheffield: Geographical Association.