Why is it so important to show your steps in the problems you solve in Maths? Why can’t you just leave them out when you know how to solve a problem in your head? Surely if you can do this then you will save time in a test? Or are there other reasons why the steps are important to do?
The fact is that you can do some steps in your head without writing them all down. And get the right answer. But this is where the trouble can begin.
If you leave out steps and make any mistakes along the way you won’t be able to see WHERE you’ve gone wrong. And you’ll have to re-think your way through the problem to find out where you made the mistakes.
But you might not be able to follow your original thought process. Or you’ll make the same mistakes as you re-think your thought process.
And all of this takes time. Especially in a test. Re-thinking a problem is much harder and more time consuming without the steps to look at. If the steps are all laid out in front of you they can be easily checked for errors. By anyone who’s checking the solutions, especially YOU.
Perhaps because you’re confident in your ability. Maybe because that’s how your teacher does Maths. Maybe you’re just trying to save time by writing less.
Maybe you just don’t know the correct steps to use. So you leave them out. And because of this you’re making more mistakes and losing precious marks.
And remember: what you practice you get good at. If you keep making mistakes because you leave out steps in your working out, then you’ll get better at making mistakes when you leave out steps.
The fact is that nearly everyone in Maths makes mistakes. Even students who find Maths easy. And they make simple mistakes because they skip steps.
I know, I do it myself and end up having to go through the problem again. And I get a bit annoyed because I haven’t done the exact thing I encourage my students to do: Show all the steps!
Sometimes it’s the students who struggle with Maths. Their main mistake is leaving out the steps in their working out. Mainly because they don’t really know the correct steps to start with.
Once they’ve been shown them they tend to keep using them. Why? Because they know they can’t do the problems without using them.
And sometimes it’s the more able students who make mistakes when they leave out steps. They usually try to do two or three steps in their head mainly to save time. But it usually costs them time to go back and find where they went wrong and fix it.
If they’re so good at Maths then why do they need to do the steps? Mainly for this reason. They don’t seem to be aware of the fact that the more times they write the steps the easier it will become for them to repeat them in similar problems.
Haven’t you noticed that in some Maths exercises that after a while the steps become repetitive? And after you’ve done about ten or so problems you get to the point where you can remember the steps.
And you start thinking about other things while you’re doing them. You’re thinking “I know how to do these now so I don’t need to do any more.”
But its this repetition of steps that will help you to remember them. And After a while the steps will become automatic. And that’s where you’ll save time.
You’ll find it easier to study for tests because revision will just be a memory jog. Because you took the time to do the steps and you understood that part of Maths better.
You either spend time upfront doing the steps which will save you time later on. Or you leave steps out to save time and end up having to go back and fix your mistakes which ends up costing you more time. Which would you prefer?
Another major benefit of using steps is that it will free up time in a test for you to think. To think about how to solve a problem.
If you know all the steps in the process of solving a problem then you don’t really have to think about what the next step is. That means you can spend more time thinking about how to solve the problem. Instead of trying to remember the correct way to solve the problem.
And it’s really thinking ability that separates the top students from the rest. They have developed their thinking ability by mastering the steps early on in Maths. Whilst other students are still making some basic mistakes because they are leaving out steps.
So if you’re consistently making simple mistakes and not getting the kind of results you want in Maths then maybe it is because you are not doing enough steps. By doing them when you’re solving ALL the Maths problems you do, you’ll find it easier to remember them.
You will also find that you will become better at solving problems. And the other thing is that if you do show all your steps, you’ll find yourself always thinking: “What’s the next step?” And this is really how Maths problems are solved. Step by step.
You’re welcome. Has the article helped your son?
As a gifted HS student, I’d say you are right about much of this. However, as a person who tends to make 100’s in the vast majority of light math assignments, this sort of thing is extremely illogical. I just got back three papers, with all problems being correct, with 70’s, only because I did not show my work entirely. This makes very little sense to me, even if the teacher is trying to force a habit so I will show my work for tasks in which I HAVE to show my work. I shouldn’t be getting minimum C’s for A+ work.
Well what I used to say to my students was “If you don’t show any working you won’t get full marks”.
And then I explained to them that if they don’t show any working out then they might not have known how to do it and guessed the answer and got it correct.
Or they might have copied off someone else’s work or they actually did know how to do it and didn’t show steps.
I understand that you find Maths easy to do but I guess it’s just part of the deal when you do Maths at school – gotta do what your teacher wants or you don’t get the marks.
should we have to show our work if we can use calculators?
It really depends on what Maths problems you’re doing and what your teacher wants.
If you really want to make Maths easier to understand then the most effective way of doing Maths I believe is to show the steps in your working and then use your calculator in the final calculation.
That way you remember the steps and you really understand the concepts much better.
Thank you for your clarity. We homeschool and this is a constant battle. I will share this with my son.