Modelling matters in mathematics, but what are the ingredients of effective adult modelling?
To answer that question, let’s begin with an example. Mrs Ahmed presents the following question to her Year 3 children.
“I am going to talk you through my own thinking as I tackle this problem. As you’re listening, think about whether you would approach it in the same way.”
“To begin, I am going to read the question carefully. “How many centimetres long is the ribbon?” I can see the blue ribbon and there are some clues shown on the number line. I can see a zero at the beginning and 1m at the end of the number line. I know that m stands for metre.
“I know that there are 100 centimetres in 1 metre. I also know there are ten intervals. I know that ten tens are one hundred so each interval must be ten.”
“Let me prove it by counting in tens.” As Mrs Ahmed counts in tens, she touches each interval with her finger.
“I am correct. Each interval is counting in tens, because when I reached the 1m, I said 100. I know that 1m is equivalent to 100cm. Therefore, I know I am right.”
“I can now work out how long the ribbon is.”
Mrs Ahmed starts from zero and counts in tens until she reaches the end of the ribbon.
“The ribbon is 70cm long.”
Modelling in mathematics
As maths teachers, our shared goal is for pupils to become effective, independent, and motivated mathematicians. We want to instil drive and determination, so that children feel empowered to tackle any mathematical problem they come across. We want them to ‘to give it a go’ and demonstrate resilience to ‘not give up.’
But motivation is complex. Factors such as a like or dislike of maths, beliefs about whether one is good or bad at maths – as well as whether it is useful or not – can all affect mathematical motivation.
Recommendation 5 of ‘Improving Mathematics in Key Stages 2 and 3’ guidance report highlights the importance of adults modelling strategies and behaviours
to encourage pupils to develop their independence and motivation towards learning maths.
Adult modelling sounds straightforward. It sounds sensible. Children are often influenced by the adults around them and as the ‘experts’ in the room, we need to be the ones modelling these strategies and behaviours to develop them within the pupils that we teach.
When we talk about adults modelling, who do we mean within school and how can we ensure all adults have the secure subject and pedagogical knowledge to model these things effectively?
The ‘MODEL’ acronym summarises these key strategies and behaviours.
This MODEL acronym could help us to reflect upon teaching practice and support us to ask questions of ourselves and of the teachers we lead.
Let’s take Mrs Ahmed’s modelling of ‘own thinking’ as an example.
- Did this problem require Mrs Ahmed to model her own thinking?
- Was she explicit and detailed enough with her own thinking?
- Was there anything that she missed?
- Did she plan what she was going to say?
- What does Mrs Ahmed expect to happen because of this modelling?
- What comes next in the lesson sequence?
- By modelling her own thinking, was Mrs Ahmed able to model her own motivation, confidence, and enjoyment of maths?
- Perhaps modelling these things aren’t quite as straightforward as we might think at first glance. They may require careful planning and deliberate thinking about what this modelling might look like.