Analysis: from poetry and sports to history, dancing and storytelling, there's an abundance of ways to teach maths in a creative manner

By Mary Scahill, Dr Cornelia Connolly, Dr Aisling McCluskey and Dr Tony Hall, NUI Galway

(1) Think poetry

Take your favourite poem or rhyme and try to notice the mathematics hidden within it. Maybe it’s a imerick or haiku or villanelle or even the spooky prophetic rhyming of the witches in Shakespeare’s Macbeth. Like all great songs, these hold a mesmerising, ordered quality which comes from the basic mathematics behind their design. Have a go at writing your own haiku. The formula is simple: the first line of your poem should contain five syllables, the second line seven syllables, and the third line five syllables.

(2) Google the Calculus Wars

Learn how one of the most important and fascinating developments in mathematical history, calculus, was jointly invented by Gottfried Leibniz and Isaac Newton, two of the most famous and brilliant minds in history. While at the time both mathematicians and their friends contested and claimed the original discovery, there is a consensus today that both Newton and Leibniz independently invented the calculus, which allows us to measure change, a very important function of maths in today’s complex and fast-moving world.

(3) Some 19th century future thinking

Computational thinking (or CT for short) is one of the big new ideas in computer science, mathematics and STEM education. As well as enabling us to do so many new activities which were previously unimaginable, computers are changing fundamentally how we think and learn.

But computational thinking was first originated in the 19th century by Countess Ada Lovelace, the daughter of the great Romantic poet, Lord Byron. Countess Lovelace was the world’s first computer programmer - or, as she called it, "poetical scientist" - and she devised a sophisticated algorithm to compute Bernoulli Numbers. What she innovated in the 1840s is what we try to do today with computational thinking when we try to come up with systematic strategies for understanding a range of problems and challenges, and then use computers to provide or simulate solutions.

Pick one of your favourite activities (such as making a cup of tea or hitting a sliotar with a hurley) and break it down into its basic, constituent activities and parts. Take away any unnecessary detail and try to notice patterns that can be repeated. There are many great and free computer applications, which you can use to program (simulate) your algorithm. Use the online version of Scratch to create a simple computer program to implement your algorithm.

(4) Tune up with Pythagoras

Best known for his eponymous theorem (you know the one: for any right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides), Pythagoras also made remarkable contributions to the mathematical theory of music. The Greek philosopher noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers and that these ratios could be extended to other musical instruments. Discovery of the chromatic, diatonic and enharmonic scales are said to be the work of Pythagoras. The next time you witness someone tuning a musical instrument, reflect on the mathematical link and if the musician is using Pythagorean tuning to get ready.

The probability of a particular athlete or team winning is just mathematics

(5) Telling stories

Storytelling is regarded as one of the most powerful formational processes in education. According to the late educational psychologist Jerome Bruner, storytelling is a uniquely human activity that serves as a key foundation for all our learning and development. It allows us to structure and make sense of our world, while also playing a very important dual role in mediating and inspiring our imagination.

Oral storytelling can transform the abstract, objective, deductive mathematics experiences in the classroom into a subject imbued with narrative, subjective feelings and meanings. Many different stories can be wrapped around mathematics, including science fiction, history, stories of adventure, fairy tales and detective stories.

Similarly, different types of mathematics such as arithmetic, measurement, statistics, and algebra can be embedded in the oral narrative through problem solving, algorithms, concepts and communication. Literature and storytelling can enrich mathematics education. Why not design your own whodunit, or fictional quest, where answering mathematical problems and questions allows the sleuth to decode answers to solve the mystery?

(6) You dancing? You asking?

There are many cross-curricular possibilities with mathematics and dance. Students can discover topological ideas while learning different dancing positions in salsa. They can use maypole dancing to investigate geometric patterns or folk dancing links with group theory and permutations. There are multiple possibilities and permutations to connect ideas and patterns in mathematics with dance.

Here’s a way for students to learn about patterns and geometry through the medium of dance. Groups make up different clapping patterns which can then be combined to create a unique rhythm. Each group then creates a simple dance, to form a geometric shape of their own choosing. To follow on from this, the groups perform a mathematical transformation through dance. For example, one group performs a translation, by using dance moves to glide across the floor, whilst maintaining their geometric shape. A second group performs a rotation and a third, performs a reflection, again choreographed with dance moves. Finally, all the choreography is brought together as groups perform their mathematical transformations and their clapping rhythms simultaneously.

Developing spatial awareness, collecting data and recognising mathematics in daily life is invaluable.

(7) Maths and sports

Statistics and probability play an important role in sports. In basketball, mathematics is used to calculate average points a player scores in a game, while mathematics is used in bowling to find out how many points were scored in each frame. The importance of player statistics is becoming more central in GAA, football and rugby. The probability of a particular athlete or team winning is just mathematics.

(8) The arts’ equation  

Mathematical tools are used in an essential way in the creation of art, architecture and in design. A simple example, that also connects art and mathematics, is where children can use partially completed diagrams to come up with the formula for the numbers to populate Pascal’s triangle. The activity can then be developed further through the medium of art with groups of children participating in a "colour by numbers" activity to create four Pascal’s Triangles, which when joined together form the image of a 3-D cube. A follow-on activity could involve students in discovering the many hidden number patterns that lie within Pascal’s triangle, again through the medium of art.

(9) Maths in nature

The Fibonacci sequence is where each number in the sequence is found by adding up the two numbers before it (ie the sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 etc). Students could be introduced to the Fibonacci sequence by connecting mathematics and nature.

The Fibonacci numbers are evident in some patterns, which occur naturally in nature. Many plants and trees replicate the Fibonacci sequence in their growth patterns. In some plants, the arrangement of leaves around a stem follows the Fibonacci sequence, while many trees exhibit the Fibonacci sequence in their growth points where branches are formed. Using craftwork to create a tree, which reflects the Fibonacci sequence, allows students to express their creativity while learning mathematics.

Encourage children to work in groups, to figure out the Fibonacci sequence for themselves, given only a set of cards containing the relevant numbers. The children can develop their knowledge by participating in an arts and crafts activity during which they each design a leaf or a flower to create a "Fibonacci Tree" (see below). In assembling the tree, the students should ensure that the growing patterns of both the branches and leaves follow the Fibonacci sequence.

(10) Vroom vroom

The three concepts of distance, speed and time bring together mathematics and science. Developing spatial awareness, collecting data and recognising mathematics in daily life is invaluable. As an example of this, children are introduced to the concepts of distance, speed and time in class and for the follow-on activity 1m strips of cardboard are covered in a variety of different materials such as cooking foil, cotton and cloth. Children use a dinky car and a smartphone to calculate the speed of the car over the different surfaces and record their findings.

Mary Scahill is a researcher at the School Of Education, NUI Galway. Dr Cornelia Connolly is a lecturer at the School of Education, NUI Galway Dr Aisling McCluskey is a senior lecturer at the School of Mathematics, Statistics and Applied Mathematics, NUI Galway. Dr Tony Hall is a senior lecturer in Educational Technology and a design-based researcher in the School of Education, NUI  Galway. Find out more about NUI Galway’s specialist teacher education degree programme in maths and applied maths here