Category Archives: 3.4 Prof. Reflection & Commitment

Discovering mathematics reflection- Have I discovered it?

www.google.co.uk/mathslove

I’m not quite sure I have the same love for mathematics as the numbers above….however, I can say that my fear of maths has reduced dramatically over the course of this Discovering Mathematics elective!

I have just finished my assignment about having a ‘Profound Understanding of Fundamental Mathematics’ and I have Liping Ma to thank for making those four elements of PUFM torment me every night for the last 3 weeks whilst trying to get to sleep – CONNECTEDNESS, BASIC IDEAS,MULTIPLE PERSPECTIVES and LONGITUDINAL COHERENCE. It has taken me the length of the elective to get my head round these 4 elements and be able to apply them to my own mathematics experiences and to our lectures. I am grateful to Ma as It has been very beneficial being able to view maths as a coherent whole. I feel through my engagement with the lectures and wider reading, I have started to repair my fragmented view of mathematics as I begin to open up the underlying network between different mathematical concepts.

ENJOYMENT

Looking back over the discovering mathematics elective, I wanted to pick out a particular lecture that I enjoyed and show how it helped develop my understanding of how mathematics can be used in wider society.

Maths – Data & Statistics (Dr Elanor Hothersall)

During this lecture we had a guest speaker, Dr Hotersall, who works for NHS Tayside as a consultant in public health. Dr Hotersall was quick to identify one of the main barriers for individuals working in the health profession – a lack of understanding of the basic mathematical concepts. This was in regard to nurses and doctors calculating drug dosages, fluid prescriptions, concentrations of medications, interpreting research and probabilities which leads to treatment decisions, biomechanics and in particular pharmacodynamics (what happens to your body when you swallow medicine). To be honest, before this talk, I never really considered the underpinning mathematical literacy that was required to work in the health field, yet I would want to be fully confident that my nurse/doctor was competent enough in mathematics to prescribe me the correct drug dose and be able to calculate the correct reduced dose if they were treating my son. Dr Hothersall also went on to discuss how in her job she regularly has to compare health information and statistics, identify patterns and anomalies in results and decide acceptable levels of variation. Overall it was a fascinating lecture and really made me think deeply about how basic mathematical ideas and concepts can be crucial when working in such an important profession.

Where do I go from here?

Although my maths anxiety has reduced from the start of this elective it is still clear in my mind that I need to participate in professional development by continuing to engage with mathematics topics, courses and training opportunities. I need to work hard to develop my confidence and understanding of basic mathematical concepts if I am going to be able to explain them well to my pupils and encourage them to explore them with confidence. It is really important to me that I do not allow my pupils to experience any negativity when it comes to maths. I want mistakes to be welcomed as long as we can work back from them, see why it went wrong and then discuss, debate and predict how we could get to the right answer. Collaboration and discussion is going to be vital to achieving success in my maths classroom! I like to talk things through and feel that children will benefit from dialogue when working through mathematical processes. I am happy with the wide variety or research I have done for this elective and I feel that my blogs show a high level of engagement with my professional development.

I want to thank Richard and Tara for all their lectures and hard work throughout the module – especially for putting up with my puzzled face and silly little questions. Also a big thanks to all the guest lecturers who provided us with a good insight into how fundamental mathematics can be applied in wider society and to other professions beyond educational applications.

Is Maths beautiful?

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The Golden Section and Mystery of Phi

When you look deeply at nature and our surroundings, you can begin to identify and analyse the role that mathematics plays in aspects of our daily life. The Golden Ratio is considered to be everywhere: nature, music, our fingerprints, logo’s, artwork and buildings. The Golden Ratio is aesthetically pleasing to our eyes. Look at the two pictures below and choose which one you like best.

In one of our recent lectures on Art and Maths, we were introduced to abstract art by artist Piet Mondrian. If you like the picture on the right, then I guess you are an exception to the rule. I drew that picture with no knowledge of how to create Mondrian abstract art and just experimented with lines and colour. If you like the picture on the left better, have a think about why? Is there anything in particular that jumps out at you? The picture on the left draws on the mathematical concepts and principles of the Fibonacci sequence. The measurements between the lines within the picture all fit in with the numbers on the sequence. To me, it is more aesthetically pleasing and it seems to have more structure to it.

http://www.tate.org.uk/art/artists/piet-mondrian-1651

It is worthwhile to bare in mind that because the golden ration is pleasing to the eye, we might show an unconscious preference to it. Artists may make choices in their work which result in approximations of the golden ration without drawing on the concept and principles directly. Could it be that the golden ration is not so mysterious and that it is somewhat learned rather than innate? Just some food for thought.

I absolutely loved the TV series 24. Kiefer Sutherland had me on the edge of my seat constantly. His new drama ‘Touch’ draws on mathematical concepts such as patterns relating to numbers and sequences. Take a look at the trailer below and see the golden ratio, and links between numbers, guide the drama and story line through exciting twists and turns.

Tennis and Mathematics

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The obvious mathematical concept involved in tennis would be counting. The scoring system in tennis is unusual as it doesn’t go up in units of one, or even units of the same amount. the follow picture depicts the different scoring options that could take place during one tennis game. As you can see, the first two scores (if won by the same person) go up in units of 15 (15-0, 30-0). However if the same person won the next point, one would presume it would be 45-0, however, due to the unusual scoring system, the new score would be 40-0.

http://mycodehere.blogspot.co.uk/2011_02_01_archive.html

Are there any deeper mathematical concepts embedded in the game of tennis?

Analysing statistics is a vital aspect for anybody involved in professional sport. Statistics can help players identify individual strengths and weaknesses and also the weaknesses of their opponents, which might inform their strategy and tactics for future matches. Percentages are the usual way of comparing players. In tennis, the typical statistics you see after each set include: first-serve percentage, service games won, break points saved, second-serve return points won, break points converted, unforced errors, forehand winners and so on.

http://www.changeovertennis.com/wp-content/uploads/2013/01/matchstatsmurraydjok.png

Before Andy Murray takes to the court to play a big semi-final against Djockovic, members of his training team will have analysed Djockovic’s match statistics from that specific tournament so see if they can identify any trends, likely predictions of play and any areas which are particularly weak so that Murray is stepping onto the court with informed information. This may not alter how Murray chooses to play, however if the match is not going as he would like, it would make sense that he would draw on the information he had been given to try and change up his tactics and play more aggressively to his opponents current weaknesses.

What about geometry?

Could tennis just be a problem of geometry? When playing a game of tennis, your aim is to win by the point by hitting the ball hard over the net, with spin, to a position where you opponent cannot return the ball. Is geometry involved in this process? In the path of the ball? The position of the player? The spin on the ball? It has been said by many commentators and some of the greats of the game that tennis is about controlling the middle of the court, cutting of angles and geometrical concepts support players in achieving this.

www.google.co.uk/tennisangles

An attacking shot in tennis why relies on the play having a knowledge of angles is the angled approach shot. Hitting a short angled ball over the net forces your opponent forward, scooping up their return which should theoretically leave you with an easy volley to put away. You create a greater number of steeper angles when you step into the court and this forces your opponent to move around playing less confident and challenging returns. The following article discusses some of the geometric concepts in tennis further and provides some interesting food for thought for the next time you step out onto the tennis court.

Geometry and the Art of Tennis

What about the impact of top spin?

www.google.com/tennisbounce

The ball bounce can greatly affect how an opponent returns your shot. Two properties which are involved in this process are Coefficient of restitution and Coefficient of kinetic friction. These two elements involve mathematical concepts such as ration, speed, distance and angles. The above diagram shows the bounce of a flat shot with no spin. The angle of incidence is approximately equal to the angle of reflection. This means the angle at which the balls impacts the ground and which the ball leaves the ground are almost the same. The ball slows down after it bounces due to the impact when hitting the surface.

www.google.co.uk/tennisbouncespin

The diagram above shows that when a ball is hit with top spin the angle of reflection is lower than the angle of incidence. The ball is not affected by the friction when impacting the surface of the court and the forward spin pushes the ball forward with greater speed after it bounces.

The following link is great for describing the effect different spins have on the ball bounce and how the different spins change the velocity, speed and direction of the ball.

The Physics of tennis

The things I love and their affair with mathematics!

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The ‘Discovering Mathematics’ module has encouraged me to identify and explore mathematical concepts that occur regularly throughout our lives. I have found it very interesting to do this with things I encounter everyday and wouldn’t normally associate with mathematics.

PARENTING

I have a two year old son who is now at the stage where he is exploring his surroundings, asking questions, solving basic problems and interacting with others around him. When I was sitting with him the other day, playing with his toys, I decided to look at how many of his toys incorporated some sort of mathematical concepts. The books that I would read to him encouraged him to identify shapes, count objects, try help the character solve problems like getting through a maze. One of his favourites is playing with shape toys and fitting them into a container. He enjoys sorting objects into shape, size or colour and I often find him counting his way up the stairs to his bedroom. All of these are very basic mathematical concepts: shape, organising and sorting, counting, simple problem solving etc. When reflecting on this, what hit home was the notion that my son enjoys doing all of these activities, he doesn’t shy away from it. The activities excite him and give him a sense of achievement and I wonder if these feelings and motivation leave children when they experience the mathematics curriculum when they start school.

HAIR & MAKEUP

Anyone that knows me well knows that I am obsessed with hair and makeup!! I am always waiting for payday to come so that I can visit the local MAC counter and purchase the latest lipstick or foundation. I decided to explore makeup and hair further to see if I could identify any mathematical concepts that are involved in these processes.

Hairdressers need to have a sound level of confidence and competence when dealing with basic mathematical principles. In their profession, they regularly work with; angles when cutting hair, ratios and percentages when mixing colours together, and symmetry when finishing off styles.

The following link shows a short video clip of how the mathematical concepts discussed above can be applied in hairdressing.

https://www.youtube.com/watch?v=GQGW6FJWfDM

In makeup, concepts such as angles, symmetry, geometry and shape are regularly used to achieve the ‘perfect look’. The following video shows how makeup artists used measurements, and a compass-like tool, to apply makeup in the 1930’s for women with different shaped faces. The artist would measure the distance between the forehead and bridge of the nose and then from the nose to the chin. These measurements would then act as a geometrical guideline for outlining where to apply makeup to the cheeks, eyes and lips.

All girls know about the ‘Big C’ when talking makeup. It usually is accompanied by a picture of Kim Kardashian. Yes, I am talking about contouring. If you are a man reading this, then you will probably want to switch off now. Contouring is a work of art. It is a mission and can sometimes feel like mission impossible. Contouring works to give shape to an area of your face and then enhance your facial structure through makeup. It can give the illusion of higher cheekbones, slimmer nose and chin, and it can be used to help alter your face shape. Similarly to how makeup was done in the 1930’s, contouring draws on concepts such as shape, symmetry and measurement.

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http://4.bp.blogspot.com/-xz83kd-zKqc/U_XppFboYWI/AAAAAAAAAg4/HLJa-xfg6o4/s1600/b1d33a589ca631d11d054eaf25b42893.jpg

Links

Cut it out and curl it up – Maths Careers

Geometric beauty

Learn for Life – Our new curriculum!

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Mind-map of our new curriculum

In our education studies lectures, we have been have been looking at the education policies of the different political parties. We were then posed the question “If you could scrap curriculum for excellence and make up an entirely new curriculum, what would it be?” and additionally “Why have you come up with the curriculum you have chosen? What are the incentives, the morals and the underpinning values and missions behind it?”

During our discussion, a main point that was widely agreed on was the introduction of ‘Life Skills’ into the curriculum. By this we mean: Cooking, Health and Safety, First Aid, Animal care, Environmental care and Parenting Skills. Now I know the latter point is a contentious one. We understand that this is a delicate issue however, we educate our children about sexual health, alcohol and drug abuse and in doing so, we are not encouraging the behaviour associated with these things. We are exposing the dangers and the negative effects being involved in these activities could cause. With the teenage birth rate in the UK at 37.7% per 1000 population in (NHS, Information Services Division, 2013) there is a need to make teenagers and young people aware of the demands and skills required for parenting. The emphasis on sexual health and family planning will of course be a priority in the delivery of health and wellbeing section of the curriculum.

Another element that we were all keen to introduce was ‘Moral Skills’. We think it is extremely important to instill respect, kindness and generosity in our pupils. We want pupils to have firm and respectful relationships built within the community and work together to provide good public services to support people who are in less-fortunate positions. It was suggested that children could be regularly involved in volunteering with local charities and homeless shelters within the community. Classes and year groups could work on projects throughout the year to help raise money or awareness for things they feel strongly about in the community. The idea is that these projects would be student initiated and student led. They should feel a strong sense of independence and have the majority of control in order to work together to achieve something great.

We highlighted team building and school trips as a brilliant opportunity to introduce more outdoor and active learning experiences. No matter the weather, we want children to have hands-on educational experiences outside, working together to problem-solve, overcome challenges and develop real-life skills. I discussed the benefits of outdoor learning in a previous blog post about education in Sweden, and I feel passionate about bringing the attitudes and values towards outdoor learning into the Scottish curriculum. Children rarely get the opportunity within school to go to outdoor learning facilities and take part in air obstacle courses, abseiling, water sports and team building challenges and if they do, it is once and year and considered to be a luxury or reward. Why should it be like this? The learning experiences that children leave with after trips like this are rich, varied and can be applied in their day to day lives.

We decided that we would maintain all of the curricular areas, however there would be major adjustment to the topics being taught and the relevance of learning. We want children to be educated about things that will help them to live their lives when they leave school. I believe we are still teaching children topics that were being taught in the 1970’s. Although the introduction of technology changes the way children are taught, the basis and reasoning behind these topics being taught is still the same. We discussed Maths as being a topic which is essential to daily life. However, in schools we do not use maths in a way which helps children develop the mathematics skills needed once they leave school. Children are not educated in budgeting, mortgages, loans and interest and even if they are, it is out of a textbook,not from real-life examples. Children are not encouraged to make the connection between the importance of school maths and the maths they deal with in their personal lives. This is a gap that our curriculum would aim to focus on.

The final area we discussed was ‘Work Experience’. One member of the group brought up a very important point. At 17/18, the majority of students apply to go to university to specialise in a subject or profession. This is a massive decision to make and most students only receive a 2- week work placement opportunity from their school to help them make their decision. We don’t believe this is enough. We want pupils to have the opportunity to take part in regular and varied work experience to introduce them to a variety of professions which they might be interested in. We want to build good connections and relationships with employers, apprenticeships and businesses in order to provide these opportunities. We thought that a morning or afternoon a week from 14 years of age would be extremely beneficial for students. It would build confidence, self-esteem, motivation and it would help many students who are unsure of the profession or subject they wish to study at university. Additionally, students who didn’t want to go on to further education would have a wealth of experience in difference areas which would help them to make an informed decision about which career they wished to pursue.

After the discussion we reflected on what we had written and we could see that the connecting and underlying theme between all of our points was the notion of ‘learning for life’. We are educating our children so that they are prepared and ready to leave school and live successfully in the world. What they learn at school is relevant and helpful to what they will experience and need to know in the future. Our Learning for Life curriculum provides the foundation of knowledge that children and young people will need to flourish and be successful. There is no taboo about this curriculum, everything we do!! 🙂

Souces

NHS, (2013) Information Services Devision. Available at: ahttps://isdscotland.scot.nhs.uk/Health-Topics/Sexual-Health/Publications/2015-07-07/2015-07-07-TeenPreg-Summary.pdf?21798342467 Accessed 30/10/2015

Modern Languages – Isolated or integrated approach?

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If I am honest, I have always felt more comfortable with the thought of a specialist language teacher delivering the modern language curriculum to my class. My justification for this was that these teachers have specialist knowledge and understanding of the language which would allow them to teach the language more effectively than I could. The children would then get an informed and specialist educated professional delivering the lessons and their learning experiences would be greater than what I could offer. I think this train of thought is encouraged by my lack of confidence in modern languages and the fear that I would teach something incorrectly.

After leaving my first Modern Languages tutorial, I was surprised at how much French I could actually remember from school and I was happy that I could follow most of the discussions. This tutorial gave us some brilliant teaching strategies for a beginners language class and the emphasis on ‘why these strategies were effective’ was really valuable. Some of these strategies were: repetition, voice modulation, clear and precise dictation (providing a good speech model), mime, gestures, facial expressions, eye contact and games. It’s all good and well choosing a teaching strategy, but if you don’t know ‘why’ and ‘how’ it is going to help pupils learn and develop, then you will not be able to deliver your lesson effectively.

After some reading and research into the strategies used to develop a modern language (ML), I have been able to identify some criticisms of my initial ‘Isolated-approach’ method delivered by a specialist. As a result of a ML being taught by a language specialist, there is very little room for embedding modern languages into the curriculum as teachers wouldn’t have the knowledge or skills to provide cross-curricular learning experiences. There is also limited opportunity for children to learn the target language in meaningful contexts as all language learning would be restricted to small slot in the timetable.

“Pupils need to encounter, process and use new language in different, meaningful contexts in order for it to be embedded in their minds.” (McLachlan and Jones 2009)

As my understanding in this field has grown, I now consider a whole-school approach as being vital to the success and effective delivery of ML. By this, I mean that class teachers have the support of their management team and other members of staff in promoting Modern Languages around the school and embedding it within daily routines. For example, this could be ML display boards in the school reception promoting welcoming phrases and increasing the status of languages for parents and visitors. Simple classroom routines such as the register, instructions, behaviour management and timetabling could be introduced in the target language. Welcome and introductions in assemblies could be done in the target language which would create a positive whole-school attitude towards ML.

“A clear and shared vision for the whole school’s present and future language provision will considerably enhance the initial classroom teaching.” (Hood and Tobutt, 2009)

This approach could be hindered by teacher’s lack of confidence in Modern Languages. Being able to provide cross-curricular learning experiences in the target language can be challenging and a daunting experience for members of staff and this could work against the integrated approach which schools are aiming for. A way in which schools could tackle this issue would be promoting professional development opportunities in Modern Languages. Schools need to give teachers the opportunity to develop their own knowledge and understanding of the languages being taught which would increase their confidence and would take a step in the right direction for embedding language in the whole curriculum. Another option would be to work with a Language Specialist, or another teacher who is particular competent in languages, to plan cross-curicular learning experiences and work through some lesson plans to ensure the class teacher felt secure in delivering them. Collaborating with other professionals is a valuable experience and one that allows you to share good practice, come up with new ideas and benefit from each other’s strengths.

An important point to consider when teaching a new language is, should my lessons be delivered only in the target language? Or, should I be using the english language to teach the new language? Teachers have differing views on this issue. Some say that the english helps to establish meaning in the target language and will prevent students from getting lost and de-motivated during lessons. Others say it doesn’t make sense to learn a new language by speaking your native tongue language. I fall in-between these two statements with a slight tendency to lean towards the latter. I do believe that children should be immersed in the target language and be able to develop the four language skills through this immersion. However, I agree that in the early stages of learning language, it is appropriate and often necessary to return to english to establish meaning, to cover tricky grammar rules and instructions and to check for your pupils’ understanding.

The video below is an interview with an experienced language teachers and she discusses her views on using the target language when teaching ML.

For my 2CM6 assignment, I am going to do further research into the use of singing, rhymes, games and story-telling to develop the target language. I want to develop my understanding of why and how teachers are slowing moving away from rote learning in ML acquisition to strategies which introduce Knowledge about language, language exploration and language comparisons.

References

Hood,P. and Tobutt, K. (2009) Modern languages in the primary school. London: SAGE Publications

McLachlan, A. and Jones, J. (2009) Primary languages in practice: a guide to teaching and learning. Maidenhead: Open University Press

Code cracker for the NSA to code cracker of the financial industry!

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What an incredible man, devoting his life to maths research and using his knowledge to identify and prove patterns, trends and connections in different fields.

This video on TED talks caught my attention when I saw ‘Mathematician who cracked wall street.’ I am fascinated by the work the NSA does in cracking codes to diffuse security threats. To be honest, I had never thought about the mathematics behind something like this. The identification of patterns, trends and anomalies are all involved in the process of cracking security codes. For Simons to go on and be able to apply these strategies to the financial industry really supports the notion of Mathematics being linked to multiple disciplines. Maybe I will enjoy developing a profound understanding of mathematics after all!

I was interested when the interview went on to talk about Simon’s involvement in supporting and encouraging maths research and development within education. The ‘Simons Foundation’ discussed in the TED video was cofounded in New York by Jim and Marilyn Simons in 1994.

“The Simons Foundation at its core exists to support basic — or discovery-driven — scientific research, undertaken in pursuit of understanding the phenomena of our world without specific application in mind.”

The foundation has a great focus on collaborating with scientists in the progression of fundamental scientific questions within major topics such as mathematics, computer science and physics. The Education Outreach sector of the foundation drives to encourage a deeper understanding of science and mathematics amongst pupils, teachers and members of the public.

In the video above, Simons states that the charity has a vision to invest in maths teachers around America.

“Instead of beating up the bad teachers, which has caused morale problems within the educational community, we focus on the good ones, giving them status and extra funding for their own professional research.”

This approach and support has had a positive effect on teacher’s morale, confidence and their desire to remain in the teaching profession. Take a look at the following link to the Simons Foundation website to see the positive work being done in Education, Life Sciences, Autism Research and Data Analysis. They also have great links with and support the development of MoMath (National Mathematics Museum, NY) in demonstrating the capacity Mathematics has to impact the world in unique and unexpected ways.

Simons Foundation – Education and Outreach

Websites:

About Us

https://www.ted.com

Inspections – purposeful or painful?

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Personal opinion – Painful!

Whilst I was working abroad as a Learning Support Assistant, our school received the dreaded phone call that we were to undergo an inspection within the next two weeks. I was familiar with inspections after seeing them take place when I was a student but I wasn’t nearly aware of the impact that the “It’s inspection time” phone call had on teachers, support staff, and most of all the school management team.

I think we received over 50 emails from management in the two weeks prior to the inspection.

“Make sure every display board is fully complete and displays the best work from the class.”

“Make sure your resources are fully stocked and that each table has the correct amount of stationary per child.”

“Teachers, please make sure that you are using your LSA effectively during inspection time and not for classroom administrative tasks.”

“Teachers, please make sure you are not found sitting at you desk on your computers during class lessons and are moving around, interacting with all the children during activities.” (Ironically, due to the constant pings from my teacher’s email inbox, she was on her computer reading the barking orders during lessons more than she was at her computer normally.)

We all felt the pressure from management for the inspection to go perfectly. However, the response from teachers was very negative to say the least.

http://static.guim.co.uk/sys-images/Guardian/Pix/pictures/2008/08/30/Stressed-teacher-460×276.jpg

‘After years of training, why do I need to be reminded to move around my classroom? I’m in a classroom more often than the management team are so I think I know how to do my job!!’

‘Do you think that I would let my classroom resources and stationary decrease enough that it would start to impact on the learning experiences that my students are getting?’ An few examples of the conversations you would overhear in the staffroom over lunch!

You could see the divide widening between teachers and the management team. A divide that you feared would be recognised by the inspectorate team as soon as they set foot in reception.

What effect did the management’s emails have on the relationships between members of staff? A negative one! What effect did they have on teachers’ self-esteem? A negative one! Did this have a knock on effect on stress levels of staff prior and during the inspection? Definitely! Was this a pleasant environment to be working in during those two weeks? Absolutely not!!

My underlying thought is as follows; if it was an extremely unpleasant environment to be working in during that time, filled with stress, tension and overall chaos, what effect did this process have on the learning experiences of our students during this time? I can only imagine it was a negative one. AND surely the learning experience of the child is what is being inspected.

I leave you with this last thought. I remember being asked by my deputy-head to take down one of the student’s work from a display board because it “looked unfinished”. I knew that the piece of work was complete. In fact, it was the only piece of work that child had completed in 2 months. This child had been having difficulties at home and this had affected his work in school. My class teacher had finally found a book that he was engrossed in and he had asked if he could write his own blurb for the book to try encourage his peers to read it. He had a great sense of pride and feeling of achievement when we put it on display. I don’t want to even imagine how he felt when he walked into the classroom the next day to see it had been stripped from the wall.

Is it worth stripping a child of their pride and achievement in order to get a glowing review from an inspectorate?

Absolutely not.

Incidentally, our school received ‘outstanding’ in every sector of the inspectorate. All members of staff were given a certificate in their cubby holes, congratulating us on our achievement.

It didn’t feel like an achievement nor did it feel like something to be celebrated. It was a horrible two weeks and I don’t feel that the division between ‘us’ and ‘them’ (staff and management) ever healed.

I’m moving to Sweden! Part 1

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I left one of my recent lectures on comparative education ready to pack me and my son up and book the next flight to Sweden! Why? They have absolutely nailed early years education and after doing further reading and research, there is no doubt that I would love my son to experience pre-school life out there.

The pedagogy within pre-schools is built on the concept of experiential learning and developing the whole child. Social interaction plays a vital role in children’s development and the learning is based on interactions with each other as well as the adults and teachers involved in education. The pre-school environment is very welcoming for the children and very much resembles the home environment. There are sofas, game rooms, kitchens and the children even take their shoes off at the front door (that is one of my favourite bits – don’t you always feel more comfortable in a place where you can take off your shoes!). When children develop this sense of security, they are able to flourish and their development soars. The children also have the freedom to go and get a snack and drink when they need to without the permission of an adult (I’m not sure this aspect would work for my son as he would probably never be out of the kitchen! )

OUTDOOR LEARNING!!! And I don’t mean Scotland’s version of outdoor learning where we are outdoors until the first speck of rain falls and then it’s a rush back into the classroom because we can’t let the children get wet and drag their muddy boots back into the school!! Heaven forbid!! Pre-school education in Sweden is outdoors! The majority of the day is spent outside running through forests, climbing trees, playing by lakes, playing in parks, climbing hills and experiencing learning in a meaningful, hands-on context. The benefits of learning like this are HUGE! Children develop independence, awareness, self-esteem and resilience. The benefits really are endless. What do you think the answer would be if you asked a 4 year old what they were most proud of: learning how to decode and read the word cat, or finally managing to climb that big tree in the park? I bet it would be the big tree! They develop a massive sense of achievement when they finally have accomplished something which they have been attempting to do for ages! They develop intrinsic motivation and they learn about challenges in a real life context. They are doing exactly what 4-year olds should be doing! I hate it when I pick my son up from nursery and I see his clothes in the clean, pristine state they were in when I dropped him off 8 hours earlier. I’m one of those parents who would be overjoyed to see him with a muddy trouser leg and little rip in his jumper from playing in the bushes, or having to buy him a new pair of welly boots because he’d worn down the soles of his ones from playing outside all the time!

One of the notable differences between our education system and that of Sweden’s is the compulsory school starting age. In Sweden, children do not start school until they are 7. There is an emphasis on the freedom to play and for children to acquire their knowledge in a playful way without the pressure of formal education. By no way does this mean that children are not involved in meaningful learning experiences. The teachers have a very important role in observing, questioning and developing the children’s understanding of the activity they have chosen to do. Teachers work with the interests of the children to develop knowledge and extend their learning. By waiting until the age of 7 to start formal education, children have been involved and immersed in quality experiences and they have developed knowledge in real life contexts. This really supports the notion of waiting until the child is ready. When a child is not ready to learn, they will not learn. When a child is ready to learn, they will learn more, and then some.

I will be doing another post on Swedish Education which will discuss The National Curriculum, the goals of Swedish Edcuation and the implications for teachers. I just wanted to share with you my views on the Swedish system from a parent’s perspective! I just love it!

Can you imagine life without counting and number names?

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In our society and culture, we use counting everyday. If we woke up one morning and had lost the ability to count or there were no longer any number names then we would struggle to function with daily activities. The number symbols on our clock would no longer have any meaning. Processing amounts of stock in shops would become a mammoth task and splitting the cocktail bill on a night out would be impossible!

Recent studies into Amazon Indian Tribes have shown that counting for them is really as simple as one, two, thee and maybe four. They do not have the counting vocabulary to specifically identify amounts larger than 4. Their counting language is the equivalent to one, two, few and many. I can’t imagine going into my local pub and asking for ‘many drinks’ when buying a round for 7 people. Our daily lives rely on our ability to use number names and our use of the Arabic numeral system. (This numeral system was introduced to Europe in the 10th century by Arabic speakers of North Africa.)

Although for us, the process of counting is so fundamental to our perception of quantity. For these tribe members in the Amazon, counting is needed very little in their daily lives. They have very little to do with transactions, trade and calculations (to be honest, I would probably love it there!).

For one of our activities during our counting and numerals workshop, we were tasked with creating our own numeral system and deciding if it would stick to similar rules as our own numeral system or if we would like to explore something entirely different. We came up with a 12 number based system which is different to our arabic numeral system which goes up to 9. We built on the foundation of a dice number system and continued from there. We decided to call our numeral system ‘Decinals’.

Unbeknown to me, there is actually a society which promotes the use of a base twelve system and they suggest that our current base 10 system is not the best system to use for humans! As the bast 10 system is so firmly embedded within our brains, it is almost impossible for me to think of counting in any other way! I find it confusing! In our recent lecture on place value, we were introduced to the dozenal system in the form of a number square and a times-tabele square! If i didn’t feel baffled before, I was certainly baffled now!

http://www.google.co.uk/imgres?imgurl=https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Dozenal_multiplication_table.

I can understand what is going on in this table up until 2×7 = 12??

I have to continually remind myself that 10 in this table doesn’t represent what we consider to be 10 in our system. Ten in the dozenal system is represented by an upside down 2 and 10 represents what we would consider to be twelve!

An interesting point to make is that young children would be able to pick up the dozenal system much quicker that we could because they do not have the base 10 system embedded in their minds. This is something they learn when they go to school.

After doing some further reading and research into this area, I am beginning to wonder myself if intact a base 12 system would be easier for us to us. I found an article which discusses the main advantages of a dozenal system and after reading it and then reflecting on the points discussed, I have to say they have very good reasonings for their initiative. I especially liked the ‘It’s All About the Factors’ section. It notes that ten only has two factors, being 2 and 5. Whereas 12 has 2,3,4 and 6. Consequently we are able to use the three most common fractions without having to employ fractional notations. Fractions was one of my weakest subjects at school and I now pose myself the question, “Do I think I would have understood fractions better if we used a base-12 system?” Of course I’ll never know the actually answer, but part of me likes to think I might have!

Take a look at the following links to support this post! I particularly like the ‘Why we should change to a bas-12 system’. It really helped explain the idea of a dozenal system and made the thought using it very appealing.

Links:

Why we should change to a base-12 system

Dozenal Society UK

Guardian article

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