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They are willing to change their mind when presented with convincing arguments.
This could lead on to a discussion about the assumptions they will need to make and then you can allow time for pairs/small groups to come to a conclusion.
If the teacher's role is more of a 'guide on the side' rather than a 'sage on the stage', then asking probing questions is of key importance.
The activity offers a context in which to discuss trial and improvement and working systematically, and the way that these two skills are often used together.
Once we have one solution (perhaps by trial and improvement), how many other possible answers are there and how do we know we have got them all (systematic working)?
How do we help our learners to become better at collaborating mathematically?
Read this article to find out more about the importance of collaborative problem solving (CPS) and the impact it can have on your pupils. If you encourage your learners to work in pairs or small groups and share ideas, they may learn to recognise that two heads can be better than one.
Part 2: The Teacher's Role It is perhaps easy to underestimate the effect teacher behaviour can have on enabling problem solving in the classroom.
Ruthven (1989) describes a three-pronged approach to teaching and learning mathematics (Exploration, Codification, Consolidation) which contrasts with the more 'traditional' model of demonstration then practice.
From this point, pupils can work backwards to find the winning approach. involves discussing how many dots pupils can see, and the strategy they use to count them.
This encourages learners to discuss how they are visualising the number patterns within the dots, and helps them appreciate that there is no 'right' way to go about this task.