Category Archives: Discovering Maths

Reflecting Upon the Discovering Mathematics Module

I would just like to take some time to look back on the past three months of this module, reflecting on how my opinions on maths has changed, and how I will moved forward with the experience that I have gained.

Beginning this module back in September, I didn’t fully know what to expect from this module. How much maths was I going to have to do? Would it help my worries about maths and improve the way I thought about it? Would it be beneficial to me as a teacher? There were so many questions that I was thinking.

Overall, I have to say my views about maths has changed dramatically over the past three months. I have gone from thinking that maths is nothing but sums and equations, to believing that maths can be truly fun across a variety of different subjects. As I mentioned in my first blog post about maths anxiety, I always enjoyed maths all the way through primary school, and only lost the excitement for it when I advanced into high school. This was the time when my view on maths changed, believing the myths that you were either good or bad at maths (me believing that I was the latter) and that you could not improve. You were either born with the ability to understand it or not. This took all joy out of maths when I was only learning formulas just to pass tests and exams, but this is not how maths should be.

Leading on from my own experiences of maths, I have always been apprehensive teaching maths in the classroom. If I did not fully understand a mathematical concept, then how can I explain it to learners and make sure they understand it fully? I do not want to be teaching maths the way that I was taught it, using textbooks and doing sums over and over until I ‘understood’ it. Maths should be fun, and not considered as the ‘boring’ subject that may children love to hate. During my placement, I did a lot of maths lessons, as I wanted to push myself to teach a subject I wasn’t 100% comfortable with. Although yes, I did use textbooks and worksheets sometimes, I tried to make many of my lessons practical, to get the children involved in their own learning. I found that the interactive, ‘fun’ lessons were the ones that produced the best engagement.

From this module I have learnt a variety of things.  One being that maths is not a singular subject that stands alone. It interconnects with every subject on the curriculum, and there are countless cross-curricular lessons that could be planned and executed linking maths with other subjects. My eyes have been opened to the fact that maths is in our lives every day, but not how we might expect it. The most interesting topic that has been covered in this module is the Fibonacci sequence and golden ratio. I find it hard to comprehend the fact that this sequence and number (phi) can be found everywhere: music, art, nature, the human body, even the galaxy that we live in. It was so fascinating to learn about and I would definitely love to take time out to learn more about it.

Overall, I feel that my confidence with maths has greatly improved as a result of this module. Seeing the fun side of maths and the many different applications of it has definitely lifted the barrier between maths and I. I will take all I have learnt in the past two months forward with me into practice and hope to use my new-found confidence to dispel the myths that many children believe about maths and show them in fact it can be fun!

Image result for maths is fun

Maths in Music

I have never played an instrument in my life or classed myself as musically talented. My brother plays the bagpipes and it amazes me how he can look at the notes and knows what it means. My musical abilities go as far as playing the recorder in primary school. So, when I found out we had a musical input, I was a bit apprehensive with what to expect.

We started off by listing some things that we think link maths and music. We came up with:

  • Rhythm
  • Scale
  • Chords
  • Tuning

It was quite difficult to think of the relations between maths and music without having a musical background, as I did not know but about music anyway. Du Sautoy (2011) said “rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry.”

The next thing we looked at was the Fibonacci sequence within music. Having previously looked at the Fibonacci sequence within art, it was interesting to see it appear in music as well.  I have written about the Fibonacci sequence in my last blog post so I won’t go into too much detail in this blog. There are 13 notes in an octave, scale is composed of 8 notes, the 5th and 3rd notes of the scale form the basic ‘root’ chord and are based on whole tone which is 2 steps from the root tone, that is the 1st note of the scale (Meisner, 2014).  This links to the Fibonacci sequence (0,1,1,2,3,5,8,13…). A piano keyboard scale goes from C to C with 13 keys, 8 white and 5, also split into groups of 3 and 2.  This 13th note as the octave is essential to computing the frequencies of the other notes (Meisner, 2012).

Here is the piano scale.

We then had a shot playing the instrument ourselves, which at first, I found a bit difficult, but after a few tries, I began to get the hang of. Getting the opportunity to play the instrument allowed me to experience it for myself and improve my understanding of notes and rhythm, which allowed me make connections between maths and music.

Finally, we looked at tuning an instrument. If a guitar is tuned perfectly, the notes that are strummed out are in perfect Fibonacci sequence. This is, however, not the same with a piano. If a piano was tuned in Fibonacci sequence, it would not sound right to the ear. Instead, it has to be tuned with a man made adaption on this sequence. This video does a great job of explaining why a piano cannot be tuned using the Fibonacci sequence.

It was not until taking the discovering maths module that I realised how many different areas maths connects to. This reinforces the ideas of Ma’s (2010) ideas of longitudinal coherence and multiple perspectives. I will take what I have learnt form this module into my practice as a teacher, showing the pupils how maths interconnects with other subjects, whilst creating some cross curricular lessons involving maths, music and art. I thoroughly enjoyed this input as it was practical and I liked getting to have a shot of it for myself.



Du Sautoy, M. (2011). Listen by numbers: music and maths. [Article]. Available at: [Accessed 27th November 2017]

Meisner, G. (2014) Music and the Fibonacci Sequence and Phi. [Online]. Available at: [Accessed 27th November 2017]

Minutephysics (2015) Why It’s Impossible to Tune a Piano[Online].  YouTube. Available at: [Accessed 27th November 2017]

Tindal, C. (2017). Maths in Art and The Fibonacci Sequence. [Blog].  Available at: [Accessed 27th November 2017]


Maths in Art and The Fibonacci Sequence

In our input with Anna, we learnt that there are many different aspects of maths within art. It was very interesting to learn about and see for ourselves.

The first activity that we took part in was drawing in the style of Mondrian. Piet Mondrian (1872 – 1944) was one of the founders of the Dutch movement De Sijl (The Art Story, n.d, b). De Stijl was an avant-garde style, that was appropriate to all aspects of modern life, from art to architecture (The Art Story, n.d., a). Mondrian was best known for being simplistic, using lines and rectangles to create his paintings.

Composition with Large Red Plane, Yellow, Black, Gray, and Blue (1921)

Here is one of Mondrian’s abstract paintings.

I then had a go at drawing my own Mondrian inspired piece of work. I started off by drawing two parallel lines about 9cm apart. I then began to draw lines within the first two lines, both vertically and horizontally, which created rectangles. I then coloured in some of the rectangles that were created and this was the result:

Here is my own interpretation of a Mondrian style of artwork.

The next thing we looked at was the Fibonacci sequence. This sequence starts with 0, and is when the two previous numbers add up to the following number, so it goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…etc. When this sequence is drawn out in squares, it makes spiral, also known as the ‘Golden Ratio’. This video looks at Fibonacci’s sequence and how it is found in nature. It also talks about the golden ratio and its relevance to Fibonacci’s sequence.

The golden ratio is the number 1.618033, also known as phi (Φ). This number is found by the formula  (a+b)/a = a/b . This relates to Fibonacci’s sequence, as ratio of each successive pair of numbers in the sequence approximates Phi (1.618. . .), as 5 divided by 3 is 1.666…, and 8 divided by 5 is 1.60 (Meisner, 2012, b).  Phi was first used by Greek sculptor and mathematician, Phidias (Meisner, 2012, a). It was Euclid that first talked about Phi as taking a line and   separating it into two, in a way that the ratio of the shortest segment to the longest will be the same ratio of the longest to the original line (Bellos, 2010).

The golden ratio was first called the ‘Divine Proportion’ in the 1500’s. Many people believed that by taking measurements of your body, and then using the formula of phi, you were beautiful if the result was 1.60. We had a try at this ourselves by measuring:

  • Distance from the ground to your belly button
  • Distance from your belly button to the top of your head
  • Distance from the ground to your knees
  • Length of your hand
  • Distance from your wrist to your elbow

Then we had to divide:

  • Distance from the ground to your belly button by distance from your belly button to the top of your head
  • Distance from the ground to your belly button by distance from the ground to your knees
  • Distance from your wrist to your elbow by length of your hand

Some of the results i got were 1.7 which is very close to the golden ratio, and others were way off with results of nearly 2.1.

Many Renaissance artists used the golden ratio in their paintings to achieve beauty. For example, Leonardo Da Vinci used it to define all the fundamental proportions of his painting of “The Last Supper,” from the dimensions of the table at which Christ and the disciples sat to the proportions of the walls and windows in the background (Meisner, 2012, a).

Image result for the golden ratio in the last supper da vinci

Here is how Da Vinci has used the golden ratio in two of his most famous paintings.

The golden ratio and Fibonacci’s sequence is also a prominent feature in nature, as mentioned in the video before. Here are some more examples:

Fibonacci’s sequence in the bones of a human hand.

The golden spiral in a hurricane.

Image result for golden spiral in milky way

Even our own galaxy that we live in is made up of  Fibonacci’s sequence.

I found this input incredibly interesting and will definitely be taking what I learned into the classroom. This input has definitely benefited me in not only seeing the link between maths and art, but also with nature, science, and much more. . Moving forward, I can see the possible cross-curricular activities that can be undertaken with maths, linking it with art or science, by creating our own artwork using Fibonacci’s sequence or looking at how plants grow in particular ways that link to the golden ration. Overall, I thoroughly enjoyed this input and can’t wait to look at it again.



Bello, Alex (2010) Alex’s Adventures in Numberland London: Bloomsbury

Meisner, G. (2012, a). History of the Golden Ratio. [Online]. Available at: [Accessed 24th November 2017].

Meisner, G. (2012, b). What is the Fibonacci Sequence (aka Fibonacci Series)?. [Online]  Available at: [Accessed 24th November 2017].

Memolition. (No Date). Examples Of The Golden Ratio You Can Find In Nature. [Online] Available at: [Accessed 24th November 2017].

Robb, A. (2017) Maths and Art. [PowerPoint Presentation] ED21006: Discovering Mathematics [Accessed 24th November 2017]

The Art Story. (No Date, a). De Stijl Movement, Artists and Major Works. [Online] Available at: [Accessed 23rd November 2017].

The Art Story. (No Date, b). Piet Mondrian Biography, Art, and Analysis of Works. [Online] Available at: [Accessed 23rd November 2017].

TheJourneyofPurpose (2013) Fibonacci Sequence in Nature [Online].  YouTube. Available at: [Accessed 24th November 2017]

Maths in Sports

In one of our inputs with Richard, we looked at exploring mathematics within sport. I was not surprised that maths was an integral part of sport, unlike art and stories, which was more surprising to me.

We were given the first ever recorded football league table to look at.


Here is the English league table from 1888.

Our first task was to take this league table and convert it into a league table that is used today. What we first noticed was that the old league table was ordered alphabetically, whereas league tables today are ordered by points. We looked at the table and figured out that Preston football club would be at the top based on points. We continued ordering the table in this way until we got to Bolton Wanderers and West Bromwich, as they both had the same points. When this happens, the teams are then ordered by the best goal difference. This also happened with the last two teams, Notts County and Stoke. We placed Stoke 11th and Notts County 12th, however, we noticed that on the old table, it was the other way round.

The reasoning behind this was because goal difference was not counted in league tables until 1970’s. Instead, if two teams had the same points, they were ordered by the amount of goals they had scored. In this case, Notts County had scored 39 goals compared to Stokes 26 goals, putting them higher up in the table.

Here is the league table we made based on modern day tables.

The next task we were given was to take our own knowledge of a sport and look at the mathematical perspectives behind it. Our group chose Taekwondo, as Amy participates in this sport and has a great knowledge of its rules and formats.

Here is the mind map that we came up with, showing the different mathematical perspectives and rules.

The rules of Taekwondo are as follows:

  • Punch = 1 point, kick to body = 2 points, kick to head = 3 points
  • 1 vs 1
  • Points lost for illegal activity
  • Divisions are based on weight


We then had to change the rules to see how it could potentially change the game.

This is the rule changes we decided to come up with.

The first aspect that we decided to change was the ring size; after each round ended, the ring size shrunk for the next round. We decided on this as some competitors may use the ring size to their advantage, by avoiding the opposition, and with a smaller ring size, they couldn’t do that. We also decided to shorten round time for this same reason. Another aspect that we changed were the divisions. Previously, the divisions were split by weight, which was changed to height. This was because if two competitors in the same weight divisions had a big height difference, it would be hard for the smaller player to achieve a kick to a head to gain maximum points. The next rule that we changed was the points. Instead we decided on: punch to body – 1 point; punch to head – 2 points; kick to body – 3 points; kick to head – 4 points. We decided to make our final rule change a bit quirky – changing the players from 1 vs 1 to doubles which we liked to name ‘two-kwondo’. We thought of it as similar to the idea of tag teams in wrestling.

As a result of this input, I feel that my knowledge of maths in sports, especially taekwondo has improved. Looking at this has also made me realise how changing the rules of a sport can dramatically change the outcome of the game. I will keep this input in mind as a lesson for when I am teaching, as this would be a really fun activity that the pupils would really enjoy as they can really get involved in it. It will allow them to see beyond the basic rules of sport, and view the mathematical concept behind it.



Wright, C. (2016) On this day in 1888: Preston the big winners as first football league results recorded. [Online] Available at: [Accessed 22nd November 2017]


The History of Time

Time. Something that we use every day of our lives. How could we possibly live without it? Everything we do is based on time, when we wake up; when we eat; when we go to work; when we sleep; when we catch the bus. But have you ever stopped and thought to yourself about the history of time?

Before Clocks

There was a period of time before mechanical clocks, when telling the time wasn’t as easy as looking at your watch or checking your phone. Mechanical clocks were first seen in the early 14th century, and the first accurate pendulum clocks were brought in in the mid-16th century (Bellis, 2017, a). So how did people tell the time with no clocks?

One of the earliest ways to measure units of time were sundials. As the sun moves from East to West, the shadows formed on the sun dial show the time. Sundials were first used by Ancient Egyptians. The Egyptians built a t-shaped sundial that consisted of a crossbar and a vertical stick. 5 hours were written on this stick. The stick would be placed facing east in the morning and placed facing west in the afternoon (Marie, n.d.). It was quickly noticed that the length of the day varies at different times of the year, due to the tilting of the earth’s axis (Rogers, 2011). If this was not accounted for, then the sun dial would not display the correct time, and each week would have different times as the earth moved around the sun. By the 10th century, pocket sundials were being used (Bellis, 2011,a).

To compensate for the inaccuracy of sundials, water clocks were invented. The earliest water clock to be discovered dates back to 1500 B.C., however, the Greeks started commonly using them around 325 B.C. (Bellis, 2017, b). The two most common water clocks were either: stone vessels with sloping sides that allowed water to drip at a constant rate from a small hole near the bottom; a bowl-shaped container with markings on the inside that were used to measure the passage of ‘hours’ as water filled into the container; or a metal bowl with a hole in the bottom. The bowl would fill with water and sink within a certain time (Bellis, 2017, b).

This video shows one of the most intricate designs of a water clock. This water clock is known as ‘The Elephant  Clock’ and was built by Al-Jazari; a scholar, artisan, mechanical engineer, and inventor, from the 13th century (Georgievska, 2017). This clock was 22 feet high and would move and made a sound every half hour or hour, depending on the size of the bowl inside the elephant. Inside the elephant was a timing mechanism and basin. Inside the basin there is a bucket, and inside the bucket is a bowl with a small hole in the base, that floats in water. After half an hour, the bowl would be full and would pull a string attached to the top of the elephant. This would cause the see-saw mechanism to release a ball that fell into the serpent’s mouth. When the serpent leaned forward, his weight pulls the bowl out of the water. When this happens, the other figures begin to move, and the driver of the elephant hits his drum. The serpent then returns to his original position and the cycle happens again (Georgievska, 2017).

Mechanical clocks took over from water clocks in the early 14th century. At this time, they began to appear in public places such as in towers. The first accurate mechanical clock was invented in 1656 by Christiaan Huygens. He created the first pendulum clock that had an error of less than one minute per day. With further adjustments, that error was reduced to less than 10 seconds per day (Rogers, 2011).


Units of Time

There are many different units of time: millisecond, second, minute, hour, day, week, month, year, decade… the list could go on. But how did we decide these different periods of time?

Time Units

This flowchart illustrates the interrelationships between the major units of time.

Most historians credit the Egyptians to being the first to divide the day into smaller parts. The sundials that they used were split into 12 sections, to measure the interval between sunrise and sunset. This division reflects Egypt’s use of a base 12 system, instead of the base 10 system that we use today.  This use of sundial most likely formed the first representation of what we call an hour today.

During the night, Egyptian astronomers observed a set of 36 stars that divided the circle of the heavens into equal parts. The period of total darkness was marked by 12 of these stars, once again resulting in 12 divisions. During the New Kingdom (1550 B.C. to 1070 B.C.), this measuring system was simplified into a set of 24 stars, 12 of which marked the night. Once both light and dark were divided into 12 parts, the concept of a 24 hour day was in place (Lombardi, n.d.).

Hipparchus, a Greek astronomer, geographer, and mathematician, devised the system of longitude lines that encompassed 360 degrees running from north to south, pole to pole. Claudius Ptolemy expanded on Hipparchus’ work by dividing each of the 360 degrees of longitude and latitude into smaller segments. Each degree was divided into 60 parts, each of which was subdivided again into 60 smaller parts. The first division of 60 was called ‘partes minutae primae’ which became known as the minute. The second division of 60 was called ‘partes minutae secundae’ which then became known as the second (Lombardi, n.d.). This is where the concept of 60 seconds in a minute and 60 minutes in an hour derived from. However, minutes and seconds were not used in everyday timekeeping until many centuries after this idea was first introduced. Lombardi (n.d.) says that “clock displays divided the hour into halves, thirds, quarters and sometimes even 12 parts, but never by 60.” It was not practical for the general public to consider minutes until mechanical clocks that displayed minutes appeared at the end of the 16th century.


Standardisation of Time

From 1792, in England, it became normal to use local mean time, rather than time from a sundial. By the 18th century horse drawn coaches were taking mail and passengers across Britain, and the guards on these coaches carried timepieces. Because of the local time differences, these timepieces were adjusted to gain 15 minutes in every 24 hours if travelling west to east and vice versa if travelling east to west (, n.d.). The use of local time was beginning to become an inconvenience, and accurate time was beginning to become more essential. By 1844, almost all towns and cities in Britain had adopted GMT, however a lot of railways kept their local time and showed “London Time” with an additional minute hand on the clock.  By 1847, the London and North Western Railway and the Caledonian Railway had adopted “London Time”. By 1848, most railways had followed suit (, n.d.).

Greenwich Mean Time (GMT) was adopted as the legal time throughout Great Britain on 2nd August 1880. It then also replaced Dublin Mean Time in 1916. GMT was adopted as the international standard for civil time in 1884 at the International Meridian Conference. It was the standard time until 1972 when it was replaced with Coordinated Universal Time (UTC), which is based on the solar time on the prime meridian (0° longtidue) (, n.d.).



Bellis, M. (2017, a). The History of Mechanical Pendulum and Quartz Clocks. [Online]. Available at: [Accessed 11th November 2017].

Bellis, M. (2017, b). The History of Sun Clocks, Water Clocks and Obelisks. [Online]. Available at: [Accessed 11th November 2017]. (No Date). Units of Measurement. [Online] Available at: [Accessed 10th November 2017].

Georgievska, M. (2017). The Elephant Clock: One of the greatest inventions of the outstanding mechanical engineer Al-Jazari. [Online]. Available at: [Accessed 11th November 2017]. (No Date). Railway Time. [Online] Available at: [Accessed 11th November 2017].

Lombardi, M. A. (No Date) Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day?. [Online] . Available at: [Accessed 11th November 2017].

Luppino, D. (2015). THE ELEPHANT CLOCK for “Science in a Golden Age” (Aljazeera English). [Online] Vimeo. Available at: [Accessed 11th Novemer 2017].

Marie, N. (No Date). When Time Began: The History and Science of Sundials. [Online]. Available at: [Accessed 11th November. 2017].

Rogers, L. (2011). A Brief History of Time Measurement. [Online] . Available at: [Accessed 10th November 2017]. (No Date). Time Zone History of the United Kingdom. [Online] Available at: [Accessed 11th November 2017].

Profound Understanding of Fundamental Mathematics

If someone asked me two months ago what ‘profound understanding of fundamental mathematics’ was, all I could tell you it was something to do with maths. PUFM sounds very confusing and complicated, when in fact it is quite the opposite. Over the course of this module, my understanding of this statement has developed greatly, and I now feel much more confident in my abilities of teaching in a classroom setting.

Ma (2010) defines PUFM as “an understanding of the terrain of fundamental mathematics that Is deep, broad and thorough.” There are four principles in teaching and learning that represent a teachers understanding of fundamental maths in the classroom: interconnectedness, multiple perspectives, basic ideas and longitudinal coherence.

Interconnectedness – 

Ma (2010) defines interconnectedness as when “a teacher with PUFM has a general intention to make connections among mathematical concepts and procedures.” Interconnectedness occurs when the learner is trying to make a connection between the mathematical concepts and procedures. Here, it is the teachers job to stop the learning from being fragmented, and help the students to develop the ability to make links between underlying mathematical concepts, and showing how maths topics rely on each other.

Multiple Perspectives –

“Those who have achieved PUFM appreciate different facets of an idea and various approaches to a solution, as well as their advantages and disadvantages” (Ma, 2010). Multiple perspectives is when a learner can approach mathematical problems in many ways, as they understand the various perspectives when taking on a maths questions, and are able to look at the pros and cons of the different viewpoints. It is the teachers job to provide opportunities for the learners to be able to think flexibly about the thinking and understanding of different concepts in maths.

Basic Ideas –

MA (2010) says that “teachers with PUFM display mathematical attitudes and are particularly aware of the ‘Simple but powerful basic concepts of mathematics’ (e.g. the idea of an equation.”  Basic ideas is a way of thinking about maths in terms of equations. Ma (2010) has suggested that learners should be guided to conduct ‘real’ maths activities rather than just approaching the problem when practising the property of basic ideas. If a teacher is implementing this principle effectively, then they will not only be motivating the learner to approach the maths problems, but will also be providing a guide to for the learners to help them understand the maths themselves.

Longitudinal Coherence –

“Teachers with PUFM are not limited to the knowledge that should be taught in a certain grade; rather they have achieved a fundamental understanding of the whole elementary mathematics curriculum” (Ma, 2010). Longitudinal coherence is when a learner recognises that each basic idea builds on each other. When a learner does not have a limit of knowledge, it is impossible to identify the level or stage that a learner is working at in maths. the learner has instead achieved a holistic understanding of maths (fundamental). A teacher who has a profound understanding of maths is one who can identify the learning that has previously been obtained. The teacher will then lay the fundamental maths as a foundation for learning later on (Ma, 2010).

The four principles are vital to having a deep understanding of maths, especially when teaching the subject. I will make sure I have PUFM before I begin teaching mathematics, as without it, I cannot teach the subject as in depth and as thoroughly as possible.


Ma, L. (2010). Knowing and Teaching Elementary Mathematics. New York: Routledge.

Maths, Play and Stories

How could maths, play and stories intertwine? How could a child possibly be learning maths whilst playing with their friends, or getting read their bed time story? Maths is all around us, even where we least expect it.

Parents as Teachers

Parents may think the only way they can engage their children at home with maths is by helping them with their homework. Some parents may not even be able to help their children with their homework due to the maths anxiety that many adults suffer. As I have spoken about in a previous blog post on maths anxiety, the negative connotations that parents have about maths, can easily be passed down to the child, and create them to have their own worries about maths. It is vital that parents provide a rich learning environment for mathematics at home, so that children can be learning at all times and reaching their full potential. Studies looking at how often numeracy activities occurred at home found that they often happened less than once a day. They also found that the activities rated by experts as having specific numeracy focus occurred more infrequently than the activities with ambiguous numeracy content (Skwarchuk, 2009). Much of a child’s early mathematical development is enhanced through communication. This is why parent should ask open-ended questions to support and challenge their child’s thinking. For example, using varied mathematical language like bigger, smaller, fewer etc.


Importance of Playanalysis, blackboard, board

Lev Vygotsky says that the learning of a child takes place in the ‘zone of proximal development’ which represents the between what a child actually knows and what the child can learn with support from those who are more knowledgeable. He also believed that the teaching of maths can be influenced by relating the subject to the child’s own experiences. This helps us to understand why play is such an important aspect of learning maths, as it allows the child to personalise it and be able to relate it to themselves. Saracho (1986, cited in Saracho and Spodek, 2003, p.77) explains that when children play, they confront social circumstances and learn to collaborate,  help,  share,  and  resolve  social  difficulties. Play is extremely important to a child’s learning for some of the following reasons:

  • Helps children to make connections in their learning
  • Allows child to experiment
  • Provides a meaningful context
  • Promotes social learning
  • Encourages perseverance

Friedrich Froebel was another theorist that also emphasised the importance of play in children. He viewed play as the ‘work of children’ and believed that children’s best thinking took place during play. During quality play, children are:

  • making decisions
  • imagining
  • reasoning
  • predicting
  • planning
  • experimenting with strategies
  • recording

Susan Issacs had many of the same views as Froebel. She saw the value in play as a way to allow children to explore their ideas and feelings freely. Through play, children can move in and out of reality, and whilst doing this, she encouraged them to be curious and express their feelings. But how does this relate to maths? Nutbrown (1994) said that “mathematics is never far away from young children’s actions.”  All the different things that happen during quality play (as listed above) all link into mathematics. Predicting, experimenting, reasoning, making decisions are all needed in maths. Children using these strategies in play will help them to have a better understanding of the approaches they must use. It will also help them to understand why they are learning maths, as they can relate the problem solving and reasoning to their real-life experiences.


Maths in Stories

Another way that maths can be incorporated into a child’s everyday life is through White Teddy Bear With Opened Book Photostories.  Stories are something that are enjoyed by children, and can help eliminate that fear of maths that a lot of children have.  They can be used to introduce new mathematical concepts, or to build on ones that are already known. By showing children that maths can be fun and interactive, they will be much more willing to engage.

Here is an example of a math story book ‘A Place For Zero – A Math Adventure’. This story talks about the number zero and place value.

Stories like this one can help children to connect with, and understand the concept being portrayed in the book. Having a visual aid will allow the children engage in the book, and listen to the story line. At the time, they may not even realise that they are actually learning mathematical strategies.

Maths storybooks are not the only way to teach maths through stories. There are many popular children’s books that can easily be adapted to fit a mathematical story line. For example, ‘We’re Going On a Bear Hunt’ can easily be change to ‘We’re Going On a Square Hunt’. Using a familiar text will allow the child to acknowledge how maths can be related to them, and used in their day to day life. It may also make the experience more comforting, by having something the recognise, especially for those that suffer from maths anxiety. You should always remember to match the book and your discussions to the mathematical abilities and development of the children in your class.

From the workshop and my own research, I now understand the great importance of play in developing a child’s academic understanding, by allowing them to freely explore ideas and express their emotions. Not only in maths, but in every aspect of schooling, play can help children relate it to their own experiences. When working in classrooms in the future, I will make sure to incorporate all that I have learnt about play and stories to make the learning as fun and interesting as possible, as I now know the benefit of them.


Ehrhart, M. (2014) A Place For Zero A Math Adventure [Online].  YouTube. Available at:–wKA1yYQ&t=487s [Accessed 1st November 2017]

Nutbrown, C. (1994) Threads of Thinking. London: Paul Chapman Publishing Ltd.

Saracho, O.N. and Spodek, B. (2003). Contemporary Perspectives on Play in Early Childhood Education. Conneticut: Information Age Publishing.

Skwarchuk, S. (2009). How Do Parents Support Preschooler’s Numeracy Learning Experiences at Home?. Early Childhood Education Journal, [Online] 37. Available at: [Accessed 30th October 2017]

Valentine, E. (2017) “Maths, Play and Stories” [Powerpoint Presentation] ED21006: Discovering Mathematics [Accessed 31st October 2017]

Is Maths a Language?

“Is maths a language?”  There are thousands of languages across the world – English, Spanish, German, French… all taught across schools and reinforced as being important to succeed in later life with jobs. So why is this attitude not portrayed with maths?

Math is a language that has been used thousands of years. It is spoken universally, and can be understood by all no matter the age, religion or culture. Sure, different countries may have different symbols or words for aspects of it, but the profound fundamental understanding of maths is the same no matter where you go. Paying for your shopping in a supermarket uses the same knowledge of maths whether you’re paying in pounds, rupees, yen or euros.

Some anthropologists suggest that the global language of maths was needed in order to trade. Many different countries were trading, and were not able to communicate with each other as there was such a wide variety of languages, so a universal language that could be understood by all needed to be implemented. Roman numerals were the most dominant number system used in trade. It was created on the base 10 system but was not directly position and did not include a value for zero (Mastin, 2010). The base 10 system is a system used today in every country, and our understanding of place value is based on this. It is thought that this system was introduced at least as early at 2700 BCE by the Egyptians (Mastin, 2010). This system is used widely and is an understood language across the world, even though it appears to have begun in Egypt.

Europeans were still using Roman numerals in the 13th Century, but found that they were difficult to work with when trying to divide or multiply. This is when Italian mathematician Fibonacci introduced Arabic numerals into Europe. These are the numerals that we know and use today to represent values of numbers. The difficulty of the Roman numerals led to merchants and bankers embracing the simpler Arabic system (Maths Careers, n.d.). This number system eventually spread across the globe, as the inclusion of zero meant that so much more could be done.

Here is a great video from Dr. Randy Palisoc, talking about maths as a language. This video also touches on maths anxiety, and how looking at maths as a language can help to eradicate the anxiety and fear around maths.



Mastin, L. (2010). Egyptian Mathematics. [Online]. Available at: [Accessed 23rd October 2017]

 Mastin, L. (2010). Roman Mathematics. [Online]. Available at: [Accessed 23rd October 2017]

Maths Careers. (No Date). A Universal Language. [Online] Available at: [Accessed 23rd October 2017]

TEDx Talks (2014) Math isn’t hard, it’s a language | Randy Palisoc | TEDxManhattanBeach [Online].  YouTube. Available at: [Accessed 23rd October 2017]

Maths Anxiety

I always enjoyed mathematics all the way through Primary, and never once felt anxious about participating in it. Even during the early years of High School, I still had no worries about maths and liked going to classes. This all began to change around about 3rd/4th year, when the maths became harder and more stressful. Trying to memorise formulas just to pass my exams without fully understanding how or why I was learning this is where my maths anxiety stemmed from. This anxiety is still something that I carry with me now.

I decided to choose ‘Discovering Mathematics’ as my second year elective, as I wanted to try and further my understanding of maths and try to get over my maths anxiety. In one of our first few workshops, maths anxiety was one of the topics that was discussed. Hembree (1990, p.45) describes maths anxiety as “a general fear of contact mathematics, including classes, homework and tests.”  This anxiety of maths can have both physical and psychological effects on students. These include headaches, muscle spasms, shortness of breath, dizziness, confusion, mind blanks, incoherent thinking and many more (Arem, 2010, p.30).This anxiety of maths can cause the pupil to become disengaged in their learning, as they lose some self-esteem, and in turn, the anxiety increases. I found it really interesting that maths anxiety can be considered a diagnosable condition, as I always felt that it was just my own fault for not being great at maths.

For most children, this anxiety continues into adulthood and can affect their confidence in tasks such as paying bills and handling their finances. If as kids they did not learn the basic mathematics as a result of maths anxiety, this could potentially affect them for the rest of their lives. This anxiety can also be transferred into their own children, giving them a negative impression of maths. Many parents will be unwilling or unable to help children with their homework, which will also greatly affect the child.

Maths anxiety in teachers also greatly affects the student’s performance. The teachers on the Maths and Science Survey (TIMSS) it is shown that Scottish P5 pupils are scoring below international average, and S2 pupils are scoring well below the international average. Even the highest achieving pupils in Scotland scoring well below the international average, which is very worrying figures for the country (IEA, 2008). As a teacher, I want to try and get over my maths anxiety, after seeing how greatly it can impact on your class’ performance, and help the children that do suffer it to see maths in a different light.

This video by TED-Ed does a great job of explaining what maths anxiety is and ways in which it can be helped.




Hembree, R. (1990) ‘The nature, effects and relief of mathematics anxiety’, Journal for Research in Mathematics Education, 21.

IEA (2008) Trends in Mathematics and Science Survey 2007. Lynch School of Education, Boston College: International Association for the Evaluation of Educational Achievement.

TED-Ed (2017) Why do people get so anxious about math? [online].  YouTube. Available at: [Accessed 4th October 2017]