From Exploration to Consolidation

Below are two pairs of tasks. Each pair offers the opportunity to put into practice the model of 'exploration, codification, consolidation', which was first developed by Ruthven.

The first task in each pair encourages learners to be playful with the mathematics and make their own discoveries (exploration). The teacher's role is then to help children articulate what they have learnt, introduce new vocabulary where appropriate, and support children in deepening their understanding by helping them link the new learning to their existing knowledge (codification). The second task in each pair then gives a new context in which children can apply what they have learnt in a meaningful way (consolidation). As a group these problems will give you the chance to develop all five strands of the rope model (understanding, skills, problem solving, reasoning and attitude). 

You can read more about this approach to mathematics teaching and learning here.