# The Nature of Mathematics

It is a common belief that nature can be understood using mathematics. Many scientists have discovered mathematical concepts and patterns in nature for example from sunflowers to snowflakes to hurricanes and galaxies.

#### Symmetry

A great example of mathematical concepts in nature is symmetry which is found in abundance in the natural world. A snowflake exhibits a six-fold radial symmetry with unique and identical patterns on each arm. Each snowflake is different as when they fall from the sky, each experiences its own unique atmospheric conditions such as humidity and wind, which ultimately affect how the crystals on the snowflake forms. Due to each arm of the snowflake experiencing the same environmental conditions, it crystallises in the exact same way, producing a symmetrical snowflake.

Honeycombs are an example of wallpaper symmetry. It is believed by mathematicians that bees build their honeycombs in a hexagonal pattern as it is the best shape for storing the greatest amount of honey while using the least amount of wax to create the structure.

Orb spiders build their webs using radial symmetry. They create near-perfect circular webs that have near-equal-distanced radial supports coming out of the middle and a spiral that is woven to catch prey. Scientists believe that these spiders build their webs in this way for strength and to evenly distribute the force of impact when a fly or other prey becomes entangled in the web.

Symmetry in nature appears to have multiple benefits.

#### The Fibonacci Sequence

There is a simple sequence of numbers that appears in many places in nature called the Fibonacci sequence. Named after Leonardo of Pisa, also known as Fibonacci. This sequence of numbers involves starting at 0 then 1 and adding the previous two number together to get the next digit in the sequence, ultimately equating to 0 1  1  2   5  8  13  21  34 and so on.

#### The Fibonacci Spiral

The pattern in sunflower seeds and many other flowers are arranged in a Fibonacci spiral which keeps the seeds uniformly distributed regardless of the size of the seeds. “A Fibonacci spiral is a series of connected quarter-circles drawn inside an array of squares with Fibonacci numbers for dimensions. The squares fit perfectly together because of the nature of the sequence, where the next number is equal to the sum of the two before it.” (Live Science, 2017) – see diagram opposite. The spirals pack florets as tight as can be, maximising their ability to gather sunlight for the plant.

The Fibonacci spiral can be found in many different places in nature for example the spiral is very evident in the chambers of a nautilus shell. The spiral occurs as the shell grows outwards and tries to maintain its proportional shape. The benefit of the nautilus’s growth pattern allows it to maintain its shape throughout its entire life.

In some plants, the leaves appear to be arranged in a Fibonacci spiral. The reason behind the staggered leaves in a spiral shape is to maximise the space each leaf has and to ensure the greatest absorption of sunlight for the plant’s growth.

Therefore, maths is everywhere in nature and has a specific purpose, either to ensure a snowflake is strong enough, a plant receives optimum conditions or even for structural purposes to save waste. Nature is spectacular in the way it uses mathematical concepts to create its own benefits.

#### References

Fibonacci in Nature. 2017. Fibonacci in Nature. [ONLINE] Available at:http://jwilson.coe.uga.edu/emat6680/parveen/fib_nature.htm. [Accessed 31 October 2017].

Live Science. 2017. What is the Fibonacci Sequence?. [ONLINE] Available at: https://www.livescience.com/37470-fibonacci-sequence.html. [Accessed 31 October 2017].

Planet Dolan | Obscure Facts About Life. 2017. 15 Beautiful Examples of Mathematics in Nature – Page 2 – Planet Dolan | Obscure Facts About Life. [ONLINE] Available at: http://www.planetdolan.com/15-beautiful-examples-of-mathematics-in-nature/2/. [Accessed 31 October 2017].

# Conquering Maths Anxiety

Many of us will be familiar with the shear panic, the sweaty palms, the headaches and the confusion that comes alongside attempting mathematical problems but not many will be aware that this is a diagnosable condition and is extremely prevalent among the population. Maths anxiety has been defined as “a feeling of tension, apprehension, or fear that interferes with math performance” (Ashcraft, M.H 2002, p. 1) and is believed to affect around a quarter of the population including thousands of school teachers.

#### Why do we have maths anxiety?

For me, the anxiety I have for maths came as a surprise as i was always very competent and able in the subject all through primary and up to secondary school. This anxiety first began when i stopped studying it at high school and saw others around me become more competent in the subject. This created a fear that i wasn’t as good as them and couldn’t understand the concepts they were learning. I felt i was being left behind in my learning and was not as smart as them. Therefore, I opted to avoid any mathematical problems that i perceived as too difficult or simply used my calculator to prevent making mistakes and looking bad.

For others, maths anxiety can often be caused by influential adults such as parents who have negative attitudes towards mathematics because they project their fears onto their children. This leads to the children adopting the same negative feelings, such as “maths is a waste of time” and taking them into school. It can also come from the teachers themselves. If a teacher is negative or afraid of maths then their teaching will influence how the children in the class feel towards it. Maths anxiety can often come from the fear of embarrassment or failure which puts the children off from even attempting the subject. If a child has been embarrassed or made to feel wrong in front of the class, it can destroy their confidence and discourage them to explore mathematical concepts in the future.

Maths is a difficult subject and needs strong support from teachers, not more pressure of succeeding in tests or appearing to be always right.

#### How does maths anxiety impact us?

Learners with maths anxiety will repeatedly go above and beyond to avoid doing maths in class and outside class, which in turn results in even poorer competences in the subject and applications of maths to real life. Children are unfortunately led to believe maths is about having right answers and are therefore too afraid of making mistakes to even try. This means as children grow up avoiding maths and not trying they are likely to have the same poor abilities in their adulthood.

As adults, a lifetime of maths anxiety can have devastating consequences. Some avoid applying for jobs which may involve some mathematical reasoning, therefore limiting their career opportunities. They may have a lack of confidence dealing with their own personal finances, their mortgage, buying/running a car etc. From these examples we can see just how important maths skills are in the real world outside of the classroom. This is why, as future teachers, we need to promote the positivity and relevance of maths to children.

#### Conquering Maths Anxiety!

As teachers, it is vital that we help children understand maths and not be afraid of it. Allowing children to experiment and discover maths in their own time is so important for their futures and the quality of life they will receive from doing so. We need to show them the relevance of maths and ensure that mathematical problems are set in meaningful contexts to the children. This will make the questions worth solving!

Making maths fun in the classroom will encourage children to enjoy discovering concepts in maths and be curious in their discoveries.

Make children feel comfortable to ask questions and explore as children should not be afraid of getting it wrong – focus more on the discovery and on the excitement!

This Ted Talk by Robert Ahdoot is a great place to start on learning how to conquer maths anxiety in the classroom!

References

Ashcraft, M.H. (2002), Math anxiety: Personal, educational, and cognitive consequence, Current Directions in Psychological Science, 11: 181–185

Atkinson, E (1992) Mathematics with Reason, Oxon: Bookpoint Ltd.

Brian, K (2012) Maths Anxiety: the numbers are mounting The Guardian [Online] Available at: http://www.theguardian.com/education/2012/apr/30/maths-anxiety-school-support [Accessed: 7 October 2017]

# “Maths is hard”

### Why is Maths Hard?

What is it that makes maths appear to be a hard subject? Is it all the rules you must follow or all the formulas you need to remember? Is it the focus on accuracy or all the strange unfamiliar symbols?

Most people you ask will tell you they found maths difficult at school and they were never very good at it. In the UK, it has now become culturally acceptable to be ‘bad’ at mathematics and we more than often overhear the words “I can’t do maths” (Kowsun,2008). Negativity towards the subject is, unfortunately, something that people take pride in and boast about. This may be due to the stereotype that maths has been given, thus leading people to believe that only the rare and gifted people are capable of doing maths. It is seen as male dominated and ‘nerdy’, all of which are untrue stereotypes.

A research study by BAE Systems found that approximately one in six adults admitted to being embarrassed by how difficult they find mathematics and one in five adults required the use of a calculator to work out simple sums. The proportion of adults struggling with mathematics has greatly increased as today, 49% of adults have the maths skills expected of an 11 year old child still at primary school (Garner, R. 2012). Low adult numeracy skills lead to many disadvantages in life such as difficulty getting a job, struggling to do their job as it may entail some form of mathematics or even just simply difficulty dealing with home finances and everyday shopping. Low skills in mathematics costs the nation around £20.2 billion (National Numeracy).

### Importance of Maths

Little do these people know how important mathematics is to them and their everyday lives and perhaps, even how much they really use maths on a day- to-day basis. For example, a routine task of crossing the road requires many mathematical processes including estimating the speed of oncoming vehicles, the speed you can walk across, the time it will take you to cross and the distance to the other side. These are all common calculations our brain carries out each day however not many would include this as being ‘maths’ .The preconception is that mathematics is all about finding a ‘right answer’ whereas in reality, “mathematical discovery relies on the same guesswork that informs our everyday maths” ( Pound, L 2008). This meaning that maths is all around us and is vitally important to our lives.

### Maths is for Everyone!

Despite all these factors insinuating that maths is hard, we as human beings are born mathematical which makes learning maths significantly easier than it would be otherwise.

Everyone can do maths and we all carry out calculations in our head every single day without our realisation. The only boundary we have stopping us succeeding in maths is our own attitude towards it. “Doing mathematics does not require any special ability not possessed by every one of us” (Devlin, 2000 p253).

References

Devlin, K. (2000) The Maths Gene London: Weidenfeld & Nicolson.

Garner, R. Independent. 2012. Almost 50 per cent of adults can’t do basic maths. [ONLINE] Available at: http://www.independent.co.uk/news/education/education-news/almost-50-per-cent-of-adults-cant-do-basic-maths-that-means-half-7469119.html. [Accessed 6 October 2017].

Hall, J (2013). Adults Struggling with Basic Maths. [ONLINE] Available at:http://www.independent.co.uk/news/uk/home-news/adults-struggling-with-basic-maths-with-one-in-five-requiring-a-calculator-for-even-the-most-simple-8532488.html. [Accessed 6 October 2017].

Kowsun, J. (2008). This innumerate isle – Article – TES [Online] Available at: http://www.tes.co.uk/article.aspx?storycode=2033102 (Accessed 6 October 2017)

National Numeracy. Attitudes Towards Maths. [ONLINE] Available at:https://www.nationalnumeracy.org.uk/sites/default/files/attitudes_towards_maths_-_updated_branding.pdf. [Accessed 6 October 2017].

Pound, L (2008) Thinking and Learning about Mathematics in the Early Years. New York: Routledge