Category Archives: Discovering Mathematics

Mathematical Terminology Used More Often Than We Think?

My first Maths and Science input of semester 2 with Tara made me challenge my way of thinking or as I thought the normal way of thinking.

When talking in social situations or even just reading simple stories it is apparent that mathematical terminology is at the forefront of them. In this lecture, Tara read us a story and asked us to think of the words she said and to write down the mathematical terms in a list on our page. Originally I only counted 10-15 words of this type but after it was explained I had the realisation that mathematical terminology is not only words associated with number, but size, positioning etc. Realising this made me feel the need to look closer at other children’s stories and rhymes.

I decided to look at This nursery rhyme in particular because numbers are prominent here and frankly to begin with I didnt think there would be many more terms other than the numbers 1-10.

I was wrong…

In this early childhood song not only do children use mathematical terminology with the numbers 1-10. There is also terminology used to describe positioning and size. I will use bold on the font to highlight the mathematical terminology.

ONE, TWO, THREE, FOUR, FIVE!

One, two, three, four, five,

Once I caught a fish alive,

Six, seven, eight, nine, ten,

Then I let it go again.

Why did you let it go?

Because it bit my finger so.

Which finger did it bite?

This little finger on the right.

Maths in Football

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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.

THE BALL

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).

Picture taken from – www.bbc.co.uk

SCORE TAKING IN THE MATCH

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.

TIME

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.

SHAPE AND DIMENTIONS OF PITCH

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.)

REFERENCES

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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Screen Shot 2015-11-02 at 16.59.51

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.

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.

References

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).

Number Systems

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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?

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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!

http://www.novelgames.com/en/ayumu/

Picture from Google Images – io9.com

References

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).