The EEF’s ‘Cognitive Science Approaches in the Classroom’ evidence review suggests that using worked examples helps to manage pupils’ cognitive load by providing clear, step-by-step exemplification which supports understanding of each stage in a mathematical process or task. This removes the need for pupils to carry out the task in its entirety, and instead allows them to focus attention on understanding the individual steps required to reach a solution.
Worked examples can also promote high-quality mathematical talk by providing opportunities for pupils to work on shared tasks to elicit collaboration and discussions around concepts, strategies and ideas. In this way, worked examples can support pupils’ transition to independent practice by providing a scaffold which can boost confidence and help prevent pupils from feeling overwhelmed.
This also links to recommendation 5 of the EEF’s ‘Improving Mathematics at Key Stage 2 and 3’ guidance report which highlights the role of worked examples in making pupils’ thinking explicit. Worked examples can be used to encourage explanation, whereby pupils articulate their reasoning and mathematical thinking, deepening understanding of the steps they take and why these are needed.
In my own classroom, before sharing the worked examples, I give pupils the task and ask them to briefly begin exploring possible approaches. This encourages pupils’ own thinking, and also provides an opportunity for my initial assessment of the strategies pupils are using, and to identify any misconceptions.
I then present the worked examples and ask pupils to consider the potential benefits and challenges of the different approaches used. Key questions include:
- How are these two approaches related?
- Which approach do you prefer?
- Is there a different way to approach this?
These questions encourage pupils to communicate their thinking around the alternatives which are open to them, drawing their attention away from over-emphasis on the solution to the task, and instead encouraging increased focus upon the approach and individual steps used.
As teacher, these discussions provide opportunities to act as a role model in using accurate mathematical terminology and language, and to encourage pupils to use this in their own discussions and explanations.
When planning which worked examples I will use in my teaching, I carefully consider opportunities for discussion of common misconceptions. I use colour-coding to highlight particular features of the approaches that I want pupils to explore.
In the worked example above, I used colour to highlight the steps which were common to both approaches. This enabled pupils to compare these, helping to develop their understanding of why particular steps needed to be completed first.
After considering the worked examples, pupils were able to identify more ways to approach the task. We discussed some of these as class, encouraging pupils to adopt a Think Aloud process to narrate their thinking as they shared their different approaches.
As pupils shift towards working more independently, this previous experience of approaches allowed pupils to select those which they feel most confident and comfortable with. In addition, because the worked examples were deliberately planned to help pupils consider common misconceptions, fewer pupils made errors of this nature during their independent work. However, where errors did arise, pupils were more easily able to link back to the worked example to help them self-correct.
In my teaching, worked examples have helped the pupils to develop their understanding of key mathematical structures and concepts, whilst maintaining confidence and addressing some common misconceptions. Crucially, they have also supported pupils to think more carefully about the different approaches they can take during mathematical tasks in order to make more careful, deliberate decisions about what they are doing and why.