Stop stressing about “how” and focus on “why”
It’s probably one of the biggest problems that Maths students across the world have. Yes, I said across the world.
It’s the reason that many students can answer any equation based question but struggle endlessly with the worded ones.
This situation is unbelievably common. In fact, when I meet new students, only 1 in 10 say they feel confident with worded problems as much as the other types. That means that 90% of Maths students feel like worded problems are out of their reach.
But my approach to fixing this is surprisingly simple; instead of teaching students how to use the concepts they’ve learnt, I focus on helping them understand why.
The difficulty of worded questions (and any problem-solving question, really) is not the Maths itself. The processes and methods are usually fine. But worded questions don’t ask a student to perform a specific set of operations – they only ask for a result. It’s up to the student to know what is required to achieve that result. Much like any real world career, students must learn to understand how to connect the result they want with the processes they learn.
“Why” separates the amateurs from the professionals.
I’m not a carpenter. But I can effectively to all the jobs a carpenter can do. I can measure precisely, cut proficiently, and operate any number of power tools.
So, what is the difference?
The difference is that I do not understand why I would do those things. I am not capable of deciding on how large a frame I would need for a job. I do not know why I would use a certain type of screw. I don’t even know why I would use a certain type of timber, even though I do know which timber to use.
I know how to use the tools, but I do not know why.
Maths provides a similar challenge. If a student struggles with worded problems or application tasks, it is because they know how to use their Maths tools, but not why.
Solution: Learn why
When a student goes through a new topic, they very often simply learn the methods in order to get through the next question or the next test and be done. There is little understanding of why. But if parents, teachers and tutors can foster a curiosity that makes them ask why, then the game changes.
It is the why that gives meaning to the formulae. But more importantly, it is definitely the why that builds an actual love for Maths. Even for die-hard Maths nerds, the passion doesn’t usually come directly from applying a theorem – it’s from understanding why the theorem works.
If we can move away from the mentality of only teaching students how to do things, and instead work on combining that knowledge with understanding of why we do things, I am certain that there will be thousands more passionate maths minds in the world.