I have had a lot of conversations with students over the last couple of weeks which made me want to write this post. I apologise in advance that it will be rather long.
It’s also important to state that this message doesn’t hold for everyone, but it is worth seriously thinking about.
Many students recently have asked me about how to go through tutorials, and how to revise. They are finding that while they are sitting down for a long time with their tutorials, the tests still feel really hard.
To an important extent, technologies have changed the way we think and act over the last couple of decades. In many ways, things were easier in my day when we didn’t have so many technological distractions. Cellphones were rare when I was a student and smartphones were still over a decade away! There was no Facebook, or Youtube, or Instagram. Google was just beginning, but most people had a Hotmail account and that was it. So this means that because of the different landscape of distractions, you now have to come up with different methods for navigating your studies.
As you read this you should keep in mind, that I am not just speculating on how things are for you, but explaining also how things are often for me!
What has this got to do with struggle? Well, how familiar does this sound?
“OK, I’ll have a go at question 3 from the extra problems…I’ll read through the question…hmmm, it doesn’t quite make sense, but let’s have a proper look at part a) and see if we can get it…ah, ok, part a) seems alright, let’s jot down a note….we think that that’s true, so we write down 3a) True. Let’s look at part b)…ok, that’s harder…hmmm…I’ll think about it for a moment…I’ll just take a look at a quick message on Whatsapp and reply to it, and then come back to part b)…nice, they replied!…ok, just a couple more messages…ok, phone down for a moment…ok, where were we…part b)? hmmm, seems tricky, let’s move on to part c and we can look up part b in the memo when it comes out.”
When the memo comes out, you look through and see that 3b) is False. You think about it for a moment and think,”yep, ok, I can believe that”, and it feels like you’ve learnt something.
What’s happened here? You’ve got into a pattern of behaviour that says “when things are difficult, it’s good to take a little break and do something which feels easy and is fun, and is just a click away”. At the end of all this you feel like you’ve learnt the answer to the question anyway, so all is ok.
Now it comes to the test. You sit there and look at a question. It’s not immediately obvious how to solve it. You think for a moment. Wow, wouldn’t it be nice to check Instagram, or to send through this question on Snapchat and show how tricky it is? OK, in the past when I came across a question like this and I couldn’t get it, I moved on to the next one. We’ll come back to it later…but when you come back to it later, it’s still just as tricky.
What has happened here? I believe that what has happened is that the line between manageable struggle and impossible struggle has been set low by the fact that you are surrounded by so many distractions now. You have not felt your true capabilities, because there was an easier path through to finding the right answer. You don’t know what it feels like to come across a question which feels really difficult, and to battle with it until you have conquered it. I’m not blaming you. It’s really hard to do this when distractions are within easy reach.
That moment of conquering a question, which at first felt insurmountable, is absolutely key to getting good at mathematics. It’s not just the practice and turning the handle, but it’s what happens when the handle gets stuck – do you stop and move on to the next calculation, or do you examine the handle with as many tools as you have at your disposal until it gets unstuck and the problem is solved. The more you use your mathematical toolkit in diverse ways, the more you will know how it feels to solve a problem which at first feels impossible.
OK, how do I know all this? Let me let you into a secret…It is the same for me. I am easily distracted by all of the social media around me. I know what it’s like to be doing some research, and to think, wow, this is tough, let’s have a look at the News and then come back to it when my brain has had a chance to rest up. Again, this builds a pattern of taking a break when the going gets tough, which is precisely the point where you should push the hardest.
So what do I do? I know that I don’t have the self-control if the distractions are in easy reach, so I put boundaries up for myself which mean that I don’t have to be controlled. The distractions are simply not there. I sit in a library without any electronic devices around me. I put a block on my internet browser which means that I can’t access certain sites. And here is the strangest one of all, and not one that I expect many to choose…I don’t own a Smartphone. I know that I don’t have the self-control to not be constantly distracted by it. Without owning one at all, I never have to be self-controlled.
Self-control is hard, and it takes mental energy. If you have your phone next to you while you are working, then there is a part of your brain which is engaged with trying not to pick it up, and you have less mental energy to actually solve the problem.
The solution: Put the phone in another room, give it to a friend and tell them that they can give it back to you in an hour, for ten minutes, and then they will take it back after that. Get together with a few friends and all put your devices in the centre of the table, and agree that you are not allowed to touch them for the next hour.
This is how I would go about working through a tutorial (having already removed the distractions).
- Try and spend time on every question
- If you come across a question that you can’t answer, write down everything that you know about it, and spend some time trying different possibilities.
- If you still can’t do it, come back to it the next day and try again.
- If you still can’t do it then, look in the notes/textbook at the section in which that type of problem is discussed.
- Now put those notes away and try the problem again.
- If you still can’t do it, take a break, take the notes out again and try and work through the problem with the notes open.
- If you still can’t do it, talk with a friend. Find out their strategy, but don’t do it immediately after this.
- Come back to it a few hours later and try and remember their strategy.
- If by the time the memo comes out, you still haven’t been able to do it, look at the memo, then put the memo away, and a few hours later do the question, without the memo.
Essentially, you want to put yourself in a position where you can only just answer the question. The harder it is to answer, the more you have strengthened your toolkit for doing maths. The easier you make it (ie. getting your notes out straight away and seeing how to do it), the less you learn.
If you come across a hard question while doing tutorials. Make a note that it was particularly tough, and that it will be a good question to use for revision. You should keep a list of revision questions as you go through your tutorials. Each question should be marked as:
- Easy – I didn’t learn much from doing this, there won’t be much point in me doing this again during revision
- Not too hard, but it was good practice – do this one again for revision
- Pretty hard – this will be vital for revision
Then, when it comes to revision, you will have a much smaller set of questions to go through, and you know that they will be optimally chosen for the time available.
You are often taught that if you struggle at something, it means that you are not good at it, but in mathematics, struggle is often part of the feeling of conquering a topic. When it comes to a test, if you have allowed yourself this struggle when studying, you will know how it feels, not only to struggle, but to make the breakthroughs and answer questions which you thought were impossible.
Give it a go – learn to enjoy the struggle, rather than think of it as a weakness. It feels amazing when you make those breakthroughs, however small they are.