Monthly Archives: October 2016

The Only One Who Wins at the Bookies is the Bookmaker

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tumblr_static_chanceOur most recent workshop was about probability and chance. This is most definitely something which we see every single day and affects people in both positive and negative ways.

So, what is probability? Probability is defined as “the study of chance” in one of our key texts: “Alex’s adventure in Numberland.”

Gambling is strongly connected to maths and is all about chance and luck and helps us see that Ma’s idea of “interconnectedness” is always apparent and important. There are so many aspects of maths in gambling such as money, probability and percentages (in particular; the amount actually paid out in comparison to what was paid in).

Here, in gambling and chance, all three topics that I previously stated need each other to allow people to win (or more than likely lose!) Think of it this way:

“How much cash should I put in to this game? How likely am I to actually win with this amount of money? What percentage of that have I won?”

There are also aspects in gambling which are linked to “multiple perspectives”. This is about having different ways to reach an answer. In the workshop we were shown an example of a made up restaurant. It had 2 choices of starter, 3 choices of main, 2 choices for dessert and we had to figure out how many different possible combinations we were. I managed to see multiple perspectives put into life here. The way I would have done it was long and confusing: I just wrote out a letter for each option and kept writing and writing until I had run out. But, another student used a “branch” type system and reached the answer a lot quicker than I did. Therefore, showed me that even as student teachers we are on our way to achieving a PUFM.

Unfortunately (in my opinion), gambling is something which affects many people’s lives on a slot_machine_cartoondaily basis and it, more often than not, involves money. Let’s look at fruit machines. These are something which are seen in almost every pub and casino that people go into and the aesthetic appeal of most of these machines encourage people to waste their money and use them. The first fruit machine was invented by Charles Fey from California in 1887. (Slot Machine History, 2010) and since then their popularity has continued to grow.

However, it’s not all fun and games. If you were to win on a slot machine there is only a 70% pay-out rate. (If you could win £10 you would actually only win £7).

This leads me on to talking about probability. For example, imagine we had a slot machine with three reels (the “screens” to see the symbols) and 15 symbols. To find the number of combinations we have to multiply the symbols by the number of symbols on the remaining reels. So, for a three reel machine that has 15 symbols per reel we have to do 15x15x15 which equals 3375 combinations of slot symbols.

If a jackpot offered on this machine pays on 7 7 7 and only one 7 symbol is on each reel, then the probability of hitting this jackpot is 1/15 x 1/15 x 1/15 or one in 3375.

When it comes to teaching probability there is much simpler way to do this: flip a coin. There is 50% or one in two chance of guessing heads of tails.

With regards to my professional development probability and chance will be taught. But, this workshop has also made me realise the importance and seriousness of gambling and that it is fun but can lead to debts and problems in later life.

References

  • Bellos, A. (2010). Alex’s Adventures in Numberland (Chapter nine). London: Bloomsbury.
  • Slot Machine History. 2010. Available at http://slotmachineshistory.com/charles-fey.htm(Accessed on: 28th October 2016)

 

 

 

 

Maths and Play

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We recently had a workshop with Wendee which was all about learning about mathematics through play. It was great as it let us pretend that we were children again!

Play has an extremely important part in a child’s development. It allows them to learn new skills, such as socialising with their peers. But, it also allows them to revise and revisit the abilities they have already learnt through previous education and interaction.

plastic

Thinking back to my own primary school experience with maths and play I always remember the little plastic blocks like the ones shown. It makes me feel quite nostalgic and no one can deny that they all smelt the same!

These blocks would be used to help us to learn how to count one by one, then move onto addition and subtraction and in later stages they could be used to understand volume and cubic centimetres.

I feel that using these blocks for play links in with Liping Ma’s theory of basic ideas. Counting is simple, to us, but this understanding of basic ideas will allow children to learn to count then move onto addition and continue to work up to more complex mathematical situations confidently.

The importance of these blocks was that children could use their senses. They could physically see addition and subtraction taking place and this would allow them to apply these skills to mathematics in the future.

But, in my opinion, play now is very different to what it was when I was at primary school. Children are so advanced with technology so using things such as iPads and computers can benefit them with their mathematical knowledge through the use of  apps and websites.

I think that technology is a fantastic way for children to learn as the majority of the time they do child-with-ipadnot even realise they are applying their knowledge because they are having fun.

Here is a website with a variety of apps that children can use to apply their mathematical knowledge to games: http://www.pcadvisor.co.uk/feature/software/best-maths-apps-for-children-3380559/

A study from Davies (1995) found a huge variety if reasons why games are beneficial in a child’s learning and understanding of maths. The one which stood out most for me here was motivation. From my experience on placement trying to motivate pupils to learn and engage with my maths lessons proved to be quite difficult. But using games in maths allowed children to totally engage because they wanted to win. I feel this was due to the very competitive nature of the pupils in my class.

Additionally, he stated that games were beneficial because it allowed children to have a bit of independence from the teacher. I agree that this is beneficial because children do like to occasionally work on something themselves or in a group in order to meet a goal or, in this case, to win a game.

Therefore, I believe that play is vital for pupils. It is important for their social development but it also allows them to realise that maths is fun.

 

 

 

 

 

The Art of Mathematics

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paintbrushes

So far in this elective I have seen that maths is used in everything we do every single day. From looking at the clock when we wake up and how much flour we should put in that cake we really shouldn’t be having. But, in a recent workshop with Wendee we have seen that maths is extremely important in art. Throughout this post I will prove that maths is used in different types of art and is in a lot of things we see everyday. Art is a subject which is about creativity and expression and, possibly, has no correct “answer” as such. So how can a subject like this be related to maths?

Throughout this elective we have been told to read the work of Liping Ma. She explains there are four fundamental properties within mathematics. She refers to one of these properties as “interconnectedness” which is how topics within maths depend on each other and work together.

Islamic art is a great aspect to look at when studying the relationship between maths and art, but also exploring the property of interconnectedness. Islamic art uses 4 main geometric shapes: circles, squares, equilateral triangles and hexagons. Richard (2015) tells us that each shape represents something islamic-artwhich is important in Islamic religion, for example, the circle represents unity and something which is never ending. Additionally Hussain (2009) states that these complex and beautiful geometric designs create the idea of continuous repetition, and this allows a person to understand the idea of the infinite nature of Allah. 

During our lecture the “Golden Ratio” was mentioned and I think this is a vital concept which is key in understanding the strong bond between mathematics and art and also maths in everyday life. To give a bit of background; the Golden Ratio is a number which is approximately equal to 1.618 and also known as “Phi” in the Greek alphabet. This is how the ratio looks visually:

golden-rectangle-ratio2

The Golden Ratio is used in geometry in mathematics and it is how symmetry is used to make a balance look in pictures. You start with a basic rectangle which is drawn using the ratio of 1.618…. If you were to draw a line in your rectangle to make a perfect square the rest of the rectangle will have the ratio of 1.618: the same as the original rectangle. You can carry on doing this on the rectangle and that is why it is so special. (Sincere apologies if that has bored you!)

The spiral is the main part to focus on here:

fibonacci_spiral

It starts at the bottom left then hits the opposite corner of each square within the rectangle. spiral4-sThis spiral is extremely pleasing to the eye and is found in a huge variety of things we look at every day such as plants and even the human face.

 

 

 

It has been found that the Golden Ratio is found in art work such as the “Mona Lisa” and “The Last Supper” by Leonardo DaVinci. By following the spiral round our eyes are drawn into the main focus of this picture. monalisa

I really enjoyed this lecture. Throughout my time at school I always loved art and I think it is fascinating how so many different aspects of maths can be used in a variety of different pieces and seen in objects we use every day.

 

 

References:

  • Henry, R. (2015) Geometry- The Language of Symmetry in Islamic Art. Available at: http://artofislamicpattern.com/resources/educational-posters/ (Accessed 4th October 2016.)
  • Hussain, Z. (2009) Introduction to Islamic Art. Available at: http://www.bbc.co.uk/religion/religions/islam/art/art_1.shtml (Accessed 4th October 2016.)