“Gleeb is a small Martian child. His farm grows 60 blue fruits, and he collects 7 of them. How many are left?”

Or

“60 - 7 = ?”

Which of the above questions do you think your Year 3 or 4 pupils would be most confident in answering? In my experience, it’s usually the second, and the research literature backs this up.

Time and time again, research shows that primary children struggle to solve arithmetic word problems; the challenge they face is understanding the problem structure and relating the quantities in the problem to each other.  

After I reflected on this with Evrim Erbilgin, an associate professor at the Emirates College for Advanced Education in Abu Dhabi, we decided to do something about it, and set about designing an intervention that would scaffold subtraction word problem-solving skills. 

First, we designed and created a digital game (which was then built by a programmer) in which pupils need to represent word problems in three different ways (visual model, bar model and number sentence). The hope was that as pupils developed their ability to represent the sum in multiple ways, it would have a strong impact on their ability to come to the correct answer. 

We had three learning objectives for pupils: to represent the action in a subtraction word problem using different representations; to make connections between different representations; and to perform the subtraction or addition operations to solve the given problems using mental strategies (for example, using multiples of 10 as a bridge).

The game is simple enough: pupils are given a word problem based around the experiences of a Martian called Gleeb. They are asked to work out the answer using the visual model (through removing the correct number of fruits from the “game board”), bar model and number sentence (see below). 

There are five levels to the game, all increasing in difficulty. 

In order to support pupils’ learning as they play the game, we developed a pedagogy framework for teachers, based on the work of researchers Cristyne Hébert and Jennifer Jenson (2019). It involves the following principles:

Scaffolding word problem-solving skills in maths

1. Teacher knowledge of - and engagement with - the game
When we were designing the game, we played it multiple times with primary school teachers and revised aspects of it to help us reach the learning objectives outlined above.

2. Focused and purposeful gameplay
During the gameplay, the teacher directed pupils’ attention to important mathematical ideas, such as how different representations are related to each other or how to use mental strategies to perform the operations.

3. Collaborative gameplay
Levels  3, 4 and 5 of the game were played in pairs to promote collaborative learning. Pupils who tended to use more concrete strategies were partnered with those who used more abstract strategies. 

4. Meaningful learning activities
The different levels of the game were played on different days, allowing the teacher to interweave additional problem-solving tasks that complemented the gameplay, and allowing pupils to cement their learning. 

5. Cohesive curricular design
The gameplay lessons were planned as part of a week-long review of the subtraction topic. Pupils worked on different subtraction and addition tasks across the week: for example, they created their own subtraction word problems, then switched with a partner to solve each others’.

6. Appropriate lesson pacing and clear expectations
The teacher structured the lessons throughout the review so that multiple tasks were completed in each lesson. The pupils were given concrete time frames to complete these tasks.

7. Technological platforms are not a point of focus
The teacher frequently directed pupils’ attention to the mathematical concepts involved in the game by asking open-ended questions, such as, “Aysha counted the fruits by tens. How can we count them differently?” These questions helped pupils to share different problem-solving strategies with each other.

8. The game is positioned as a text to be read
Connections were made between the game and other learning materials. For example, the pupils were asked to use the models from the game during regular problem-solving sessions, completed using worksheets.

9. Connections to prior learning and the world beyond the game environment
During the game, teachers encouraged pupils to use mental strategies they had learned previously. Outside of the game, children were reminded of the strategies and representations used in the game.

More teaching and learning:

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So how effective was this approach? We enlisted 26 seven- to nine-year-olds across China and Turkey. The pupils played this game over a two-week period, playing it three times per week.

It was a small study, but our results showed great impact. We found that as children played the game, their performance improved a great deal. In the pre-test the average performance was only 68 per cent, but by the time we did the post-test, it averaged 95 per cent.

Of course, there may be other factors at play here: for example, pupils may have been doing extra subtraction and mathematical representation study at home, which could have skewed the results. However, assigned homework during this time was not related to subtraction, and it was not being taught simultaneously in other parts of the curriculum at the time. 

The research is clearly limited by the number of children involved in the trial, but I think there are takeaways for teachers, with or without the use of the game.

The main one is that when teaching maths, it is important to get pupils to represent their answers in more than one way. Rather than simply asking children to create a number sentence, including the use of a visual model, such as blocks that can be coloured in, is a good idea. 

I’d also urge teachers to consider the effectiveness of letting pupils lead their own learning on arithmetic word problems through game-based learning. In my own teaching, I have already put this into practice, and I ensure that all maths lessons have multiple representations for children to understand, and for them to use in their answering of questions and problem-solving. 

Gregory Macur is a head of primary Cambridge curriculum and Year 3 teacher in China