Primary National Strategy

1. PrimaryNational Strategy Mathematics3 plus 2 day course:Session 8

2. Objectives • To discuss approaches to teaching problem solving • To consider the tasks for Day 4 of the course (the second self-study day)

3. Approach A • Start work on a problem during an initial whole-class discussion • Ask pupils to continue the activity, often in pairs or small groups, developing it to a level appropriate to their attainment • Collect pupils’ responses in a plenary, and work through the solution, encouraging individual or pairs of pupils to contribute • Draw attention to particular features of the solution and the strategies that pupils used • Stress the stages and steps used, and how these might be applied to similar problems

4. Approach B • Work through a problem during an initial whole-class discussion, demonstrating ways of being systematic in approach and recording • Follow this by providing related problems that lend themselves to similar approaches • Give pupils at different levels of attainment harder or simpler problems, as appropriate • Draw together solutions in a plenary, working from the simpler to the more challenging tasks • Highlight the strategies used in the solutions, stressing the steps and stages, and how these might be applied to similar problems

5. Discussion points For each approach: • What scope does the approach offer for pupils to make their own decisions? • When and why should teachers intervene in what pupils are doing?

6. Approach A: • is less directed • offers good scope for pupils to make own decisions • may require mini-plenaries throughout main part of lesson • may require a greater level of intervention in group work • allows the teacher to draw on the approaches used by pupils to highlight what it means to be ‘systematic’

7. Approach B: • offers less scope for pupils to make own decisions • enables pupils to apply and practise the approach of the teacher • may help pupils to work independently in a sustained way after the guidance at the start • allows a teacher to focus on a group working at a particular level • requires the teacher to draw out the common elements of related tasks in the final plenary

8. Day 4: a self-study day • Following up the day on problem solving • Teaching problem-solving lessons • Preparing for Day 5 Allow about 4 hours 15 minutes plus some normal teaching time with your own class.

9. TASK 1: Following up the problem-solving day • Identify two pupils whom you believe are at the same level of attainment in AT1. • In your daily mathematics lessons over 2 weeks, observe each pupil. Keep brief notes on evidence of the pupils’ attainment in AT1. • After your observations, think about: • the similarities and differences in the ways that the two pupils use and apply mathematics; • the teaching strategies that might help each of them progress in AT1. Allow about 1 hour, plus some normal teaching time with your own class, for this task.

10. TASK 2: Teaching problem-solving lessons • Prepare and teach two lessons on problem solving – one to your own class and one to a different age group. • Choose the lessons from those in Participant’s pack 4. Adapt them to suit the pupils that you will teach. • After each lesson, collect some samples of pupils’ work. Complete one of the two evaluation forms provided in the pack. Be prepared to discuss the lessons on Day 5 of the course. Allow about 2 hours, plus 1 hour of normal teaching time with your own class, for this task.

11. TASK 3: Preparing for Day 5 • Read the articles Communicating in mathematics and Mathematics reasoning. • For about half an hour, observe two pupils (in your own class or a colleague’s class) working on an activity involving an aspect of AT1. • About every 3 minutes, record the kind of activity the pupils are engaged in, identifying opportunities they have for mathematical communication and reasoning, using the recording sheet in the pack. Allow about 1 hour 15 minutes for this task.

12. Lessons on problem solving • Fives and tens • Buckets of water • Addition and subtraction problems • Area and perimeter problems • Problems involving patterns and sequences • Multiplication and division problems

13. TASK: Lessons on problem solving Look at one of these lessons. Consider possible modifications that you might make to suit your pupils. Year 4 teachersLesson 1: Fives and tens Year 5 teachersLesson 3: Addition and subtraction problems Year 6 teachersLesson 5: Problems involving patterns and sequences Other teachersChoose one of the above.

14. Teachers have found it helpful to ... • start the class or group on an activity and stop them after a short period of time to discuss the initial approaches that they have used • set pupils to work initially in pairs, then put the pairs into fours to share what they have done • when intervening, focus on systematic approaches rather than specific mathematical content, e.g. • ‘Gitali, can you show David the method you are using?’ • ‘Kevin, can you explain to me what Jodie has just said?’

15. Teachers have found it helpful to ... • gather the class or group for a mini-plenary to discuss or explain something, with opt-out points when pupils can choose whether to stay for more of the discussion or return to continue their work • after the class has completed the work: • put the class into groups to share results, methods or solutions, and agree which answers are correct or which approaches or forms of recording are the most helpful or effective • ask one or two pupils to describe to a group or the whole class how they approached the work and what conclusions they reached