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Eight Problem Solving StrategiesEIGHT PROBLEM SOLVING STRATEGIES.

1. WORK BACKWARDSTo solve some problems, you may need to undo the key actions in the problem. This strategy is calledWork Backward.

Working backwards is a standard strategy that only seems to have restricted use. However, its apowerful tool when it can be used. In the kind of problems we will be using in this web-site, it will be mostoften of value when we are looking at games. It frequently turns out to be worth looking at what happensat the end of a game and then work backward to the beginning, in order to see what moves are best.

2. GUESS AND CHECKSome problems cannot be solved directly. You need to use a strategy called Guess and Check.Guess and check is one of the simplest strategies. Anyone can guess an answer. If they can also checkthat the guess fits the conditions of the problem, then they have mastered guess and check. This is astrategy that would certainly work on the Farmyard problem but it could take a lot of time and a lot ofcomputation.Guess and improve is slightly more sophisticated than guess and check. The idea is that you use yourfirst incorrect guess to make an improved next guess. You can see it in action in the Farmyard problem.

In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess.In some problems though, where there are more variables, it may not be clear at first which way tochange the guessing.

3. LOOK FOR A PATTERNIn many ways looking for patterns is what mathematics is all about. We want to know how things areconnected and how things work and this is made easier if we can find patterns. Patterns make thingseasier because they tell us how a group of objects acts in the same way. Once we see a pattern we havemuch more control over what we are doing.

4. DRAW A PICTUREIt is fairly clear that a picture has to be used in the strategy Draw a Picture. But the picture need not betoo elaborate. It should only contain enough detail to solve the problem. Hence a rough circle with two

marks is quite sufficient for chickens and a blob plus four marks will do for pigs. There is no need forelaborate drawings showing beak, feathers, curly tails, etc., in full colour. Children should be encouragedto use this strategy at some point because it helps children see the problem and it can develop into quitea sophisticated strategy later.

5. MAKE A TABLE

There are a number of ways of using Make a Table. These range from tables of numbers to help solveproblems like the Farmyard, to the sort of tables with ticks and crosses that are often used in logicproblems. Tables can also be an efficient way of finding number patterns.

6. MAKE A LIST

Making Organised Lists and Tables are two aspects of working systematically. Most children start offrecording their problem solving efforts in a very haphazard way. Often there is a little calculation orwhatever in this corner, and another one over there, and another one just here. It helps children to bring alogical and systematic development to their mathematics if they begin to organize things systematically asthey go. This even applies to their explorations.When an Organised List is being used, it should be arranged in such a way that there is some naturalorder implicit in its construction. For example, shopping lists are generally not organised. They usuallygrow haphazardly as you think of each item. A little thought might make them organised. Putting all the

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meat together, all the vegetables together, and all the drinks together, could do this for you. Even moreorganisation could be forced by putting all the meat items in alphabetical order, and so on.

7. ACT IT OUTMeaning that two strategies combine together because they are closely related.Young children especially, enjoy using Act it Out. Children themselves take the role of things in theproblem. In the FARMYARD problem, the children might take the role of the animals though it is unlikelythat you would have 87 children in your class. But if there are not enough children you might be able topress gang the odd teddy or two.There are pros and cons for this strategy. It is an effective strategy for demonstration purposes in front ofthe whole class. On the other hand, it can also be cumbersome when used by groups, especially if alargish number of students are involved. We have, however, found it a useful strategy when studentshave had trouble coming to grips with a problem.The on-looking children may be more interested in acting it out because other children are involved.Sometimes, though, the children acting out the problem may get less out of the exercise than the childrenwatching. This is because the participants are so engrossed in the mechanics of what they are doing thatthey dont see through to the underlying mathematics. However, because these children areconcentrating on what they are doing, they may in fact get more out of it and remember it longer than theothers, so there are pros and cons here.

8. USING SYMMETRYIt helps us to reduce the difficulty level of a problem. Playing Noughts and crosses, for instance, you willhave realized that there are three and not nine ways to put the first symbol down. This immediatelyreduces the number of possibilities for the game and makes it easier to analyze. This sort of argumentcomes up all the time and should be grabbed with glee when you see it.