2 Constructing stories to help make sense of mathematical concepts
Traditionally, word problems appear in textbooks or in classroom teaching at the end of a chapter. Often, little time and attention is spent on making sense of these word problems. Letting students create their own stories, or word problems, to narrate a mathematical sentence like 3 + 4 = 7 can help to build an understanding of the mathematical ideas and lead to greater problem solving skills. It can help students overcome the difficulties of making sense of the context of the word problems, because they will construct their own context and focus on making the story fit the mathematics. In that way it also helps them with identifying which mathematical representation to use.
Before attempting to use the activities in this unit with your students, it would be a good idea to complete all, or at least part, of the activities yourself. It would be even better if you could try them out with a colleague, as that will help you when you reflect on the experience. Trying for yourself will mean you get insights into a learner’s experiences that can, in turn, influence your teaching and your experiences as a teacher. When you are ready, use the activities with your students and once again, reflect on the way the activity went and the learning that happened. This will help you to develop a more learner-focused teaching environment.
The next two activities give ideas to help your students create their own stories for mathematical number sentences.
Activity 1: Making stories
Preparation
Read Case Study 2. Adapt the mathematics in the questions to fit the level of learning of your students. Think about how you will organise your students when they work on the activity. You may wish to have a look at the key resource ‘Using groupwork [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] ’.
The activity
Tell your students to choose a problem from Table 1 and use their imagination to create a story around the given problem.
| Maths problem | The first line of a story |
|---|---|
| 4 + 7 = … | A girl was playing ‘Snakes and Ladders’ with her brother … |
| A box has three white balls and six red balls. How many balls are there in all? | Shyam is very fond of collecting balls … |
| 9 – 7 = … | My aunt lives a few houses away from my home. Her house is … |
| If 5 is subtracted from 8, what is the answer? | Our dog … |
| 2 × 4 = … | A group of friends were playing cards … |
Then ask the students to get into pairs, tell each other their stories and comment on them.
- Some more complex examples:
- 4 + 7 = 3 + 8
- 2(3 + 1) = 2 × 4
- 2(3 + 1) = 6 + 2
- Make up some more of your own. At least one should be an easy one to work out, and at least one should be a difficult one. Remember you have to be able to work out the answers yourself as well!
Activity 2: Making many stories for the same number sentence
Tell your students the following.
Consider this number sentence:
3 + 4 = 7
This number sentence could be represent by several mathematical relationships, such as:
- adding 3 and 4 together makes 7
- 4 more added to 3 gives 7
- the total number of things is 3 + 4 = 7
- 4 less from something leaves 3.
Now ask your students to formulate a story or word problem for each of these relationships. Encourage them to use their imagination! For example, for the first relationship, the story or word problem could be something like this:
- Mohini and Rohini were playing together and making balls from clay. Mohini made three balls from the clay and Rohini made four balls. They wanted to know how many balls they had made in all. They kept them together in a box. Can you help them to find out how many balls they made in total?
To link in with Bruner’s modes of representation, you could also ask the students to make a drawing depicting their stories.
Case Study 2: Mrs Meganathan reflects on using Activities 1 and 2
This is the account of a teacher who tried Activities 1 and 2 with his elementary students.
For both activities, I asked my students to work in the groups of three or four because I thought that would give them more ideas to share. They could also support each other if one of them was stuck. We had a go at the first three questions of Activity 1 as a whole class because my students never had done something like this before. I think this helped them to understand what I wanted them to do. It also opened up their imagination to think of all kinds of examples. Some involved monsters, stars, going to the market or being in a Bollywood movie. I then ask them to come up with their own group examples and that they were not to use the examples we had already mentioned as a whole class. I did change some of the harder questions because my students have not come across brackets in mathematical sentences yet.
The students did not find the second activity that easy to start with. They could understand the differences in mathematical relationships when I read them out, but found it hard to come up with stories that would fit these relationships. I decided to write it up on the blackboard instead of just reading it out to them, and then asked one of the students to read out loud what I had written. That seemed to help them realise that there were subtle differences.
When each group had come up with something for every equation, we shared them with the whole class. I asked the students whether they agreed with each of the examples. This helped to clear up some misconceptions.
I then asked them ‘Which one was most difficult and why?’ This meant that the students had to think about how they thought about their mathematics – that is called ‘metacognition’, I think. Asking them to take this overview also meant I became more aware of what they found difficult, and therefore where more practice would be needed.
Reflecting on your teaching practice
When you do such an exercise with your class, reflect afterwards on what went well and what went less well. Consider the questions that led to the students being interested and being able to progress, and those you needed to clarify. Such reflection always helps with finding a ‘script’ that helps you engage the students to find mathematics interesting and enjoyable. If they do not understand and cannot do something, they are less likely to become involved. Use this reflective exercise every time you undertake the activities, noting as Mrs Meganathan did some quite small things that made a difference.
 Pause for thought
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1 Word problems seen as stories