Heuristics methods used in Mathematics - Part 1

Part 1

The word ‘heuristic’ is taken directly from the Greek verb, heuriskein which means ‘to discover’. In Mathematics, there are usually different ways to go about solving problem sums. These ways or methods are known as heuristics maths.

Heuristics can be divided into 4 main types, which will be covered in this 2-part article.

One: Giving a representation

·         Pupils can transform word problems into pictorial representations and represent information with a diagram/model. This skill helps pupils to understand the question better when they see the visual representation of the word problems.
·         A systematic list should be made for word problems that require pupils to identify patterns such as repeated numbers or a series of events that repeat. This skill helps pupils in identifying patterns easily as the list organises all possible answers systematically.

Example: Michele saved $150 on the first month. On the second month, she saved $60 more than the first month. On the third month, she saved $70 more than the second month. On the fourth month, she saved $55 more than the third month. How much did she save in four months? Solution: Making a list: 1st month → $150 2nd month → $150 + $60 = $210 3rd month → $210 + $70 = $280 4th month → $280 + $55 = $335  Total amount saved = $150 + $210 + $280 + $335                               = $975  She saved $975 in four month

Two: Making a calculated guess

·         The ‘guess and check’ method is used for word problems when certain information is lacking. It requires them to make a guess first and check it, and making subsequent guesses and checks until the correct answer is derived. It is often used together with a systematic list as it helps pupils to narrow down the possibilities within a short time frame.

Example: Jenny has a total of 7 dogs and parrots. The animals have 20 legs altogether.                 How many dogs does she have?  Solution: Using the ‘guess and check’ method, Number of dogs Number of legs Number of parrots Number of legs Total number of legs Check 1 1 x 4 = 4 6 6 x 2 = 12 4 + 12 = 16 X 2 2 x 4 = 8  5 5 x 2 = 10 8 + 10 = 18  X 3 3 x 4 = 12 4 4 x 2 = 8 12 + 8 = 20  √ She has 3 dogs.

·         The ‘look for patterns’ method is usually used by pupils when they have to identify a certain pattern in a number sequence.

Example: 12 4 5 13 11 9 16 18 16 12 3  X Solution: Making a list of possibilities:  12 - 4 + 5 = 13 11 - 9 + 16 = 18 16 - 12 + 3 = 7 The value of X is 7.

Hence by using the systematic list, it is more effective to find the underlying pattern.