Liz Woodham, NRICH Project & Michael Hall, Open University 2014 - 2015

1. Developing teachers’ mathematics subject knowledge in primary schools to improve the attainment of all pupils Liz Woodham, NRICH Project & Michael Hall, Open University 2014 - 2015

2. In between face-to-face days … Don’t forget https://nrich.maths.org/haringey

3. Day 6 – 11 November 2014 9.15-9.30 Welcome 9.30-10.45 Project update and working on mathematical tasks togetherUpdate on project achievements to date and points to consider for this academic year Tackling tasks and reflecting on them in terms of subject knowledge and pedagogy 10.45-11.00 Break 11.00-11.45 Working on more mathematical tasks together Tackling one or more tasks and reflecting on them in terms of subject knowledge and pedagogy 11.45-12.15 Sharing experiences since last time 12.15-1.00 Lunch 1.00-1.20 Planning for/sharing ideas about staff meeting 1.20-2.20 Curriculum priorities and curriculum development work In pairs, planning for at least one task back at school 2.20-3.10 Working on another mathematical task together 3.10-3.15 Reflection

4. Common themes from mathematical needs identified on day 1 The following were flagged up by at least two schools: • Fractions/decimals/percentages • Problem solving • Place value • Time • Algebra • Word problems • Application of calculation strategies • Subtraction

8. ‘ I think that the opportunities to explore mathematical thinking is key and my class were great models of how to speak mathematically and there were opportunities for my SEN children who were on 2s to match the rest of the class. There was an air of increased confidence’.

9. Helping children to become competent and confident problem solvers As teachers we can support this process in three principal ways: • Through our choice of task • Through structuring the stages of the problem-solving process • Through explicitly and repeatedly providing children with opportunities to develop key problem-solving skills. See ‘Developing Excellence in Problem Solving with Young Learners’ article http://nrich.maths.org/10865

10. Poly Plug Rectangleshttp://nrich.maths.org/7511 The computer secretly makes a rectangle using equal rows of spots on the 5 by 5 grid. The aim is for you to find the rectangle by testing spots on the interactivity. If the chosen spot is part of the rectangle, it will turn yellow.  If it isn't part of the rectangle, the spot will turn blue.

11. What makes ‘Poly Plug Rectangle’ a rich task?

12. The Problem-solving Process • Stage 1: Getting started • Stage 2: Working on the problem • Stage 3: Going further • Stage 4: Concluding

13. Problem-solving skills • Getting started try a simpler case draw a diagram represent with model act it out 2. Working on the problem visualise work backwards reason logically conjecture work systematically look for a pattern trial and improvement 3. Going further generalise verify prove 4. Concluding communicate findings evaluate

14. How does the activity Poly Plug Rectangle support the three National Curriculum aims of fluency, reasoning and problem solving?

15. Before we meet again … • Continue to try out rich tasks with your learners and colleagues • Take a look at the Problem Solving feature on NRICH, particularly the articles: http://nrich.maths.org/10334 • Look at NRICH’s curriculum mapping documents: http://nrich.maths.org/8935

16. Liz Woodham emp1001@cam.ac.uk Michael Hall wichaelhall@gmail.com