1. Subject Leader Development Meeting June 2010

2. Programme Session 1 – Problem Solving This session will consider the principles of effective teaching and learning as well as the importance of problem solving in the mathematics curriculum. 1030Tea/Coffee Session 2 - Group Work This session will explore a group task and discuss the implications that this has for teaching and learning.

3. Objectives:   To discuss approaches to problem solving in the classroom and experience problem solving activities   To consider approaches to group work in the mathematics classroom and experience group work activities

4. Starter Jim asks 100 students if they like biology, chemistry or physics best. 38 of the students are girls 21 of the girls like biology best 18 boys like physics best 7 of the 23 students who like chemistry best are girls. Work out the number of students who like biology best.

5. Looking back to the future Session 1

6. Cockroft report 1982 para 249

7. What’s already been happening?   National Strategies materials (2001 – present)   New KS3 National Curriculum (MPA)   Rich tasks   New tasks for old   Bowland Trust materials   Functional Skills   Quality of written communication (QWC)   Success for All materials (Standards Unit)

8. Some principles for effective learning   Pupils learn about and learn through the key mathematical processes   Pupils work collaboratively and engage in mathematical talk   Pupils work on sequences of tasks   Pupils select the mathematics to use   Pupils tackle relevant contexts beyond the mathematics classroom   Pupils are exposed to the historical and cultural roots of mathematics Improving learning in mathematics: challenges and strategies Malcolm Swan

9. Some principles for effective teaching   Build on the knowledge pupils bring to a sequence of lessons   Expose and discuss common misconceptions   Develop effective questioning   Use cooperative small group work   Emphasise methods rather than answers   Use rich collaborative tasks   Create connections between mathematical topics   Use technology in appropriate ways Improving learning in mathematics: challenges and strategies Malcolm Swan

10. Mysteries Pupils are presented with data on slips of paper about a situation where there is a single open question or problem for them to resolve. The statements can be general or background information, specific details and sometimes ‘red herrings’ or irrelevant information. Pupils work in groups to read and sort the statements, link information and come up with a solution to the mystery question. Adapted from ‘Leading in Learning: developing thinking skills at Key Stage 3’ Handbook for teachers

11. It’s a Mystery   What strategies have you used whilst solving the problem?   What strategies might your pupils use whilst tackling the problem?

12. Problem Solving in Action Watch the video clip and consider   the barriers experienced by the pupils   the skills that we need to teach for pupils to be able to tackle this type of problem   how support could be given to enable the pupils to acquire these skills

13. The Problem Solving Cycle

14. What’s the problem about? Have you seen this type of problem before? What did you do? What are you trying to find out? Could the problem be solved in a different way?

15. Developing progression in thinking skills   Increase the difficulty of the task   Reduce the amount of support for the task   Increase the complexity of the group work   Increase the level of challenge in the plenary Adapted from ‘Leading in Learning: developing thinking skills at Key Stage 3’ Handbook for teachers

16. It’s another mystery In pairs, create your own set of mystery cards.

17. Mysteries Consider the mystery tasks and discuss how you might incorporate them into your existing schemes of work.

18. Session 2 Group work and problem solving

19. Starter  The mathematical farmer

20. A ‘Cog’native problem!

21. Counting Cogs http://nrich.maths.org/7014&parthttp://nrich.maths.org/7014&part= http://nrich.maths.org/7014&part

22. Working in Groups   What are the benefits of pupils working in groups?   As a teacher, what are the issues and what strategies can be used to minimise them?

23. Working in Groups When productive group work is a regular feature of lessons, pupils:   fully develop their understanding of an idea because they have tried to explain it to others or argue a point of view;   are more likely to ‘have a go’;   are persistent and develop perseverance;   are more likely to develop social and team-working skills. Group work gives pupils opportunities to:   practise and to learn from each other;   develop a sense of empathy and to understand other views;   have the opportunity to make decisions and justify them;   develop problem solving skills.

24. Working in Groups   What are the benefits of pupils working in groups?   As a teacher, what are the issues and what strategies can be used to minimise them?

25. Resolving the Issues Pupils are more likely to work effectively in groups if the teacher:   provides clear structures in which groups can operate;   uses strategies that support positive behaviours and develop group-work skills;   establishes clear rules and procedures;   introduces tasks so that outcomes are clear and linked to the behaviours required;   selects groups to suit the task;   maintains momentum by effective intervention;   sets group goals.

26. Effective mathematical collaboration depends on these skills   Listening   Asking questions – to help you understand your thinking   Asking questions – to help you understand what someone else is saying   Explaining by telling how and why   Helping others - by responding to their needs   Helping others - to do things for themselves   Showing others how to do things   Finding out what others think - asking for, listening to and making sense of their ideas   Thinking about and making use of what has been said   Being clear when telling others about your thinking   Giving reasons for ideas   Allowing everyone to take part   Pulling ideas together - sharing listening, valuing everyone’s ideas   Finding out if the group is ready to make a decision.

27. The Future for Problem Solving …?   Consider the problem solving skills that you want your pupils to develop and how might you achieve this?   Create a mission statement that summarises this, in less than 30 words

28. The Future for Problem Solving …? Our mission statement…   Pupils can look at a problem, decide on the most appropriate strategy, make links to similar problems and then persevere to find a solution Staffordshire Secondary Mathematics Team 2010

29. Possible Resources   Logic problems: http://www.puzzles.com/projects/logicproblems.h tml http://www.puzzles.com/projects/logicproblems.h tml   Nrich http://nrich.maths.orghttp://nrich.maths.org   Ken Ken www.kenken.com www.nytimes.com/ref/crosswords/kenkenwww.kenken.com www.nytimes.com/ref/crosswords/kenken

30. Next Steps   CPD – Developing Problem Solving in the Mathematics Curriculum - 16 Feb 2011, MAB52901   Discuss one or more of the 4 tasks with your department, trial with a group of pupils, retain any evidence for use at the district/cluster APP meeting in the Autumn term 2010.   Next Subject Leader Development Meeting (SLDM) 23 rd November 2010 Kingston, MAN51701, MAB51601 or 16 th November 2010 Seabridge MAN51702, MAB51602