We began by considering interior and exterior angles in a polygon, then following the principles of needing to convince:
a) ourselves
b) a friend
c) a sceptic
We then looked at the different ways in which the task could have been designed:
It was noted that no formulation is necessarily "better" than another, but they each can be considered in terms of the outcomes desired and the students themselves.
The following ideas were discussed:
Option 1
- question suggests it should be easy to find out
Option 2
- invites investigation
- like proving your answer to a friend
- students might responds with 'no'! - but then ask why not
Option 3
- what does the word investigate mean
- difficult to lock program to ensure focus on task
- self-differentiating
Option 4
- may not get this exact formula, therefore might assume they are wrong
- when give the formula, students may not feel the need to prove it themselves
- takes away the opportunity for discovery
At the end of this session, Gabriel asked us to fill in a questionnaire to help for a section that he is writing for a book on teacher education. This prompted me to discuss the following ideas:
- considering my own proofs: think about how I am going to introduce a concept to the class; do I want to prove it beyond all doubt or do I want to leave that as an exercise for the students to do?
- possible lesson idea: introduce an idea and then have 5 minutes silent thinking about the concept - find out who is convinced and who is not then get the convinced people to prove to the 'sceptics'
- task design: think carefully about the outcomes desired from the task and how to structure it to achieve these outcomes
