Learning mathematics is the same as learning rugby.
Have a think back to what a mathematics class was like when you were last at school. Were they streamed and had an A class, a B class, and so on? Did the teacher show you a mathematics problem on the board, you copied it down and then answered questions from the textbook into your workbook? Then you were probably tested on that topic later on and given a grade based on how many you got correct? And it was this grade that labelled you as being ‘good’ at mathematics or not. That was probably a familiar experience for most people doing mathematics at school and is still the case in Australia today.
I think what the worst thing for myself in that process was telling my parents what I got on the test. In my mind anything less than an A was a failure because I got a lot of questions wrong (I was a ‘C’ student throughout most of my years at school). The usual response I got from them usually consisted of “just try harder next time”. When I think about that response now it is a rather odd thing to say. This is because I did try hard in class, I did exactly what the teacher had told me to do, but I had still gotten some of the questions wrong. I would also agree that this is the case with most students, they do try hard in class and it is not their effort that is at fault.
If “just try harder next time” is not the correct thing to say, then what is? Let’s change the context slightly. Imagine that instead of learning some Pythagoras and completing some problems in a test, it was playing rugby and passing the ball to the open person on the wing and they could run the ball down the field to score a try. Let’s say that pass went too high, they had to jump to catch it, and this meant that the other team had time to catch up to tackle them, preventing the try. “Just try harder next time” still doesn’t apply here because I’m sure that player was trying hard to pass that ball to the winger. In most instances the player and the coach would analyse what happened in that scenario to determine why the pass went high. Could be timing of when the ball was released, could be direction of the hands were pointing during the pass, or it could have been how they were holding the ball.
In this case the player and the coach are looking at the skill of throwing and how to improve it. If we go back to the mathematics class, I remember I never applied this mindset to my lessons or my tests. I never looked at my ability to do mathematics as a skill and identify exactly what I needed to do. If it was Pythagoras I was working on (a2 + b2 = c2), were my mistakes coming from squaring numbers or finding the square root, was I able to successfully transpose the equation, or correctly identify the correct sides on the triangle to use the equation? And if I had identified that mistake I would have been able to find some resources such as youtube videos to see how to develop that skill (…well youtube wasn’t around when I was at school…but you get the idea).
The great thing is, this ability to reflect on learning as a skill is not specific to mathematics but is applicable to all subjects at school and even co-curricular activities. Educational research in this field has been growing and heaps of books have been written on this topic. If you are interested, just search ‘fixed mindset vs growth mindset’.
If “just try harder next time” is not the correct thing to say, then what is? Why not try: “what skill do you/I need to develop to improve?”.
Zach Holmes
Acting Head of Mathematics