Problem Solving Revisited

Age 16 to 18
Challenge Level
If you've been working through the STEP Prep modules since Module 1, you may remember our article A Guide to Problem Solving. I'd like to refresh your memory about some of the advice offered in that article.

First, if you're not already in the habit of asking yourself questions while working on solving a problem, it's not too late to build it into your problem-solving routine. A reminder of the problem-solving heuristic from the article mentioned above:

Understanding the problem
  • What area of mathematics is this?
  • What exactly am I being asked to do?
  • What do I know?
  • What do I need to find out?
  • What am I uncertain about?
  • Can I put the problem into my own words?

Devising a plan
  • Work out the first few steps before leaping in!
  • Have I seen something like it before?
  • Is there a diagram I could draw to help?
  • Is there another way of representing?
  • Would it be useful to try some suitable numbers first?
  • Is there some notation that will help?

Carrying out the plan

  • Try special cases or a simpler problem
  • Work backwards
  • Guess and check
  • Be systematic
  • Work towards subgoals
  • Imagine your way through the problem
  • Has the plan failed? Know when it's time to abandon the plan and move on.

Looking back
  • Have I answered the question?
  • Sanity check for sense and consistency
  • Check the problem has been fully solved
  • Read through the solution and check the flow of the logic.
As part of your final preparation, read through these questions, pick out the ones you find most useful, and remember to ask yourself them while you are sitting in the examination room.

The other part to remember is the set of questions about how you are feeling and whether you are in control:
  • Am I getting stressed?
  • Is my plan working?
  • Am I spending too long on this?
  • Could I move on to something else and come back to this later?
  • Am I focussing on the problem?
  • Is my work becoming chaotic, do I need to slow down, go back and tidy up?
  • Do I need to STOP, PEN DOWN, THINK?
Working through this checklist, and remembering that it's a three hour examination so you have time to stop and think, should help you to cope with any exam anxiety. Don't forget to breathe!

Finally, make some time to do some enjoyable maths. You've spent the last few months working very hard to prepare yourself for STEP, so why not explore some of the problems on the NRICH site just for fun? And of course once the exam is over, there's a whole summer to spend on reading articles, preparing for university maths, and solving mathematical sudoku puzzles...