Category Archives: 3.4 Prof. Reflection & Commitment

Where did it all begin?

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.]

Teamwork makes the dream work

As part of today’s TDT we were encouraged to engage with peers posts which has prompt me to keep on top of my ePortfolio more.  I do engage frequently with mine however it is more for TDT’s rather than professional thoughts and opinions. By looking at my peers posts it has inspired me to engage with my ePortfolio outwith my TDT’s.

Prior to the Christmas break I was beginning to really getting into the swing of writing posts and commenting on my peers posts. However this began to fall away when assessments and presentations were coming up as all my focus was on them. The lack of engagement from my peers and lecturers on my post also made me lose my confidence. When I am posting a blog it takes me ages to write it up as I am constantly re-reading and re-writing it. The amount of time I together-everyone-achieves-more-teamwork-quotespent on my posts and the lack of feedback I received really made me think, whats the point?

However after today’s lecture with Derek my “what’s the point attitude” slowly began to fade. After engaging with my peers post I was made aware that people did not engage on every single post and they still continued to post outstanding blogs so therefore why shouldn’t I?One blog that particularly stood out for me was – 5,6,7.. Dance. I found this post really interesting as Lauren’s passion and enthusiasm for her love of dance really shone through. I liked how she incorporated pictures from her own dance experience into her blog to make it that bit more personal. Her lesson plan really showed how much experience she has in dance and I am sure her enthusiasm would really motivate the children.

For me to improve my blog personally I feel I need to be more open to share my posts on edushare. I still feel very apprehensive when posting my work on their for everyone to see and for my professional development I feel this is something I must work on. I also feel I need to include more interactive sources such as videos, pictures and my professional reading into my blog to show I am really meeting and understanding the Standards for Registration.

The ePortfolio’s are a great tool to use as it is a space in which your thoughts and feelings are gathered. It allows you to reflect and engage in professional dialogue with peers and university staff providing you with the opportunity to expand your professional knowledge, thoughts and opinions.  After engaging with my peers posts this has really spurred me on to engage with my ePortfolio more and also my peers. By working together as a cohort and really engaging with one another’s ePortfolio’s we can flourish and grow together as professionals and make this a huge learning success.

Dance like nobody’s watching..

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.

 

 

 

 

how secure are you?

During our psychology lectures one lesson I particularly enjoyed was studying the theory of attachment. I found it interesting that your sense of security and attachment is connected with the development of you as a person. Attachment is a bond in which a person has a special sense of security  and comfort to another person which is usually the Mother. However in the modern day attachment can be formed with many different people such as the child’s father or the child’s grandparents.

I looked further into some studies regarding attachment and one that I thought was interesting was Freud and Dunn (1951) study on war orphans. Freud and Dunn studied six war orphans who’s parents were killed in the concentration camps. The infants were looked after as-well as possible from fellow prisoners however it was difficult to form any sort of attachment as people were never around long enough. The conditions the children lived in were hard and they had limited food and no toys to play with. After the war had ended the children were moved to Bulldogs Bank Reception in the Lake District. The children couldn’t communicate much except a few German swear words. Freud and Dunn found that the children were very hostile to the adults trying to help them and the children would do everything together, if one did not eat nor did the rest. They appeared to have formed attachment to one another. The children progressively developed relationships with adults and slowly recovered from the deprivation they suffered however still remained very much attached to one another. For me I thought this study was a real eye opener as to how key attachment is for development. The infants missed a crucial period for creating attachment therefore their social skills were affected.

An attachment theory I feel can be really beneficial in the classroom is Mary Ainsworth Strange Situation study. Ainsworth studied children’s reaction when a stranger was in a room with and without their mother present.As a result of the experiment she came up with three different attachment types; insecure avoidant, securely attached and insecure resistant. Insecure avoidant  is when the child has little interest in their caregivers and aren’t phased when alone with a stranger, they also aren’t looking for comfort when the caregiver returns. Securely attached is when the child gets upset when their caregiver leaves and seems distressed when alone with the stranger, however is quickly soothed when their mother returns. Insecure attachment is when the child doesn’t want to explore the room and they cry when their caregiver leaves and when left alone with stranger. There is however mixed responses when their mother returns they want to be soothed but they can also reject their mothers comfort and be angry. Children with a secure attachment don’t need all the teachers attention on them and are happy for other children to receive some of that attention. These children are able to wait their turn, with belief that their teacher will be able to meet their needs.  This allows the child to take risks and tolerate frustrations in the learning process. However, children with attachment difficulties will typically show distrust within in their teacher and classmates, and many put this down to  lack of concentration rather than attachment difficulties. A child who constantly talks can be using this a strategy to keep bad thoughts away. These children may also have difficulty dealing with unstructured situations such as playtimes . If they make mistakes, these children may have explosive reactions.

Overall for me I feel that having the knowledge of the attachment theory is crucial for teachers. Having the ability to spot that a child is acting up as they have trust issues because due to not having that attachment figure in their life, and not because they are trying to show off or be the “class clown”. As teachers having the knowledge and tools to deal with this situation can only insure a better learning experience and future for your pupils.

Reflection

Reflection is when you draw from your experiences, beliefs and emotions and by reflecting back on these better yourself as person. I believe that being able to reflect is crucial in teaching. The Standards for Registration states that student teachers must, “reflect and engage in self evaluation using the relevant professional standard.” This shows how vital it is for teachers to be able to reflect.

As teachers in order to be able to reflective we have to be open-minded and responsible. We need to have the ability to be critical of ourselves. If a particular lesson did not work well we must be able to reflect by looking a the lesson and identifying what did not work well and learn from this in order to prevent the problem arising again. Reflection leads to change and adaptation; without reflection I feel education would never progress.

I feel the key to becoming a successful learner is having the ability to reflect. If children are taught from a young age to look back and reflect on a particular situation within their learning provides them with a staggering amount of opportunities through development. Reflection is also vital in allowing people to recognise and consider other people’s beliefs and values. Having the skills to take a step back from your own values and see other people’s perspectives is a vital skill throughout life.

In brief, we need reflection in order to improve as teachers. If teachers are constantly improving this gives the students a even greater education.