Category Archives: 3.2 Classroom Organisation & Management

Can Mathematics be Beautiful?

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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/

https://www.google.co.uk/search?q=classroom+layout&tbm=isch&source=iu&ictx=1&fir=WPv9o2SVAH3AsM%253A%252CbTLiokDsO1T1KM%252C_&usg=AI4_-kRDyvtGzbDweqgy0q8h9lsLZI_84w&sa=X&ved=2ahUKEwidt6-Oz8LeAhVBKewKHcCsB8IQ9QEwBHoECAYQDA#imgrc=WPv9o2SVAH3AsM:

Resource Allocation Workshop

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Recently we took part in a resource allocation workshop. Here we were split into 5 groups, each receiving an envelop with resources inside. I was in group 1, which we were first to receive our envelop. Straight away we realised that we had the fullest envelop but didn’t really think much of it. We were then asked to make something which would be useful for a first year student at university, using only the resources we were provided.

My group loved this task as we were giving coloured pens, pencils, coloured card/paper, sticky notes, sellotape, blue tack, more envelops, paper clips etc. We started of by going around the group, each giving our ideas of what we could make. We decided on a pin board which had a timetable on it, a reminder section, a map and an events section. Firstly our tutor got each group to stand up and just explain their ideas. Our tutor seemed very pleased with our idea compared to the rest of the groups, however again, we didn’t really think much of it and just thought it was down to our team work.

We then had to make our idea. Again our team worked really well together and found it easy as we had more than enough resources to make it. Throughout the process of making our idea our tutor kept coming to our table and giving us a lot of praise but again we just put this down to good teamwork and inclusion of everyone in the group. We didn’t really pay attention to what the other teams were making and what resources they had as we just concentrated on getting our idea made. (looking back now we should of noticed that not everyone had enough resources and maybe could of shared the resources we weren’t using or needing out.)

When it came to presenting our ideas, this is when we began to notice that our group was the only ones that had been giving coloured pens and paper and genuinely much more resources to make our ideas. Our tutor gave us so much praise and attention and it made us feel, as a group, that we had done a great job at the task and had really worked well together.As the other groups began to present their ideas we began to realise that the tutor was being really horrible and snidey towards them and not giving them very much attention and no praise at all. This is when as a group we clicked and realised that this was all a fixed task and it wasn’t at all about what we had designed it was about the principle of how sometimes people/children who have everything and need the least amount of help receive all the tutor/teachers attention when really it should be the people/children without.

This task made me really think about how to begin with my group didn’t even really notice that the people around us didn’t have as much as us and weren’t getting the same amount of attention as us. Therefore not realising that this was making the other groups feel as though their ideas weren’t good enough or that they couldn’t do what they were asked to because they didn’t have the resources or the extra support.

This then made me think about this in a classroom setting, in that not every child is going to have all the resources they need, from physical resources like pens and pencils to mental resources like support and encouragement from parents and family. This task has really pointed out to me that it is absolutely vital that I as a teacher make sure that no child, no matter how much or little they have got, is left behind and left feeling like they arent good enough. This may mean that those children with much less will need more support and more attention than those children that have much more, however this is crucial as no child should feel like they arent good enough, especially not at school.