Can Mathematics be Beautiful?

Maths, beautiful? Before I would have never of put these two words in the same sentence. Now I will say maths can be beautiful. After allowing myself to really understand how this can be and how maths can make things more pleasing to the eye I can put maths and beautiful together.

The Rule of Thirds

The rule of thirds is the first thing that introduced my thinking of mathematics being beautiful. The rule of thirds is where an image is broken down into thirds- both horizontally and vertically- so you end up with 9 parts on the image (Rowse, 2006). Like this:

We then place the thing of interest (whether that’s a person, animal, object or even just a specific part of scenery/image) on one of the third lines or on one of the four intersections of the third line which will give a more aesthetically pleasing result rather than if we just centralised the thing of interest (Roswie, 2006). Roswie (2006) furthers this by highlighting that in 1797 John Thomas Smith explained that by using the rule of thirds makes our eyes naturally drawn to these intersection points and thereby makes the image more pleasing to the eye. Therefore, by framing an image in this way, using this rule, works with our natural direction rather than against it (Rowse, 2006).

After my lecturer in Discovering Maths explained this rule of thirds I wanted to explore this further to see if in fact this well-known rule of photography was being applied in the wider world and to see if by using this rule of thirds actually works.

Here is an example of an image using the rule of thirds where the wasps eye has become the point of focus.

Wasps, more often than not, are seen as not the most beautiful creatures however from using the rule of thirds within this image I think the image itself can be looked at as beautiful. I am aware however that this rule of thirds is not the only thing that impacts upon this image and I understand that there are other factors that contribute such like lighting and timing (Amirshahi et al, 2014). However, it is interesting to think that this “old” rule has been impacting on us when looking at images unconsciously, as before this Discovering Maths input, I had never heard of this rule before.

Another thing that can allow me to use ‘maths’ and ‘beautiful’ in the same sentence is when looking at intervening with our faces. It is thought that the more symmetrical our face is the more ‘beautiful’ our face is (Bader, 2014). One of the reasons for this is because it has been suggested by the Evolutionary Advantage Theory that the more symmetrical the face is the better a person’s health is (Bader, 2014). Dr. Stephen Marquardt (undated), along with many other facial surgeons and mathematicians, furthers this through his findings where he too found that people do find more symmetrical faces more attractive/beautiful. The Perceptual Bias Theory (Bader, 2014) agrees with this as it states that our brains work in a way that allow us to process symmetrical images easier than asymmetrical ones, thereby indicating that maths unconsciously effects our day to day lives in as much detail as what we find beautiful/attractive to look at (Perrett, 2001).

These two ideas – the rule of thirds and facial symmetry- are only just two examples of how maths is beautiful.

This then got me thinking even more. If we can use the rule of thirds to make an image more pleasing to the eye and by making a face more symmetrical we can make it more beautiful, can we make the same outcomes within the classroom?

Have a look at the layout of this classroom:

You can argue that this particular classroom, shown in the image, has slight symmetry and the use of the rule of thirds. For what I have previously researched and found out about the rule of thirds making things more pleasing to the eye (Roswie, 2006) and the that symmetry makes things more beautiful/attractive (Bader, 2014), can this be the same for this classroom? Would this make a difference to the learning and teaching which is created? This is what I now ask myself. It could be argued that because the rule of thirds makes thing more pleasing to the eye, if we were to layout our classroom using this rule of thirds, it could in fact make the room have a more pleasing feel to it. Dr. Sheryl Reinisch (2017) furthers this by saying that if then the classroom has a more pleasing feel to it this can impact greatly on the teaching and learning that goes on in this classroom. This is due to helping the children feel safe, secure and valued. Just by the way we layout our classroom can have a real impact on creating a more pleasing environment allowing children to feel more motivated and engaged (Reinsch, 2017).

If I am completely honest, before learning and researching about this I would be very likely to layout my classroom the way it would look the prettiest to me and not really have a huge thought about it. However, now this has really made me think twice about this as it could have a real impact on the children’s learning before they even sit down.

Furthermore, this rule of thirds has also allowed me to begin to think on my wall displays in the future. Using this rule could make them much more pleasing to the eye and therefore more meaningful, as children would tend to refer to them more because they are pleasing on their eye. This would also allow for the discussion to take place on how, yes maths is used in everyday lives, but not just using the usual examples of counting money to buy sweets or working out bus timetables so you can get places. This would directly show the children that we use maths for almost everything, even when just take or displaying a simple photo.

References

Amirshahi,S et al. (2014) Evaluating the Rule of Thirds in Photographs and Paintings. Available at: http://booksandjournals.brillonline.com/docserver/journals/22134913/2/1-2/22134913_002_01-02_S11_text.pdf?expires=1540566335&id=id&accname=guest&checksum=3055FC5FFDC8C1AD326C6AB654328732 (Accessed: 6 November 2018).

Rowse, D. (2006) Rule of Thirds. Available at: https://digital-photography-school.com/rule-of-thirds/ (Accessed: 6 November 2018).

Bader, L. (2014) Facial Symmetry and Attractiveness. The Evolution of Human Sexuality. Available at:  https://sites.psu.edu/evolutionofhumansexuality/2014/03/24/facial-symmetry-and-attractiveness/ (Accessed: 6 November 2018)

Perrett, D. (1999) Symmetry and Human Facial Attractiveness.

Dr. Sheryl Reinisch (2017) https://education.cu-portland.edu/blog/classroom-resources/welcoming-classrooms-better-students/

Could the Curriculum for Excellence be a ‘Sunk Cost’?

Could the Curriculum for Excellence be a ‘Sunk Cost’’?

The aim of Curriculum for excellence and the reason it was put in place was to help children and young people, across Scotland, gain knowledge, skills and attributes needed for life as well as the skills needed for learning and work (Education Scotland, 2018). The Curriculum for Excellence has been the framework for Scottish education for the past 8 years, and was created by government officials over a long period of time to give teachers more flexibility over what and how they teach (BBC, 2017). Although the government would argue that the Curriculum for Excellence has a purpose to create successful learners, confident individuals, responsible citizens and effective contributors, formally known as the 4 capacities, and further framework to create the seven principles, to ensure children’s learning is specified to them, many people would argue that it has many flaws. One of the arguments that is made is that the Curriculum for Excellence could in fact be widening the attainment gap, not closing it, therefore it is failing (BBC, 2017).

What is a ‘sunk cost’?

A sunk cost is defined as something which has had a lot of time, money or effort put into it however if it starts to fail, those who have invested the time, money or effort, carry on with it as they don’t want it to appear wasteful (Arkes and Blumer, 1985).

Can this be what has happened with the Curriculum for Excellence?

For me what stands out the most from the arguments that have been highlighted about the flaws of Curriculum for Excellence is that it could in fact be widening the attainment gap and not closing it (BBC, 2017). Paterson (2018) makes this apparent when he highlights that Scotland use to be well ahead of the OECD (the programme for international student assessment) average however this has declined drastically. Paterson (2018) furthers this by summarising the results from the annual Scottish Survey of literacy and numeracy which show a fall in attainment in both of these curricular areas. This evidence then brings the realisation that the Curriculum for Excellence is not closing the attainment gap in this sense as attainment as a whole is falling from where it was before Curriculum for Excellence was introduced. Paterson (2018) then goes on to explain that on comparing the Curriculum for Excellence to other international educational structures, CfE can be seen to ‘neglect’ knowledge and focus more on skill. Hirsch (2016) furthers this and explains just how much knowledge matters. He does not dismiss the fact that skills do matter however shows the best way to gain skills is through gaining knowledge. Paterson (2018) goes on to highlight that schools provide the opportunity for children to gain knowledge who would not get it from home. Therefore, if schools stopped teaching structured knowledge, the inequality of knowledge will widen because the children of the well-educated and the wealthy will receive this structured knowledge in other ways. This then makes me indicates to me that curriculum for excellence can do better within this aspect and therefore makes me consider that is could in fact only be the start of its sunken cost.

On the other hand of this argument is that the Curriculum for Excellence is so deeply embedded, that removing it and creating something new would cause enormous upheaval. There would never be an easy way to change it and would mean that a whole generation would have been disadvantaged even more so within their education (Paterson, 2018). Therefore, meaning that the children of Scotland would be at an even bigger disadvantage within education if we were to move away from the Curriculum for Excellence compared to if we just stick to it and try and work on it.

Furthermore, looking at an opposing argument, the Scottish Government (2017) published information suggesting that those children because of Curriculum for Excellence are achieving within areas of reading, writing and numeracy. This then provides evidence that in fact the Curriculum for Excellence is providing the children of Scotland with a fairly good education however, it is the question of could it be better?

Overall, from my research I would say that arguably the Curriculum for Excellence is a sunk cost as it could be better. However, when looking at changing the whole education framework this is a very unrealistic approach as it would disrupt too much learn for very long period of time. The time, effort and money that would be spent creating a new framework, re-educating teachers would be significant. Having spent so much time, effort and money on the Curriculum for Excellence I feel we are in too deep now to change it. No child’s education should reduce due to a failing curriculum; therefore, I feel the best approach to this issue is that the Curriculum for Excellence is used as a very basic framework and we now begin to develop and work on the sections of it that are just not quite working.

References

BBC (2010) New curriculum could be ‘disastrous’, says education expert. Available at:  https://www.bbc.co.uk/news/uk-scotland-scotland-politics-41134835 (Accessed: 1 November 2018)

Education Scotland (2018) What is Curriculum for Excellence. Available at:  https://education.gov.scot/scottish-education-system/policy-for-scottish-education/policy-drivers/cfe-(building-from-the-statement-appendix-incl-btc1-5)/What%20is%20Curriculum%20for%20Excellence? (Accessed: 1 November 2018).

Arkes and Blumer (1985) The Psychology of sunk cost. Available at:https://www.sciencedirect.com/science/article/pii/0749597885900494 (Accessed: 2 November 2018).

Paterson, L. (2018) Scotland’s Curriculum for Excellence: the betrayal of a whole generation.

Hirsch, D.E. (2016) Why Knowledge Matters. Available at: https://eric.ed.gov/?id=ED568821 (Accessed: 2 November 2018).

Scottish Government (2017) Achievement of Curriculum for Excellence Levels 2016/2017. Available at: https://www.gov.scot/publications/achievement-curriculum-excellence-cfe-levels-2016-17/  (Accessed: 2 November 2018).