Category Archives: Discovering Mathematics

Have I Discovered Mathematics?

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If you had asked me this time last year whether I would have chosen to do a mathematics module at university I would have said no- absolutely not. Fast forward 6 months and if you asked me how I was feeling about the upcoming new semester and the Discovering Mathematics module I had in fact chosen to do I would have said I was dreading it. Maths has never been something I’ve ever been particularly excited about (as you can see from my very first maths blog post). However if you asked me today how I feel about maths- after having just submitted my discovering mathematics assignment- I would say it excites and intrigues me.

Over the past three months, I have found myself getting excited about our mathematics inputs. I have had my mind expanded by learning about the origin of numbers, the mathematics behind board games, the universe in which we live and so, so much more. I’ve learnt different teaching techniques, I’ve built my knowledge and most importantly, I’ve built my confidence.

At the start of this module I completed the Online Maths Assessment  and scored 76%. Before starting this blog post I completed it again and scored 76%. Although I got the exact same score in both attempts, in my second I felt a lot more confident (even getting a little bit excited when a question about the Fibonacci sequence came up!). I have realized that maths can be fun and as someone who has always described themselves as ‘creatively minded’ I have realized that I can use this to my advantage when teaching mathematics rather than seeing it as a hindrance.

Although I did teach maths lessons whilst on my first year placement- even choosing to teach maths for my summative assessment- I think in the future I will be able to incorporate different subject areas within my lessons and be a more enthusiastic teacher. I believe this will allow me to engage the children in my lessons better and will hopefully allow them to feel a similar excitement when learning mathematics.

But what about that dreaded maths anxiety-is it any different? I do believe my maths anxiety has been seriously reduced, I don’t get a rush of worry when anyone mentions sums and I don’t panic when thinking about teaching it in the future. However I do think it would be very easy for me to slip back into a maths anxious frame of mind. In order to stop this from happening I must continue to engage with the subject, whether this be through the OMA or just doing maths in my head rather than using a calculator.

So, throughout the discovering mathematics module I’ve gone from feeling like this…

to feeling a bit more like this…

 

Board Games- Mathematical? No way!?

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I’m going to start off this post with a little bit of honesty… During our recent input about the maths within board games I was kind of (very) distracted by a ‘Where’s Wally?’ jigsaw puzzle so I didn’t quite manage to make a lot of notes on the subject… But never mind! it’s time to explore the mathematics within some of the nations favourite board games!

Throughout my childhood I would always get a new board game for Christmas- without fail. The whole family would sit and play the newest edition of ‘Monopoly’ or ‘Guess Who’ instead of watching the Queen’s speech. But little did I know that these board games weren’t just a way to escape the Christmas TV but were actually forcing me to use mathematics even during the holidays (sneaky…)

I feel like the best place to start when talking about board games is obviously with Monopoly. Although it may seem like a game you can win using luck, it’s actually a lot more complicated! Monopoly uses chance, probability, percentages and much more. There is actually a science behind winning the game so, if you want to impress (and probably annoy) your friends and family this Christmas just watch this short video, follow the rules and you’ll be sure to win every time!

However, monopoly is not the only game which uses maths. Jigsaw puzzles (just like the Where’s Wally one I was so easily distracted by) also use maths. Jigsaws use tessellation to ensure all the pieces will fit together, they use distribution and fractions.

So, if you, your son, daughter, sibling, etc is ever asked to take a board game into class on the last day of school, it’s only because they’re mathematical!

Spend Money to Earn Money

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Money. it sometimes seems as though our world revolves around it, the human race probably does revolve around it but how can someone make it?

Many people have their rags to riches stories; Lord Alan Sugar, Duncan Bannatyne, and Sir Richard Branson. But how did they do it? What is the secret to money success. Spending it.

Yes, you have to spend your hard earned cash before you can make more, seems crazy but it works.

In a recent Discovering Mathematics workshop, the MA2 student teachers were given an Apprentice-style task- demand planning. We split into pairs and were (theoretically) given £5000. We had to use this money to plan what we thought would sell in a shop at different times of the year and buy it accordingly in order to make the biggest profit.

Katy and I decided to work strategically, we thought we would only spend a couple of hundred pounds and save the rest ‘just in case’. We spent roughly £300 on stock for the first three months and made a profit of £900- great! We decided to stick with this tactic of spending a little and making, what we thought, was a great a profit.

At the end of the task we had £10,000 meaning we had made a profit of £5000 over the year, doubling our original sum of money!

We thought we had done brilliantly until other people started reading out their profits. Other pairs had made hundreds of thousands of pounds and how had they done it? They spent thousands of pounds on items such as tins of beans in the first three months of the task. They had managed to make more money because they were spending more money and therefore had more stock for people to buy.

So. if you’re thinking of quitting the day job to start a business, maybe start saving so that when you’re ready, you can start spending!

Please Mind The Gap…

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Sun, Mercury, Venus, Earth, Mars, Asteroid Belt, Jupiter, Saturn, Uranus, Neptune, Pluto, Kuiper Belt Objects- it’s the solar system!

But what’s wrong? I’ve included the belts of comets, I’ve even included downgraded dwarf-planet Pluto but there’s still something missing…

The same thing that’s missing from this picture of the solar system… But what is it..?

The gaps! We’re missing the masses of space between the planets which make up space. (funnily enough…) Planets are like grains of sand spaced out in a large outdoor stadium.

When teaching children about the solar system and using images like the one above it is fundamental to ensure you also teach about the gaps between the planets.

But how do we teach about the gaps between planets when it would be near enough impossible to fit them all on a page? its all about scale and proportion.

One way I found to be effective was to line the planets up in a setting I knew (this also links to the CfE principle of relevance). For example, when explaining to a room full of confused-looking student teachers, Dr Simon Reynolds used Dundee and the surrounding areas. If, scaled down, the sun was at the Dundee Science centre, the furthest away planet (that we know of), Neptune would be way past St Andrews and into the Scottish waters. (See below)

Screenshot (7)

 

This image shows how difficult it is to show the planets and gaps between them in a single picture. With the planets proportionally sized and spaced out you can barely even see the inner planets (Mercury, Venus, Earth and Mars) which are all scattered across the Tay Road Bridge.

Another activity Dr Simon Reynolds engaged us in was using different balls to show the difference in size between the different plants. For example, if the sun was the size of a beach ball, the Earth would be a small bouncy ball and Neptune would be a football.

So, even if using pictures like the first one in the blog post to teach children about the planets in our solar system, it is equally important to teach about the gaps and sizes of each of the planets using a number of different activities.

Mathematics and Art

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You can either be mathematically minded or creatively minded, you can’t possibly be both, right?

Wrong.

Maths and art go hand in hand, they’re like apple and cinnamon or cheese and crackers.

Throughout school maths and art were always completely separate subjects, they took place in completely different parts of the school and even in primary school they were taught by different teachers. I could never have imagined them going together. That was until a very eye-opening input about their connections throughout time.

Artists have been using maths to create masterpieces for hundreds, if not thousands of years. Ancient Greeks used the Golden Ratio to ensure buildings and sculptures were pleasing to the eye. Renaissance painters used mathematical  to ensure facial features and body parts were in proportion and a lot of religious art in heavily mathematical with tessellation and geometric shapes featuring heavily.

Islamic art is possibly my favourite kind of mathematical art, so far… I think it’s eye catching and beautiful. Islamic art uses tessellation to create stunning images which paint the walls and ceilings of buildings.

Tessellation is the arrangement of shapes closely fitted together to create repetitive patterns. However, tessellation can not be done with any shape, it can only work if all of the angles of the shape add to make 360° such as squares, hexagons and equilateral triangles.

 

The power of 0

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It is greater than God, it is more evil than the devil, the poor have it, the rich need it and if you eat it you’ll die. What is it?

Nothing.

Zero- arguably, the most important number in mathematics. Think of the number seven hundred, seven thousand or seven million, what you’re thinking of is the digit 7 followed by a number of zeros- right? Zero is a place holder, without it numbers would lose great value, imagine having a zero taken off (or added on!) to your salary! But what is it’s history? Where does the number zero come from and has it always been important?

The Ancient Egyptians were one of the first civilisations to practice mathematics and used symbols similar to their well known hieroglyphics to symbolise numbers (as shown below). However, the Ancient Egyptians did not have a symbol for 0 and even without this, they became very well respected mathematicians.

 

 

 

 

Some, maybe less well known, mathematicians are the Babylonians. They made a huge first step in coming up with a place holder or a number 0. They’re number system was a base 60 system with one symbol for units and one for tens (as shown below) but still there was no symbol for 0. The Babylonians continued without a ‘zero’ for many years using just a blank space as a place holder. However this could get confusing and mathematicians could easily forget to leave the space. So, during the fourth to first centuries B.C Babylonian mathematicians and astronomers developed two signs to represent a ‘space’.

 

 

Babylonian Zeros (above)

 

 

Despite the Babylonian’s great step towards finding a place holder within mathematics, many sources credit the Indians for first imagining the idea of a ‘zero’. In the 7th Century, Indian mathematician, Brahmagupta wrote some very important works on both mathematics and astronomy. A text called ‘Brahmasphutasiddhanta’ which contains many different mathematical ‘rules’ was written by Brahmagupta. This is the earliest known text which attempts to define zero as a number in its own right and not just as a place holder as the Babylonians used it. Brahmagupta established, what are now considered as basic rules for dealing with the number zero (i.e 1+0=1, 1-0=1, 1×0=0).

Throughout my time researching for this blog post I have found that the origin of the number zero is a lot more complex than I had first thought it would be. Many of the sources I found contradicted each other and it is clear to me that nobody is 100% sure where the number zero originated or who invented it. What has been made clear to me through this blog is that numbers are very complex and many people have been developing them over many years.

 

 

References:

http://discoveringegypt.com/egyptian-hieroglyphic-writing/egyptian-mathematics-numbers-hieroglyphs/

http://www.und.edu/instruct/lgeller/zeroph.html

http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_numerals.html

http://www.storyofmathematics.com/indian_brahmagupta.html

 

My Relationship with Mathematics- Maths Anxiety

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I’ve always had a very love/hate relationship with mathematics. Throughout primary school I was always in the top maths group, coped well with the work I was given and, as far as I can remember, thoroughly enjoyed the work I was doing. Upon entering secondary school, I still felt confident with my maths abilities however I think some of the enjoyment started to die down, this may have been due to the work I was given or the way it was being taught in a secondary school setting. Despite this, I still felt very confident throughout my first and second year.

Going into third year, I was put into a credit/general Standard Grade class. Again, I felt very confident throughout my third and fourth year studies and began to enjoy it more which I believe was due to my teacher’s style of teaching. Admittedly, there were some aspects of the course which took me longer to grasp than others but I managed finish the two years with a credit grade 1.

My time in Higher Maths is where I believe my maths anxiety began. During Higher Maths we would be given a homework worksheet most weeks which we would have a week to complete and were not allowed to leave any questions unanswered without a valid reason (“I couldn’t do it” was not a valid reason). So, every week I found myself at my maths teacher’s classroom door asking for help with one or two questions on that week’s homework. A vast majority of the time, once the method had been clearly explained to me I managed to solve the equation myself. Looking back, this makes me think it wasn’t the numbers and equations I found difficult but the problem solving and the words used in the questions. Despite my difficulties throughout Higher Maths I did manage to pass all three NABS and was able to sit the exam. I think this also proves that I do have skills in maths and I am able to do the arithmetic I just need to build my confidence within the subject.

But how do I build my confidence? One of my goals for this year is to build my confidence in mathematics so I do not feel high levels of anxiety when teaching it in the classroom. I aim to do this by completing the Online Maths Assessment multiple times throughout the year, hopefully improving each time. Additionally, I plan to do some reading around the subject in order to familiarise myself with some of the vocabulary used.