The title of this post is a question I hear almost daily in my Maths classroom. I could retire a happy man if I was given a dollar for every time I have heard it "When am I ever going to use this?". The question bugs me a bit, because they don't ask the question anywhere near as much, if ever, in Science and I am sure it doesn't happen very often in other subjects either. There is something about Maths that makes people believe that everything they do, every lesson will be a mathematical concept that they can take out and immediately apply to their everyday life, this just doesn't happen and to be honest none of my answers in the past have necessarily hit the mark for the students.
Take for example solving quadratic equations. More than 95% of all students who walk through the door will only need to solve quadratic equations for the purposes of year 10 Mathematics they will never need to apply it to any job they have or any task they will need to complete as part of their lives, at least not solving quadratic equations in the manner they occur in class. Even if it is something they will need for their job, in most cases they will have a piece of software that will solve it for them. So how do you justify studying it to students who will only ever use this concept for 5 weeks of their lives or will have a computer do it for them?
My new thinking on how to tackle this question has two trains of thought. Firstly is to show them how they are already unconsciously using the Maths that we are studying. For example lets take the situation of a person kicking a football to a running player. This is an incredibly complicated situation as essentially you are kicking the ball into empty space with the hope that the person that the person will be there to catch it by the time it lands. As the person kicking the ball you have to pick a spot to kick to, you then need to judge how fast the person is running and use this to estimate how long it will take them to reach that spot. You then need to determine how hard to kick the ball and at what angle to make sure the time of flight of the ball is exactly the same as the amount of time for the running person to reach that spot from their current position
Complicated huh? it involves estimation, extrapolation, solving linear equations, solving quadratic equations, probably a bit of physics and trigonometry. The maths in this sort of problem would be too much for most high school maths classrooms, but yet our mind does it almost seamlessly through a mixture of experience and practice. Part of addressing this question of where will I ever use this is to show them how they are unconsciously already using this maths, the lesson then becomes about putting a formal mathematical construct to what their brain is doing automatically. Therefore the question then is answered by showing them how much maths actually permeates their lives, whether they like it or not, the universe the live in, is written in the language of mathematics.
The video below illustrates this point well. What I like most about it however is that it was made by high school students for a video contest called Math-O-Vision. Therefore it shows they maths that they see in day to day life.
I think the second part of addressing the idea of "when am I ever going to use this?" is in getting students to rethink the purpose of maths education, what it really should be about. For me mathematics is about learning to think in a logical way and it is also learning to think in a completely different way to most other subjects. Ideally a maths class presents you with a complex, messy, complicated problem and it requires you to look at what you have, what you need, and then to proceed with solution that follows a clear line of logic, it is not about the continual accumulation of a range of skills. In approaching maths in this kind of way, it is about trying things, making mistakes, learning from them and trying again, it is not about following the carefully structured approach that the teacher has given you. Therefore I think if students see mathematics is a way of looking at problems they may encounter in a completely different way, if they realise that mathematics is about teaching them how to think, then to some extent the question may also go away.
Senior Leader of Pedagogical Innovation and Mathematics Coordinator in Regional South Australia.
Opinions in this blog are my own and do not necessarily represent the views of my employer.