1 Issues with word problems
Students can find understanding how to work with word problems hard to do (Morales et al., 1985). They can become distracted by the narrative, which might claim to be based on real life, but is actually unrealistic. For example, consider the following word problem, of which there are many adaptations:
Eighty-two people are queuing for the lift on the ground floor of an office building. The lift can take a maximum of nine people at a time. How many trips will it take the lift to clear the queue?
The word problem seems to be based on a real-life situation – people in an office building queuing for the lift. It does not represent reality, however: with such a long queue, there might be people who will choose to take the stairs instead of waiting for the lift, or people who will decide to wait until later to travel to the upper floors of the building.
However, in a mathematics word problem, such aspects of real life are usually not considered relevant. Hence sometimes students need to be helped to consider what is part of the context that is relevant to the mathematics and what is not – in other words, to pay attention to what is important and to disregard the rest. Students need a set of tools to:
- make sense of word problems
- notice the mathematics elements
- be aware that word problems are a case of modelling mathematical ideas.
Word problems are usually an example of mathematical modelling. It may be important to remind the students that this is how a lot of mathematics is used in careers beyond school: to model what happens (or may happen) in the world so that complex situations and often awkward numbers can be manipulated more simply and solutions to problems found. Students can become aware of this by ‘decoding’ word problems, and also by making up word problems themselves.
Pause for thought
Thinking about your classroom, how are word problems perceived by your students? Do they like them? Do they struggle with them? Why do you think this is?
Thinking back about your experiences as a mathematics learner, how did you perceive word problems? What helped you to understand how to approach them?