Heuristics Methods Used in Mathematics - Part 2

Part 2

Heuristics can be divided into 4 main types, which another 2 types would be discussed in this article.

·         The heuristic ‘act it out’ requires pupils to use physical objects or manipulatives to represent information. This skill is used to introduce new concepts and to allow pupils to explore the concepts using manipulatives.

Example: The figure is made of 17 sticks. Move 4 sticks to form 8 squares. Solution:

Pupils can use matchsticks to represent the information and use the matchsticks to find the solution to the problem.

Example: There were some chocolates in a basket. Michael and three of his friends took 8 chocolates each. 25 chocolates were given to Shirley. There were then 11 chocolates left in the basket. How many chocolates were there in the basket at first? Solution: Using the ‘work backwards’ method, first find the number of chocolates taken away by Michael and his three friends. 4 × 8 = 32 chocolates Then, find the total number of chocolates taken away from the basket. 32 + 25 = 57 chocolates Number of chocolates in the basket at first = 57 + 11 = 68 chocolates

·        Pupils can use the ‘before-after concept’ for problems that provide information given before and after the event to find the unknown. This skill allows pupils to compare the information and relate different events together to solve the problems.

Example: Jacky had $56 more than Jill. When he spent $108, Jill had thrice as much as what he had left. How much did Jacky have at first? Solution:   2 units → $108 - $56 = $52   1 unit → $52 ÷ 2 = $26  $26 + $108 = $134 Jacky had $134 at first.

Four: Changing the problem

Example:Find the sum of 10 + 12 + 14 + … + 146 + 148 + 150. Solution:           There are 75 numbers in the sum 2 + 4 + 6 + … + 146 + 148 + 150.   There are 4 numbers in the sum 2 + 4 + 6 + 8. 75 – 4 = 71 Hence, there are 71 numbers in the sum 10 + 12 + 14 + … + 146 + 148 + 150.    There are 35 pairs of 160 and a ‘80’. 10 + 12 + 14 + … + 146 + 148 + 150 = 35 × 160 + 80  = 5680

Thus, do try to keep in mind the various heuristics and apply them when you are doing problem sums. With regular practice, you will be able to handle problem sums with ease.

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.

Three: Going through the process

·        Pupils can apply the ‘work backwards’ method when given a problem that provides the final result and that requires them to find the initial quantit

·        By restating a problem in another way, pupils can view the problem in another perspective.

·        When facing a complex problem, pupils can split the problem into smaller parts and start by solving the simpler parts. After doing so, the problem is simplified and solving the problem is much easier.