Imagine the following scenario. You have recently received a promotion at work. You feel upbeat and enthusiastic. However, with this promotion comes added responsibilities, and you quickly find yourself suddenly under a “time crunch”. Your boss is nervously pacing up and down at his work station, scratching his bald head, waiting for your document to appear on his desk. However, you only have a limited timeframe to complete this work. So you do what could loosely be described as research, pull out the relevant bits, highlight the key information – sure, it’s a bit rough around the edges – but it does the job. The boss is happy when you hand in the document on time, as there is a demand on him as well to relay the information in the report to his boss.
Taking shortcuts can be important in order to complete tasks quickly and efficiently. It is not only relevant in business but also education. For example, you might be able to solve a maths problem in an exam with two different methods, and it would obviously benefit you to take the shorter route of explanation. Students, just like people in the world of business, are under a “time crunch”. Children often have an abundance of homework, extra-curricular activities, family activities, and have to do all of this in a short space of time. They are forced to think quickly. The problem is that in education, when we are learning something for the first time, fast thinking generally won’t cut it since learning something properly requires a deeper understanding – which of course takes time. It requires slow thinking.
Here it is useful to draw upon Daniel Kahneman’s (2011) distinction in his International Bestseller, ‘Thinking, Fast and Slow’. Fast thinking is automatic and intuitive, our first reaction to something which takes little effort, e.g. interpreting somebody’s facial expression as anger (p. 19). In contrast, slow thinking is deliberate, orderly, and takes effort (p. 20). This can be measured physically. For example, imagine trying to solve a certain maths problem without a calculator. In attempting to do so, your blood pressure rises, pupils dilate, muscles tense up and heart rate increases etc. (p. 20). Working through a problem manually takes physical and mental effort, and this is akin to slow thinking.
Maths relies upon a good deal of slow thinking. Consider the secondary student learning algebra. It takes time for the student to digest the new mathematical language being introduced, and it is very important that the student takes the time to master the basics. In fact, if the student succeeds in grasping basic algebraic concepts then they should subsequently be able to work more quickly in later stages. Hence, by becoming good at slow thinking and establishing solid foundations, the student can ultimately become a faster thinker, with the help of a greater conceptual understanding. Moreover, if students do not take the time to gain a firm foothold, then they may develop what is commonly referred to as “maths anxiety” whereby maths equations can appear quite foreign, or even alien to the student.
Maths also relies on fast thinking, whereby students instantly recognize patterns, make calculations based on memory, or solve a problem mechanically on the calculator. This is important too, but we need to ensure that students do not become lazy and rely on fast thinking all the time. Sometimes amidst the chattering of the keyboard, or the punching of buttons on the calculator, we need to slow our thinking pace down. For instance, students should question whether they understand a certain graph that has been automatically sketched on the calculator. Otherwise, they may lack the deeper understanding that is necessary to help them solve the more challenging problems.
In short, to become really good at maths, you need to have the conceptual understanding – and this, I argue – stems from slow thinking. So it’s worthwhile taking a little extra time on your maths to gain a deeper understanding. It might be a harder slog at first, but will prove to be more rewarding for you in the long-term. Slow thinking ultimately leads to faster thinking later down the track.