According to Kahneman (2011), our thought process is determined by two different systems – impulsive/automatic and thoughtful/deliberate – also considered as system 1 and system 2. He makes apparent that for the majority of the time we should be using our system 2, however, this is not what happens. In fact, the reason we don’t use system 2 all of the time is because it is more exhausting, therefore, we resort to using system 1 (Kahneman, 2011).
To show how these systems work my lecturer used a very easy but clear example. He put this on the board:
We’ve used our system 1 process and immediately thought the answer is £10 – which is wrong. The answer in fact is £5- HOW?? Due to our system 1 thinking it automatically creates the calculation of £110 – £100 = £10, however, if and when we use our system 2 thinking –our thoughtful and deliberate thinking – we can see where we are going wrong. If we used system 2 thinking from the beginning, this is how we would work out the answer:
This isn’t “hard and complex” maths which makes us get the wrong answer. This has then made me wonder is it in fact Kahneman’s (2011) system 1 and system 2 approach to the way we think which affects the answer we first give?
The ideas that Kahneman’s (2011) Thinking Fast & Thinking Slow give, really make up the whole spectrum of human thought, action and behaviour.
After getting my head around the “Thinking Fast & Thinking Slow” approach (Kahneman, 2011), it led me to further thinking on how, the way we think and process what we read, can affect the answers we give and its not nesessaraly because we do not know the answer. This got me thinking about exams within maths, in particular, and how the reason we give the answer may not be due to if the maths is ‘easy’ or ‘hard’. It could be caused by using only our system 1 (Kahneman, 2011) thinking.
Furthermore, still thinking about exams, this time multiple choice, our counter-intuitive thinking becomes apparent. This is when you put an answer but then go back and think it might be a different answer. Do you stick with the first answer you put or do you change to the other answer you think it might be?
Brownstein et al (2000) make apparent that those who go ahead and change their answer actually change it to the wrong answer. However, Kruger et al (2005) creates an alternative argument to Brownstein et al (2000) and highlights that over 70 years of research which has been focused on changing answers and this belief that if you change your answer your more likely to change to the wrong answer, that this is not the case. In fact, Kruger et al (2005) make clear that people who have this counter-intuitive thinking, and who then go on to change their answer, majority of which end up changing their answer from the wrong one to the right one. This then improves their overall result/mark.
So why is this the case? Well my lecturer presented a problem to prove how this can mathematically work. He asked us this:
Straight away, using our system 1 approach (Kahneman, 2011), we think the answer is 50/50. He then showed us the mathematical proof that there is more chance of winning the car if you switch doors.
After my lecturer explain why this works, making me use my system 2 approach, it got me thinking even more about Kahneman’s (2011) Thinking Fast and Thinking Slow approach in that is our counter-intuitive thinking really just questions tricking our system 1 thinking so we then use our system 2 thinking. This meaning that when it comes to changing your answer, really we should change it because as Kruger et al (2005) state, there is more a chance of us changing it to the correct answer and there is more of a chance this is us then using our system 2 thinking which Kahneman (2011) would argue is the system we should be using all of the time. Finally, this has highlighted to me that throughout teaching mathematics we should really consider this Thinking Fast & Thinking Slow (Kahneman, 2011) approach as this could be a major factor which affects a child’s answer being wrong and not actually how difficult the mathematics is.