1 Word problems seen as stories

Pause for thought Thinking about your own classroom, how are word problems perceived by your students? Do they like them? Do they struggle with them? Why do you think this is? Think back about your experiences as a mathematics learner, how did you perceive word problems? What helped you to understand how to approach them?

Word problems can play a significant role in making school mathematics meaningful and contextual for students. Along with connecting everyday reasoning with classroom context, they can also connect school mathematics with everyday situations and everyday problems, and vice versa. It is therefore very important that students are exposed not only to solving word problems, but also to constructing them themselves.

When working with word problems, difficulties can occur as students try to make sense of the context and come across words and expressions that are not familiar to them, or when they cannot visualise the context of the word problem.

An effective way to help students is by considering word problems as stories. Students tend to like stories and are familiar with them. Stories often catch the interest and attention of the students, who might even be well versed in creating stories themselves. They know that stories can be completely fictitious – but equally they can take place in contexts that are familiar to the students.

Research shows that asking students to develop a story or narrative as part of their learning activities can help understanding. Bruner (1986), an influential educationalist, argues this is the case because ‘human beings are essentially narrative beings, telling stories to themselves and others as a way of making sense of the world’ (Mason and Johnson-Wilder, 2004, p. 68).

Making drawings or using hands-on teaching aids (manipulatives or props) to depict the story or word problem can also help students to understand the problem and physically see the relationships between different variables.

The first case study describes how Mrs Chadha used stories to introduce the mathematical concept of addition to her students.

Case Study 1: The story of Aditi

I am Mrs Chadha, a teacher of Class I.

I planned to start teaching addition to my students. I believe that for mathematics to make sense to the students, they need to place mathematical concepts in a context; hence, I try to give plenty of concrete experiences whenever I start with any new mathematical topic. So when starting my lessons on addition, I told a short story about a girl named Aditi who loved collecting marbles. I had a box of marbles on my desk.

One fine day Aditi was playing in the garden and saw some marbles lying on the ground. She was very happy and decided to collect them. She found three marbles at first. (Now I ask Varun, a student, to count three marbles loudly and take them out of my collection of marbles.)

I continued with the story: as Aditi moved around and looked for more, she found four more marbles. (Now Varun takes out four more marbles.)

I then asked the students: how many marbles did Aditi find in total?

Varun raised his hand to answer. I asked Varun to share with the whole group how he found the answer. Varun explains how he counted to find out the total number of marbles.

Continuing the story, I said that Aditi kept moving as she thought she should check the whole garden. As she neared a bench she saw that there were some more marbles lying under it. She found two more marbles. I then asked the students to count and tell me how many marbles Aditi would now have. I added two more similar steps.

I then shared similar short stories with my students and asked them to find out the total number of things, such as buttons, pencils, pebbles, etc.

After this I started asking how many biscuits there will be in total if one student has three biscuits and another one has two biscuits, and so on. For each problem, I first drew the objects [see Figure 1].

Figure 1 Three biscuits and two biscuits

Then I wrote the numerical representation on the blackboard as I spoke:

Three biscuits and two biscuits together become five biscuits.

3 biscuits + 2 biscuits gives 5 biscuits

At this point, I introduced the symbol ‘+’ for addition and then I introduced the symbol ‘=‘ for equivalence [Figure 2].

Figure 2 Three biscuits and two biscuits, with ‘+’ and ‘=‘ symbols added.

Then I wrote the expression ‘3 + 2 = 5’.

I then reminded the students of the story of Aditi and the marbles, and asked them how I should draw this. On their instructions I drew the marbles on the blackboard and wrote the mathematical expression. Together we drew many more ‘adding’ stories on the blackboard using the ‘+’ and ‘=’ symbols.

Video: Storytelling, songs, role play and drama

In Case Study 1, Mrs Chadha is building links between the mathematical concept of addition and a real-life context that is familiar to the students. At the same time she lets the students be active participants in the narration of the story.

Bruner (1966), an influential educationalist, suggested that learning for understanding happens by going through three modes or stages of representation: enactive (activity-based), iconic (image-based) and symbolic (symbol- or language-based). He argues that these modes of representation are the ways in which information or knowledge is stored and encoded in memory (McLeod, 2008).

Mrs Chadha first provides actual marbles so that the students can physically count and add marbles to find the answers. Later, she represents the same on the blackboard with the help of images of the objects (biscuits), and then moves to write what he says first in words and then in symbols.

At the same time, Mrs Chadha links these three representations by constantly talking about them. For example, she introduces the words ‘add’, ‘altogether’ and ‘plus’ gradually, and associates these with the action of addition. This gives the students an opportunity to encounter the vocabulary many times in different contexts.

Pause for thought Can you think of an example in your own teaching practice where you could use a similar approach to that of Mrs Chadha? How might Mrs Chadha have adapted these activities to make help all of the students remain fully engaged throughout the lesson?