Show your working – it really helps

“Show your working” is a common request in high school maths exams.  Yet, in the modern learning environment, where worksheets and workbooks are common place, students don’t get a lot of practice at this important communication skill.  With so much content to deliver, there is little time left for teachers to teach students how to craft a good solution.  Furthermore, textbooks with answers at the back generally do not show any working.  It’s no wonder so many students find writing out mathematics both difficult and puzzling.

So, why should you bother to show your working?  Here are some points worth considering.

1. In a written exam, there is no kudos in working everything out in your head or getting the wrong answer quickly.  It gets you no extra marks.  In fact, if working is required, writing down only the final answer will cost you marks.
2. Getting the right answer is not as important as understanding the steps you took to get there.  That’s not to say that getting the right answer isn’t important.  Quite the opposite.  It’s so important that you want to be confident you’ll be able to get the right answer every time you encounter the same type of question.
3. Showing your working is not supposed to be a nuisance.  It is meant to explain, with justification, how you arrived at your final answer.  Rather than being a nuisance, it should actually help both you and your teacher/marker to understand your work better.  Whoever is marking your work is not a mind reader.  Even you might have trouble understanding what you did when you look back at your work, sometime later, if you haven’t provided enough detail!  But if you have made a mistake and the steps are written out clearly, it will be much easier to identify where the misunderstanding occurred and correct the mistake.
4. Use your brain power wisely.  Most students are faster and more accurate when they write things down because they can focus on the accuracy of each step rather than holding everything in their heads.  If you think that not showing your working will save you time, think again!  What if you make a mistake?  You won’t save any time if you get a wrong answer quickly and then have to re-do the calculation.  And that’s only if you notice.  If you’ve written down your steps, you are more likely to spot any mistakes and only have to re-do part of the calculation.
5. If, in an exam, you’ve written down nothing but an incorrect answer, you’ll get no marks.  However, if you’ve written down an incorrect answer but have shown your working, there is a chance that your marker will be able to find something in there to justify giving you a partial credit.  In fact, if you made only a tiny numerical slip, it might be overlooked and you might still be awarded full marks.

Hopefully, you are now convinced that showing your working is a good idea.  Here are some tips on how to get started:

1. Read quality worked solutions, and then practise writing out solutions in a similar manner.
2. Articulating your ideas in writing helps you to understand better what you are doing.  You need to start practising this skill with the easy questions, when you know what all the steps are.  If you can’t do it for the easy questions, you won’t be able to do it for the harder questions either!  In actual fact, the harder questions might not be as hard as you think, if you are well practised at breaking down a problem into smaller steps.
3. Knowing how much working to show requires a bit of judgement.  Again, refer to quality worked solutions for guidance.  Here is a good rule of thumb: when you are writing out a solution, imagine that the person reading your solution is someone in your class who doesn’t know how to solve the problem.  Would that person be able to follow your solution and then understand how to solve the problem?  Try it yourself: swap solutions with a friend and see if you can understand each other’s solutions.  It might give you a better appreciation of what it takes to write a clear and coherent solution if you try reading someone else’s work.
4. Solving word problems is generally a test of whether you can extract information from the question and apply it correctly. So, identify when you are making explicit use of information or numbers supplied in the question and make this clear in your solution. For example, if you are calculating the area of a circle with diameter 6cm, a good written solution might be:
   

   Radius r = × 6cm = 3cm

   Area of the circle = πr2 = π × 32 = 28.27cm2

5. Understand the precise meaning of the equals sign (=) and use it correctly. The equals sign does not mean “Here is the answer:” or “Here is my next line of working:”. The equals sign means “is equal to” or “has the same value as”. Naturally, as the words suggest, it only makes sense to use the equals sign to indicate that two expressions (not equations) are equivalent or have the same value. For example, if I wanted to multiply 3 by 4 and then add 17, I would write:
   
   3 × 4 + 17 = 12 + 17 = 29
   

   and not: 3 × 4 = 12 + 17 = 29. The latter is what I call a running calculation.  It might be how we think through the calculation in our heads, but, as written, it is nonsense because it says that 3 × 4 is the same as 12 + 17.

The benefits of writing out your mathematics solutions in full cannot be understated. With continued practice, you will understand things better and have more certainty of your answers, particularly when attempting harder questions. Ultimately, you will feel better prepared and more confident when you go into your exams.

Dr Audrey Tan, Mathmo Consulting