Why do losses attract more attention that gains? Why do our brains stick with the original answer in a multiple-choice test? These are questions that were picking through my brain when we spoke about Counter Intuitive Maths. Such as the two ways our brains function answers such as System 1 and 2 which I will discuss further through my blog post.

Loss Aversion

As we look into the multiple perspectives explained by Liping Ma (2010) which shows the idea that people have different ideas and approaches to similar outcomes. It shows both the advantages and disadvantages to various concepts. This can be related to Loss Aversion and the idea that most people do not like to lose anything that they own as it conveys negative emotions and fear. It can be seen that there are multiple perspectives in the idea of loses attract more positivity than constant gains. For example, we are far more upset about losing a £20 note rather than gaining one. This is because our idea of loss produces a stronger emotion and we gain the feeling that we do not want to give something up (Heshmat, S. 2018).

This video explains the concept of Loss Aversion in a simple form which makes us realise that a loss can be more painful than a gain. A similar example we can expand on could be Netflix giving you 4 free months trial which you are happy about but then eventually they cancel, and give an upsetting thought of having to give it up and lose out on something you like to have.

Both our brains running

When we look into the question of “Why our brains stick with the first answer in a multiple-choice test”, this is through the terminology of System 1 and 2. These systems are processes which are carried out in our brain where one system is automatic, and the other is thought processed. System 1 occurs with our automatic responses once we see a question and put down our initial thought. System 1 proposes the idea without us going into further depth of the concept of the question (Kahneman, 2011). This can be linked to our memory bias as this system suggests we can recall studying this kind of question before and the content of the answer is remembered. It can show a context effect as the person/pupil sitting the test have memory of being in this same situation and recalls the same information that has been learned before (Cohen, 2012).

System 2 involves thought processing and decision making to occur in our brains. This system allows us to take time to think over the question and the outcome of the answer, for example whether it would be beneficial or not to change the original answer in a multiple-choice test or not. Quite often in these situations our brains look at a question initially but after further reflection it shows the main point of attention (Kruger et all, 2005).

An example such as “Emily’s father has three daughters. The first two are named April and May. What is the third daughter’s name?”. Have a think about it! When we look at this question our intuitive answer (system 1) is going to be ‘June’. This is often people’s initial thought when they read the question as they are trying to follow the pattern of the question and have fallen into the trap. Where-as the considered question (System 2) is actually ‘Emily’. The third daughter can only have this name as it states in the question that ‘Emily’s father has three daughters’.

Overall, I have thoroughly enjoyed looking at this topic in our module as it gives a deepened insight as to how our brains process questions in different ways. There are many debates about whether it is more efficient to stick with your original answer or change it in a multiple-choice test. In my opinion I have never thought about this discussion before but reflecting on experience I would always stick with my original answer although my views have changed after research. Kruger et all (2005) states that research has shown that those who change their answers have shown an increase in test results and regardless of your system 1 answer which was shown in the example your first instinct is not always correct.

My perspective about counter intuitive maths relates to Ma (2010) and her explanation of fundamental maths and how we view equations through the 4 properties which all relate to the way of counterfactual thinking. Such as connectednesswhich provides a link between the 2 systems and through deep understanding of the question we are able to represent the correct answer in the end. Multiple perspectiveswhich was discussed through the discussion of loss aversion and how many people have different approaches to situations such as some would rather gain a £10 note rather than losing it. Through the idea of considered questions relates to Basic Ideasand how we are guided towards the depth of the real mathematics behind the question and are aware of the simple strategies needed to convey the final answer. Lastly Longitudinal Coherencecan relate to the knowledge of those who may sit these multiple-choice tests and use all their knowledge gained and take opportunities to use their mathematical progress to put down the correct answer.

Cohen, H. (2012) What is memory bias? Available at:http://www.aboutintelligence.co.uk/memory-biases.html(Accessed 25 October 2018).

Heshman, S. (2018). Psychology today. Available at: https://www.psychologytoday.com/gb/experts/shahram-heshmat-phd(Accessed 25 October).

Kahneman, D. (2011) Thinking Fast & Slow. New York :Farrar, Straus and Giroux.

Kruger, J., Wirtz, D., & Miller, D. T. (2005). Counterfactual Thinking and the First Instinct Fallacy. Journal of Personality and Social Psychology. Available at: http://dx.doi.org.libezproxy.dundee.ac.uk/10.1037/0022-3514.88.5.725(Accessed 25 October 2018).

Ma, L. (2010) Knowing and Teaching Elementary Mathematics – Teachers’ Understanding of Fundamental Mathematics in China and The United States.London: Routledge

When I first read the title of the first presentation I thought “No way? How can mathematics be creative?”.  This is when I began to realise that I did not “hate” maths in the way I thought I did because it is actually an extremely powerful subject which is used in everyday life which we do not realise.

Tessellation

As learned in our previous lecture, Tessellation is the repetition of shapes that fit together without any overlaps or gaps and for the shape of tessellate it must be able to exactly surround a point or a shape. It can be made through the use of 2D shapes although there are different types of tessellation which include regular and semi regular. The video below shows examples of how tessellation can be used to create patterns and how different 2D shapes can be used to show this.

Islamic Art

The key concepts of Islamic Art include texture, colour, pattern and calligraphy. It is often very easy to pick out a piece of Islamic art and is outstanding for someone to look at. This kind of art does not necessarily follow a religion but includes traditions of art used by the Muslim culture. Islamic Art provides meaning in its repetition and variation and shows the relationship between maths and art. The art avoids human and animal forms and instead uses different mathematic tools such as reflective symmetry and how many lines there are (BBC,2014).

Geometric Multiplication Circles 

These are made through geometry which is the heart of Islamic Art. These circles can be formed by using times tables to create patterns such a stars which I have attached below. The procedure works for example by using the 6 times table. 6 x 2 is 12 which simples down by completing 1 + 2 which leads to the final answer being 3. Similarly by working out 6 x 6 is 36 and therefore 3 + 6 equals 9 which is the answer. This allows children in classrooms to use creativity and enjoyment in their times table work and helps them develop transferable skills to work out the final answers. These digital root patterns which we can describe them as allow children the opportunity to learn new maths techniques without realising they are doing them (Warner, N/A).

Ma’s (2010) idea of connectedness shows that tessellation and creativity in art shows how individual aspects of maths can be linked together which can allow children to understand the concept of maths in a more efficient way. Also the idea of basic ideas, allows the idea of joining different aspects in maths together to structure a simple strategy for example multiplication, and how these quirky creative styles can be remembered by children.

Examples 

5×1=5

5×2=10=1

5×3=15=6

5×4=20=2

5×5=25=7

and so on…

6×5=30= 3

6×6=36=9

6×7=42=6

6×8=48=12=3

6×9=54=9

6×10=60=6

References

Ma, L. (2010) Knowing and Teaching Elementary Mathematics (Anniversary Ed.) New York: Routledge.

Warner, M. (n/a) Digital Root Patterns. Available at: https://www.teachingideas.co.uk/number-patterns/digital-root-patterns/  (Accessed 1 October 2018).

BBC (2014) Islamic Art. Available at: http://www.bbc.co.uk/religion/religions/islam/art/art_1.shtml (Accessed 1 October 2018).