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.
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.
You can ask them to arrange the dominoes on the table to show you that they have/have not got a full set and then all children can have an opportunity to look at others' arrangements.
By inviting the learners themselves to justify their answers, you can draw out the key features of the dominoes and the systematic approach that is required.
This is the codification stage, where you are highlighting key learning points and perhaps introducing specific vocabulary.
Consolidation of the ideas comes in the form of another task, Amy's Dominoes, which also involves finding out whether a domino set is a complete one, but this time the information focuses on the number of dots.
' and 'how many jelly babies would fill the school hall?
') can also be a useful vehicle for 'holding back' in the mathematics classroom and giving children the opportunity to explore a situation freely.