Category Archives: edushare

Magic Beans

Yesterday our maths workshop involved looking into the maths behind supply chain and global food. We talked about food miles and how some of the food we buy in supermarkets travels thousands of miles from countries on the other side of the world like New Zealand. Food that has had to ravel a long way to reach our supermarkets are said to have a large carbon footprint.

The Game

Richard had us play a business simulation game which required us to work in pairs and act as demand suppliers. Each pair was given €5000 to start with, and a list of items (SKUs) that we could spend this money on. We were allowed to order a maximum of 5 SKUs per sales period (which was quarterly, starting in April). It was important that when choosing our stock, we considered what time of year it was, as there were items available such as turkeys and selection boxes, which would probably be silly to buy in April, May and June, but very sensible in October, November and December! So for this first quarter, the items that caught my eye were ice cream wafers (summery), bananas (also summery), bread and milk. We didn’t spend all of our €5000 budget on this and made sure we had €1500 left over in case some of our stock wasn’t fully sold. Richard read out the sales figures by giving us the percentage that was sold. We had left over items across the board, but unfortunately with our bananas, milk and bread, we could not carry these over into the next quarter as these items go off quickly. Which meant we ended up wasting quite a bit of money. Regardless, we now had €8820 to take into the next quarter.

Moving into the second quarter (July, August, September), we kept our ice cream stock from the first quarter, stuck with our bread and milk (decreasing the quantity of units due to wastage in first quarter) and introduced soft drinks and beans into our stock list. Our thinking behind the soft drinks was that the weather is pretty hot at this time of year, people are going to be buying more soft drinks! We considered adding beer to our stock list for the same reason, but it was adding the beans that turned our fortunes around. What I noticed about the beans was the striking difference between the purchase price (€0.25) and the seasonal selling price (€2.00). This was 8 times the purchase price!! I wondered if anyone else had noticed this…. and it definitely encouraged me to look closer at the differences between the purchase and selling prices for the next two quarters. I had overheard some people talking about the champagne, and how it had such a high selling price, which I had originally fallen into the trap of thinking. However looking at the purchase price for champagne, it was €10, half of the selling price, which compared to the beans was nothing special. Funnily enough, for that quarter, the beans ended up giving me back the most amount of money (€9600), having only invested €2000.

We continued to use this method, of mainly investing our budget into buying more of the tins of beans. In the third quarter we invested in Christmas selection boxes, Turkeys and Hampers (due to the time of year), which proved a good decision because 100% of all of those units were sold. We also increased our bean quantity from 8000 to 10,000 units, giving us €18,000, and €57,965 in total at the end of the third quarter. In the final quarter we went back to our milk and bread, figuring that at this time of year people are short on cash and are therefore buying the basics, and upped the quantity of beans to 40,000. This was because now, instead of the beans being sold for 8 times their purchase price, they were being sold for 10 times. This ended up giving us back €100,000, due to 100% of the beans being sold that quarter.

At the end of the task, we ended up managing to turn our initial budget of €5000, into €184,440, mainly thanks to beans! This task definitely taught me not to jump into looking at the face value of things. Yes, the Champagne had a very high selling price in the first two quarters, but just looking at that factor would be silly.

Many basic mathematical topics and ideas were used in this task, such as multiplying, dividing, adding and subtracting, percentages and decimals. We were also encouraged to think about wider society, what the public may be buying at certain times of the year and basing our decisions around that and importantly, the purchase and selling prices. This task involved a lot of trial and error, but I think that was a very important part of the game. it made me realise that with maths you might not get it perfectly right straight away but by adjusting things and thinking back to basic ideas it can be made clearer. I feel it is crucial to portray this message to the children we teach, especially those who may feel they have some anxiety towards maths.

The Maths Behind Netball

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In our maths in sport input we had the opportunity to either take a sport that already exists and improve it somehow, or make up our own sport with its own rules. My group decided we would try to improve on a sport that already exists, and therefore I suggested netball, which is my favourite sport. I started to consider the rules of netball, and it was here I realised how many mathematical concepts were involved.

Dimensions of the Court:

A netball court is split into thirds, which are each 10.14 metres long, making the whole court 30.5 metres (100ft) long. This is just a bit longer than a basketball court.The centre circle in the middle of the court is 3 feet in diameter which is also the exact distance a player needs to be from their opponent when marking them when they have the ball. The semi – circles (shooting circles) at either end of the court are 32ft in diameter and have a radius of 16ft.

When a player’s opponent has the ball and is ready to make a pass, that player can mark with her hands up in order to try and defend the pass. However, the defending player must be at least 3 feet away from the player with the ball, otherwise the umpire will pull her up for obstruction.

Taking this to a teaching level, I feel that this would be an ideal way of introducing topics like area, perimeter, circumference, diameter and radius of a circle. By linking the topics to things that the pupils enjoy (favourite sports), it will encourage them to make their own links and connections between maths and wider society.

Ball Size:

A netball is around 8.9 inches in diameter and 27 – 28 inches in circumference and compared to a football this is ever so slightly bigger. A netball weighs between 14 and 16 oz (397-454 grams) which is around the same as a football but far lighter than a basketball.

An average females hand length is 6.77 inches, which is almost a quarter of the circumference of a netball. This could mean that it takes great hand-eye coordination and skill to be able to catch a netball with one hand which players quite often have to do.

Timings:

A netball match is 60 minutes long and is split into quarters, which are each 15 minutes long. Their is a 3 minute break between the first and second and third and fourth quarters but a 5 minute break at half time, for a team talk and a rest for players. This means that there are 900 seconds in a quarter of a netball match (15×60) and therefore 3,600 seconds in a full game of netball ((15×60)x4) (not including breaks).

Once a player has caught the ball, they have 3 seconds to pass it on again or score a goal. If they fail to pass to another player on their team within this time, a penalty is given to the other team.

Height of Players:

Netballers are preferably tall in height, as sports with a hanging net in the air usually require tall players. For a sport like netball, a coach should really find players with great height and strong build in order to intercept and defend passes. However, shorter players often have better quickness and agility, which is key for some attacking positions in netball. The average height of netball players is usually between 1.7 metres and 1.9 metres, which is well above the average height of a Scottish female (5ft3 – 1.6 metres).The height of a netball post is 10ft, therefore a shooter who is tall will have a much better chance of getting the ball in the net than a player that is shorter, hence the preference for tall players.

Conclusion:

Again, this module has allowed me to look at the mathematical side of something that I would never have linked to maths before. Taking one of my passions (netball) and analysing it from a mathematical perspective has allowed me to dip into all sorts of maths topics (area, perimeter, height, length, breadth, time, speed and the measurements of a circle). This highlights Liping Ma’s principles of connectedness (making simple connections with topics and wider parts of society) and basic ideas (taking simple concepts like length, breadth, height, width and using it in a more complex yet still relatable concept like sport). In terms of developing my understanding of mathematics, it could help to look at the mathematics in sports that I don’t play regularly, which could be more of a challenge and allow me to give netball something to be compared to.

Being Born Lucky

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Our maths input today was on data and statistics. It was mainly based on health care and hospital statistics, but our lecturer (Dr Ellie Hothersall, from the university’s medical school), also brought up the topic of University attainment in terms of students from the least deprived areas of Scotland, typically being the ones to attend University. She gave her view from a medical school angle, telling us that historically student doctors were only white males, and that over the late 20th century females were being accepted to medical school more and more. However what the University of Dundee are now trying to do, and have been for several years, is accept students that aren’t necessarily from wealthy middle class families, which is what most people are guilty of picturing when we think of a stereotypical doctor. To me, this makes a lot of sense. People of all ethnic backgrounds and cultures go to see doctors, and I personally feel more at ease when I see a doctor that I feel I can relate to and vice versa. Therefore everyone should have the opportunity to be able to relate to the medical profession, and not see doctors as a completely alien and elitist group of people.

I wanted to think about this further and consider that Universities across Scotland are taking this approach when admitting Students. The Scottish Government have recently published that ‘A Record Number of Students from Deprived Areas Get in to University’. The article states that the number of acceptances for students from the 20% most deprived areas is up by 13% in 2017. According to John Swinney (the deputy first minister) “our goal is that everyone with the natural talent and ability has the chance to go to university”. So even if you are from a very deprived area of Scotland, if you get the grades and have that natural ability, you should get to go to University. Which I think is fair. However according to a BBC News article from May 2016, Young Scots are four times less likely to go to University if they are from a disadvantaged area, than those from wealthy backgrounds.

Why is this?

Is it just pot luck or chance that depending on the family you are born into and the area you are brought up in, that determines the quality of your future education?

From my perspective, every member of my family has attended university. Grandparents, mum and dad, aunts and uncles…. therefore university for me was inevitable. Ellie said the same about her family, and that she expects her two young children to attend university and hadn’t really considered any other options. Perhaps this is the initial step that young people take when considering university for their future. Maybe those who have grown up with family members not having gone to university don’t consider university as readily. So is it just down to chance? If you are ‘lucky’ enough to be born in a wealthy area, into a well-off family, you are already leaps and bounds ahead of those who weren’t given that same opportunity?

An article by Steve Hargreaves called ‘Making it into the Middle Class’ looks at some statistics. Of people born into lower income households, few will ever make it into the middle class, according to a recent study from Pew Charitable Trust. A small percentage makes it into the high earners bracket, which is shown clearly in the diagram below. It shows that 70% of the people from lower income households remain that way, and still only 26% rose to middle class.

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The report the goes on to say that even those that moved on to become slightly higher income households shared various traits in common such as, being college graduates, coming from two income families, being white and not experiencing not unemployment.

I then went on to the Pew Research Centre website and found an online calculator that was able to tell me if I was middle class in Western Europe or not.It asked me for my nationality, my annual household income and the number of family members I have living in that house. Even doing this very simple online calculation can determine what class you supposedly fall into and therefore, according to society, decide how successful your future looks.

Looking at statistics in this way has made me want to use more statistics in my learning and understanding of topics in the future. I feel that using graphs and charts that contain data is a very effective and visual way of summing up larger pieces of information and making them easier to understand. Having Ellie come to speak to us about the data and statistics they collect in the medical school setting gave us a different perspective than if we were to hear from one of our own lecturers from education. This emphasises Liping Ma’s fundamental principle of mathematics – multiple perspectives. She effectively showed us how statistics are used and related it to something which we, as a class, could all relate to – exams! I feel that that is what teaching mathematical concepts is all about, making sure you can relate ideas and topics from everyday life and link it to somewhat ‘scary’ things like statistics and data analysis.

References

BBC News (2016) Scots Students Face ‘Shocking’ University Access Gap. Available at: http://www.bbc.co.uk/news/uk-scotland-36392857
Hargreaves, S. (2013) Making it into the Middle Class. Available at: http://economy.money.cnn.com/2013/11/13/making-it-into-the-middle-class/
Pew Research Centre (2017) Are You Middle Class in Western Europe? Available at: http://www.pewglobal.org/interactives/european-middle-class-calculator/
Scottish Government (2017) Record Number of Students from Deprived Areas Get in to University. Available at: https://news.gov.scot/news/record-number-of-students-from-deprived-areas-get-in-to-university

History of Time Keeping

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Before clocks were invented, time was kept using different instruments to observe the sun passing through the meridian at noon (the meridian is an imaginary line running from the North to the South Pole). The earliest instruments used for timekeeping that we know of are sundials and water clocks.

Sundials– (3500BC) A sundial is able to tell what time of day it is depending on the position of the sun. Ancient Egypt was the era which held the oldest known sundial. Sundials have their origin in shadow clocks, which were the first devices used for measuring the parts of a day. Shadow clocks divided daytime into 12 equal parts and these parts were divided into even smaller parts. This shows that Egyptians must have understood the concept of division. They also must have understood that the earth was spinning or the stars were moving, at a constant speed, and that that is the key to telling when time is passing. Although shadow clocks were perfectly accurate during the day, they relied on the movement of the sun and therefore when the sun went down or it wasn’t a very sunny day, they became useless. Due to this, the Egyptians developed different timekeeping instruments, including water clocks, and a system for tracking star movements.

Water Clocks- (1092) One kind of water clock was a small bowl with holes in the bottom of it, which was floated on water and filled up at a constant rate. The markings that were made on the side of the bowl indicated how much time had gone by, as the surface of the water reached them. Water clocks were commonly used in Ancient Greece.

Candle Clocks- (1400BC, introduced in medieval Europe in 885) again, this uses equally spaced markings, that when burned, indicate the passage of periods of time. This solved the problem of when there was no sun present in the sky, as candle clocks did not require the use of the sun. Which meant these were used mainly on cloudy days or at nighttime. Clock candles were used in Japan in the early 10th century. You Jiangu’s device consisted of six 12 inch long candles all of the same thickness and were divided into 12 sections (one inch thick). Each candle burned away completely in four hours, making each marking 20 minutes. Again, this shows the mathematical concept of division being used.

Wristwatches- From the early stages wrist watches were mostly only worn by women, while men used pocket-watches up until the early 20th century. Wristwatches were worn initially by military men around the end of the 19th century, when it was crucial that the men synchronised their watches in order to time manoeuvres during war without potentially revealing the plan to the enemy through any signalling actions were discovered. Pocket watches were seen as impractical and not secure enough, therefore they strapped them to their wrists in the heat of war.

There is a lot of debate of whether children in schools need to be taught how to read an analog clock, or whether they can rely on using digital time. According to Jennie Ito, who is a child development expert, “analog clocks help children understand the passage of time because they have hands that are consistently moving”, whereas a digital clock only shows numbers changing as time goes by. Analog clocks also represents time in multiples of five, again, creating links between mathematical concepts is really important here. I feel that without using analog clock in classrooms and revealing these links between maths topics, children will not have as broad a knowledge of mathematics. Telling the time on an analog clock is essential for wider society and I believe that without having that skill, children would be at a disadvantage. By giving children a history of time keeping, it will allow them to have a better understanding of the concept of time and why we need to keep track of it.

The Pentatonic Scale is Everywhere

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As I discovered on Thursday, maths and music have many links, far more than I had previously considered. Seeing myself as reasonably musical, I had not given much thought to linking music with maths and if I’m honest I didn’t know there was such a thing. As a group we were asked to reflect on some of these links, and the first thing that came to me was reading music. Each note has a value depending on how it looks, and we have to assess what each symbol means just like we do with maths (+, x, -, £ etc ). We must also consider the speed and temp of music, tuning, pitch, scales and arpeggios. All of which hold some mathematical substance. In music theory scale is any set of musical notes ordered by fundamental or pitch. Typically scales are listed from low to high pitch.

Scales

We discussed the different types of scales there are in music, again something I had never thought about before this workshop. There is a monotonic scale, consisting of one note, ditonic, tritonic and tetratomic (2, 3, and 4 notes) which is mainly limited to prehistoric music. The pentatonic scale ( also known as the “black note scale”) is 5 notes per octave, which is lacking semi-tones and common in folk music, and I will go into more detail about this later. The Hexatonic scale is 6 notes per octave (you get the idea now…) and is common in Western folk music. The Heptatonic scale is the most common modern western scale and the Octatonic scale is used in jazz and modern classical music.

“The number of the notes that make up a scale as well as the quality of the intervals between successive notes of the scale help to give the music of a culture area its peculiar sound quality.” Nzewi, Meki, and Odyke Nzewi (2007). This quote emphasises the point that different types of scales can create different sounds and vibes, creating genres such as folk, western and classical.

The Pentatonic Scale

Pentatonic scales are found all over the world and are a key part of many, many musical genres, some of which I hadn’t heard of until researching. This is what grabbed my attention the most about the Pentatonic Scale is that it really is everywhere. What really blew my mind was the youtube video we were shown, which involved Bobby McFerrin (Singer of Don’t Worry Be Happy) demonstrating just how powerful and predictable the Pentatonic Scale truly is. In the video he is stood in front of a crowd of people, and he pretty much uses them as his musical instrument. He demonstrates one note to the crowd which they imitate, he then moves up and down the stage, which requires the crowd to sing higher and lower, moving up and down notes. Eventually the crowd are so good at predicting the notes that he manages to get them to sing a tune, all in the space of around 2 minutes.

What I found fascinating about the pentatonic scale is that it is applied within tonnes of popular songs, it is everywhere in music culture no matter what genre. Below is another video that I have found which really emphasises this. It features someone trying to see how many songs they can play using the C major pentatonic scale (notes C, D, E, G, A). The guy manages to play all sorts of music, songs by Jimi Hendrix, Drake, Bill Withers, Britney Spears and even nursery rhymes (Mary had a little lamb).

I think the key point I took from this workshop was that maths can be applied in many musical ways. It also made me consider how different mathematical ideas and concepts intertwine in music. Liping Ma’s fundamental principle of mathematics, interconnectedness, is really highlighted in this topic as it is so crucial as a teacher to reveal connections among mathematical concepts. And this doesn’t just mean within maths itself, hence the musical link. Liping Ma discusses having a profound understanding of fundamental mathematics as “taking something to the most basic principle you can”, which I agree with but I also feel it is about taking maths and stretching it to make links with other subjects like art, music , computing, and in and around everyday life.

References

Nzewi, Meki, and Odyke Nzewi (2007), A Contemporary Study of Musical Arts. Pretoria: Centre for Indigenous Instrumental African Music and Dance.

Discovering Mathematics – Counting Animals and Number Systems

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On Monday we had an input with Richard about the origin of number systems. The first question we got asked was whether or not we believed animals could count or not. My initial reaction was “no? obviously not.”, but when we discussed the possibilities of it it did not seem as ridiculous as I had first thought. We looked at a study to do with ants, and how they could possibly know exactly how many steps were needed to be taken in order for them to reach their nests. In the study, the ants’ legs were shortened and lengthened, and when this happened they went just short, and further than the nest, which could represent the ants actually counting! We then considered that perhaps ants and other animals can’t actually count but have in fact memorised a pattern or sequence that they have done over and over again. We also looked at Ayumu the chimpanzee, who was able to recall the order of eight separate digits in the correct numerical order when the numbers were only displayed for 0.21 seconds and the order of 5 digits recalled when displayed for 0.09 seconds. This sounded impressive, and the video footage we watched made that even clearer. However when we considered that at the London Olympics, Usain Bolt’s reaction time to the starting pistol was 0.165 seconds, it was even more impressive. I personally didn’t believe that Ayumu knew the correct order of the numbers, but instead could recognise the shape of each number and simply memorise that the shape of 1 comes before the shape of 2, etc.

After looking into a few studies on animals and whether they could perhaps count or understand the concept of counting, I considered that perhaps, as humans, we see numbers in a very similar way to animals. Realistically when we count we are just memorising a series of numbers, and when we look at these numbers we are really just recognising shapes and associating them with their numerical value.

Richard then asked us to come up with our own number system. This could consist of a variety of symbols, and we were allowed to create this and present our systems to others in the class.

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This was the number system that Erynn and I created. Our system works on bases of 10, therefore the circles represent numbers between 1 and 10, the triangles represent numbers from 11 to 20 and the squares represent numbers from 21 to 30 and so on. The lines coming out of the shapes are how you identify which specific number it is, i.e 1 line = 1, 11, 21 etc. Our system is not the easiest to write down and seems to require a lot of thought, unlike our own number system where we automatically recognise a shape and associate it with its numerical value. In hindsight I found creating a number system a lot easier and less daunting than I had first anticipated and feel that the whole input gave me a different perspective on counting and number systems as basic ideas of mathematics.

Unit 1 – B: Managing My Learning

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Managing My Learning – in this task I was asked to think about what helps me to learn and what hinders my learning. Once I had thought of a few examples I then thought about how I could manage these things.

Activity 1

Complete the table below to identify and reflect on those factors and plan actions for each.

Recognition/ Reflection	Action
What helps my learning?	How can I utilise this?
Example: “Discussing the topic with others”	· Set up a study group of like-minded peers · Engage with the online community
Asking for help when I need it	· Email lecturers and tutors to get assistance with whatever I am struggling with instead of ignoring the issue.
Reading	· Borrow as many books from the library as is necessary to help me to further understand certain topics and broaden my knowledge.
Taking a break	· By taking a break by playing a sport I am able to relax my mind.

Recognition/Reflection		Action
What hinders my learning?	How can I address this factor?
Example: “I’m easily distracted”	· Study in a place where distractions are minimal · Read lecture notes before the lecture and then take notes lectures to keep me focused
Panicking about deadlines	· Keep a diary so I know exactly what needs to handed in and when · Manage my time carefully so that I leave plenty of time for assignments to be completed well.
Not taking detailed notes	· Try to write notes that explain the point in as little words as possible so I am not writing big paragraphs that I don’t need.
Tiredness	· Ensure I have a steady sleeping pattern

First Values Workshop

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Last Tuesday we had our first values workshop. I went in completely clueless as to what we would be doing for the next hour, and I was eager to find out. Carrie split us into random groups and gave us all a huge envelope. We were told to use the resources inside our envelope to make something that would be useful for a student in their first week of their first year (a situation we were all very familiar with).

I was in group 3, and inside our envelope we had four post- it notes, two pens, 3 pieces of paper, a handful of paperclips and some blue-tac. I did wonder why we had been given so little but it didn’t occur to me to look at what the other groups were given. I thought we all had the same things in our envelopes and that the task would help figure out which group was the most resourceful. After sitting and staring at our resources for a while, we decided to make a survival pack that would help guide a first year student through their first week at university. We designed a map of the Dalhousie Building, created a timetable, wrote a few motivational post-it notes and a list of essentials that should be purchased in your first week of being a student. We presented our creation back to Carrie and the other groups. I noticed Carrie wasn’t overly impressed with what we’d come up with but I didn’t think anything of it. I wasn’t overly impressed with what we had made either to be honest! What I did start to notice however, was that each group’s resources were of very different qualities and quantities. As I watched group 4 present their idea to the other groups, it dawned on me that Carrie wasn’t even facing their direction. She kept checking her watch and yawning as if she couldn’t wait for them all to stop talking. That’s when I put two and two together and realised that this task was fixed in a way that would create a hierarchy between the groups.

As we packed up to leave I began to think about how I view people who have a lot and people who don’t have anything (which was obviously what the workshop was designed to do). I think I am guilty of not always viewing everyone equally, and I feel that it is really important to view each child at school equally, no matter what their background may be. In a classroom there should be no hierarchy. Just because one child has a flashy iPad and another hasn’t even been provided with a pencil to come to school with, it doesn’t mean they should be treated any differently.

Why Teaching?

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It wasn’t until the beginning of my 6th year at high school that I realised that teaching was the profession for me. Many factors led up to my decision to apply for teaching at university, the main one being my love for working with children. Since starting my job as a Kids Coach at David Lloyd, I have become fascinated with the way children learn and in general, find them a pleasure to be around. Due to this, I knew I definitely wanted to have a job where children were involved.

I look back on my primary school days fondly, mainly because I had such great teachers. One teacher stands out in particular who taught me for my last two years of primary school. His lessons were always well planned and thought through, he seemed like he really loved his job and was thrilled to be there teaching us. As an 11 year old, seeing my teacher enjoying what they do was a really positive thing. It certainly made me enjoy school more and inspired me to want to give others that same experience. The work experience that I have done in a classroom setting has also played a huge part in my decision to want to become a teacher. Learning about all the different ways to teach and discovering that teaching isn’t as traditional as it used to be, really broadened my mind. Working with children from different backgrounds and realising that every child is different was interesting too.

I have always found that I have a solid grasp of most subjects that are taught in school, rather than standing out in one particular area and so I felt that Primary Education was perfect for me, due to the wide range of things that I will be teaching. This also means that hopefully every day at work will be different and that really appeals to me.