This post is a response to the article, ‘Why 5+5+5 doesn’t always make 15: Maths exam question divides the internet’.
Mathematical symbols convey information for the reader to interpret. In the example of question 1 shown above, is it fair for the child to have one mark deduced for ‘wrong’ representation?
When does ‘5 x 3 = 15’ be presented in form of 5 + 5 + 5 = 15 or 3 + 3 + 3 + 3 + 3 = 15?
5 x 3 = 15 in form of repeated addition; 3 + 3 + 3 + 3 + 3 = 15
- 5 times of 3, when ‘times of’ is represented by the multiplication sign ‘x’
- 5 groups of 3, when ‘groups of’ is represented by the multiplication sign ‘x’
5 x 3 = 15 in form of repeated addition; 5 + 5 + 5 = 15
- 5 multiply 3 times, though this is usually not used in communication but the statement stands true.
Hence, both 3 + 3 + 3 + 3 + 3 = 15 and 5 + 5 + 5 = 15 are correct, depending on the interpretation of the reader. In the case of the paper setter, he/she interpret it as ‘5 times of 3’ / ‘5 groups of 3’. The child interpret it as ‘5 multiply 3 times’. Though the syllabus focuses on the former interpretation, that does not mean a child should be penalised for another logical interpretation.
If the required answer is 3 + 3 + 3 + 3 + 3 = 15, this question can be modified in the following suggestions:
- Solve 5 x 3 by completing the repeated addition statement.
5 x 3 = 3 + 3 + ____________________ = __________. (Answer: 3 + 3 + 3 = 15) - Based on the diagram below, solve 5 x 3 by using repeated addition.
(Answer: 3 + 3 + 3 + 3 + 3 = 15)
This kind of questions reminds me of a comic I posted before in my post ‘Do schools kill creativity?’
What’s your thought?