When learners ask ‘Why are we doing this?’ it is often because they feel that they are not succeeding. (‘If you can’t give me a reason, I don’t want to carry on.’) Whether or not learners feel that they are successfully doing whatever it is, they may genuinely be looking for reassurance that persevering with it is justified by the need to know it in the future, which might be in a test. But whether the question is a disguised protest, or a genuine request for information, saying that it is a fact, rule or procedure that they need to know is, at best, an inadequate response, and, at worst, is likely to reinforce a view of mathematics that undermines successful learning.
When learners are told that they are doing something in mathematics because it is a fact, rule or procedure that they need to know, an incorrect belief about the source of authority in mathematics may be encouraged, or reinforced. A teacher’s dogmatic assertion about the value of an activity contributes to learners’ dependence on the teacher, and on other adults such as authors of text books, as authoritarian ‘deliverers’ of mathematics. This makes it hard for learners to move to understanding that the true, and sole, source of mathematical truth and correctness is mathematics itself; the source is logic and reasoning, not adult ‘say-so’. To divide by 1/3 you multiply by 3 not because someone says so, and not because the textbook says so, but because there are three thirds in a whole. And you see that this must be so when you think of dividing as finding ‘how many … there are in …’.
Instead of sending learners the message that they cannot be expected to know why they are doing particular tasks, it is part of the teacher’s role to engage learners in the kind of self-motivated activities in which they know why they are doing them. If the teacher is providing situations in which learners are stimulated by their natural powers to want to do tasks, the question is unlikely to arise. A learner asking ‘Why are we doing this?’ is an indication that something is wrong.
But, if learners do ask why they are doing something, it will always be better in the long run, not to give in to the temptation to attempt to satisfy learners by saying that they just need to do it.
Instead, it may help, as an immediate temporary measure, to remind learners that mathematics has been a fundamental aspect of human activity since before recorded history. Always people have been seeking general methods of solution of problems that arise in life while, for example:
- designing and making objects
- carrying out transactions involving exchanging goods
- inventing means of transportation.
An essential characteristic of human beings has always been the desire to investigate the processes of problem solution that they develop, enquiring into the nature of number and geometrical relationships, looking for general methods, properties and relationships. Mathematical puzzles have always intrigued people. Human beings have natural powers that they have always applied to these things. It is your role as a mathematics teacher to provide situations in which learners can use their natural powers, and to guide them so that they learn which powers to use when. An appropriate temporary response might therefore be ‘I’m hoping that you will eventually always be able to decide for yourselves why you are doing things in mathematics.’
The fact that learners are asking why they are doing something is a signal that learners have a distorted view of what constitutes learning and doing mathematics, and can act as a prompt for you to start thinking about what you can do to change that view.
Mathematics as a Human Activity
Themes Which Pervade mathematics
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, RoutledgeFalmer, London.
Mason, J. & Johnston-Wilder, S. (2006 2nd edition). Designing and Using Mathematical Tasks
, Open University, Milton Keynes.
Pólya, G. (1945). How To Solve It: a new aspect of mathematical method
. Princeton, USA: Princeton University Press.
Pólya, G. (1962) Mathematical Discovery: On understanding, learning, and teaching problem solving (combined edition)
, Wiley, New York.