During our Exoressive Arts module at university, creating a drama bag (character bag) was one of the tutor directed tasks we were given. Where we were asked to fill a bag with objects to represent a variety of characters which could be used as stimuli for role-play or improvisation. However, i decided to create my charcter bag based around an event in a detective story.
Information given to children, to prompt questioning, and reasoning.
‘Someone had stolen the princess’ crown and this was the evidence left at the scene of the crime’
“Without mathematics there is no art.” said Luca Pacioli, a contemporary of Da Vinci.
Mathematics and art are two subjects which many would think would never connect. However, following a recent input of our ‘Discovering Mathematics’ module, we learnt that in fact maths and art link quite closely in various aspects.
Golden Ratio
Without going into too much detail, here is the basic concept.
The Golden ratio is a number which is found by dividing a line into two parts, so that the longer part divided by the smaller part, is also equal to the whole length divided by the longer part.
The Golden Ratio is present in various ancient Greek architects work, a common example is the Parthenon in Athens. Where the pillars and roof shape are all equally proportioned into the Golden Ratio, purely for the purpose, that it is pleasing to the eye.
However, you might still be wondering, how does this relate to art? The Golden Ratio creates the idea of pattern, which is an important aspect of bt art and maths. However pattern shown using the Golden Ratio in art may not be as obvious as a polka dot pattern accross a painting. The Golden Ratio is present in Renaissance painters portraits. The most famous of these being the Mona Lisa. Again here the various aspects of the face are perfectly proportioned and equal to the Golden Ratio.
Therefore, to relate this to fundamental mathematics, the Golden Ratio would be perfect to incorporate in a cross-curricular activity of maths and art, whilst also relating to the world beyond education. Hawkin (2005, page 39) states, “Teachers are therefore increasingly looking for appropriate and mathematically rich contexts in which mathematics can be used to describe and explain the world. Art is one such context which is rich in pattern and other relevant concepts.” Through studying the Golden Ratio in mathematics and art, students can develop their knowledge of ratio, multiplication and pattern.
Cheerleading is a sport which was a big part of my life for many years – from seven years old until I was seventeen years old. So, of course the title of this blog is written light-heartedly and with complete sarcasm, as this can be a common misconception. However, although it may not be obvious to the outsider, mathematics is a big part of cheerleading, and covers many of the basic principles of mathematics; such as counting, shape, angles, measurement.
Counting
Basic knowledge of counting is used in cheerleading of counting up to eight, which must be kept at a steady pace, and in time with music. To confuse things, as you progress into higher levels of cheerleading, the music and pace of routines becomes faster and eight-counts must be counted only using the odd numbers off the number sequence. For example, 1, 3, 5, 7…….1, 3, 5, 7, in comparison to 1, 2, 3, 4, 5, 6, 7, 8. Therefore, there must be a knowledge of odd numbers, or counting in two’s. An example of the basic cheer count is demonstrated by the video below (the first 8 seconds of the video should give you the right idea). Another important point of counting in cheerleading is to ensure stunt groups are in groups of five or four. There must be basic knowledge of division, knowing how to divide your team up to create an equal amount of stunt groups.
Shape and angles are an important aspect of cheerleading, as all the motions used have to be tight, precise and in the correct position. By cheer motions I am referring to the various positions your arms and legs are held to create a shape. Below is an example of some of the motions used in cheerleading, to aid me in my explanations.
As you can see shape and angles play a big part in all of these. For example the motion ‘T’, you have to ensure that both of your arms are at a right angles, and your legs are tight toghether to create the perfect ‘T’ shape. However motions are not the only time that shape and angles come into cheerleading. During stunting, the way the base (person on the bottom of the pyramid) holds their posture, arms and legs is also extremely important. The base’s legs must be shoulder width apart (measurement) and the bases arms must be be held tight in towards their chest and their hands held at a right angle, in order to hold the flyers (person on top of the pyramid) foot. Again below is an example of how bases and flyers must stand and hold their posture whilst stunting – drawing in key aspects of shape also with the flyer holding her hands in position known as ‘High V’.
Moreover on shape and angles, bases must ensure they are standing creating a box shape with their feet, and their feet are facing directly towards one nother – knows as toe-to-toe. Therefore, creating more right angles.
Measurement
Back to the idea of positioning in stunt groups – stunt groups must ensure they are the correct distance appart so as not to bang in to one another. This is usuually measured by around and arms length or markings are shown on the mats of where to stand. This rule is also important during floor work, cheerleaders must enure they are at least an arms length apart from one another, so as not to collide whilst dancing and cheering. Lastly, during floorwork, position is important to as to create shape. For example, cheerleaders standing around the mat in a square or circle before a tumbling sequence.
Are cheerleaders dumb?
So, there you have your answer, cheerleading is not as easy as people may think and cheerleaders need to have a good concept of mathematical principles in order to carry out their routines, stunting and floor work. Therefore, no, cheerleaders are not dumb, they could in fact be budding mathematicians.
How has the ‘Discovering Mathematics’ module helped?
Through engagement with the ‘Discovering Mathematics’ module I would not have taken the time to reflect on my experiences as a cheerleader, and I may never have known how relateable it is to maths. To further my development in the future, I intend to be more aware of links where mathematics is present in daily life and routines that I may have turned a blind eye to previously.
Here’s a video of a the world champions in cheerleading below – Top Gun.
During one of our Discovering Mathematics lectures we disccused the idea of mathematics being present in the food industry. Through supply chain and logisitics, we discovered that the food we eat everyday has had a considerable amount of mathematical thought put into it before it reaches our fridge. Everything that you touch and use has come from a supply chain, and you are therefore guaranteed to come accross it in a job role in the future. However this particular discussion was on the supply chain regarding food.
Firstly, we discussed food miles. Food miles relates to the comparison of energy and CO2 emissions used for our food to be transported from different countries within the world. We were given a comparison of Lamb, and whether it would be more cost effective to purchase it from New Zealand or the United Kingdom. This is an important factor that shop owners must be able to work out in order to get the best deal. In the end New Zealand used lower energy and lower emissions in the transportation of lamb, than the United Kingdom. Therefore it would be be an increased benefit to purchase lamb from New Zealand – and this was all worked out through the knowledge of basic maths.
However this is not all that should be considered when transporting food. Factors and fundamental principles of mathematics mentioned in the lecutre, included;
mass (weight)
size (bluk,length, height, depth)
strength
temperature requirements
distance travelled/time taken (shelf life)
Secondly, we took part in a business simulation, where we became demand planners. It was our job to pick which items to stock in a shop based on the time of year and how successful we thought the sales of the products would be. We were given a list of products and a budget, we were to pick five products which we believed would sell well at the particular time of year. For example, during the Christmas period my team chose to spend a large percentage of our budget on selection boxes. During this period we sold 100% of the selection boxes, therefore we made a successful profit and reduced wastage. We had to take into account wether food was perishable, how long it would stay in date and popularity. Again, this all linked in with the fundamental principles of mathematics as we were using our knowledge of quantity and addition and subtraction.
This is, therefore, a prime example of the fundamental principles relating to every day life, without us even realising.
One example of mathematics being used in day to day life is in cooking – an essential skill that children need to learn as they grow up, and a skill that I am still to learn. However, aside from the fact that I cannot cook without a side portion of food poisoning, I do understand the basic concepts of mathematics in cooking. Therefore, I am going to discuss some of the important mathematics present in cooking, through the eyes of a recipe book. Let’s bake a cake.
Conversion
Firstly in the recipe, there will be a serving suggestion, however this may not always fit the individuals needs who is baking the cake. For example, the serving suggestion for this cake is 5 people, but we want to bake a cake to serve 10 people. Therefore, there must be a basic understanding of units and ratios in order to convert the measurements supplied, to the measurements required.
Measurement
Secondly, there will be the ingredients list. Once the conversion has been carried out, and the calculations are all correct, there must be a basic understanding of how to measure out the various substances. For example, the amount of sugar required will be weighed in grams, and thus there must be an understanding of weight and how to operate scales. Another measurement which may be required is that of liquid form: for the cake, milk measured in millilitres. Again, there needs to be a basic understanding of how to measure liquids, understanding the symbol for millilitres and using a measuring jug.
Shape
Another area of mathematics covered in cooking, is the concept of shape. Shape is present when baking a cake in many aspects. However, next in the recipe book, would be the shape and size of cake tin to be used in baking the cake. Shapes can be circular, square or rectangle. Size will be measured for the cake tins in various ways – a circular cake tin can demonstrate knowledge of diameter, and square and rectangular cake tins can demonstrate a knowledge of perimeter and length and breadth. All this can be used as examples for millimeteres or centimeteres, and again examples of conversion may need to be applied.
Temperature and Timing
Lastly, in the cake baking process, is temperature and timing. You must understand the temperature of your oven, in order to know how high or low a heat to bake your cook in the oven on, which can be in degrees celcius or degrees farnheit. Timing will then come into the equation, as you will have to time your cake and know when to remove it from the oven. Thus you will require the mathematical knowledge of telling the time.
The End Result……
OR…… if your baking is as good as mine, your end result can vary.
Therefore, cooking and baking can be a key ingredient in developing your mathematical knowledge, and possibly one which I should practice with more precision.
“Maths after break boys and girls”. The class let out a reluctant sigh. Why is it in 2015 that some school children still dread the thought of a maths lessons? When we (as teachers) should be creating engaging and interactive lessons with the children, why are some classes continuing to copy from a textbook in silence? Are our efforts in mathematics failing the children of today?
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