Category Archives: 2 Prof. Knowledge & Understanding

What Would Life be Like if we Lived in System 2?

Despite the fact I was aware that my brain is a house full of many rooms that do many different things, I was unaware that unconsciously my brain was making choices for me from either my system 1 or system 2.

David Kahneman (2001) discusses the concept of system 1 and 2 and the fact that we are living the majority of our lives and decisions within system 1. System 1 works automatically and very quickly. We don’t have voluntary control over when we use system 1 (Kahneman, 2001). Whereas system 2 provides analytical and slower processed thinking, more in depth into our real abilities and knowledge (Ranadive, 2017).

Here is an image which I feel displays key words and situations that the two systems work individually but also how they can also relate.

System 2 is activated in situations where System 1 does not have the answer (Kaheman, 2012). A scenario that we looked at in recent lecture in Discovering Maths, the question left me stuck in system 1 for a lot longer than what I would like to admit. it is as follows;

A cup and Teapot set costs £110. The teapot costs £100 more than the cup. How much does the cup cost?

Our first instinct and therefore the answer from our system 1 brain is £10, but this is wrong!

When we use our system 2 brain, we can make sense of the problem we can understand (long-story-short) that the correct answer is £5. (reference lecture notes) I find this concept interesting to look at when considering life decisions. Kruger and Wirtz (2005) discuss the concept that in exams or tests, our first answer comes from system1 – the instinct answer. however, if we then hum and hay about weather to stick with our first or analyse the question more and change it, we are in fact, increasing our chances of getting the answer wrong! Yep- that’s right, even if we think over this answer and dig deep into our brains, when we change the answer we shoot ourselves in the foot. I have been in situations myself when taking exams at school or even when completing the Education numeracy and literacy tests. When I am in doubt about my answer, I have sat before and dictated if I should in fact trust my gut or take a risk and change my answer. Kaplan (1999) says that we should exercise with great caution if we decide to change our answer. I wonder now, how many times my indecisiveness has cost me a mark or two in exams, or even a whole grade!

This concept made me think about how our lives could be lived or the impact it could have on day to day decisions, if we lived at all times in system 1 or all times in system 2. Experiments have been done that show if we are asked to retain a sequence of 7 numbers, told that this is the most important thing to remember (keeping occupied system 2). Then if we are asked questions such as what pudding we would prefer between the healthy fruit salad of calorie filled chocolate cake, we pick the cake. Our system 1 means that we make decisions that are impulse, less thought through and often more selfish (no name, 2012). Alcohol has the same impact also. So therefore, we may live a unhealthier life.

System 1 brains may result in us all making decisions that are not rational, not considerate of other people. How far would our system 1 brain allow us to take it? System 2 would mean that every single decision we make would be thought through, weight up and rationalised of every aspect. How long would bar ques be if we had to consider every single drink there?

Kaplan (1999) p.37 cited in Counterfactual Thinking and the First Instinct Fallacy. Available at: http://psych.colorado.edu/~vanboven/teaching/p7536_heurbias/p7536_readings/kuger_1stinstinct.pdf (accessed on 4.11.18)

J, Kruger and D, Wirtz (2005) Counterfactual Thinking and the First Instinct Fallacy. Available at: http://psych.colorado.edu/~vanboven/teaching/p7536_heurbias/p7536_readings/kuger_1stinstinct.pdf (accessed on 4.11.18)

J, Smith (2017) What is ‘System1’ thinking – and why do you need to learn it? Available at: https://observer.com/2017/09/what-is-system-1-thinking-and-how-do-you-do-it/ (accessed o n 4.11.18)

A, Ranadive (2017) What I Learned From ‘Thinking Fast and Thinking Slow’ Available at: https://medium.com/leadership-motivation-and-impact/what-i-learned-from-thinking-fast-and-slow-a4a47cf8b5d5 (accessed on 5.11.18)

D, Kanheman (2012) How Thinking Fast and Slow Thinking SHape Perception and Choice. Available at: https://www.scientificamerican.com/article/kahneman-excerpt-thinking-fast-and-slow/ (accessed on 5.11.18)

D, Kahneman (2012) Available at: http://codolc.com/books/Thinking,_Fast_and_Slow.pdf (accessed on 8.11.18)

How Does Maths Affect Beautiful Things?

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I would use many words to describe maths, however beautiful would not have been one of them, until very recently. Once I allowed myself to understand how maths can make one thing more pleasing to the eye, I was opened up to a world of beautifully mathematic possibilities.

‘The Rule of Thirds’ (ROT) is the first concept that blew my mind. What it is, is the idea that when we divide a photo, art or scene into 9 equal parts, horizontally and vertically, then we place the thing of interest (weather this is a person or a animal or even just the part of the photo/art that is the focus) at one of these cross points the photo then we create a more pleasing and balanced photograph than if we were to frame it otherwise such as centrally. (Roswie,2006) The theory first talked about by John Thomas Smith says about how naturally, our eyes are drawn towards these intersection points, so framing an image in that way is working with our natural direction rather than working against it. When Googling ‘beautiful pictures’ I found that again this was followed and I was so unware.

I wanted to explore if in fact this well known and older ‘rule’ of photography was being applied, and if so having an impact on interaction on a popular social media site ‘Instagram’. I had found a popular photographer called Chris Burkard, he captures amazing pictures in nature.

On pictures where he seems to have followed the ROT more obviously than others, his likes were increased. However, I am aware that this may not be down to the ROT alone, because of factors such as timing of the post or peoples interests being drawn to what he is photographing. It is interesting to see that the ROT may still be impacting us unconsciously on platforms of social media.

A twist to this concept has taken a hold where businesses are trying to reach the same goal by looking more appealing to customers by being/looking more interesting. Breaking down their social media platforms into threes (J. Grace, 2013). The businesses aim to divide the content up to allow them to deliver both necessary information but also with things that will draw in their customers such as advertisements.

However, despite the emphasis and importance highlighted on this golden rule, there has been research done in evaluating the real impact of this rule. Amirshahi et al. (2014) undertook research into how the ROT impacted peoples rating on art. They used a computer-based approach to get their findings. Amirshahi et al. found that despite the importance in the composition of art the ROT played only a slight impact on the scoring of both aesthetically pleasing aspects of the art but also overall ratings.

Another beauty concept that maths intervein with is our faces. There is an idea that a more symmetrical face results in a typically more physically ‘beautiful’ face. It has been proposed by the Evolutionary Advantage Theory that a more symmetrical face represents good health in a person (Bader, 2014). Elder (2001) an orthodontist supported this idea stating that symmetry in a face represents ‘freedom from disease’. Since many diseases may leave scars or marks on someones body or face. This could be the case, however, when we consider how much maths is unconsciously effecting our day to day decisions and perceptions of things I believe that there is maths possibly ‘wired’ lets say within us that means our brains think and see like like this. The theory of Perceptual Bias agrees with this idea. This theory states that our brains do work in a way that allow us to process symmetrical images easier than asymmetrical ones (Bader, 2014).

When looking at computer modified images, I personally found that the original images were in fact more ‘beautiful’ and there was something odd looking about the trialed faces. This may just be due to the inaccuracy or the fact that I have seen these faces before however take a look for yourself;

Despite my opinion however there has been many facial surgeons and mathematicians that have looked into this concept. Dr. Stephen Marquardt (undated) found throughout his studies that ranged from older members of society right to modern day agree with this theory. The faces that do follow typically more symmetrical frames are rated better in attractiveness. Marquardt has linked his research to the rule of Pi (or the golden ratio). He has created beauty masks which he shows examples of how this rule is applied to faces of beauty across ethnic variations, historical figures but also modern well known faces.

Before we have seen the rule of Pi applied to beautiful things within nature, drawings and now faces.

These ideas are two examples of how maths in fact can and is affecting beautiful things within out world. The idea of maths relating to reconstructing and allowing us to rethink what we see as beautiful fascinates me. The rule of thirds has already impacted how I look at posting even my own pictures ‘does the see divide the picture into a third?’ ‘should I capture my friend at a different angle to see if it does impact the interaction with my social media?’ Finally I am starting to see that I am not just using maths to count my coffee money or figure out the bus times!

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

Grace, J. (2013) The Rule of Thirds for your social media strategy. Available at: http://jenntgrace.com/rule-of-thirds/ (Accessed on 29.10.18)

https://www.google.co.uk/search?q=beautiful+pictures&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjRqZKSrqzeAhWsIMAKHYi2AiYQ_AUIDigB&biw=1366&bih=651

Edler, R. J. (2001). “Background Considerations to Facial Aesthetics”. Journal of Orthodontics 28 (2): 159 Zaidel, D.

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 1.11.18)

No name (2012) ‘Is beauty really in the proportions?’ Everyday Evolution. Available at: http://evolutioneveryday.blogspot.com/2012/01/is-beauty-really-in-proportions.html (Accessed on 5.11.19)

Me and My Maths Anxiety

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Throughout my journey to being where I am right now, training to be a primary school teacher, I have had to persevere and overcome some hurdles on the way. The biggest and baddest of them all is MATHS. I tried to ignore it and avoid it but when the choice came up for me to ‘Discover Maths’ as a module in 2nd year I thought, I need to face this head on before maths takes over me.

Turns out however, I am not alone. The Organisation for Economic and cooperation and Development (OECD) raised awareness for close attention on math anxiety after recognizing that around 30% of Scottish learners reported that they feel very tense and nervous when doing maths work and more than 50% worry that maths will be difficult. (Scottish government, 2016). The whole way through school I knew how uncomfortable I felt about maths, so why was it never recognized as a problem. Recognizing the ‘problem’ as such may have allowed me to look at it from a different point of view. I may have been able to establish that maybe I am not just rubbish at maths.Mark H. Ashcraft talks about how he witnessed upset when It came to asking simple as 15 – 8. He linked this problem to the simplicity of spelling ‘cat’. (2002) This is where I found a clear link with my problem. despite me not having great confidence within spelling, it has never stopped me or discouraged me to try my hardest within literacy based subjects such as English or History. So why has this maths fear hit be so hard? Why is it that I don’t tackle the parts of the maths problem I can do and work it from there?

The University of Dundee have made efforts to research ways into targeting maths anxiety. An Online Maths Assessment has been introduced to allow Education students to take an opportunity to improve their levels and confidence within Maths (Henderson, 2010). Teaching us students about the issue and providing us with resources is taking steps to reduce the fear that is taking over.

The Scottish Government have also put out recommendations of what parents/careers, teachers, practitioners and pupils can do to improve maths standards. – improving maths skills for employment. I feel we fail to recognize the importance that maths can play within future opportunities, the job possibilities that maths can open us up to. When you google ‘maths and jobs’ it comes up with 3 recommended jobs, 2 of which are math teachers. what kind of idea does that present to children? That we only learn maths to teach it?

There are many questions I feel I still have surrounding maths and anxiety but what I hope this module allows me to do is investigate and gain more knowledge about how I can save my future pupils from the fear that overtook my experience.

Scottish Government. (2016) Transforming Scotland into a maths Positive Nation. Available at: https://www.gov.scot/Publications/2016/09/3014/4 (accessed on 5.10.18)

Ashcraft, M. (2002) Math Anxiety: Personal, Educational, and Cognitive Consequences. Availabe at: http://www.mccc.edu/~jenningh/Courses/documents/math_anxiety.pdf (accessed on 5.10.18)

Henderson, S. (2010). Mathematics Education: The Intertwining of Affect and Cognition. Unpublished doctoral thesis. D.Ed. University of Dundee.