Sunday, May 24, 2015

[MathsEd] The Secret to Mathematical Problem Solving

     Many students treat mathematics problem solving either as a mystery, or they like to shoot at random from a set of formulas or recipes that they have memorised and just see whether it works or not.  When this strategy does not work and after working for a few minutes, they just give up.  They wonder how all those maths geniuses get it.  Many do not know that even the professional mathematicians take many years or evencenturies to solve mathematics problems.  The mathematician George Polya has written a book “How to Solve It” in 1945, describing how mathematics problems are solved.  Since then many people have adapted and modified the steps slightly but they basically boil down to the following steps.

Step 1: Understanding
     Try to make sure you really understand the problem first.  If it is an examination question, read and take note of the given information.  Ask what is known, what can be known and what is to be found.

Step 2: Planning
     This is where you plan your strategy of attack.  Can you organise the information into a table or a diagram?  Heuristics(rules-of-thumb or guidelines) are usually useful to help you formulate yourstrategy, especially if you have not seen this type of question before.

Step 3: Execution
     Carry out your plan.  Make sure you are conscious of what you are doing.  Are you able to explain it to yourself, or younger brother/sister?

Step 4: Evaluation
     Check your calculations and logic.  Are there any careless mistakes?  Is your answer plausible or believable?  Are you on the right track?  Are you getting somewhere?  You also need good number sense.  For example, if you are calculating with a triangle with sides  4 cm,  5 cm  and  6 cm,  and you get an area like 1 000 cm ²,  does your answer even taste and smell right?  Do not continue doing the same wrong thing.  If you catch yourself making a mistake, go back to step 2 and change your strategy.  Try another approach.

Step 5: Reflection
     After solving the problem, think back at what lessons you have learnt by attempting / solving this problem.  How could you have done better?  Did you discover anything that can be applied in other problems?  What if the numbers are changed?  What if the conditions are changed?  You can test your own understanding by setting yourself a similar or modified question.  Can you generalise your results?  Can you link what you have learnt to daily life or to other subjects?

Suitable Levels
all levels, all topics !!!

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