Ambitious mathematics: Ratios, decimals, fractions and time for Ta’ovala:The Connect: Reinforcing the learning
David Ahlquist rounds the lesson off, connecting the work the students have done to the associated big mathematical ideas. He constantly refers the students back to their own thinking and strategies, affirming what they have done: ‘Well done… I really liked your thinking’.
Professor Roberta Hunter explains the significance of the Connect being done at the end of the lesson:
‘Often teachers will think ‘I’ve got to tell them everything they need to know at the beginning of the lesson’ … David trusted they would come through with what he could pick up … at the end he picked up on what they said and he took them to the next level, almost summarising so that they could walk away with a new thinking tool about what they had done … What you see in classrooms where teachers begin with that … he did it at the end!’
The effect of this strategy is demonstrated in an unexpected and dramatic way. As part of the filming process the film crew ask the teacher and class to recreate their group work, aiming to get more footage to help the editing process: ‘We hoped to get more footage of the learning in the groups’.
During the lesson itself, none of the groups reached a final answer to Problem (b). However, in their reconstruction all groups reached a final and correct answer: ‘Our students couldn’t unlearn what they had had just learnt … they had developed their understandings to a new level’.