Scenario: you have been given a problem in mathematics. You are expected to solve it. For some reason, you have consulted E2 beforehand.
Math problems (or, as I like to call them, "maths problems") come in all shapes and sizes and it would be futile for me to try to account for all the many tactics that you may come use during your mathematical life. Therefore this node will be made as general and all-embracing as I can make it.
- First off, study the question to find out what regions of mathematics you are likely to be using. In many cases, it's probable that you have just (i.e. mere hours ago) covered this topic in class or in lectures, so if you a) have them available and b) are allowed to (i.e. not an examination), dig out your notes or textbooks on these regions and have them open and available in front of you. If you think the problem relates to an area you've never encountered before, but you're still expected to solve it, then a trip to the library might be in order, or you could consult a teacher/tutor/lecturer for guidance.
- If you're not already sufficiently conversant with the subject matter to understand the problem you've been given, then study your notes until you are.
- Consult all your sources for similar-looking problems that you may have already covered. With textbooks and worked examples at your disposal, you should now have a kind of "toolbox" of skills and techniques which you can use to attack the problem.
- Read the question properly, analysing it for data. Write out this data (not simply the question itself) in a format you can understand, possibly a diagram. (People who are better with whatever is the more creative side of the brain may find it much easier to comprehend a problem in diagrammatic form.) This will simplify the question and possibly allow it to congeal into some kind of comprehensible form in your head. Make sure you do this bit carefully: write down the wrong data, and your effort is doomed from the start!
- Find out exactly what the question is asking for and write down this piece of information too. Sometimes it will simply be a "show that:" question, where the answer is given you and you just have to prove it correct, but sometimes the answer is an unknown. If not explicitly stated in the question, you may have to invent a name for this unknown.
- Study the data for familiar patterns and/or "chinks" where you may be able to apply the tools you have learned.
- Figure out a way, using the tools and methods you have at your disposal, to navigate from the data you HAVE to the answer you REQUIRE. In most circumstances, there will usually be a clear (or at least logical) route through this maze, in steps that individually should make sense to you. However, sometimes a problem will require a little more than this: a flash of inspiration, a leap of deduction that you probably weren't taught about. There is no foolproof, easy way to spot these kinds of tricks - it's more down to practice and natural talent.
- Do not make unnecessary stops on the way. Though this question may look exactly like one you may have encountered before, the answer it's looking for may be very different (and that can mean easier OR harder to find). Try not to end up solving for variables that you really don't need. I slip over this kind of stuff all the time.
- If there is no obvious route from the data you have to the data you want, then just try to "widen the hole" a little. Attack the problem anyway, seeing if you can get it to yield a little more data about itself. This extra data may be enough.
- If the question allows, then you can work on the answer using the same methods. This way, you can work to bridge the gap between question and answer from both directions, hoping to meet in the middle. Sometimes, working backwards from the answer is actually infinitely easier than the usual method; if you're cunning, you can spot this right from the start.
Finally, remember: you are not in this alone, and there is always, ALWAYS, someone out there who is better than you at whatever you are doing (with one exception, you know who you are). These people are willing to help you and a small minority, many of whom can be found on E2, might prove to be actually helpful. So if you get irrevocably stuck, ask for help. Compare notes with others who are stuck with the same problem. Don't let them grind you down, daylog your pain. And remember that, as long as you put in lots of effort, it's okay to write "I couldn't do this question" as your answer sometimes!