When I consider Mathematics as a curricular area, I automatically think of sitting in a classroom, at a desk, copying from a textbook! It was draining and unenjoyable – not to mention sore on the old wrist as I tried to speed my way through multiple equations. The idea of having a profound understanding of Maths was not important to me until I began this module. Ma (2010), suggests that basic ideas within Maths is essential to set us up for the future.

Whilst on placement I had a lot of issues trying to come up with creative maths ideas, I really struggled to steer clear of the textbook approach as this was what I knew and also the school I visited was very textbook focused. However, from the children’s reactions when a maths lesson was introduced, I could tell they already had a negative attitude towards the subject and this would potentially lead to problems later in life for them. It is suggested that people who do not have adequate numeracy skills are more likely to be unemployed (BIS research paper, 2016), and as a practising teacher this is not the setup I wish to give my pupils. Throughout placement I introduced lessons to them that offered a more hands on approach using magazines, internet searching and allowing them to create shopping lists within a budget. Which the children did begin to enjoy, although I wish I had considered the outdoor learning approach after taking part in this during an input.

Richardson (undated, p.1 ), states how outdoor learning is very beneficial for children “supporting children’s developing problem solving reasoning and numeracy skills through good use of natural and manmade materials in the outdoor environment”.  She believes that not only will out door learning help progress children’s problem solving within maths abilities but also contribute to their development in communication, imagination and ultimately enjoy the experience (Richardson, undated).

Studies show that adults who were taught by the basic practises of maths teaching (jotter, textbook, pencil, rubber) feel that what they learnt in school did not set them up for successful use of maths in their future. They believe it did not prepare them for everyday life, and they were unsure how they would use the maths they were being taught later in life (National Numeracy, 2018). Further studies suggest that adults of today struggle with finances due to lack of mathematical knowledge which suggests that the issue lies with the way in which maths is taught in school (Burns, 2012). Taking this into consideration, a solution for mathematics being taught in the classroom successfully needs to be carefully assessed, could outdoor learning be the answer?

The idea of outdoor play is also stated within the Curriculum for Excellence document. It discusses how children are able to experiment which will lead to a more thorough understanding of mathematics as well as other curricular areas (CfE,2010).    

Taking all of this into consideration I believe that the idea of mathematics being taught outside of the classroom will be extremely valuable to pupils and help them to progress successfully within this subject area. Children will be introduced to maths in their daily lives instead of just doing as the textbook asks of them. However, I am not disputing the fact that at times classroom-based lessons and textbook use may be crucial to develop a particular skill. Ma (2010) further suggests this as she states that outdoor learning would be a great opportunity for children to achieve a deeper understanding of the world around them.

So, the moral of the story is try to use as many different approaches whilst teaching numerous subjects not only maths.  And most definitely use the world around us as one of them!

References

Burns, J. (2012) Poor numeracy ‘blights the economy and ruins lives’. Available at: https://www.bbc.co.uk/news/education-17224600 (Accessed: 20 November 2018).

BIS Research Paper Number 267 (2016) Impact of Poor English and Maths Skills on Employers: Literature Review. Available at: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/497550/BIS-16-48-impact-of-poor-english-and-maths-skills-on-employers-literature-review.pdf (Accessed: 20 Novermber 2018).

Curriculum for Excellence Through Outdoor Learning (Learning and Teaching Scotland, 2010) Available at: https://education.gov.scot/improvement/Documents/hwb24-cfe-through-outdoor-learning.pdf (Accessed: 20 November 2018).

Ma, L. (2010) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. New York: Routledge

National Numeracy (2018) Why is Numeracy important? Available at: https://www.nationalnumeracy.org.uk/what-issue (Accessed: 20 November 2018).

Richardson, G. R. (undated) Open Up to Outdoor Mathematics! Available at: https://www.ltl.org.uk/nsgw/documents/LTL-Maths-Early-Years-Booklet-final1432742138.pdf (Accessed: 20 November 2018).

Apparently so, when we first began this input, I was very sceptical that I could be won over by thinking maths in fact can create beauty. I was unsure what the outcome of the lesson was going to be. Little did I know that by the end of it my mind would be blown.

From thinking back to school all I remember in my maths jotter was pages of equations, sums, decimals, multiplication… the list goes on! But maybe it is possible to create something in maths which is not purely number based? Children would most likely be motivated by maths if we used ways in which are creative and exciting rather than boring equations.

In fact, maths can be used to improve and progress in our artistic skills. It is suggested that maths and art work in partnership together and that majority of art is all founded upon mathematical concepts (Barrow 2014). Patterns created by artists all have their own individual processes, these are known as algorithms in mathematics which is basically a set of instructions to follow to successfully create a pattern.

Self portrait

By using measurement in maths, it allows us to create far superior portraits than if we simply guessed where our facial features are positioned on our face.  We can use basic mathematical concepts – shape, measure and fractions – to improve our drawing skills and make portraits look more realistic by ensuring the facial features are in proportion. The human face is naturally symmetrical anyway so to create a better and more realistic image it makes sense to mirror this when drawing a portrait.

It is believed that symmetrical features make a more “beautiful” and “healthy” face. These ideas are suggested by (Bader, 2014) who believes that a more symmetrical face displays good health.  Is this just a coincidence? When we think how Mathematics affects our lives daily without actually realising could our brains be made up in a way that makes us think and see in this particular way?  There is an idea that supports this thinking. Bader (2014), explains how our brain functions in a way in which we interpret images that are symmetrical a lot easier than asymmetrical.

Another mathematical term we can use for creating the perfect image through measurement is “the golden ratio”. This term is a Mathematical ratio whish is used to create a more beautiful and aesthetically pleasing image. It is usually found in nature, and when used in designs it gives natural looking structures that are pleasing to the eye (Gross, undated). There are many designs and creations that have been developed with the use of the golden ratio, these include The Mona Liza, Pyramids of Giza and even Social media logos including Twitter! (Gross, undated). An example of how our bodies and faces follow the Mathematical ratio can be seen below:

It is suggested that or brains are “hard-wired” so that we favour items and pictures which are created with the golden ratio (Gross, undated).

The Rule of Thirds

Another way that is probably slightly easier to create images by using the golden ratio is “The Rule of Thirds”. Although it isn’t as accurate as the golden ratio it has a very similar effect (Gross, undated). To follow the rule of thirds divide your photo into 9 equal parts with 2 vertical and 2 horizontal lines. The rule implies that the most important object in your photo should be positioned at the point of intersection. By placing the main object off–centre it is believed to create a more interesting photo to the human eye.

After looking at some photos online I have realised that in fact this idea may very well be true! I looked into some professional photographers on a social media sight where I seen the rule of thirds used in many pictures. When looking at the pictures which followed the rule of thirds and then again and images that did not it became clear that other people had the same opinion. The volume of “likes” were sometimes almost doubled when the image followed the rule of thirds, compared to when it did not.

To be sure I had been in fact influenced into this belief I decided to try it for myself by editing some photos that were already in my library. Below you can see that by following the rule (in my opinion … well slightly … as he is always beautiful in my eyes) the image does indeed become even more beautiful.

Image 1 – not following the rule.

Image 2 – edited to follow the rule.

To sum up my thoughts and feelings towards this lecture, I can believe how much my eyes have been opened to maths covering so much more than sums and equations! It has developed my thoughts further in to how Maths surrounds us, unconsciously, EVERYDAY! It has most definitely impacted my thoughts on how I hope to introduce maths as a teacher, and it most definitely will not follow my memory of textbooks, jotters, pencils and rubbers.

References

Bader, L. (2014) ‘Facial Symmetry and Attractivness’ The evoluation of human sexuality. Available at:https://sites.psu.edu/evolutionofhumansexuality/2014/03/24/facial-symmetry-and-attractiveness/ (Accessed on 13.11.18)

Bourne, M. (2018) The Maths Behind The Beauty , Available at: https://www.intmath.com/numbers/math-of-beauty.php (Accessed on 05.11.2018)

Gross, R. (undated) What is The Golden Ration? What you need to know and how to use it, Available at: https://www.canva.com/learn/what-is-the-golden-ratio/ (Accessed on 13.11.2018)

Pete, P. (undated) Top 10 Photography Composition Rules, Available at: https://www.photographymad.com/pages/view/10-top-photography-composition-rules (Accessed on 13.11.18)

Maths, can it only be taught from a textbook or are there more creative ways? Having left school more than 10 years ago I feel like I have forgotten a lot of what maths is really about, I remember it as being split into groups of abilities and when you didn’t pass a test you were automatically moved down to less able groupings. This is something which I experienced and would never want any student of my own to feel as low as I did back then. Throughout Secondary School my experience of maths was copying from a textbook and memorising formulas simply to pass a test and not have to be reduced levels again! Maths for me was a big stress factor within my studies and to help me deal with this my parents had a private tutor to try and overcome these worries. With this help it enabled me to eventually pass higher Maths – but really with still no understanding of what or why I had to learn these useless pieces of information.

After being in my first-year placement I found that maths was something that I enjoyed teaching the class. I got so much from the children when I could see they were enjoying more creative learning ways instead of simply copying from a textbook, I tried to use as many different creative ways as possible to help enhance my lesson plans. I feel that undertaking this module will help me further in finding more interesting ways to deliver maths to pupils as I become closer to my profession.

I feel like Maths anxiety is a common feeling within majority of pupils due to class teachers and schools setting expectations that maths is a priority subject and must be undertaken to allow for employment or further study at university. There has to be changes made to remove this negative stimulus that the word maths brings.

A big turning point for me already within this module was when we looked at tessellation or tiling, this is when shapes are composed of repeating patterns without any overlapping or gaps (Coolman, 2015). I would never have thought that “tiling” could be looked at as an act of mathematics. Tessellation can be seen every single day without anyone being remotely aware that it is around us – it makes up the floors we walk on, its in nature around us and even in food that we eat.  Having a partner who always doubts his learning abilities – especially in maths – but actually does tiling for a job and doesn’t realise that he is using maths on a daily basis. The word “tessellate” means to arrange small squares in a mosaic form. It originates from the Greek “tesseres” which means four. The first tiling’s were created from square tiles and created as an art form. Tessellation is very rich in mathematics and has ties with geometry. Cultures around the world have all encountered tiling at various levels of intricacy (Coolman, 2015).

There are however many different kinds of tessellation, these include; regular, semi-regular and other. If we look at semi-regular tessellation this is when two or more shapes are repeated to create the piece of art and only regular shapes can be used. Regular tessellation is when only one shape is repeated and all shapes have equal sides and equal angles. Other tessellation is when many different shapes are repeated and fit together smoothly, these shapes can even include curves (Math is Fun, 2018). Below are examples of these different tiling ways:

Semi-regular tessellation.

Regular tessellation.

Other tessellation.

After the input I went home and had a further conversation with him and his thoughts on his job being strongly related to mathematics. His first response was very defensive as he couldn’t see how “sticking things to walls or floors” could be maths! We discussed the measuring element he has to do daily to ensure jobs are completed to a high standard, we discussed how he uses different shapes and styles and creates patterns. Soon he came to terms with the idea that in fact he does use maths every single day without realising it and I believe that children need to learn from a young age that maths can be enjoyable and is used in many different ways – not just to pass exams.

Drawing upon all of this it is believe that children should take a positive approach to learning mathematics and this should be influenced through their parents, teachers and daily tasks. If we are able to decrease these negative opinions related to maths through the way it is taught by more supportive teachers creating les pressure on the children and develop more creative and enjoyable ways of learning maths. This will ensure children feel more comfortable whilst learning maths and will allow them to relate it to many different careers instead of just passing exams!

References

Coolman, R. (2015) Tessellation: The Geometry of Tiles, Honeycombs and M.C. Escher Available at: https://www.livescience.com/50027-tessellation-tiling.html (Accessed: 10 October 2018).

Ma, L. (2010) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Available at: https://ebookcentral.proquest.com/lib/dundee/detail.action?docID=481154. (Accessed: 5 November 2018).

Maths is Fun (2018) Tessellation.  Available at: https://www.mathsisfun.com/geometry/tessellation.html(Accessed: 5 November 2018).

“What have I learned?”

When I was initially faced with this question I was very unsure as to how I was going to answer it. To be honest I wasn’t entirely sure what I had learned until we were introduced to artefacts and the stories behind them, which gave me some food for thought. If this is what helped me to understand various religions by touching and actually seeing then of course it would be much easier for the children to learn in this way whilst being much more engaging for them. I even learned how to wear a sari in the last input.

The artefacts brought much more discussion; what is the object? How do you use it? What religion does it relate to? These are all great opening questions to create discussion and enquiry in the classroom with the children.

These lessons have most definitely opened my mind to teaching RME. My memory of this subject at school was visiting the church on special occasions and simply re telling stories from the Bible about Jesus of Nazareth, which to be honest was very of putting and boring for me. However living in a Muslim country for a year opened my eyes to religion and made me realise how important it is to be culturally aware. I most definitely don’t know everything about all religions but this excites me as I can learn with the children and hopefully make lessons as exciting and enjoyable as possible.