Category Archives: Maths Elective

The Land Before Time

During one of our most recent inputs with Richard we discussed a bit about time which eventually led us into a discussion about timetables and how they work.

We began talking a bit about the study of time- also known as Horology, and it’s importance to humans. The more I thought about it the more I began to realise that pretty much our whole lives are influenced by time, from the moment we get up to the moment we go to sleep at night our whole day is based on this mathematical concept without bus even thinking about it. If we really think more into it it’s not just humans that base their lives on time, what about animals? do they have any idea about time?

If we firstly think about household pets such as our beloved dog, many of us can say that when it reaches a certain time in the day the dog goes wild demanding food or their daily walk. This could be referred to as a “body clock” so we could say that animals have some concept of time, although it is hard to say whether its their internal clock or just when their tummy starts to rumble. When we think about other animals, if their routines aren’t influenced by humans, for example an owl, how do they know that they should come out at night? They have special eyesight for night time so we could say that it is just in their genetic makeup to know when to go to sleep and when to wake up. Hibernation is a similar concept, how do animals know to stock up on food and when to go to sleep for the winter?. Birds also know when to migrate, most of this could just be down to the weather being simply too cold for them to cope with so every year they come up with the same ideas of hibernation and migration? Or we could say that time is embedded into their instincts telling them when it is time to change their behaviour to suit their surroundings.


So before we had created our mechanical clock that we still use today how did we tell the time? was it just embedded into our instincts? Well Marie, N. (2016) helped with my understanding of the early use of time by speaking about sundials. A sundial uses shadow to track the movement of the sun which then gives us the time of day according to its position. Within our input we discussed just how much maths really applies to this, before using it people would have needed to be clear about what speed the sun moved at, did it travel at the same speed all day? This shows us that there was an understanding of maths and how to link mathematical concepts to apply it to real life.


Overall this input helped me to understand what it means to have a “profound” or “specialist knowledge of fundamental mathematics” as it has given me yet more examples of how maths can be used beyond the classroom without us even thinking about it!

Marie, N. (2016) When Time Began: The History of Science and Sundials. Available at: [Date Accessed: 10/11/16]

Maths in Art

Throughout the Discovering Mathematics module we have learned that there is a lot more to maths than just timetables and textbooks, maths is all around us! It’s in space, nature and even in art. Who would’ve thought? In our recent lecture about maths in art all I could think was wow, in a subject once considered boring we can combine the fun and enjoyment of art to completely change children’s attitude towards mathematics.

In Liping Ma’s idea of a “profound understanding of fundamental mathematics” she mentions “interconnectedness” and this is great example of how we can connect two topics that at first glance, seem completely unrelated.



If we look at the above example of Islamic art it is clear that mathematics came into play during its creation, art of this origin is usually stuffed to the brim with beautiful geometric designs that include mathematical concepts such as shape, repetition and rotation. symmetry plays an extremely vital role and many Islamic pieces allowing these mathematical concepts to develop, whether it be one main line of symmetry down the middle or several to create an endless number of beautiful patterns.


As well as within the patterns in Islamic art, mathematics is present within the ideas behind many of the creations, components of shapes are unpicked within the subject however within this art many of the components have meaning.

The equilateral triangle represents the ideas of “harmony” and “human consciousness” whereas a square is seen to represent the world and the four corners stand as the four directions (NORTH, EAST, SOUTH and WEST) also as the four elements (WIND, WATER, EARTH and FIRE). The third main symbolic shape throughout Islamic art is the hexagon which represents heaven. finally, the star is seen as a central area with the spread of Islam through its points.

Of course Islamic art is just one example of how maths and art intertwine, there are a number of ways that we could incorporate the two subjects to get children excited about maths again. Using them together will also encourage children to develop a specialist knowledge of the subject and will help them to see that their are multiple perspectives within the subject and they can use what they know to find out more about the world, not just to achieve the required answer to a problem.

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

University of Leeds International Textiles Archive.(2008)Form, Shape and Space: An Exhibition of Tilings and Polyhedra. St. Wilfred’s Chapel: Leeds.

How Many Socks Make a Pair?

During one of our workshops Richard presented us with the question “In the dark, how many socks do we need to take out of a drawer to make a pair?” Not to my surprise, the group’s first answer was “two” because who really has the time to rummage through their sock drawer to find a matching pair of socks? However, once it had been cleared up that the socks had to be matching it soon became obvious that there was more to this problem than I first thought.

So, if we have 2 different colours of socks in our drawer, pink and blue for example(guaranteed visit from the fashion police if one of each is worn) and we have three of each colour, how many do we need to take out before we find a matching pair? it took me quite a while to get my head around this but I finally managed it.

So basically, we would need to take 3 socks out of the drawer to guarantee a pair! just 3! because if there are six socks and three of each of the two colours we could either pull out one of each colour or a pair within the first two, in the case of the first two being two different colours no matter what colour we pull out next we will make a pair! my mind is blown!

So what about writing a formula to help all of our fellow sock wearers out there? basically what we did was pull out a number one more than the number of colours of socks that we have, still with me? So if we represent the number of colours of socks with the letter “n” then the formula should be n+1.

So if were to try it with different numbers, if I have 3 colours of socks and 3 of each colour I would need to pull out 4 socks to guarantee that I had a pair, the extra sock is to support me if I am unlucky enough to pull out one of each colour within my first 3, the back up sock has to be one of the colours therefore this guarantees a matching pair!

While this is a fun concept, it is actually a great example of why having a “profound understanding of fundamental mathematics” is so important. It is easy to look at the question and come up with the answer “2” but if we really unpick the question it soon becomes obvious there is more to it. I used my previous knowledge of maths and applied it to this problem, this highlights that when teaching children about maths we should build up their conceptual understanding rather than just their procedural knowledge. This will give them better foundations for attempting problems without a set procedure and solution, it will build confidence and generate innovative thinking.

Eastaway, R.(2010) How Many Socks Make a Pair? Surprisingly Interesting Everyday Maths. London: JR Books.

Maths is More Than Meets the Eye

Since starting the Discovering Mathematics module I have been completely shocked and amazed at how interesting and relevant to real life the subject actually is!

For one of our tutor directed tasks we were asked to take a look at Liping Ma’s Knowing and Teaching Elementary Mathematics chapter 5. This chapter really made it clear to me what it takes to be able to teach Maths successfully in the primary school. Ma, L(2010) frequently uses the term “Profound Understanding in Mathematics” or “PUFM” and in chapter 5 she explains what it means to have PUFM and how to promote it through teaching.

A teacher’s knowledge of mathematics should go beyond the set topic areas, it should be extremely wide and thorough Ma, L.(2010, p.133). There should be clear connections between topics that also link directly to everyday life. I strongly agree with this as I believe that children find it harder to stay engaged with a lesson if they can’t see themselves using it in the future. Whereas if it is linked to real life situations or even just to an area of interest such as football or any other hobbies that the various pupils may have then they are far more likely to tune in and gain more from the lesson.

Ma, L.(2010, p.134) presents four key elements to teaching in this way.

1. Firstly she uses the term connectedness, a teacher should be able to create and display links between various concepts within mathematics, the subject should not be learned as isolated topics but as a combined chunk of knowledge.

2. Secondly, we should provide pupils with multiple perspectives, encouraging them to find various approaches to reaching a solution, however it is important to put emphasis on the importance of justifying their methods, this will then lead to a more flexible understanding of mathematics.

During one of our Discovering Mathematics inputs we were lucky enough to be visited by someone from the Dundee Science Centre. This was extremely interesting a greatly backed up Liping Ma’s idea of multiple perspectives. As humans on Earth we have a pretty big influence upon our environment. However if we look at ourselves as humans on a planet in our solar system within space, we are tiny. Even compared to the Sun the Earth seems pretty insignificant! This displays that at first when we reach a solution in maths it is important to explore a little more so that we can gain a wider understanding of the concept and not just start celebrating because we got the number that’s in the answers at the back of the book.


3. The third aspect Ma, L.(2010, p.134) highlighted was that teachers should reinforce basic ideas within mathematics, this will then encourage pupils to carry out real mathematical activity instead of just finishing a topic, moving on and forgetting everything that has been learned.

4. Finally, she talks about longitudinal coherence which to me, seems to be one of the most important. We should drop the attitude that certain topics are taught at certain stages in a child’s primary school life. We should always be referring back to previous learning and seizing opportunities to lay the foundations for the future. This one particularly stood out to me as many teachers may just teach the class what they need to know until they are no longer their responsibility.

I feel as though Liping Ma has really encouraged me to look at Mathematics in an entirely different way, in the future when I am about to teach a Maths lesson I will think more about what concepts are behind the topic that I am teaching, what parts of the children’s previous knowledge can I pull from to make it clearer for them and how can I link it to everyday life to make it more relevant?


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

Why Choose Maths?

When we were given the opportunity to pick our elective for MA2 I can easily say it was a tough decision for me. Throughout my time at high school I never really excelled in one particular subject, I feel as though this was mainly due to a general lack of enthusiasm, people are always saying “a good workman never blames his tools” but I do believe that my teachers were partly to blame. In MA1 we were asked to write a post explaining how we feel about mathematics and I wrote a bit about how my teacher had an impact on my lack of confidence within the subject. Throughout school the teachers only really seemed to concentrate on the pupils that were either extremely “smart” and enthusiastic or on those who were extremely challenging and I always found myself floating in the middle of the scale struggling to get hold of the class teacher when I needed help. However, it would be unfair to just blame my teachers for my feelings towards mathematics as I could have definitely shown more enthusiasm myself.

So how did I eventually reach my decision to pick the Discovering Mathematics elective? I decided to think back to my experiences of various subjects at primary school because I felt this would be more relevant as I do eventually want to teach at that level. I really excelled at maths throughout primary because I found it extremely fascinating. I don’t know if this was because I was fortunate enough to be placed in the top group and maybe we got more attention because of that. Due to these experiences I decided to choose the Mathematics elective because I want to ensure that the children I teach enjoy it just as much as I did. I feel as though maths is a big part of our everyday lives and we really don’t think about it enough, this morning the first thing I did was switch off my alarm that I had set the night before using skills that I had acquired at primary school! It is important that children understand that mathematics goes beyond the set topics within the school curriculum and I would like to gain knowledge on how to stop that collective sigh from the class when they find out that they have Maths after break. In the end, all of these reasons made it clear that this elective was the right one for me and so I had reached my decision!


My Maths Journey

I could confidently say, throughout primary school I was one of the best in my class at maths, I was bursting with confidence in the subject and I found every aspect of it painfully easy. On my final day of primary school I even received a prize for maths, I was that good at it.

However, after my transition into high school it all went downhill. I began to find maths extremely difficult and I seriously lacked the confidence to progress in the subject. I was never bad at maths, I still remained in the top class for my year group but something had changed. I was now the worst at maths in my class and I felt too stupid to ever ask my teacher for help.

A well-known saying is: “a good workman never blames his tools” but I am going to contradict that by placing most of the blame on my high school maths teacher for my lack of confidence. He snapped at me whenever I asked him for help and he even told my mum at parents evening that there was no chance of me passing the subject. He was wrong, I sit here today with a C in higher maths, a very low C, but still a pass.

In my experience, those who were good at maths were regarded much smarter than someone who was good at history or art. I think this is a main reason as to why the subject intimidated me slightly when it came to secondary school. Another reason is that I strongly believed the myth that we were born with either a mathematical or a literacy brain, I was always good at history so I then decided that it just wasn’t in my genes to be talented at maths.

There is also another myth circulating that people wont need maths once they leave school. I feel very strongly against this as we use maths in many aspects of life. When I get on the bus every morning I have to deal with money which is pretty much basic maths that I learned in primary school. When I become a teacher maths will be a large part of my job so that directly proves that this myth is rubbish.

I aim to incorporate group work into my maths lessons because I feel that children will be more likely to ask for help when they are in a group rather than on their own. As well as this speaking out in class is much less daunting because it wont be as humiliating giving a wrong answer when it is a group effort.

In today’s maths input there was an extremely interesting saying:

I hear, I forget

I see, I remember

I do, I understand

This backs up the idea that group work among other things, may be beneficial. Children learn better by actually trying things out instead of just working from textbooks. If they can apply their maths to everyday life and make it interesting they are more likely to remember it in the years to come.