From the Editor’s Desk
16th October 2023
“Critical thinking” is a term that is thrown around a great deal in the field of education, but often, people do not stop to question what this term means exactly. When faced with a new set of information, the act of critical thinking involves not blindly accepting a piece of information, but rather questioning its base assumptions, examining whether the new information coheres with existing literature, and evaluating its implications and consequences.
Mathematics as a discipline can be shown to improve critical thinking as it tests assumptions, proves statements, and can be used as a tool to give a statement empirical evidence to back it up. Mathematics should be viewed as a tool to provide answers to questions arising from critically thinking about something – critical thinking does not often involve intense mental gymnastics, but rather questioning assumptions and asking “How do I know what I know?”
1. Testing assumptions using statistics
Firstly, there are many assumptions that are made, as humans are creatures who like to generalise and put everything they observe in neat categories or boxes to make the chaos of life easier to comprehend. For example, if we experience a particular phenomena many times (such as encountering many red cars on the road), we may believe that there are many more red cars on the street than they actually are. Furthermore, if we have never seen something (like perhaps a rainbow holographic car), we may believe that it does not exist – this is called the Black Swan effect. As such, to improve our critical thinking, we should always found our perceptions based on statistics to provide ourselves with a more educated assumption.
2. Extrapolating using Mathematics
Extrapolation is a natural aspect of human life – people want to know how much they have in future. For example, if a farmer buys a new machine, he wants to know how much he could produce with that new technology as opposed to on his own, even though he does not have the machine yet. This is called extrapolation, which is refined using Mathematics. Extrapolation is an important part of critical thinking, as it is important to consider how (if any) the past influences the future to better prepare for it.
However, extrapolation is not a wild guessing game, but it needs to be based on existing data. If we want to predict the population of a country in future, it stands to reason that with the current medical technology and food security, the population of a country will likely go up. How much will it go up by? We then need to look at existing population data to observe how much it has increased in previous years to get a rough estimate of how much it will increase this year.
3. Tethering abstract concepts using Mathematics
Economics is the social science which studies how to use limited resources and allocate them amongst competing people. There are many theories in Economics which govern the allocation of resources, and these theories remain in the abstract until Mathematics is involved. The field of Econometrics involves quantifying these theories so their effects in practice can be better examined. Abstract theories about what happens in the economy hold no water until they can be shown in numerical terms, which shows the weight of Mathematics in tethering these ideas.
The aforementioned techniques are just some ways of improving critical thinking with Mathematics. However, less focus should be placed on the quantitative aspects of improving critical thinking, but the emphasis is instead on asking the right questions. By asking the right questions, such as how the piece of information is derived and how information is portrayed, the quantitative tools can be bent and melded to answer these questions, which is the foundation of how to think critically.