So what is meant by Counter Intuitive Mathematics?

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’.Image result for system 1 and 2 thinking

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

 

1 thought on “So what is meant by Counter Intuitive Mathematics?

  1. This was an interesting post and I liked you link to PUFM. It’s interesting that Sunk Cost and Loss Aversion can override basic mathematical thinking if we are not careful.

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