Where Would We Be Without Maths?

Where would we be without maths?

Now that is a big question! Throughout the Discovering Mathematics elective my eyes have well and truly been opened to just how important maths is in society. At school maths was never my favourite subject but I understood it was important in the way I had to gain my qualifications to get into my prefered university course. Now its apparent that its more important that first thought!

Maths in Science

In science everything has to be  carefully calculated and measured to make sure everything is exact and precise.Biology, Chemistry and Physics all use maths in this way. Science is used by ALL DOCTORS, NURSES AND RESEARCHERS in medicine and drug discovery. Without maths in this context, different medicines and drugs may not be found. Therefore we may not have near the amount of cures for diseases and treatments for other medical conditions than we do with mathematics. As well as this if Doctors were not able to   measure medicines accurately no patients would be treated correctly and this could potentially be fatal like Micheal Jackson.



Photo Taken from Google Images – www.smh.com.au

Maths in Hairdressing

Chemistry is also apparent  in hairdressing as without chemistry hair would not get dyed. Hairdressers need to be trained with the right solutions to use and which ones to mix so that the client will be happy with the colour and to make sure that it is the colour that they asked for.imgres

Photo Taken from Google Images – www.lifesurebeauty.co.uk

Are Different Aspects of Maths Connected?

Liping Ma (1999) states that after she carried out her research in China and the USA, she realised the 4 principles of fundamental mathematics. One of which interested me quite a bit was that of CONNECTEDNESS. At first I thought the most logical idea would be to connect the learning to the children’s interests but after reading more into this principle i realised it was the connections between maths itself! Obviously,I had many questions…

What could possibly connect in maths?

What links could be made?

and lastly…

Why didn’t I realise them earlier?!?!

Addition and Subtraction

Firstly, In primary school there is always the challenge of learning addition and subtraction, later to be followed by multiplication and division. I think its apparent that no matter how many times children try to hide their fingers under the table we all know they use them to count up and down. Addition usually comes first followed by the slightly more difficult process of subtraction. (Maths Steps, no date)inverse_operation

Picture Taken from Google Images – www.elearnclass.org

In my opinion this pictures sums it up completely, If children are taught addition sums first they should completely understand the structure as to see how subtraction can be made simpler.For example, an addition sum can be changed to a subtraction sum by first changing the sign then secondly swapping the positions of the first and last numbers. This would be the same for subtraction to addition. THEY ARE LINKED… OR YOU COULD EVEN SAY CONNECTED!!


Picture taken from Google Images –www.education.com

This worksheet I found, could be a great resource and be used as a way to explain this to the children to allow them to get a feel for the inverse operation! The fact its called families is also quite helpful as in my opinion it can show how they can find the “families” for multiple sums and use this to help them sole problems in other areas of mathematics or even just life in general! Like money for example!!!


Ma, L. (1999) Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in china and the United States. United States: Lawrence Erlbaum Associates.

Maths Steps (no date) MathSteps: Grade 1: Inverse relationship between addition and subtraction: What is it? <!– hide script from old browsers if (document.images) { nav1off = new image nav1on = new image nav1off.src = ‘/math/mathsteps/images/nav/nav_wii.gif’ nav1on.src = ’/m. Available at: https://eduplace.com/math/mathsteps/1/b/index.html (Accessed: 4 December 2015).

Maths in Football

Maths and football would not necessarily be two things you would put together but through the Discovering Mathematics module its become apparent that mathematics is everywhere. Liping Ma (1999) suggests that connectedness is one of the four properties of the teaching and learning of Fundamental Mathematics which led me to believe that if the teaching of mathematics  was made relevant and somehow connected to what children are interested in they would be more inclined to want to gain knowledge about the topic. Football was the sport that most children in my class shared an interest inso this is why i chose to look into football in particular.

Before this I did not believe there was much maths in football at all. Maths is a sport, sports fall under the Physical Education category and as far as I was concerned that was that.Apart from the obvious score taking, shape of the pitch, angles at the corners, number of flags and players but looking into this further i realised there was so much more than I first thought.



Picture taken from – http://www.hoist-point.com/soccerball.htm

The football in which most people are familiar with is that of the typical  black and white patterned ball. it is made of lots of leather pieces- 12 black pentagons and  20 white hexagons, all of which are regular. (Yakimento, 2015)  On this football the 2D shapes are tessellated together as to leave no gaps between the shapes. The pentagons an the hexagons must have the same length of sides for this to happen. As well as this for all shapes to tessellate the angles on the corners need to add up to 360 degrees.

Tessellation, 2D Shapes and Angles are all mathematical factors involved here.

As well as this maths can be used to calculate many different things involving the ball for example… Distance the ball travels (Equation 1), Time it takes for the ball to travel (Equation 2) and finally the speed at which the ball travels at (Equation 3).701b935ef4072b0f79c429a0d461a6cce437f1c2

Picture taken from – www.bbc.co.uk



Score taking is another part of football where maths is involved. The points system is simple if you score a goal you get a point against the other team. For example, If Dundee and Dundee United were to play against each other and Dundee scored the points would be 1-0 Dundee. If another goal was scored by Dundee the score would be 2-0.

Counting and addition are involved here.


Each football game lasts for approximately 90 minutes or to put this into a different format can be 1 hour 30 minutes. In my opinion, this is a difficult concept for children to grasp. The idea of conversion is an idea which children may find confusing. Conversion also has to be recognised by children in fractions to understand that, for example, 2 is the same as 2/1.

Time and conversion are the elements of mathematics that are involved here.



Picture taken from – www.conceptdraw.com

The football pitch is rectangular in shape which has a length  from 90-120m and a width from 45-90m. However, a rectangle is not the only 2D shape visible on a football pitch. There are also circles and semi circles and more rectangles. Shapes can be used in many forms of mathematics for example, shape tessellation with the pattern on the football, calculating areas and measuring distances. The Pie symbol can be introduced to show children how to calculate the areas of circles and semi circles. As well as using the A= LxB equation format which can be used to find the areas of squares and rectangles. A follow up for this could be to change the units from metres to kilometres etc. to give children a grasp of the decimal system and working with smaller numbers. This would come under Ma’s Longitudinal Coherence property. As well as this, the older children could be introduced to Pythagoras’ Theorem on finding the areas of triangles if they have got a good understanding on how to find the areas of the other shapes found on the pitch. ( Although there are no triangles necessarily in football.)


Ma, L. (1999) Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in china and the United States. United States: Lawrence Erlbaum Associates.

Yakimento, Y. (2015) Mathematics of the soccer ball. Available at: http://www.hoist-point.com/soccerball.htm (Accessed: 25 November 2015).

Happy Birthday George Boole!

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Picture Taken through a screen grab of www.Google.com

I am not sure if this is entirely relevant but after searching Google for information to add into my languages assignment I came across the fancy “Google” logo. The logo was a type of maths related design, which when clicked on took me to a search of George Boole, whom I read was an English mathematician. Normally, things like that would not interest me and I would just click back to what I had intended to search but the incredible similarities between George Boole and Colin Firth were too obvious, in my opinion, to not find out who George Boole was and his input in the world of mathematics.


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Pictures from Google Images

1 –www.bbc.com   2-www.bbcamerica.com

George Boole was born on the 2nd November 200 years ago!! ( which makes this post a little more relevant as it is the 2nd November today). He is known for “laying the foundations of the computer age” (Mortimer,2015) Boole created the  Boolean system which allowed all maths variables  to either be true or false/ on or off. 70 years after he died another man, Victor Shestakov from Moscow State University, used the Boolean code in relation the computer systems and its to this day still relied on in technology.

George grew up in Lincolnshire, England where he went to school until the end of his primary education. However after his primary years George had to help in his fathers business, as a cobbler, to try to stop it from failing. George was largely self taught as he had an interest in books so began to teach him self languages and mathematics. He then went on to open a school, at the young age of 20, where he taught mathematics and became so much more inspired by it that he went on to learn more.  (George Boole facts & biography | famous mathematicians, no date) In 1849 he was made a professor in Queens College in Cork due to others in the field recommending him for the job even although he had no university degree himself, which caused contreversy in . Others reccommended him due to the fact he was becoming more and more famous and well known in his own right. He had published many maths works at the age of 26. He accepted the position and began working on his most famous work;  An Investigation of the Laws of Thought, then within 2 years he was made the Dean of science . Boone married his wife Mary Everest and had 5 children with her. He tried to encourage Mary to study at the university also but he did not succeed. Sadly, Boone died from pneumonia in 1864 after he walked to the college, where he lectured, in the rain and returned home after. This is what was thought to have started the condition.

It is apparent that Boole did not realise how important his work would be to todays society. The technical age in which we live would not be as it is without him and his work.



George Boole facts & biography | famous mathematicians (no date) Available at: http://famous-mathematicians.org/george-boole/ (Accessed: 2 November 2015).

Mortimer, C. (2015) George Boole: Five things you need to know about the man behind today’s Google Doodle. Available at: http://www.independent.co.uk/news/science/five-things-you-didn-t-know-about-george-boole-a6717401.html (Accessed: 2 November 2015).

Differences Between Sweden and UK


Photo taken from Google Images – www.ucl.ac.uk

A few weeks ago we had an input where we discussed comparative education. We mainly focused on the differences between Sweden and the UK and the different perspectives they had on learning in the early years.

The Swedish School system contrasts with the UK school system in so many ways. The first one being their school starting age. In Sweden, children do not start school until they are 7 years old, which is a whole 2-3 years after we do in the UK. When this was first mentioned I assumed that they would be so far behind in their learning compared to children in our country who start so much earlier. However, I was shocked to discover that this is not the case. According to The Guardian in 2010, Sweden has over taken the UK in reading and  Maths! They also are not to far behind the Uk in the science rankings either. (Shepherd, 2014)

Sweedish Children attend Pre-school from the age of 6 where they place a strong emphasis on the importance of play. However, In most other countries play is looked at as more of a chance for children to relax and relieve stress. As in the Uk children are in school at this time trying to build on their reading, writing and numeracy. Sweden’s pre school prioritises play and social skills as well as sharing, being considerate and tolerant towards others. (Swedish Institute, 2014) These are qualities and values which I feel are extremely important to learn at this age. Tolerance for reasons which seem obvious to me, Children learning how to be tolerant of others makes them realise that people are different (whether by skin colour, disabilities or things as simple as the clothes they wear)  and understand how to deal with those differences effectively so they will not be causing anyone to be left out because of this. Consideration is also important as it allows children to consider other peoples feelings and show a level of compassion and kindness for others and situations they may be in. In my opinion, so many more children (in our country, specifically) should be taught these important values and social skills before starting school as I am sure this would lower rates of bullying in and around schools, and even just to help ease everyday stress on the teachers in the teaching practice. Swedish pre-schooling is now viewed as the foundation stages of life long learning as it is well known for the high impact it has on the children’s dialogue, interaction and communication.

Picture Taken from Google Images – globalpublicsquare.blogs.cnn.com

Outdoor Education is another HUGE focus in Swedish schooling as children play outdoors any opportunity that they have. No matter what the weather may be. (Swedish Institute, 2014)  In  my opinion, this is what children should be doing at that age rather than being stuck in a classroom, children need to explore the environment and the weather first hand instead of being shown flashcards of rain and different types of weather… go out and feel it!

The homely environment in Swedish pre schools is something else which is to be desired in British schools. The staff are called by their first names instead of their last which makes everything more casual and gives the children a sense of security and comfortability. Just more of a friendly atmosphere I would say although it can be argued that first name terms does not show children how to be respectful.  The room itself is also very homely. There is huge amounts of space for the children to  play  and a kitchen where they can snack in when they would like.   They eat all meals and snacks around a table as if it was a sit down family dinner with pupils and staff.  As well as this, children and staff members both remove shoes on entrance to the building as if it was their own homes. Comparing this to British schools, everything seems to happen at a certain time and things are a lot less relaxed. Children are allowed outside to play at 2 distinct times of the day and only weather permitting as they are made to stay inside if the weather is “too bad”.  Now comparing the 2 school systems, it seems to me, that UK schools need to allow children  a little more freedom in this regard.

Money is also an issue in the UK as childcare is becoming more and more expensive.Over the last Parliament the cost of a part-time nursery place for a child under two has increased by 32.8 per cent. A family paying for this type of care now spends £1,533 more this year than they did in 2010, while wages have remained largely static. (Rutter, 2015)

This quote from the Family and Care Trust article shows us just how expensive child care in the UK is and how much a family would have to pay to have their child to be in a nursery so they can go work to make money to provide for their family. When in actual fact the money they make from work will most likely be spent on the actual child care facilities. In Sweden there is a maximum fee policy which makes childcare affordable for everyone. The price is capped for the highest amount  families  can pay for childcare  SEK 1260  per month (which works as just about £100 per month) where as low income families will pay nothing. (Swedish Institute, 2014)

From my research on the subject, I feel that Swedish children have more opportunity to learn first hand and  in a more enjoyable way. Even starting school a few years  later than what we are used  has shown not to make a huge impact on the learning of the child. Maybe the UK should begin to follow in the footsteps of the Swedish Schooling System?


Rutter, J. (2015) Family and Child Care Trust. Available at: http://www.familyandchildcaretrust.org/sites/default/files/files/Childcare%20cost%20survey%202015%20Final.pdf (Accessed: 23 October 2015).

Shepherd, J. (2014) World education rankings: which country does best at reading, maths and science?. Available at: http://www.theguardian.com/news/datablog/2010/dec/07/world-education-rankings-maths-science-reading (Accessed: 22 October 2015).

Swedish Institute (2014) Play is key in preschool. Available at: https://sweden.se/society/play-is-key-in-preschool/ (Accessed: 22 October 2015).

Number Systems

Numbers are everywhere we go but why do we have them? Time, temperature, weight, height, phone numbers and even on the front of buses. Something  I learned from this input was that in fact numbers were thought to have came about through trading a long, long time ago.

Number Systems have never crossed my mind before this recent maths input, to be honest. I have always just assumed that people everywhere stuck to the “normal” , being the European system i am used to. I was aware of Roman Numerals  from past school projects and some watch collections. However, I was not aware it was still used, as such, but now that I have looked into this,  I see that I must have been pretty narrow-minded to think that maths and numbers would be the same worldwide.


Picture from Google Images – education.scholastic.co.uk

From further research after the workshop, I realised there was far more number systems that again I had never heard of such as Hindu- Arabic, Roman, Greek, Egyptian, Babylonian, Chinese. Which are displayed in the chart below.



Picture from Google Images – www.earth360.com

The task in this workshop was to create our own working number system. Our group decided to use a line per number and join them up… it worked but the higher the number the longer it would take to write. So we decided to stop at 9  and put a simple dot next to our number 1 to make 10. Our number system was a success.


Can Animals Count?

Can animals count?  NOT A CHANCE.

Animals such as Chickens? NO

Horses? NO

What about Monkeys? Hmmmm NO

These being my first responses to the burning questions Richard asked in the Discovering Mathematics workshop a few days ago. Although other students and the video clips played were very convincing, I just couldn’t begin to believe this could be the case.

Video taken from youtube – https://www.youtube.com/watch?v=aq_mVmai56g

First we encountered Clever Hans the horse from 1891. This horse was put on show for the public after his German owner, William Von Osten, claimed his horse could count by stamping his hoof the number of times that the answer was to be. (Jackson, 2005) His owner believed that animals were capable of counting so started to test the theory with other animals. However, it was only Hans that was capable. Later, after psychologists ran tests on Hans and viewed Von Osten’s show it was concluded that the horse only reacted from the facial expressions given off by the questioner.(Jackson, 2005) Therefore, I concluded, by no surprise, that horses can not count under any circumstances. I believed it to be more like training a dog to do tricks, but training a horse instead.

The next one got me thinking a little bit … Ayumu the chimpanzee.

I thought maybe through evolution, chimps, or monkeys etc. would be the most likely  animals to be able to count (if any). I was still so closed off to the idea until a video clip was played. Chimps vs Humans. Numbers from 1-9 were flashed on a screen in a mixed up format. They were displayed for a very short amount of time  then quickly (after a fraction of a second)  covered up with boxes. (Roast et al, 2013) Ayumu and the humans would both have to click on the boxes in  the correct order where the numbers 1-9 would have been. This was a test to see whom responded in the fastest time and all correctly. If they were all identified correctly they would be rewarded with a peanut. Surprisingly Ayumus time (210 milliseconds)  was amazingly better than the humans , whom were not often able to complete the challenge. When it was tested between other chimps in the family Ayumu was the one who had the best ability to recognise shapes, order and positioning. (Roast et al, 2013) This seems to me, to be a memory game and with a food reward…animals were guaranteed to win.

I mean, maybe animals are more clever than we think … but can they count?

I wouldn’t say so!

Ayumus Challenge!



Picture from Google Images – io9.com


Jackson, J. (2005) Home. Available at: http://www.critical-thinking.org.uk/psychology/the-clever-hans-effect.php (Accessed: 7 October 2015).

Roast, A., Shrotri, K., Mobley, E. and Stoker, N. (2013) Counting chimp. Available at: http://www.isciencemag.co.uk/features/counting-chimp/ (Accessed: 7 October 2015).

My Reflection On Being An Undergraduate!

I am Samantha Macdonald in the University of Dundee studying for an MA (Hons) in Education. I arrived here by, first of all checking all of my available options for the Higher grades I achieved in my penultimate year of high school. I was then given an offer from my depute head teacher,  to go on further work experience at a different primary school as I had previously volunteered at in my 3rd year of school. I took her up on the offer and loved every minute, from that moment on I knew that education was the route I wanted to go down.

After researching my options further, now narrowed down to my course of choice, Primary Education. I decided to apply to all Scottish Universities with Dundee being my first choice as it is close to home. Following my UCAS application I continued to go on school placements to build my experience working with children in a school environment. I went on placement at two local schools, one of which was a school that incorporated children with additional support needs. I learned so much on this placement and gained a whole new understanding of the importance and effectiveness of the inclusion of students suffering with these difficulties. By the end of my year long placement here, I had already received my interview for my first choice university. At the interview, I had to give a presentation explaining, “The teacher that I would like to become…”. Immediately I was swarmed with ideas about how I could portray my response in the most effective way possible. I prepared a poster and asked the children from my Primary 3 placement class of their own ideas of what a good teacher would be. I then incorporated them into my poster and took it along to my interview to present to the university panel and other eager applicants. After the long and worthwhile wait for a response and offer from the university I received a conditional offer to study my dream course at my first choice university. This is what pushed me to achieve my condition of one higher A in my last year of school. I was determined.

After completing my sixth year of high school in 2013 I decided to defer my entry for a year so I would be able to take part in FLAGs transatlantic student exchange. I lived in the USA for the whole school year attending an American High School and living with a typical all American family. Throughout the year I travelled to over twelve different states and experienced so many once in a lifetime opportunities. Aswell as all of this, I made lifelong friends with so many people from all around the globe and enjoyed learning about their amazing way of life and extremely different cultures.

My goal is now to continue working hard and to keep learning about all different walks of life so that in the long run I can become an enthusiastic teacher who can influence future generations in a positive way. I want to help make a change in the world for the better. My main aim is to hopefully teach children abroad or children with additional support needs.

How Did Gender Affect You As A Child?

As the youngest daughter in my family I was always brought up with a love of the colour pink, Barbie dolls and Disney princesses. I was the typical girl with typical childhood fantasies of growing up living in fairytale castles are marrying a handsome prince. I would not say that I was affected by gender or that it played a huge part in my growing up, I guess my views were stereotypical in a sense, that I played with dolls and always seen myself as the mother role to them, but nothing in the way of my parents, or any other important role model for that matter, forcing these stereotypical views onto me.

However, at primary school it was different. We had assigned seats, boy girl boy girl formation, as well as a line up routine of girls before boys or again you had to find a partner of the opposite sex when either entering the building, an assembly or going on an excursion. Whereas at High school it was a lot less gender oriented. In high school, gender divisions were only noticeable in sports teams and Physical Education as the class would be split by gender from which the boys would play football and girls would do something more feminine like dance in the fear of them getting hurt. I find this wrong as I feel like girls should be able to decide this factor for themselves. Gender does not matter.

Integration of Special Needs in the Classroom

Integration within the primary school is a big concern for many people in our society, children and adults, but I do not see the issue with it. In my opinion, I feel that children from the age of 5-12  need to be able to see the world for what it is. They need to realise and understand that there are children, just like themselves, that face extreme struggles every single day. These by mental difficulties or physical disabilities some of which are long term.  However, that does not necessarily mean that problems will not occur with this. Sometimes we can notice that other children look at the Additional Support Needs children differently simply because of their disability. This is why I feel that inclusion of special needs should happen very early on in the children’s school experience, as by the later years of their education they will be looked at as no different from anyone else.image036

Picture found on Google Images from cnotinfor.imagina.pt

On my MA1 placement  and my previous experiences in the primary school, it is clear to see  that with inclusion of ASN children they are still looked at by their peers  as “different” but we can not make this any worse by not including these children in “normal”activities which could make them stand out more. Yes we will come across certain activities that these children will not be able to do but there will still be some way in which they could take part. For example, a disabled child that is in a wheelchair will not be able to take part in a class game of rounders on either the batting or fielding team. However, this child can still be made to feel important by giving the child the role of time keeper or score taker, therefore working on other skills which are just as important in a team sport. This way they will not be made to feel discouraged as they are still a valued member of the class game.


Picture found on Google Images from www.haltontennis.co.uk

“Special” schools are looked at as a good thing, for better use of money/ shared resources, but i do not necessarily see them as beneficial to all children either. Although the pros of this could be one to one support? …but would children really achieve the one to one support they need in a school of this kind, where all children have a need for extra help?

However, putting my views aside, research shows that sometimes the inclusion of pupils with additional support needs can have non-inclusive outcomes. (Dyson and Millward, 2001)   When Inclusion fails it can be down to the lack of training for teachers on how to handle and prepare for children, of all abilities, inside the classroom, as well as limited funding for resources. (SEDL,1995) This is where the need for specialist teachers come in. Again on my placement the class teacher was appointed an ASNA who was in the class to aid the ASN children. All children bonded with her, even more so the ASN children. She was a huge asset to the class and the class teacher, although I realise that due to staff shortages this will not be the case in all schools.

Although I realise that cost, training would be factors for inclusion to not take place everywhere. I think inclusion of these children pose many benefits to other children and teachers. We can learn a lot from their strengths and teach to their weaknesses.

Me, I would hope that if my child was born with special needs they would not be made to feel singled out, discouraged, disheartened or looked at as different in anyway. My child would be loved for who he or she was, their strengths, weaknesses and personality just like any other child in their school or community.


Dyson, A. and Millward, A. (2001) Schools and Special Needs: Issues of Innovation and Inclusion. 1st edn. United Kingdom: Paul Chapman Educational Publishing.

SEDL (1995) Concerns About and Arguments Against Inclusion and/or Full Inclusion – Issues …about Change, Inclusion: The Pros and Cons, Volume 4, Number 3. Available at: http://www.sedl.org/change/issues/issues43/concerns.html (Accessed: 7 October 2015).