The Climate Classroom - Infiltrating MATHS!

Ideas for Infiltrating the MATHS Classroom!

We might think that only some subjects naturally lend themselves to climate education – understanding our changing climate and weather patterns in geography, for example, or learning about aspects of the climate and ecosystems in science. But this is a world crisis that underpins everything, and as such, all subjects have a role to play.

Baba Dioum, Senegalese poet and environmentalist, famously said: “In the end, we will conserve only what we love; we will love only what we understand; and we will understand only what we are taught.” The subject of mathematics, developed over centuries, can be a creative and highly inter-connected branch of learning that provides a groundwork for understanding our beautiful world, helping pupils (and staff) to celebrate and deepen our love for nature.

Is Maths Even Real?

A recent TikTok video from an American high school student, showing her deliberating (whilst applying make-up) whether or not maths is actually real, quickly went viral. Why? Because she had inadvertently re-ignited a very ancient and unresolved philosophical debate: What, exactly, is maths? Is it invented, or discovered? And are the things that mathematicians work with—numbers, algebraic equations, geometry, theorems and so on—real?

Educators love these sorts of curious enquiries from students; it keeps subjects fresh and alive, and reinforces the relevance of the subject for our modern world. An educator seeking to embed climate education into their maths lesson can use these as a starting point when exploring our impact on nature – through analysing real data from the energy that we use, for example. We can also use this curiosity to explore astonishing mathematical patterns that occur throughout the natural world; as David Attenborough says, “People must feel that the natural world is important and valuable and beautiful and wonderful and an amazement and a pleasure,” because when we value nature, we want to protect it.

Maths: The World’s Dominant Language

As an English teacher, it is utterly fascinating to me that the first ever writing system which can be traced to its earliest prehistoric origin - the cuneiform script, created in Mesopotamia, present-day Iraq, ca. 3200 BC – is a numerical system of counting and recording goods with clay tokens: in other words, maths. How amazing, too, that this has become the world’s dominant language: almost all states, companies, organisations and institutions – whether they speak English, Hindi, Mandarin, or Spanish – use mathematical script to record and process data, in a way to make sense of information and ideas.

This theoretical system, borne of economic necessity, has evolved into a complex theory that seeks to understand truth. The development of this incredibly useful trading tool into an increasingly refined science of structure, order, and relation, helps us to understand the question of whether or not maths is real. Consider Einstein’s famous quotation: “How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably appropriate to the objects of reality?” This gets to the heart of it: the invented mathematical numbers and theories that exist within our imagination can – and do – describe the world around us in a remarkably serendipitous and accurate manner.

The Fibonacci Sequence

What connects a nautilus shell, the way seeds are positioned on a sunflower, the whorls of a fingerprint, a satellite image of a building storm, even a swirling galaxy? The answer is visually obvious – all contain a glorious spiral.

This is probably one of the best example of maths successfully describing physical reality: through the Fibonacci sequence, in which each number is the sum of the two preceding ones (named after the Italian mathematician who introduced the sequence to Western European mathematics in 1202, but interestingly first described in Indian mathematics as early as 200 BC). When you make squares with these widths – squares that fit very neatly together – you get this splendid spiral.

In maths lessons, this is a truly awesome way to demonstrate how intrinsic maths is when exploring patterns in nature, and cannot help but spark your students’ wonder and curiosity. They appear everywhere in biological settings, so often that you can easily take your class outside to find immediate examples – look at the branching in trees, the arrangement of leaves on a stem, an uncurling fern – or bring items into the classroom for your students to explore: the fruit sprouts of a pineapple, the flowering of an artichoke, or the arrangement of a pine cone's bracts.

The Golden Section

The maths department at The Chase introduce this remarkable design at the start of KS3, presenting the puzzle of recognising the recurring pattern, and igniting a simultaneous appreciation of nature. It doesn’t stop there – any two successive Fibonacci Numbers has a ratio very close to the Golden Ratio, a truly special number (approximately equal to 1.618) that appears many times in mathematics, geometry, art, architecture ... pretty much everywhere. Also known as the golden section, golden mean, or divine proportion, this mathematical ratio seems to be so inherently natural that it fosters a pure and organic composition that is aesthetically beautiful.

As well as opening up obvious cross-curricular links with biology, we can also create connections with Art and Design Technology – the Pyramids of Giza, the Parthenon in Athens, Michelangelo’s The Creation of Adam on the ceiling of the Sistine Chapel, Da Vinci’s Mona Lisa, even Twitter and Pepsi are all designed using the Golden Ratio. Pupils can be asked to think about what they consider proportionately pleasing – be it posters, adverts, paintings, album covers, film sets, background gaming images – and conduct an experiment whereby they overlay the golden spiral to see if (or where) it fits.

And it doesn’t stop there: even our bodies and faces follow this mathematical ratio:

As Galileo says, it seems that “Mathematics is the language with which God has written the universe.” – a quotation that can open up a cross-curricular mathematical discussion in Religious Education or Philosophy and Ethics!

Fibonacci in Music

There have been studies that suggest this sense of pleasing beauty is partly innate, hard-wired into our genetics. This harmony, demonstrated visually by architecture, paintings and sculpture, can also be heard.

An octave on the piano consists of 13 notes: eight are white keys, and five are black. A scale is composed of eight notes: the third and fifth create the foundation of a basic chord.

In a scale, the dominant note is the fifth, which is also the eighth note of all thirteen that makes up the octave ... look at these numbers! 3, 5, 8, 13 = all numbers in the Fibonacci sequence. And 13 / 8 = 1.618 = the Golden Section!

Our maths department show the pupils violins designed by Stradivari in such a way to fit the ratio as much as possible, play Mozart’s piano sonatas (arranged so that the number of bars in the development and recapitulation divided by the number of bars in the exposition equals 1.618), and further engage them by demonstrating how this mind-blowing theory is still used today by playing Lady Gaga’s ‘Perfect Illusion’, which features a bold key change at 111 out of 179 seconds (for those without a calculator, that’s equal to 1.618).

The Geometry of Plants

There is something so pleasing about exploring this innately natural pattern; the combination of synchronised items to create something that works beautifully as a whole mirrors nature’s ecosystem, where plants, animals, and other organisms, as well as weather and landscape, work together to ensure life can thrive. Every factor in an ecosystem depends on every other factor, either directly or indirectly; changes in the temperature will affect what plants will grow there, in turn affecting those animals that depend on the plants for food and shelter, and so on. An ecosystem works in harmony.

A teacher concerned with embedding climate education into their maths lessons will use the natural world as an innately fascinating context within which to learn mathematical concepts.

The Council for Learning Outside the Classroom highlights how taking pupils outside ‘has been proven to raise attainment and achievement, improve behaviour and improve the engagement of all groups of pupils, including those who are hard to engage inside the classroom environment’; it is also excellent for directly engaging pupils with nature.

Take pupils outside in any green space, on or near school, to explore the geometry of plants. Simple questions can reveal lots of patterns and shapes, allowing pupils to understand and witness key mathematical concepts such as symmetry, space and shape:

What is the arrangement of the leaves on their stems?
Do the leaves grow opposite to each other?
Do they alternate along the stem?
Do they grow in a spiral (whorled)?
Find some fallen leaves. Fold them in half along the stem - Is the right side is the same as the left side?

The human-made elements within the natural green areas can be explored, too: shapes in pavements, pathways, benches, picnic tables etc.

Connecting Pupils with Locality

Just as my previous article explored how we can teach the same skills in English, with a focus on climate content, so too can the key skills for maths be taught using content that will connect pupils with nature. Observing mathematical designs in nature that is specifically local to the pupils will strengthen these connections even further, fostering a deeper bond that will lead to a sense of pride and desire to protect; look at local trees, comparing the shapes, design and arrangement of their leaves. Measure the girths of trunks at top and bottom, calculate length of leaves, map out the local area – this not only also encompasses the maths topic of handling data, as findings can be put in table and graphs, but also offers serendipitous links to geography.

Data Sharing

Pupils can explore how companies are sharing data with researchers to help support investigations into policies that reduce emissions; requiring companies to openly publish data on their greenhouse gas emissions can also help hold companies accountable to their sustainability pledges, and can provide a new and powerful resource for innovative public policy research, supplying the evidence for much-needed environmental practices within schools, businesses and society.

Meaningful Data

Even better, get pupils to collect their own data. As author Dan Heath says, “Data are just summaries of thousands of stories—tell a few of those stories to help make the data meaningful.” Collecting, recording and representing data in maths can be made more meaningful to both the students and the planet if we collect and use pertinent data that corresponds to how our pupils live. Students are naturally more interested in learning about something if they understand how it relates to them personally, and we can help students feel connected to what they’re being taught by making the content they’re learning relevant to their own lives.

In addition to the collection of natural data discussed already, there are multiple ways to do this. EDF Energy’s schools programme, The Pod, has lots of ready-to-go resources and ideas, such as an activity that involves collecting and investigating food packaging waste, which is a huge problem in the UK (if we don’t improve recycling rates, there is the possibility of running out of landfill space). The Pod activity involves students conducting a practical activity of collecting and sorting empty food containers and packets into different materials and non-recyclable groups, then analysing the contents by calculating the average (mean, median and mode) and range, then interpreting and presenting the data, creating graphs, learning how diagrams can be misleading, and practising interpreting the average from grouped frequency tables.

Real Data – Real Change

This sort of data collection and analysis lesson can involve any number of real-life environmental approaches: using year-group or whole-school questionnaires to collate data on the number of people travelling sustainably to school, for example, or who have their own re-usable water bottle, or who don’t eat meat. Making good use of free technology and software that is easily available to all makes this step much more simple and straightforward – last year, our travel ambassador in year 12 created Google Form questionnaires asking how staff and students get to school; sharing these during tutor time reached the vast majority of pupils, and the outcomes formed the basis of our School Travel Plan:

At The Chase, we have increased the number of solar panels we have

(fortuitously on the maths roof!); soon, screens will be installed that will show our school’s actual daily energy use, linked directly to our solar panels. We can use this real data within our maths lessons, which will offer teachers a powerful tool in demonstrating how much actual, real energy we use, at what time of day and what times of year, how much it costs, and where we can potentially lower our use.

Information is Beautiful

There has never been a time where there is so much easy to access information; all we have to do is go on our phones, type a question into a search engine, and we are presented with millions and millions of results: data, information, statistics, numbers – it can feel incredibly overwhelming. Writer and designer David McCandless creates infographics in an attempt to make sense of this endless data; beautiful, useful diagrams and graphics that are ever changing as more data emerges.

His website Information is Beautiful has a whole section dedicated to Nature and Climate, with key questions and engaging statements such as ‘How is the World’s Energy and Electricity Created?” and “Exploring how many Gigatons of Carbon Dioxide have we released to date / can we safely release.” These can be explored in a maths class, and emulated with the pupils’ own data, creating wonderful, easy-to-access graphs and images on the school’s specific use of carbon, for example, or which year groups feel more confident in their understanding of climate change.

Reducing Anxiety

Being deep consumers of media can increase anxiety, and empowering pupils with manageable knowledge can be a powerful tool in dealing with this. When asked whether the use of statistics has dramatically changed his opinion or preconceived nations about something, David McCandless’s response was that researching and visualising statistics and data has substantially reduced several anxieties around topics such as air travel and infectious diseases. He goes on to say, however, that “Sadly, the only topic where the stats haven’t reduced my anxiety is climate change.”

But lots of his infographics offer hope through achievable solutions, such as his graph entitled “Food Waste is a big climate problem we can actually solve”, with everyday useful hints and tips to help reduce waste, and “What can we do personally to reduce emission?”, with genuinely impactful suggestions listed in an easily accessible bar graph format.

Instigate Behavioural Change

One of the best benefits of utilising real data is that it can, and does, instigate those much needed changes in behaviour, which are essential if we are to get to grips with the climate crisis. It is crucial that we enable students to explore the impact that lifestyle choices have on the environment, and that we facilitate their understanding of the contributors to global emissions.

Enabling students to acquire the ability to read data is an essential skill that will be more and more necessary within a society increasingly overwhelmed with information; numbers to do with carbon emissions occur again and again in the public space, and it's important to be able to compare and contextualise them. Developing students' carbon numeracy can offer a springboard for follow-up conversations in and outside of the classroom; and showing them the incredible mathematical wonders of nature will instil a love of the environment that will lead to the need to cherish and protect it.

As Albert Einstein said, “Look deep into nature, and then you will understand everything better.”

Sarah Dukes is Sustainability Coordinator and English Teacher at The Chase School in Malvern. She passionately feels we must adapt our school curriculum to include explicit teaching on the climate crisis, sustainability, and nature connectedness. She has spoken on Green and Climate Education (WEF), has contributed to the World Wildlife Fund’s Sustainability Schools Guide (2022), and is co-writing a chapter on embedding Climate Education within the PSHE curriculum. Twitter: @ecodukes; @TheChaseEco1

References and further resources:

The Centre of Learning With Nature:

https://www.learningwithnature.org/math-through-nature-nature-through-math/

Some great ideas here: https://www.dropbox.com/s/41acj9kdl4g4pdx/Gantry%20Plaza%20State%20Park%20Math%20Trails.pdf?dl=0

Nature’s Hidden Prime Number Code: https://www.bbc.co.uk/news/magazine-14305667

Importance Of Prime Numbers In Nature, Popular Culture and The Internet: https://www.scienceabc.com/pure-sciences/importance-significance-of-prime-numbers-nature-real-life-examples.html

Peculiar pattern found in ‘random’ prime numbers: https://www.nature.com/articles/nature.2016.19550

https://nrich.maths.org

Fibonacci & The Golden Ratio:

https://www.youtube.com/watch?v=9mozmHgg9Sk

https://en.wikipedia.org/wiki/Fibonacci_number

https://www.mathsisfun.com/numbers/fibonacci-sequence.html