Category Archives: 2 Prof. Knowledge & Understanding

Where did it all begin?

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The history of mathematics is a topic which I have never really giving much thought, until our lecture the other day. I understand the way mathematics works within in my own country but I had no idea of the process that was involved for mathematics to be the way it is now and how long mathematics has been around for.

ishango_bone No one can know for sure how long mathematics or numbers have been around but it is believed that the working systems and the use of symbols for numbers has been around for about 10,000 years. (Bellos, 2011, p15.) Although there may not have been actual numbers systems prior to this time it is believed that our ancestors would have had some understanding of amounts. For example, they would have been able to distinguish between one animal or two animals’ (Bellos, 2011, p15.) Some of the earliest evidence of numbers are dating back from 35,000 to 20,000 years ago in Africa when they counted on bones. (Mastln, 2010.) This shows that for generations there has been some understanding of amounts and numbers.

Sumer – modern day Iraq –  developed the earliest known writing system and were one of the first generations to assign symbols to numbers (Mastln, 2010.) One of the reasons for the development of symbols associated to numbers was a response to the needs of the country and developed agriculture (Mastln, 2010.) They were dealing with larger numbers such as plots of land or taxation therefore they needed symbols for larger numbers. Sumerian and
Babylonian mathematics was a base 60 system, which means that number 60 was the base number. This is still used in modern day society with aspects of mathematics such as time babylonian_numerals(Wikipedia, 2016.)  The Babylonians also discovered a mathematics revolution by acknowledging zero as a number and symbolising it (Mastln, 2010.) It also believed there was evidence of some type arithmetic exercises in Sumerian and Babylonian schools. It is believed that Babylonians were one the first to invent multiplication. As their society grew there was a need for more sophisticated mathematics and this led to the invention of multiplication tables. They created multiplication tables on tablets and carried them around to speed up calculations (Marcus du Sautoy, 2014.) Another example of mathematics from thousands of years ago being relevant in today’s society.

There are many different number systems from all over the world and that have developed over time and that play a part in mathematics today. The Egyptians created one of the first fully developed base 10 number systems, the system we use today, as well as fractions (Mastln, 2010.) The Rhind papyrus was discovered by Henry Rhind, in the 19th century. It was a book filled with problems and solutions which included a section on fractions. The Egyptians used fractions such as 1/4, 1/2 and 1/8 (Shuttleworth, 2012.) This is another area of mathematics which stems from thousands of years ago which we use frequently in today’s world.  Greek mathematics was based on geometry. The Greek’s have established well known and used theories such as Pythagoras Theorem (Mastln, 2010.)

It is fascinating to see how far mathematics has developed from Babylonian number systems too today’s number system. However, there are still places in the world which are not as numerically developed as us. The Munduruku tribe in the Amazon only have the numbers ‘1 to 5’ after the number five it is just referred to as many (Bellos, 2011, p15.) We live in a society where numbers and mathematics play a large part in our everyday lives that I found the concept of only having five numbers completely alien. Pierra Pica went to live with the Munduruku tribe for many months and on his return he had lost the ability to describe the world in terms of numbers (Bellos, 2011.) I found this fascinating as he was a highly intelligent man living in the 21st century, how can you lose the concept of numbers so quickly? Due to numbers not being a huge part of day to day life such as time or counting, he simply learned how to survive without numbers. This made me wonder, as a society why are we so “obsessed” with numbers and time? Is this due to the fact that we are surrounded by it much more. I am intrigued to experience what life would be like where numbers play a minimal part in your day to day life. If others can live by it and survive, surely we can?

During our lecture we were asked to complete an activity where we had to create our own number system using symbols, and I tell you I take my hat off to those who have created number systems as it is definitely not as easy as you would think. Me and my partner Hannahunnamed thought it would be a good idea to use a circle as our symbol and one whole line within the circle would represent the amount. We quickly figured out that our system was too complex as by the time we reached number five we were both confused. Some of our classmates came up with really good examples and were
very simple to follow.

 

So how does this all link to Liping Ma’s profound understanding of fundamental mathematics?

Connectedness – In order for me to understand the way different number systems work I had to make connections with different mathematical concepts such as different base systems. I made these connections with concepts which I was familiar with such as time which is a base 60 system to understand my new knowledge in more depth. I also had  to make connections with real life in order to understand how number systems have developed over time and how they are different to the numbers I deal with daily.

 

References

Bellos, A. (2011.) Alex’s Adventures in Numberland. Bloomsbury Publishing PLC, London.

Mastln, L. (2010) 20th Century Mathematics – The Story of Mathematics. Viewed at: http://www.storyofmathematics.com/20th.html [Accessed on 7 October 2016.]

Shuttleworth, M (2012.) Egyptian Mathematics – The History of Mathematics. Viewed at: https://explorable.com/egyptian-mathematics [Accessed on 7 October 2016.]

Du Sautoy, M (2016) The Guardian. Viewed at: https://www.theguardian.com/lifeandstyle/2014/may/17/ask-a-grown-up-who-invented-times-tables [Accessed on 7 October 2016.]

Dance like nobody’s watching..

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Ever since I was a little girl I always loved dancing therefore when I saw we had a dancing input I was excited. I danced from a very young age right through to around 16 so I have a quite a broad experience of dance. My experience however is very much learning how to dance and 13682601-Word-dance-with-colorful-and-funny-letters-Stock-Vector-dance-cartoon-kidsperform rather than actually teaching dance so the prospect of this excited me.

I was very unaware of the amount of skills you actually develop through dance and through gaining this knowledge I feel that Dance is a really important curricular area. Dance allows children to build social skills such as team work and creating friendships. Some of the people I met through dancing have been lifelong friends. You learn to support one another through the good and bad times and this is skill which is valuable throughout life. Dance also allows time for children to really think outside and bring out their creative sides. It can provide a time for children to express their thoughts and feelings through dance movements.

From a teaching perspective I understand the spectrum of ability and anxiety which may appear when planning and teaching a dance lesson. From my own experience of dance in schools, girls liked dance more than boys. In my professional reading I discovered that “dance levels are highest in S1 with 62.4% of girls taking part in dance compared to only 11.5% of boys.” (Get Scotland Dancing, 2012, p17.) I found this interesting as it is around an age range which is similar to those in the upper years of primary schools. There is a stigma attached to dance that it is a “girls sport” and this may be the reason for the lack of male participant in dance. However there also girls who do not enjoy dance. When planning for a lesson I believe you have to consider the confidence of children within your class, their ability within dance and also age. The older children become their self awareness develops and they conform to fit in with their friends. This can prove as a challenge as many may not be fully committed to the lesson. I believe you have to slowly build up their confidence within dance and not make it all performing in front of one another.

For a Primary 5 class and through my understanding of the Curriculum for Excellence I aim to create an exciting and fun lesson for all.

Curriculum for Excellence Outcome: I can explore and choose movements to create and present dance, developing my skills and techniques. EXA 2-08

Learning Intention (LC): To be able to create a short dance routine related to a specific mood through the use of different movements which will be explored in the lesson.

Success Criteria (SC): To successfully create a short dance routine through actions such as travelling, gestures and stillness. To understand how these actions portray the mood which has been chosen. 

How will I achieve my LC and SC:
Warm up: Gather the children in to a circle and begin to warm up the children’s body by loosing off their body. I will also incorporate some rhythm exercises into the warm up by asking the children to walk, run, jump or clap to a piece of music. This allows me to evaluate the stage each child is at and also to examine if a child is carrying any injuries.

Main body: I will talk the children through different actions within dance e.g. travelling and ways ti travel such as; striding, skipping and hopping. This is to show creative ways to travel rather than walking and running. I will also demonstrate different gestures such as twisting, flop and stretching. Stillness is another aspect of dance I aim to examine is stillness. I will explain to the children the power stillness such as a freeze, sleep or pause can have in dance. Finally we will look into different levels of dance such as high, medium and low levels. Once we have examined different actions of dance the children will split into groups of around five to six people. In these groups they will be provided with a certain mood such as happy, sad, worried or excited and work together as a team to put together a short dance routine in which they will incorporate the different actions they have learned. I will half the class and ask them to perform in front of the other half of the class. This will allow the children to see how different actions create a certain mood and also the contrast of different moods performing together. Performing alongside peers rather than one group at a time can reduce children feeling embarrassed or anxious about performing and can allow them to flourish fully within the lesson as it is not all eyes on them.  This lesson may be conducted over the course of a few weeks depending on the pace the lessons go at.

Cool Down: Gather the children back in a circle to stretch out their bodies and to regain their focus. We will then discuss as a group if we feel we have all met the LC and SC. 

Assessment opportunities: Through the children’s performance I aim to examine if they have met the success criteria but also allow their peers to examine if they feel they have meet the success criteria too.

As stated in the Standards for Provisional Registration as a student teacher I must “develop tasks and set pace of work to meet the needs of learners, providing effective support and challenge.” I feel through dance lessons I can achieve this. I understand the range of abilities that pupils in the class will have and to take this into consideration when planning in order to provide a challenging but supported lesson. I understand the challenges I may be faced with also such as lack of motivation to participate, anxiety and also children who have  experience of dance, providing a lesson which can challenge them. I believe I could successfully  support the needs of the pupils in my class by motivating them and encouraging them to challenge themselves and step out of their comfort zone.

 

 

 

 

Be smart, stay safe!

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For one of our ICT inputs we were looking into internet searching and safety. This is a topic I feel is so important to incorporate into schools, the internet plays such a huge part in our day to day life. The internet is such a great tool and provides so many opportunities and learning experiences, however, there also many dangers and hazards which our children must be aware of searching online and also communicating online. Children are beginning to use the internet younger and younger now and providing children with information on what to do and what not to do on the internet can help keep them safe.

Sharon introduced us to some websites for internet safety such as ChildNet and Doople Me. I looked further into these and found them very useful. Child Net  provides information to teachers about teaching children how to use the internet safely. It also provides information for teachers how to remain professional online and within the workplace. ChildNet also gives helpful advice to parents with on how to encourage their children to use the internet safely.  I feel its so important for parents to be aware of what their children are doing online and if parents have more knowledge about internet safety they can really help keep children safe. Child Net provides a area in which children can access games and tips about internet safety. There was an acronym of SMART I found on Child Net which I thought would be great for children to use as a way of remembering how to be smart and stay safe online:

SAFE: Do not give out person information such as phone number, house address or passwords when chatting or posting online.
MEET: Do not meet someone you have only been in touch with online as this can be very dangerous. Only do so with parents’ or carers’ permission and even then only do so if they are present. Online friends are still strangerUntitleds even if you have spoke to them for a long time.
ACCEPTING: Do not accept friend requests, messages or emails from people you do not know, They may contain viruses or nasty, inappropriate messages.
RELIABLE: Some people or websites may lie about who they are or the information may be false. Always check information by looking at other websites or books. If you like to chat online it is best to chat to people you know.
TELL: Tell a parent, carer or adult if there is something oavatarr someone online which makes you or someone you know feel uncomfortable or asks you to do something you are not happy about.

I also thought Doople Me was a very useful tool. This is a website in which the children can create an avatar which represents the way the look. This allows the child to use this as a picture online rather than an actual photograph of themselves. This protects the children identity. I feel that this website is also a good tool to witness how the children view                   themselves. I made my own one and it was very simple and straight forward!

Throughout this input I also learned a few valuable skills when it comes to searching online. I am the number one culprit for using google for any questions or help I need. I was aware that some websites you have to careful of as they can portray false information. However I was not aware to how to condense your search so you are not getting so many results and also the other search engines available to use. After the input I felt that it was my job to educate children how to search correctly and also the other search engines such as AOL Kids.  AOL Kids is a search engine which caters for kids. On the homepage it provides popular and suitable websites that kids can use such as Disney and Fun Brain. I feel this would be a good search engine to use in school as search engine such as Google can sometimes have content which is not suitable for children.  Sharon also introduced to us some presentation tool such as Prezi and Animoto. These are different ways and ideas of putting together to make presentations more fun and interactive. These would be both beneficial for teachers and children to use.

Overall, I feel this input was very useful as it give me an insight to different resources available to keep children safe on the internet without scaring them completely of using the internet. It also provided me of different resources to use in class with the children not just for internet safety but across the curriculum areas. The internet is a wonderful resource which we are so lucky to have and having the knowledge to use it appropriately will help to keep children safe online. Be smart, stay safe!

The dreaded maths lesson..

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Maths has always been a subject I have associated with anxiety and fear. During my time at school maths always filled me with dread and I used to get myself worked up about going to it. I feel one of the reasons why I did not enjoy maths was the teaching style. The teacher would always go around the room and make everyone answer maths questions. This type of teaching did not suit me at all I needed time to think and process what was being asked of me.

When I arrived at university and there was maths on my timetable I thought, oh no!! However the maths input really surprised me and also comforted me to see how many students teachers also shared my anxiety about maths and how nervous they felt about teaching maths. I was shocked to find out that one of the reasons why so many people have anxiety about maths is due to the way they were taught it in school. This then made me think, how will I reduce these feelings of anxiety make maths fun and exciting for my pupils?

From my personal experience I feel I did not enjoy maths because it was very much read out the text book. However I do remember one maths lesson in primary school. We were doing measurement and it had been snowing, our class teacher took us outside and we built snowmen and then measured how tall they were. To this day I still know how many feet are inches etc as I can relate it back to the snowmen. I believe that by making maths more interactive and fun increases the chance of children not feeling so stressed and anxious about maths.

I feel its so important for children to have a concrete knowledge of maths and have confidence in their ability. Maths is in everyday life and also evident across the curriculum. It is heavily evident in subjects such as science and technology however it also appears in other subjects such as; geography for map work and history for timelines. One way I feel can be beneficial for securing a child’s mathematical knowledge is having them explain the solution to you. It is important for children to get the correct answer. Having the ability however to understand how they got to that answer and being able to do it again is when you know if they have really understood what you have taught them.

In my personal opinion, in order to change this perspective of maths I feel we have to make maths more interactive and creative. Instead of a child just reading out of text book and answering the questions actually put maths into action. If your studying measurement ask the children to measure something, if your doing fractions use plasticine and make pizza’s and get the children half their pizzas. A child will always remember more when they have something to relate it to, like myself with the snowman. There will be times in maths when it is just a case of using the textbook but when you can bring your maths lesson to life. Maths is such a crucial part of life and it is so important for everyone to have confidence within their maths ability.

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Oh Science..

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When we received an email instructing us to create a small science experiment for our lecture a wave of stress and anxiety swept over me. I have never been good at science and I was totally disengaged during science lessons at school which made this task particularly difficult. I researched some experiments and decided I would make a rainbow. It was a very simple experiment all you needed was a sunny day, however, in Dundee they are very few and far between so I therefore settled for a torch, blank piece of white paper and a glass filled with water. You shone the torch into the glass of water and a rainbow was projected on to the paper. I chose this experiment as I felt it would be appropriate for a classroom as a fun task when studying the water cycle and I may be able to use it in the future.  Rainbow Experiment

As I said previously my time studying science was not an enjoyable experience and I feel this was due to the lack of input we had during our primary years. Throughout my whole time at primary school I cannot remember a single science lesson. With science comes high amounts of facts and figures and this can scare many people, myself included. I feel that many teachers may feel anxious about teaching science due to this. Personally I aim to overcome my anxiety with science now which will allow me to become more confident within the subject and therefore will not be so hesitant about teaching it.  This not only improves my own professional knowledge but broadens the knowledge I can provide my pupils with.

In order to improve my knowledge  I will research different areas within science. I aim to do this in various ways by visiting places such as Dundee Science Center or beginning  to look at the Curriculum for Excellence experience and outcomes and begin to research the topic areas and plan lessons for them. I will achieve this through researching and by asking my peer, lecturers and teachers on placement for support and advice.

What is an Enquiring Practitioner ?

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An enquiring practitioner is some who grows as professional “by challenging or ‘disrupting thinking’ and ‘ingrained habits of mind.” For me this means someone who is open to change, someone who seeks to gain more knowledge and someone who reflects on their teaching styles and aims to better these in order to  provide their pupils with the best learning experience.The best way to better yourself as person is to reflect and learn from particular situations.

Some benefits of being an enquiring practitioner which is stated on the GTCS is that it “enables teachers to bring about fundamental changes in pedagogy and curriculum and thereby significantly improves the quality of students’ learning experiences in educational institutions.” Seeking further knowledge regarding the curriculum and incorporating different teaching styles allows teachers to grow as professionals but also improves the learning environment for children.  Another benefit I thought was of importance was that it “enable teachers to collaboratively develop the curriculum.”  The saying “two heads are better than one” comes to mind for this, working with someone allows you to see a situation from a whole different perspective. By reflecting together it allows people to share different experiences and ideas which can develop whole new opportunities for learning. Also to be a enquiring practitioner you have to ask why and having the ability to challenge certain ways of thinking. There are however some challenges which may be faced when being an enquiring practitioner such as some people may feel uncomfortable. As an enquiring practitioner the aim is to continue to better yourself as a professional through research and reflecting; this means there may be new skills and challenges being faced which can be daunting especially if you have been in the practice for a long-time. Another would be that It can be difficult to question your own assumptions  therefore many can start looking for problems in products, strategies and pupils. To be an enquiring practitioner you have to be critical of yourself to learn how to adapt to different ways of teaching.

I feel that learning now, how to be an affective enquiring practitioner will really benefit me as a student teacher . Within the University set up for example, in lectures not just believing everything you are told. Having the ability to go away and research theories and challenge them will allow me to grow as professional.  Another example would be whilst observing your classroom teacher on placement having the confidence to ask why they done that particular lesson plan or why they dealt with that behaviour in that way. Not just accepting that, that’s the way it is done. Then having the ability to reflect on this and either use it in your own lessons or deciding you may do something differently. I feel this will all set me in good stead for becoming an enquiring practitioner.

Active and Co-operative Learning; Is it effective?

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Personally I am a huge supporter of active learning and co-operative working.I feel that active lessons through things such as play or investigating and exploring are much more effective for children rather than the teacher standing infront of the class dictating to them. I believe active learning is effective because when it comes to a time in which they have to reflect on their learning they can think back to the exciting lesson that they really enjoyed and it will stick with them. I can say this from personal experience; when I was in primary 6 we were discussing Victorian Britain as a topic. My teacher set up a life-like Victorian Classroom at the back of the class. We each got a chance to sit in there for the day to experience what it was like for children in Victorian Britain. That is now a matter of years on and that lesson still sticks with me. Children enjoy interacting with their peers and by creating a environment where are working alongside their friends excites them and really draws them into the content of what you are saying. I can understand that people can argue it is not effective. If we rewind fifty years children were taught by the teacher standing infront of them dictating the lessons and back then it did work. However now we have an amazing opportunity to change the way learning is taught through the use of technology and play.

Through my own experience of learning I believe that co-operative working is really effective. When I could not understand what the teacher was trying to get across I would go to one of my peers who did understand and they would simplify what they were trying to say. As teachers I feel we can sometimes over complicate things so through co-operative learning children have the chance to help their peers. I also feel through co-operative learning a lot of life skills can be taught such as; learning to work in a team, co-operating with other people and listening to other peoples opinions. These are skills that you use in everyday life and by using them from a young age really gives children the chance to develop these. Working together also gives children time to process what you have just taught them. Letting them go away and discuss what they have just been told allows time for the information to actually sink in rather rushing on to the next part of that days lesson.  Once again I understand that this is just my views on active and co-operative learning and that there can be disadvantages to this. One disadvantage I do understand is that children can go off task when working with peers and starting chatting about things other than the lesson. However my personal view is that the advantages to outweigh the disadvantages and when I am planning lessons I will try to make them as active as possible.

Personal vs Private

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The GTCS states that teachers have to use social media wisely and in a correct manner. Even though they are entitled to a private life; what they say on social media or how they use social media can be classed as unprofessional and seen as going against the GTC code. Teachers have to maintain the trust of both pupils and parents. This trust is maintained through behaving in an appropriate way both in there personal and professional life.

For me personally I feel it would be difficult to marry up both your personal life and private life on social media and I prefer to keep both mine separate. All my personal social media accounts such as; Twitter, Facebook and Instagram are private. In your private life you could say something on social media which you see as harmless however others may think you are being inappropriate or unprofessional. I also feel it would be difficult to maintain a professional boundary if you tried to marry it up with you personal life as people can see you in a different light. My personal view is that people have very high standards regarding the way teachers behave and are quick to pick up on any negative behavior and come down hard on this.  I feel marrying the private and personal life can make a teacher vulnerable to scrutiny.

The use of social media professionally however I feel has great aspects. Social media is the forefront of everything these days and children are heavily involved within social media. I feel introducing social media sites into the classroom such as Glow makes learning more modern and relevant to the children. However I feel its so important to stress to children the dangers of using social media and that they should be taught how to use social media safely and appropriately. I looked into some statistics regarding social media and young children and one that really sprung out at me. On Guardchild (http://www.guardchild.com/social-media-statistics-2/) it stated that “Only 10% of parents of children aged 10 and under had frank talks about appropriate online behavior and threats” Children are using technology and social media from such a young age that this should be drilled into them especially when they do not get told in depth at home about appropriate use of social media.

There are many challenges to social media and I feel that social media is portrayed in a negative way. This could be due to all the horror stories you hear regarding it or that because its relatively new that some people of older generations see it a bit alien like. However I feel it is a very positive aspect of learning. Websites such as Glow allow you to communicate safely and appropriately with pupils. It expands pupils literacy skills e.g by using blogs. I feel there is always going to positives and negatives of using social media however it is the future and I believe we have no choice but to embrace it.