1. NCETM National Conference Engaging with Mathematics - A journey for teachers, learners and families 1 st December 2009, Nottingham Making use of Cognitive Conflict Lucy Sayce lucy.sayce@reading.gov.uk lucy.sayce@reading.gov.uk & Zofia Frasinski

2. A IMS OF THE PROJECT To consider the effects of experiencing cognitive conflict on learners. To produce a toolkit - “How to get Learners from Arghhh to Aha!”- to aid teachers in planning for positive outcomes from instances of cognitive conflict in the classroom. (This will be a companion document to “The Route to Cognitive Conflict”.) To consider how to manage the long term development of learners’ responses to cognitive conflict. To provide CPD to further develop participants as reflective practitioners.

3. M ETHODOLOGY Active learning group model for CPD 1 8 teachers from 4 schools + consultants 2 whole study days separated by 3 months experimentation Twilight refresher meeting between study days using Reflective Groups model 2 Funding for time out to think and reflect NCETM closed community to support collaboration 1. Jackson, P.Z. & McKergow, M. (2007) The Solutions Focus: making Coaching & Change SIMPLE. Nicholas Brearley Publishing, London. 2. Revans, R. (1998) ABC of Action Learning. London: Lemos and Crane.

4. A MOMENT OF COGNITIVE CONFLICT

5. C ONFLICT RESOLUTION : How did you feel? How did you try to resolve your conflict? What would have helped?

6. H OW DID YOU FEEL ? (P UPIL QUOTES ): I was dazed and confused. I felt like falling down a never ending hole. Confusing at first but okay when I thought of a way to do it. I don’t understand.Oh, I get it. I was confused because I thought I knew what I was doing but I actually didn’t. It felt weird, but it was really interesting. It was fun. Confused, new way of thinking. It felt like we were blind because we had not idea what to do. It was also exciting trying to think what to do. I was quite confused at first because I did not know what to do. It was slightly intimidating What have we got to do? A bit annoyed.

7. H OW DID YOU FEEL ? (P UPIL QUOTES ): I was dazed and confused. I felt like falling down a never ending hole. Confusing at first but okay when I thought of a way to do it. I don’t understand.Oh, I get it. I was confused because I thought I knew what I was doing but I actually didn’t. It felt weird, but it was really interesting. It was fun. Confused, new way of thinking. It felt like we were blind because we had not idea what to do. It was also exciting trying to think what to do. I was quite confused at first because I did not know what to do. It was slightly intimidating What have we got to do? A bit annoyed. Eliciting strong emotions

8. W HAT DID YOU LIKE ABOUT THE ACTIVITY ? (Q UOTES FROM Y EAR 8): The freedom and investigating. I liked that we were allowed to talk and had a lot of thinking time. That we had a lot of independence. The fact we were just left to do it. I quite liked being able to work independently. It was a nice change. Was it helpful to team up with other groups? No, because we will only be cheating.

9. H OW MIGHT LEARNERS TRY TO RESOLVE CC? Learners might engage with someone else’s CC to help them solve it. Is this as powerful? Lots of different questions arise in group work which might frustrate those who just want to solve their own problem. Find someone else with the same conflict. Ask for help from other learners or the teacher. Listening to others resolving their conflict. Explaining ideas to another Need to share ideas with a wider audience but unable to put thoughts into words. Using existing knowledge helps with vocabulary. Existing knowledge can be a hindrance, stifles creativity. Try to fit problem with systems we already know. How many of these depend on opportunities for discussion?

10. T HOUGHTS ABOUT RESOLUTION OF CC FROM S TUDY D AY 1 “Experience is what you get when you don’t get what you want.” (Anon, quoted in Greenfield, 2000, p31). “Thinking and feeling are not two separate processes” (Shayer & Adey, 2002, p52) The model of mathematical behaviour is a product of the prompts and questions used. Insights can be gained into how children understand their world. Do you have to be conscious of the learning for learning to take place? You don’t know what question you’ve asked until you get the response An unexpected response to a question can cause CC for the teacher “Cognitive Dissonance ≡ Cognitive Conflict” – discuss.

11. The need to move around and ask others – how does the teacher manage this? (Envoys, timed wandering.) Do pupils all listen when there is class sharing of ideas. Is this the best way to share ideas? Is confusion necessary to start the thinking process? Do pupils recognise what helps? Does knowing too much maths stifle creativity? Do you need lots of ideas to enable a rich discussion? Using CC takes the fixation away from the activity and enables you to concentrate on the thinking. Are younger children more open to conflict? (Older pupils want to just know the answer?) R EFLECTIONS FROM S TUDY D AY 2 :

12. A TIMELINE FOR EMBEDDING CC IN YOUR CLASSROOM :

13. W HAT NEXT ? Cognitive conflict across the curriculum?

14. F URTHER READING Adhami, M. (2007) Cognitive and Social Perspectives on Surprise. Mathematics Teaching (200) p34-36. Bell, A. (1986). Diagnostic teaching 2: Developing conflict: discussion lesson. Mathematics Teaching, 116, 26-29. Dweck, C.S. (2000) Self-Theories. Their Role in Motivation, Personality and Development. Psychology Press, Taylor and Francis Group, Hove. Greenfield, S. (2000) The Private Life of the Brain. Penguin Books. Shayer, M. & Adey, P. (2002) Pupils’ understanding of what helps them learn, in Learning Intelligence. Open University Press. p51 – 64. Swan, M. (2006) Theories/metaphors for learning mathematics, in Collaborative Learning in Mathematics: A challenge to our beliefs and practices. NRDC & NIACE. P53 - 79.