Problem-solving approaches to teaching and learning in Maths

1. Problem-solving approaches to teaching and learning in Maths Fran Wilson

2. Two schools in central Cambridge –Coleridge CC and Parkside CC Differing demographic of catchment Very different achievement levels in Maths Coleridge A*-C – 33%, Parkside A*-C – 75%(2005 cohort – first year of federation) Very different styles of organisation and teaching. Parkside Federation

3. Mixed-ability classes Pupil-centred exploration Problem solving Discussion and groupwork Thinking Maths Three part lesson focusing on cognitive progress/ learning styles Parkside CC

4. Classes set by ability Teacher-led instruction based teaching and learning Three-part lesson focusing on curriculum content Practice heavy activities Coleridge CC

5. Students learn better from each other than from their teacher Students have the ability to solve problems if they are given the time to think about them Students need to be able to work out what to do independently to create their own scaffolding Ethos for Learning

6. Resolving conflict may require students to struggle Discussing methods is crucial to increasing understanding All students can benefit from the progress of some students Students can approach learning in different ways Ethos for Learning

7. You can analyse problems You can interpret descriptions You can work out what you don’t understand You can see when different ways of showing something are related Having these skills will mean that: You see how things work in general You are good at explaining what you think You ask good questions What it means to be good at Maths?

8. Which will mean that: You can work out which method you should use You can make links to reallife You can work out a way to improve So that: You can find a way to solve problems. What it means to be good at Maths?

9. Teachers help students to develop group work strategies by allocating roles Students discuss how they’ve worked on their role in the plenary Students set targets in their group on how they will improve how they work together in the future Ethos for Group Work

10. Each member of the group takes or is given one of the following roles: Organiser Resource Manager Inclusion Understanding The plenary is then used to discuss how the group worked together, which roles they did well and which they need to work on to improve. Group Roles

12. For example – first problem of the topic

14. Realisation that you don’t have all the information that you need Identification of what information is needed Different strategies for working together Successful completion of some of the task Discussion of process What happened?

15. Excerpts from a lesson

16. The answers!

17. Students more open to working things out for themselves Developing confidence in solving problems Greater commitment to achievement More positive approach to maths lessons Higher aspirations and belief Better results! The changes

18. Coleridge Results - GCSE

19. In the best lessons, ‘pupils were expected to work productively in pairs or groups, discussing their learning, trying out new skills and exploring concepts’ ‘In the most effective lessons, teachers often presented new topics by challenging pupils to apply their mathematics to solve problems, drawing ideas from them and using probing questions to gauge their initial understanding and develop it.’ ‘Good teaching ensures that … important connections are forged, but the most effective teachers enable the pupils to make the links for themselves. ‘ Mathematics: understanding the score (OFSTED, 2008) What do OFSTED think?

20. fwilson@parksidefederation.org.uk Nrich May Issue The Elephant in the Classroom – Jo Boaler More information?