Tag Archives: maths

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

2 Replies

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).

Differences Between Sweden and UK

1 Reply

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?

References

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

1 Reply

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?

1 Reply

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).