1. Managing discussion

2. Aims of the session This session is intended to help us to:
experience discussion of mathematics;
reflect on how discussion can be used to promote learning;
explore the characteristics of purposeful discussion;
explore the management skills that are needed to implement purposeful discussion.

3. A group activity
Decide whether each statement on the cards you have been given is always, sometimes or never true.
Stick your statement on a poster and write your explanation next to it.
If you think a statement is ‘always true’ or ‘never true’, then explain how you can be sure.
If you think a statement is ‘sometimes true’, describe all the cases when it is true and all the cases when it is false.
Make up a statement that your learners could discuss in a similar way.
Use Statements sheet and give out glue, sugar paper, pens and scissors.

4. Always, sometimes or never true?
Numbers with more digits are greater in value
The square of a number is greater than the number.
When you cut a piece off a shape, you reduce its area and perimeter.
A pentagon has fewer right angles than a rectangle.
If you double the lengths of the sides, you double the area.
Multiples of 11 are always palindromic numbers (i.e. they read the same backwards as forwards).

5. Always, sometimes or never true? (contd.)
Quadrilaterals tessellate.
If you add together the digits in a multiple of 9 the digit sum is divisible by 9.
A triangle can only have one right angle at the most.
If you add together even numbers the answer is always even.
If you add together odd numbers the answer is always odd.
Triangles tessellate.
Discuss responses and the quality of the discussion

6. Reflect on your discussion
Who talked the most? Who spoke the least?
What was their role in the group?
Did everyone feel that all views were taken into account?
Did anyone feel threatened? If so, why? How could this have been avoided?
Did people tend to support their own views, or did anyone take up and improve someone else's suggestion?
Has anyone learnt anything? If so, how did this happen?

7. Why is discussion rare in mathematics?
Time pressures
“ It’s a gallop to the Sats.”
“ Learners will waste time in social chat.”
Control
“ What will other teachers think of the noise?”
“ How can I possibly monitor what is going on?”
Views of learners
“ My learners cannot discuss.”
“ My learners are too afraid of being seen to be wrong.”
Views of mathematics
“ In mathematics, answers are either right or wrong – there is nothing to discuss.”
“ If they understand it there is nothing to discuss. If they don’t, they are in no position to discuss anything.”
Views of learning
“ Mathematics is a subject where you listen and practice.”
“ Mathematics is a private activity.”
Use DVD clip on Thinking about learning/ thinking about discussion from over view DVD

8. What kind of talk is most helpful?
Cumulative talk
Speakers build positively but uncritically on what each other has said.
Repetitions, confirmations and elaborations.
Disputational talk
Disagreement and individual decision-making.
Short exchanges, assertions and counter-assertions.
Exploratory talk
Speakers elaborate each other’s reasoning.
Collaborative rather than competitive atmosphere.
Reasoning is audible; knowledge is publicly accountable.
Critical, constructive exchanges. Challenges are justified; alternative ideas are offered.
Examples to explore and classify.
What kinds of difficulties might you encounter in using discussion on your classroom?
What ground rules might you set?

9. Ground rules for learners
Talk one at a time.
Share ideas and listen to each other.
Make sure people listen to you.
Follow on.
Challenge.
Respect each other’s opinions.
Enjoy mistakes.
Share responsibility.
Try to agree in the end.

10. Managing a discussion
How might we help learners to discuss constructively?
What is the teacher’s role during small group discussion?
What is the purpose of a whole group discussion?
What is the teacher’s role during a whole group discussion?
Putting a session into action and reporting back – sheet 4.9

11. Teacher’s role in small group discussion
Make the purpose of the task clear.
Keep reinforcing the ‘ground rules’.
Listen before intervening.
Join in, don’t judge.
Ask learners to describe, explain and interpret.
Do not do the thinking for learners.
Don’t be afraid of leaving discussions unresolved.

12. Purposes of whole group discussion
Learners present and report on the work they have done.
The teacher recognises ‘big ideas’ and gives them status and value.
The learning is generalised and linked to other ideas and the wider context.
Look at transcripts of talk in primary mathematics lesson and consider the teacher’s role in each case.

13. Teacher’s role in whole group discussion
Mainly chair or facilitate.
Direct the flow and give everyone a say.
Do not interrupt or allow others to interrupt.
Help learners to clarify their own ideas.
Occasionally be a questioner or challenger.
Introduce a new idea when the discussion is flagging.
Follow up a point of view.
Play devil’s advocate; ask provocative questions.
Don’t be a judge who:
assesses every response with ‘yes’, ‘good’ etc;
sums up prematurely.

14. Planning a discussion session
How should you:
organise the furniture?
introduce the task?
introduce the ways of working on the task?
allocate learners to groups?
organise the rhythm of the session?
conclude the session?

15. Follow up task
Plan and try out a discussion based activity with your class
Come to the next session ready to share you experiences and reflect on the quality of the discussion