Whether I tutor in a lesson, give homework or let students practice for their exams, I always give them answers, too (well, if I have them, of course). What is it good for? Let me explain...

When I was in school, I always hated when I couldn't check my answers. I wasn't one of those who would just copy answers to make my life easier (that's how much I enjoy maths — I do maths voluntarily). But I wanted to be sure it was all alright and never wanted to wait for the teacher to mark it (it took ages sometimes).

So, besides the fact some (less responsible) students would use answer sheets to skip the process and finish their work without any pain (yes, training your brain and doing maths hurts, I know =), I'm trying to plant the right idea into their heads by explaining WHY they should have answers provided (not during a test or an exam, of course).

Self-learning is the best way to remember things. Every learner has a different approach; some are more visual (and will draw many sketches), others need to hear things (and may repeat them aloud), and others have their own special ways of learning and remembering.

But how would you know you got there and tackled the topic if you can't check your work? And what if you have something wrong? What if you don't know how to get to the correct answer at all?

Here are a few scenarios and how to use answers well:

1. You're quite confident with the topic. You do your work, check answers, and will probably get them correct; there might be some error, though. Have a look at the incorrect answers – where did you make the mistake? Is there any mistake repeating?
   The most common reasons are wrong formulae, wrong calculations (always think about and use BIDMAS/PEMDAS), not enough attention (that causes a lot of silly mistakes), and answering something other than what was being asked in the question... Check your mistakes, correct yourself, and identify the weak parts of your work and math processing. This will guarantee your future improvement.
   
   
2. You need to learn a topic by practising, but you're not really sure whether you're doing your maths correctly. The best way is to do one or a few questions and check answers. You don't want to end up doing an A4 (or more) full of questions and get them (mostly) all wrong. Such a waste of time and energy, right?
   But if you see that your "maths is not mathing" after one or two questions you've done, you can stop and analyze first what you need to do (and learn) to fix it before attempting to solve more examples.
   
   
3. You don't have many ideas on how to do the work. So, you can have a look at the answer and think "backwards" – how to get to the correct answer? (This works really well with trickier topics such as probability...)
   Sometimes, you won't just get the answer, but also a bit of work or a few steps explained (often in past paper mark schemes), which may also help give you some ideas on how to work out that question.
   

In all scenarios, you're expected to do your own work. So even if you don't know what to do, it doesn't mean you just copy answers, and you're done.

Either way, answers show you what you need to learn. Either on your own or perhaps arrange an extra maths help.