Author Archives: Zoe Boomer

I’m Going Back to Nursery!

The last time I even stepped foot in a nursery classroom was 16 years ago when I was there as a learner. I have nothing but fond memories of nursery- playing in the sand pit, making new friends, playing houses or schools, playing outside in all weather conditions and even sitting in the reading corner by myself with a picture book.

Tomorrow I’m going back as a teacher. Throughout the rest of this university semester I will be visiting a Dundee City Council Nursery every Wednesday afternoon to talk and play with the children. The purpose of this is to help my own transition into my official early years placement next semester. The vast majority of my teaching experience is with the upper years of primary school and with secondary school pupils. My first year university placement was in a P.7 class and during my Learning from Life placement in second year I mainly taught high school and college classes. Although I wouldn’t ever change the experiences I’ve already had- as they’ve all been hugely beneficial in building my confidence as a teacher- I’m excited to get some brand new experience and have some brand new opportunities to learn and grow as a teacher and as a person.

I’m also very interested to see how a nursery may have changed over the past 16 years. Do the children have more or less time to play and learn freely? What games will the children be playing outside? What will the children’s discussions be about? Will there still be a reading corner and will there be children using and enjoying it? The world has changed incredibly quickly over the past 16 years and I’m intrigued to see how this comes across when I compare the generation of children I will be working with to the generation I grew up with.

Despite my lack of experience working with children in the Early Years I don’t feel at all nervous. Personally I think working with and talking to younger children comes a lot more naturally to me than working with older children (hopefully I’m not proven wrong..!) and I’m very excited to get stuck in and play all the games children’s imaginations can think of!

 

 

Have I Discovered Mathematics?

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!?

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

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…

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

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

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

 

Languages- Scary or Intriguing?

Willkommen!

Did the language change scare you away from this blog post or intrigue you? Did it make you want to hide, never to hear another language again or did it make you want to continue and learn more? What if you were a young child in school- then how would it make you feel?

This is a subject brought up during a recent German workshop. How should children be welcomed into a modern foreign languages classroom? Should they be welcomed with a cheery “Guten Tag!” or “Bonjour!” or just a simple “hello”?- What do you think?

Before being in a room of completely mixed ability German speakers I would have said “yes! Use the language as much as you can, it can’t do any harm, right?” I believed hearing a language regularly, even something simple such as hello, would help children feel more comfortable with learning and speaking the language. I would have thought; if they hear and see it regularly they’ll be able to pick up the pronunciation and see which letters make which sounds.

However, the tutor of our German class decided not to welcome us all in the language, instead opting for a simple “good morning”- why? She didn’t want to scare anyone. At first I thought the idea of being ‘scared’ by language to be silly but maybe that’s because I spent six years learning German. Through discussion within the group, I soon learned that not everyone had such an extensive background and some had none at all. This made me think back to when I first started secondary and first walking into a German classroom, after having spent three years at primary studying French and hearing my teacher welcome us in a language I had never heard, did it make me feel anxious? Yes. So imagine how it could make a primary 1 child feel.

With the introduction of the 1 + 2 modern foreign languages scheme, I feel it is even more important not to scare the children with language. With children starting learning languages at a younger age than ever before, I believe it is important to settle them in. Begin by having words in the language dotted around the classroom, beside their English translations and images or real life objects of the word. For example, labelling the scissor box with both the English and foreign language word for ‘scissors’. This way the child will begin word association and may become curious about the language. Continue to work your way from there, insuring differentiation so that every child is able to take part. I believe it is the role of the teacher to ensure no child is ever scared of learning, no matter what the subject may be. It is the teacher’s responsibility to encourage positive learning throughout the class and ensure progression and depth- two of the main principles of Curriculum for Excellence.

So I ask you again, is learning a new language scary or exciting? And what do you think we, as teachers, could do to make it less scary for children?

My Relationship with Mathematics- Maths Anxiety

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.

 

 

My Educational Philosophy

I believe education is a tool to be valued across the world, it should be available to every child, teenager and adult who wants and needs it. I think education should be centred around the pupil and their needs. I greatly value the skills education brings to the world, without it we would have no doctors, no lawyers, no politicians, no shopkeepers, no farmers and no society.

In my interview for the University of Dundee, I was asked to prepare a presentation based on a quote from Malala Yousafzai’s UN speech. This quote was: “one child, one teacher, one pen and one book. Can change the world.” My interpretation of this was that she believed that no matter what race, gender, religion, etc. a child is, they should all have the right to an education and, if they are given this right, they will be able to do whatever they please, even change the world. I did, and still do, agree with this statement and believe Education is a powerful tool which, if given correctly and universally, can be used to achieve anything.

I think children should have a say in their learning and that their ideas and interests should be taken on board within the classroom. Children can be very creative and I believe this should be encouraged and they should come up with their own ways of taking in and sharing knowledge. In my opinion, it is important for children to work together within the classroom as this does not only help them accumulate knowledge but it gives them vital skills for later in life. Collaborative working will help the children gain confidence and prepare them for working in teams when they have left education and entered the working world. Not only does working together help the children but it will also benefit the teacher. Through my time in the Working Together social work module in first year, I learnt the importance of collaborative working between professionals such as teachers, social workers, health workers and the police. Despite this, I also believe independent working is also very important as it teaches the children not to rely on others and helps them build confidence in themselves.  Therefore, I believe it is important for teachers and pupils to be able to enter an equilibrium of independent and team working.

In my opinion, discipline is very important within the school, without it there would constantly be disorder and disruption. I think it is important to find the correct form of discipline and I believe it should be implemented throughout the entire school. However, I also believe it is important to look at each child individually and find a form of discipline that suits them. I believe the best form of discipline is positive reinforcement. I think it is much better to reward the good than to punish the bad as this means the well behaved children are getting the majority of the attention rather than the misbehaved ones. This would hopefully encourage the misbehaved children to behave well in order to gain attention from their peers and from the teacher. I attended two different primary schools as a child, both of which had very different ideas towards discipline. My first school was very much focussed around a reward system, we had a whole school star chart and the class with the most stars at the end of the week were given 5 minutes extra playtime on a Friday morning. My second school was much more focussed around a punishment system. Each class had a behaviour sheet and for every time your name was written on this sheet you would lose 5 minutes of golden time on a Friday afternoon. I think the star chart system was a much better way of dealing with behaviour, not only did it include whole class achievements but also personal achievements. I think it also encouraged good behaviour as nobody wanted to get no stars and possibly cost their class extra playtime. I think this also encouraged teamwork and friendly competition between classes.