Category Archives: Discovering Mathematics

It’s all over!!

I have always enjoyed mathematics. Inside and outside of the classroom I enjoyed doing mathematical activities and games and I was good at them! My main reason for enjoying maths in the past has been because there is always only one answer. It does not matter
how you get to this answer as long as you get there somehow. I was taught by my maths tea b2d6ed7853ac1e89ddb6c2756ecce1b8 cher that even if you had to look at the answer and then work backwards then that was okay. As long as you found how to come to the answer after working backwards. I found this useful to know as it taught me that you can come at things from different
angles and still get the right answer.
I was always told “Oh, you have a maths brain” or people were shocked to find out I enjoyed math, saying things like “You like maths?!. Liking math is mostly a foreign concept for a lot of people. I was always use to this. I did not realise how much anxiety several people held on to relating to maths until I started this module. Several people think that they are bad at math without even trying maths activities. This must be a massive issues for teachers when they teach maths to children that hold on to these mentalities.

I cannot believe that this module has came to an end. Even though I picked it because of my love of math, I did not realise it would be as interesting as it was. This module has made me look at the world in a completely different way. It has made me see the mathematics in the world around us. At times, I have felt extremely confused, shocked or disbelieving after lectures or inputs from this module. This was mostly because I could not believe the areas that we were being told mathematics related to. However, the best feeling was when I would feel confused halfway through a lecture and then understand what we were being taught by the end. I have seen the whole class, even those who did not enjoy maths usually, go through these feelings. The nicest thing at the end of this module is to see the people that had math anxiety at the beginning say that have enjoyed this module.

Lastly, I would tell anyone to take this module. I have thoroughly enjoyed it as well as enjoyed being able to tell my family where there is mathematics in the things that they do. If you have not previously been good at math or hated it. Take this module! It will change your life!

My Understanding of PUFM

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Liping Ma (2010) suggested that in order for mathematics to be understood correctly teacher’s must have a profound understanding of mathematics (PUFM). Ma said that there were four key concepts that you needed to understand in order to have a profound understanding of mathematics. These concepts are basic ideas, multiple perspectives, longitudinal coherence and connectedness. i am going to discuss my understanding of these in this post.

Basic Ideas

Ma (2010, p.122) describes this as ” Teachers with PUFM display mathematical attitudes and are particularly aware of the “simple but powerful basic concepts and principles of mathematics” (e.g. the idea of an equation). They tend to revisit and reinforce these basic ideas. By focusing on these basic ideas, students are not merely encouraged to approach problems, but are guided to conduct real mathematical activity.”

The basic ideas of mathematics are really important as children need these basic ideas to be able to continue to more complex areas. The basic ideas are similar to the foundations a building. If these basic ideas are not taught correctly to children or some areas are missed out that will make it more difficult for children to learn the more difficult areas of mathematics that are built on top of these basic ideas. These basic ideas need to be reinforced so that children have a sound understanding of them. For example, children need to learn addiction and subtraction before they can move on to more complicated areas like money and time.

Connectedness

“A teacher with PUFM has a general intention to make connections among mathematical concepts and procedures, from simple and superficial connections between individual pieces of knowledge to complicated and underlying connections among different mathematical operations and subdomains. When reflected in teaching, this intention will prevent students’ learning from the being fragmented. Instead of learning isolated topics, students will learn a unified body of knowledge.” (Liping Ma 2010, p.122)

Connectedness is a mathematical concepts that means math is connected to other subjects. I have realised through this module how important this principle is as there is math in everything.
In order for teachers to achieve connectedness they need to teach mathematics beside the areas that it can relate to and not as a single subject. Since math is laced through nearly everything that we do, that is how it needs to be taught. For children to have a thorough understanding on mathematics it is best to teach it alongside the other subjects that it is connected to.
A teacher could teach a music lesson and whilst doing different values of musical notes could do some work on counting and addiction. Another example would be a baking lesson, weight and measurement could be taught while measuring the ingredients. This gives the children some context to their lessons rather than just weighing random items that they do not care much about.

Multiple Perspectives

Liping Ma (2010) discribes multiple perspectives as “Those who have achieved PUFM appreciate different facets of an idea and various approaches to a solution as well as their advantages and disadvantages. In addition, they are able to provide mathematical explanations of these various facets and approaches. In this way, teachers can lead their students to a flexible understanding of the discipline.”

Multiple perspectives means that children need to have several ways to get to the answering not just one. This is useful for children as not everybody’s brains work in the same way. This means that if a child does not understand the first way that a new mathematical area is taught then the second or third way might make more sense. By multiple perspectives being provided in the classroom, it makes mathematics less restrictive and easier to understand.

Longitudinal Coherence

Lastly, Ma (2010, p.122) states that longitudinal coherence is needed to have a profound understanding of mathematics.
Ma describes this as “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. With PUFM, teachers are ready at any time to exploit an opportunity to review crucial concepts that students have studied previously. They also know what students are going to learn later, and take opportunities to lay the proper foundation for it.”

This concept is the one I found most difficult to understand. However, it is still important but just takes a little longer to understand. This principle says that what a child learns should not be limited because of their age and year that they are in. Ma says that a teacher should be able to teach any mathematics to suit the level of his/her children. I think that this is vitally important for in the classroom as children should not be limited just because they are a certain age. If a child understands all of the areas that they “should” know in their year then why should they not be moved on to the next area even though it is normally done in the next year up. This means that teachers need to be prepared to teach children of all levels.

References

Liping (2010) Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in china and the United States. 2nd edn. New York: Taylor & Francis.

Demand Planning

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We think of ourselves as individuals but in fact what we do can be predicted. Every time we text, use our credit cards and shop data is created that allows our movements and plans to be tracked.

Temperature can change how we act and how we eat. When it is colder we eat more. We also want to eat and drink hotter food and drink when the temperature drops. Porridge sells millions more when the weather is cold. Demand planners are people who have to predict what we will buy all year round. They have to know how much advent calendars will sell at Christmas so that they have enough for everyone but are not left with lots of stock. Demand planners also have to be able to work out where the most advent calendars will sell so that they have the correct amount of stock in each shop. However, demand planners do not need to be able to work out what we will buy at special times of the year, they need to do this all year round. Demand planners need to constantly predict how much stock each shop with sell all year round. To do this they need to analysis previous stock sold, the temperature outside, the area of the country and the time of year. If we eat more or crave more hot foods when the temperature drops then that means that demand planners need to be able to predict when this is going to happen. During “Human Swarm” on Channel 4 they talk about how weather affects what we buy. Ross Eggleton who works at the biggest warehouse in the UK tells us that “we basically capture every single transaction that every individual makes in every single store every moment of every day. And if you overlay that then with what the weather conditions were outside at the time they made the purchase,

it obviously gives you a lot of information and data that you can then use to build a picture of what those patterns are going to be the next time.” This shows how the food that we buy correlates with the weather outside and shows how demand planners then use this information. Eggleton also says that the hardest time to predict what we are going to buy is when there is a sudden change in the weather. On a low temperature weekend 246% more pies were bought than on a normal weekend. This shows how important demand planners job is. If they were not able to predict this, then the supermarkets would run out of these popular items like soup and pies that we like to eat when it is cold. This is a perfect example of how important mathematics is. Without being able to collect all of this data, demand planning would not be able to happen. This is another example of how math is used in the real world and it shows how important it really is.

Business simulation

During this input Richard came up with a way for us to have a go at demand planning. He gave us a selection of product that we could buy and a budget to start with. in groups we got to decide what to buy, how much of each thing to buy and how much we were going to spend. Richard then told us what percentage of stock we had sold, what we could carry over (non-perishable items) and is any stock was discontinued. I found this simulation lots of fun but the buying the items was pretty stressful incase you picked the wrong items. Finding out how much of the stock was sold was also nerve wracking as you might have picked the wrong items then they went off. We did this over a full year so that we got a different idea of the seasons. At the end, my group actually did pretty well and we had the third highest amount at the end out of everyone.

Below are my groups sheets from the simulation.

I think this is a fun thing that you could do with children in a classroom. Using a more simple version of this would be a great example for children how maths can be used in this industry in the real world. It would also give children an insight into food ordering and supermarkets would could be useful for their future.

References

BBC (2002) Autumn’s Supermarket Secrets. Available at: https://learningonscreen.ac.uk/ondemand/index.php/clip/27113 (Accessed: 21 November 2016).

Doherty, J. (2013) Human Swarm. Available at: https://learningonscreen.ac.uk/ondemand/index.php/prog/037BDBED?bcast=97003675# (Accessed: 21 November 2016).

Logistics and Supply Chain

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Richard’s last input with us was all about logistics and supply chain. Is there any maths behind these two things? Well yes of course there is! Logistics and supply chain is the managing of planning, implementing and controlling the process of the shipment of goods. This includes how far the food had travelled to how the food is travelling.

Food miles

Food miles is vitally important when it comes to our food. How far has your food travelled before it gets to your plate? Food miles is the distance all of your food has travelled before it gets to your plate. That includes every single ingredient. So has your chicken came from 40 miles down the road or has it been flown over from New Zealand? Are your vegetables from your local farm or Europe? These things are all important. Food miles includes every mile that your food has travelled, from producer to the supermarket and then to the consumer. However, other factors can come into play. For example, Saunders, Barber and Sorenson (2006) did a study that compared how much energy it took to produce lamb in the UK and New Zealand. She found that New Zealand were using less energy to produce their meat then the UK. This included the energy used to get the lamb to the UK as well. But why is this important? This is important because of climate change. Climate change is a massive thing worldwide with big companies wanting to do what they can to decrease their carbon footprint. If importing lamb from New Zealand is actually better for the planet than producing it here than is what supermarkets are going to buy. This shows that food miles are not as important to supermarkets anymore as they are concentrating more on their carbon footprint.

Food miles are important to a lot of consumers though as many people like to buy locally produced food. This will be a challenge for supermarkets as they will need to work out what products are better to get from local producers and when it is best to import them. What will the consumer buy? This is the role of Demand Planners.

Teaching children about food miles is important. If a child knows where their food is coming from then that might help them with knowing the right things to eat. This emphasises the fundamental understanding of mathematics as it shows connectedness between mathematics and health and wellbeing. Profound understand of mathematics’ concept of basic ideas can also be shown when looking at food miles. Children can learn about distances – miles, kilometres, metres and centimetres using the context of where their food comes from.

Shipping

When shipping products many different factors have to be considered – mass, distribution of this mass (the truck or ship needs to be evenly packed), size, temperature requirements, distance travelled and time taken to travel this time (shelf life of the products), and shape and volume. All of these things need to be taken into consideration when products are moved about. Food tends to be moved in shipping containers. The creation of these shipping containers has changed international shipping. These containers can be filled with different food products. Each different container can be a different temperature so that the food inside can stay at its best as it travels. This solves the problem of food going off while in transport because of the temperature it is stored at. Shipping containers also solve the problem or shape and volume. Shipping containers are all the same size and shape which means that they fit together and can be pilled high on the back of a boat. Since they can be stacked together with no space that means that companies are not shipping air and the boats can be evenly packed to distribute the mass evenly.

Who knew that so many mathematical concepts are needed to import and export food! This relates to the PUFM basic concepts. Children need to learn about the basic idea of volume, shape, weight, size, temperature and distance. These are all basic concepts that underlie primary school mathematics. Yet, here they are in a real life setting. This, again, shows me how much math is needed in the real world. The fact that there is so many mathematical ideas in something that seems simple has left me shocked.

References

Saunders, C., Barber, A. and Sorenson, L.-C. (2006) Food miles, carbon Footprinting and their potential impact on trade 1 food miles, carbon Footprinting and their potential impact on trade. Available at: https://researcharchive.lincoln.ac.nz/bitstream/handle/10182/4317/food_miles.pdf (Accessed: 21 November 2016).

Time for Maths

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Time is a funny thing. It is something that we all use but we have no idea where it originates from.

Why do we use the time system that we do? How before clocks were invented did we know what time it was? How do animals know what time it is?

Well let’s try and answer some of those questions.

Horology is the study of time and the measurement of time. The word ‘Horology’ originates from Greek words hṓra (hour, time). Horology also look at how time is important to humans and is this idea of time innate in animals.

When you think about it, time is enlaced though everything that we do. What time do we go to sleep; what time do you get up; how long did you sleep for, which makes a huge different to how you feel that day; the time that you eat at throughout the day. Humans are not the only ones that go through these different time routines everyday, so do animals.

For example, if you look at my dogs. My dogs in the morning and evening are very vocal about needing fed. They will come and sit staring at myself or my mum until we go and feed them. Now, does this mean that they have an innate idea of time, which is referred to as a “body clock” or do they just start to get hungry? There is no way to really know.

However, what about animals that’s routines are not influenced by humans, for example, nocturnal animals. How do they know that it is time for them to come out? it is said that they “just know” when to sleep and when to eat but that “just knowing” would be their innate idea of time. Another example of animals understanding the concept of time is hibernation. How do hibernating animals know when it is time to stock up for food and find a suitable spot to hibernate in?

A suitable example for this time of year is migrating birds. If you look up in the sky in the mornings and evenings the sky will be full of geese migrating for the winter. In the spring, the sky will again be full at these times of day as the geese migrate back to Scotland. But how do these birds know when it is time to migrate? Is it that it simply gets too cold for the animals hence why migration and hibernation happens? Or is it that the concept of time is imbedded into these animals’ natural instinct which tells them when it is time or change their behaviour to suit their surrounding or move elsewhere. I use the migrating geese over Scotland as my own way to tell time. When I see them migrating south I know that it is getting colder and that winter is coming and when I see then migrating north I know that spring is near. This means that I use an animals innate time telling to clue me in on what time of year it is.

We tell time using the traditional mechanical clock. However, this is not what has always been used to tell the time. Sundials and obelisks are the oldest known device for measuring time. Sundials worked by tracking the sun as it moved from east to west. As the sun moved it created shadows which then predicted what time of day it was. A pillar or stick called a gnomon was put in the middle of the sundial and time was then calculated depending on the length of the shadow (Marie,2016).

This is the shadow of the sun revealing the time on a sundial.

The Egyptians created an obelisk. There were similar to a sundial but they divided up the days into parts. This was the first time days had ben formally divided up. These worked the same as sundials but the enabled citizens to partition their day into two parts by noon. Obelisks also showed when the longest and shortest days of the year were (Bellis, 2016)

Looking at time has given me even more idea of how math is used in the real world that I do not even realise. Hence this has given me a better understanding of what it means to have a “profound understanding of mathematics”.

References

Wikipedia (2016) ‘Horology’, in Wikipedia. Available at: https://en.wikipedia.org/wiki/Horology (Accessed: 21 November 2016).

Bellis, M. (2016) The history of sun clocks, water clocks and Obelisks sun clocks, water clocks and Obelisks. Available at: http://inventors.about.com/od/famousinventions/fl/The-History-of-Sun-Clocks-Water-Clocks-and-Obelisks.htm (Accessed: 21 November 2016).

Marie, N. (2016) When time began: The history and science of sundials. Available at: https://www.timecenter.com/articles/when-time-began-the-history-and-science-of-sundials/ (Accessed: 21 November 2016).

Common Myths of Mathematics

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There are several different myths that are associated with math. These myths are the reason that children do not enjoy or even try at maths.

Myth 1 – Some people get maths because they have the ‘math gene’ and others don’t.

There is no such thing as a ‘math gene’. Nobody is born knowing everything about maths and just ‘getting’ mathematical concepts. Some children have just been exposed to mathematical situations more than other children. However, this is something that is difficult to explain to children.

How can you explain to a child who is adamant that they do not have the ‘math gene’ that there is not such thing? Simple answer, you don’t! They will see one child understand a new maths area straight away and they will not. Weeks later they will start to understand the new area while the other children have moved on to something else.

Dispelling this attitude in a classroom can be extremely difficult if children have already decided that this is the case. This makes the teachers job even more difficult when teaching math.

Myth 2 – You are cheating if you use any tools.

This myth is one of the most irritating out of all if them. A common myth within math is that you are cheating if you use something to help you. Not everyone can do maths in their heads very quick. Me personally, I struggle with doing maths quickly in my head and I would much rather write it down on a piece of paper to work through it and use a calculator.

There is no shame in using your fingers or a calculator to help you. Why shouldn’t you use all of the tools that you can if you are struggling to understand something. The fact that a child cannot add up in their head should not stand in their way of working out a bigger, harder problem. They should be able to use a calculator, number square or their fingers if it helps them.

If children are told that they can not use a tool or that using one is ‘cheating’ then they will disengage with what you are trying to teach them as they cannot use the only thing that is helping them through.

Myth 3 – Nobody actually uses maths in the real world anyway.

This myth is one of the most common and is the one you hear most throughout society. A lot of people think that you do not need math in the real world so what is the point in learning about it. The myth comes from several different angles. Parents or guardians may tell their children when they are struggling with their homework ‘It doesn’t matter; you wont use it anyway’. This then shows children that disengaging with math is okay as you do not need it.

This myth could not be further from the truth. I have always known that we need math in the real world but never have I realised this more than since I have started this module.

And lastly,

Myth 4 – You must always know how to get the answer.

Many associations with math is that you need to show everything that you did to get the right answer. But you don’t! If you can get the correct answer several times for the same kind of problem then you know wheat to do, you should not need to explain that.

There are many myths to do with mathematics but none of them are true. These are the myths that come in between children being open to learning math. In my classroom I hope to have no preconceptions about math and let children use whatever they need to understand the subject.

Math is linked to Music!?! What!!

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Every input in this module I realise how much math is laced through nearly everything we do. I did not realise how much math interlinked with so many other curricular areas.

“The astronomer Galileo Galilei observed in 1623 that the entire universe ‘is written in the language of mathematics’, and indeed it is remarkable the extent to which science and society are governed by mathematical ideas” (Rosenthal, 2005). This shows how mathematics has been known to run through several different areas for hundreds of years.

Music has always been hugely important to be. I have always sung or been sung too. When you are learning to read music and play an instrument math is not something that you think you are doing anything with. But in fact you are! Apart from the obvious mathematic part of music like how long notes are held for; how many beats are in a bar or how to pitch a piece of music or a song. There are many ways in which maths runs through music in ways you would never realise.

Patterns are an important and huge part of maths as I have already spoken about (see Maths is Pretty!). They are a huge area in which math can be used in the real world. However, math and music can also be linked through patterns. Many different musical pieces are made up of different patterns of notes. These do not tend to be called patterns though as musicians tend to call them motifs, melodies or sometimes rhythmic patterns. Pieces of music consist of these patterns.

Maths also comes into music when you look at octaves. An octave consists of eight notes. Notes are an octave apart when they are the same named note but played in a different frequency. A note played an octave higher is played at double the frequency while a note played an octave lower is half the frequency than the middle note. For example, High C and Middle C are an octave apart but when played together they sound great. This is the same for all notes. Several famous songs play notes together that are an octave apart – the initial “I’m singing” of “Singing in the Rain”; the first two notes of “Somewhere over the rainbow”; and the first two notes of the third line of “Happy Birthday”. (Rosenthal, 2005) This is a perfect example of how these pairs of notes go together.

The Pentatonic scale is made up of five notes. If you are playing a piano these five notes are your black keys. Every piece of music will have these five notes in it somewhere. It is suggested that we are genetically programmed with these five notes just as we are language (Goodall, 2008). These five notes are innate within us. Several famous songs use the pentatonic scale including, “Mull of Kintyre”, “Auld Lang Syne”, “Swing Low” and lots of rock songs use the pentatonic scale in their guitar riffs including “Whole Lotta Love” by Led Zeppella. If you are using the oentatonic scale to write a song you are not just stuck with these five notes but they can be used to develop from.

Bobby McFerrin demonstrates how this scale is genetically within humans.

He does not tell the audience what is the next note to play but they are able to sing the next note in the scale.

The Pentatonic scale is the perfect notes to give children as they will always sound good together no matter what order they are played in. Is that how these five notes become programmed into us? By music teachers who want children to create a nice sounding piece of music, who knows!

Fibonacci Sequence

The Fibonacci sequence (mentioned in a previous post, Maths and Art) can be seen throughout musical sequences as well. Including all notes in an octave there are thirteen. In a scale there are eight notes, the fifth and the third notes make up the basic foundation for the chords. On a piano keyboard scale there are thirteen keys, eight white and five black, these notes are then split into groups of two and three. All of these numbers are from the Fibonacci sequence.

The Golden Ratio and Phi can be seen in music instruments as well. Violins are designed using the golden ratio.

References

K. (2012) Bobby McFerrin demonstrates the power of the Pentatonic scale. Available at: https://www.youtube.com/watch?v=_Irii5pt2qE (Accessed: 13 November 2016).

Rosenthal, J. (2005) The magical mathematics of music. Available at: https://plus.maths.org/content/magical-mathematics-music (Accessed: 13 November 2016).

ScoobyTrue (2008) Howard Goodall on Pentatonic music. Available at: https://www.youtube.com/watch?v=jpvfSOP2slk (Accessed: 13 November 2016).

(No Date) Available at: http://www.goldennumber.net/music/ (Accessed: 13 November 2016).

Maths and Art

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“Maths is everywhere”

I have heard this quote several times throughout my life. I have always known that mathematics is used in day to day life but I did not realise how much math was around us in nature. I did not realise that there was maths in the plants and animals in nature and in the buildings around us.

In a recent input in my Discovering Mathematics module we were looking at how maths and art connected. We looked at the Fibonacci sequence, golden ratio and the golden spiral. Out of these three things I had only heard of the golden spiral before this input. I had heard of the golden ratio prior to this input in relation to photography but I did not know where it came from or the numbers and equation behind it.

The Fibonacci sequence is a sequence of numbers where the next number is the previous two added together. For example, to get the number 3 the numbers before (2+1) are added together. The same is then done again to get the next number 5 using the 3 and the previously used 2. This continues on and on! The sequence starts with the numbers 0,1,1,2,3,5,8,13,21,34,56,90 and so on. This sequence of numbers can be seen in many different places throughout nature including the reproduction of animals.

The Golden Spiral is linked to the Fibonacci sequence as using the numbers of the Fibonacci sequence to draw square boxes linked to each other. Using a protractor, you can then draw a spiral going through all of these boxes. The Golden Spiral can be found in nature in insects’ wings, sea shells and flowers.

This can be linked to Liping Ma’s ideas of having a Profound Understanding of Mathematics.

Connectedness this idea links using mathematics and creating a beautiful piece of artwork with it. This means that you are using basic mathematics procedures to understand the world around us.

Basic Ideas if you do not know the basic mathematic skills of being able to measure, count, work out the next number and using a protractor at certain angles. If you did not have these basic skills in math, then this task of creating the Golden Spiral would have been really difficult. Even though I have these basic mathematic skills I still struggled to see what I was trying to create.

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From the Golden Spiral you can work out the Golden Ratio. T notre-dame-paris-golden-ratio he Golden Ratio is 1.61803398875. If you take any of the numbers in the Fibonacci sequence and divide the bigger one by the smaller one you will always get close to the Golden Ratio. If I take 34 and 21, the result is 1.61904 which is the Golden Ratio! The Golden Ratio can be found in several buildings throughout history though there is no evidence whether these buildings were built purposely using this ratio. Buildings that are an example of this are Notre Dame, Taj Mahal, the Parthenon in Greece and even the Egyptian Pyramids.
These are all examples of how maths and art link in the real world. This input made me realise how big a part maths plays in our world around us. Prior to starting this module, I knew that we used mathematics a lot in everyday life in areas like cooking and banking but I did not realise how much math was around us in the buildings and animals. I look forward to discovering more ways in which math is in the world around us as I continue through this module.

References

Ma, L. (2010) Knowing and teaching
elementary mathematics: Teachers’ understanding of fundamental mathematics in china and the United States. Anniversary Edition edn. United Kingdom: Routledge.

The Fibonacci numbers and golden section in nature – 1 (1996) Available at: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html (Accessed: 3 November 2016).

(No Date) Available at: http://www.goldennumber.net/architecture/ (Accessed: 3 November 2016).

A New Number System!!

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Recently, in our Discovering Maths module we were asked to come up with our own number system. This proved to be a lot more difficult than I thought it would be. How can you come up with another symbol rather than the numeral we are use to to represent a number?!

Myself and my partner Holly, managed to come up with a system but this was based on the base 10 system.

This is the system that we came up with.

We decided to use circles and squares to represent our numbers. We used circles to represent odd numbers and circles inside squares to represent even numbers. After, we had came up with this we realised we had not included a symbol for zero. We were not sure what to use for zero, and after a while we decided zero would be represented by a plain dot.

I underestimated how hard it would be to come up with my very own number system. To think ‘outside of the box’ and away from the numerals that we are use to to represent our numbers was really difficult. It look a long time to think of what we could use. It also took a few attempts of trying different ideas and trying to think of a system that could be easily used. We did not go as far as what we would do for any numbers past nine as it was hard enough to get to nine. We would more than likely use the symbols we already have to create other numbers.

Even though we did not manage to go further than nine, other people in the class did manage to go further up the number line.

Math is Pretty!!

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Even though I have always loved math I did not realise how pretty maths could be. Symmetry is what we use to make this ‘pretty maths’. This symmetry is the most significant area of math the makes a connection between science, art and maths. Symmetrical patterns can be used in several different areas. Artists use symmetry to create patterns and use maths to help create these patterns. By using simple fractions and a computer software symmetry can be used to create amazing intricate patterns that artists put on anything from canvases to items of day-to-day use.

Islamic tiling is a unique way the symmetry is used to create fascinating patterns and designs. Islamic art is created by using extravagant geometric decoration expressed by using texture, pattern. colour and calligraphy. These patterns are not just used for a decorative purpose they are used to represent a spiritual version of the world – “Unity of God”. These Islamic tilings are always created of three simple shapes – the square, the hexagon and the equilateral triangle.

This is an example of Islamic Tiling,

This kind of pattern is called tessellation and is a great way to show children how math can be fun. Using Islamic Tiling, pattern and symmetry can be taught through a series of lessons starting with showing the children examples of Islamic tiling, showing them how they can be created on the computer and the history and meaning behind these works of art. After the children have learned about the history they can move on to create their own designs. This is showing the children how math and art are linked and how math is not always about numbers. This lets the class have fun with this new area of math and lets them try and use simple shapes to create intricate designs. Tessellation can also be shown to children through looking at buildings and all over the world. Tasks can be set as homework for the children to find tessellation around their city. A programme could also be downloaded on the computer and this can be used with real life pictures to create patterns

The concepts in this post relates to Liping Ma’s principle of connectedness as whilst the children are learning how to make symmetrical patterns and how to use simple shapes in these patterns, they are also learning how to fit these patterns together in tessellation. This means that the children are learning more than one area of knowledge and not just the topic of tessellations. This allows children to see how all of their learning is connected.

References

Liping (2010) Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in china and the United States. 2nd edn. New York: Taylor & Francis.

Why would you want to discover maths?!

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When we were asked to choose an elective for MA2, it was not a hard choice. The minute there was a module that mentioned mathematics I knew that was the one I wanted to do. To me, mathematics is the subject that makes the most sense. The fact that I enjoyed mathematics in school was always something that my family and friends did not understand. The minute that math is mentioned as something that you love mathematics, people give you strange looks and ask you ‘Why?’. Many people struggled to understand why I would enjoy a subject that is all about numbers and equations. They struggled to see why I would choose to understand the language of numbers rather than the language we are all use to in standard English reading books. Well, why would I not choose the world of numbers? If you cannot understand the numbers around you then you will not be able to understand the world.

One common dislike of mathematics is that there is only ever one answer. That is always my answer to why I love mathematics so much. I have always loved that if you follow through an equation correctly then you will get the correct answer. Compared to English texts which could be interpreted in any way depending on the person and how you understood the text. However, this is not always the case. Some areas of mathematics are not as structured as always having one answer. In fact, some areas of mathematics might not even be about getting a correct answer but about what you can create using mathematics.

The way our curriculum is structured why would anyone see the fun and adventure in numbers. When mathematics is mentioned, the general response tends to be ‘why do you like it?’ or ‘when are you going to use it in day-to-day life?’. Most mathematics that you learn in secondary school may never be used unless you go into a certain career. However, mathematics is used very differently in normal day-to-day life. How can we get children to enjoy mathematics and see the fun in it if they only think of mathematics as times tables or algebra? Children need to be shown the fun in mathematics. They need to be shown how mathematics is weaved throughout several of their other subjects. Maybe if children were shown how people in history discovered how to work out the area of a shape or how symmetry is used in architectural they might be more interested in learning mathematics (Sautoy). If the curriculum brought in a context to mathematics rather than children learning an equation, how to use it but they think they will never use it again. Having more of an understanding of the background to math would help engage children in mathematics a lot more than simply sitting learning from a textbook.

Professor Marcus du Sautoy described mathematics as a language that you needed to work on to understand just like Shakespeare. I think this comparison describes mathematics and what you need to do to understand it perfectly. At school, I always struggled to understand Shakespeare but several people struggle to understand the language of mathematics. If the children that struggle with math are sat down and helped to understand the language of numbers, just as those who do not understand an English book or Shakespeare are treated then I think we would have a lot more people in the world who would see mathematics as a good thing and not something not worth learning.

References

du Sautoy, M. (2009) The secret life of numbers. Available at: https://www.theguardian.com/education/2009/jun/23/maths-marcus-du-sautoy (Accessed: 14 October 2016).

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