For many, it's the maths equivalent of the chicken or the egg conundrum: Which should come first - teaching students how to do something or explaining why it works that way?
To help untangle this mathematical mystery, let's decipher what it means to understand the ‘how’ and the ‘why’ and the benefits of both.
In maths, we often learn how to follow a pattern and do written computations. This can be extremely useful, and its value shouldn't be underestimated.
In fact, sometimes it helps to learn the how first, and if needed, the understanding comes when putting the knowledge into practice days, weeks, months, or even years later. I saw this happening a lot with online class teaching during lockdown where the student could practice and internalise a process as they didn't have ready access to discussions or the option of getting their questions answered.
This is why many believe that learning the how is a gateway to understanding the why as having an understanding of the process or concept makes it easier to gain an understanding of why it works.
There are also times (such as written ways of + - x and / for whole numbers and fractions, angles, and sums) where there's no need to ever understand how something works. We simply need to know what they do.
There are also occasions where understanding why something works is essential. For example, it's only when we truly understand why a procedure works that we can better:
- adapt it
- vary it
- apply it
- extend it
- recall it
Another advantage of understanding why a procedure works is that we can differentiate it from other similar procedures. As a result, we can avoid using the wrong one at the wrong times (very common in percentages, volume, area, sequences, histograms, and cumulative frequency).
At other times, understanding why is a prerequisite to success in the topic, whether it's solving equations, sequences, word problems, iteration, or histograms. Too little why can result in confusion as to which rule to use when.
A happy medium
As with learning styles, the final answer to the how/why conundrum comes down to the individual learner and the individual topic.
I know from experience that too much how too soon can be confusing to students and too much why too soon can muddy the waters and cloud the issue.
That’s why for many people (and subjects) the best approach is a mixture of the two. It can be helpful to start out with the goal of communicating the basic reasons of why, adapting and extending according to the needs of the student as the topic progresses, so that ultimately the student fulfils their potential.