Fiona Allan fiona.m.allan@gmail

2. Fiona Allan fiona.m.allan@gmail.com

3. Think of a number • Add 6 • Double your answer • Subtract 4 • Half your answer • Take away the number you first thought of • And the answer is … It’s A Kind of Magic David Crawford pub. The Mathematical Association ISBN 978-0-906588-67-3

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5. Teachers: ‘I enjoy teaching Mathematics’ % change

6. Teachers: ‘My learners are responsive in my classes’

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8. Teachers : ‘I don't know where to find new resources’ % change

9. Teachers: ‘I get frustrated if my learners don't keep up’ % change

10. Teaching is more effective when it • Builds on the knowledge learners already have • Exposes and discusses common misconceptions and other surprising phenomena • Uses higher-order questions • Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work • Encourages reasoning rather than ‘answer getting’

11. Uses rich, collaborative tasks • Creates connections between topics both within and beyond mathematics and with the real world • Uses resources, including technology, in creative and appropriate ways • Develops mathematical language through communicative activities • Recognises both what has been learned and also how it has been learned Mathematics Matters

12. Build on the knowledge learners bring to sessions Write down at the top of a sheet of A4 paper something that you already know 5 x 8 = 40 100 centimetres = 1 metre 50% of £20 = £10

13. If I Know This I Also Know: 50% of £20 = £10 25% of £20 = £5 50% of £200 = £100 5% of £20 = £1

14. Expose and discuss common misconceptions • Working in a group, sort the cards. • Now sort them in a different way. • Discuss in your group how this sorting activity could expose misconceptions. What Makes a Good Resource – Understanding and Ordering Decimals

15. Develop effective questioning North Hertfordshire College project • Attendance in the classes taking part was 90% compared to 78% for those not taking part • The pass rate for GCSE Mock increased to 77% in the classes taking part, compared to a College pass rate of 52% in 2009/2010. • In an AS Level mock exam, learners achieved an average of 1.57 grades higher than the grades predicted by their GCSE scores. Professional development opportunities for mathematics teachers in Post-16 colleges

16. Use cooperative small group work Make appropriate use of • whole class interactive teaching, • individual work and • cooperative small group work

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18. Teachers: ‘I prefer one teaching method for teaching maths’ % change

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20. Emphasise methods rather than answers Percentages (Encouraging reasoning rather than ‘answer getting’) Mathematical Moments

21. Use rich collaborative tasks Integrating Rich Tasks

22. Create connections between mathematical topics Making connections to other topics in mathematics – for example, between fractions and decimals real-life problems or the world of work National STEM Centre E-Library and NCETM

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26. Use technology in appropriate ways • Give it the time that it needs • Start small • Just get on with it ‘The use of the technology has had a positive effect on the engagement of the students and the enjoyment of Mathematics.’ ICT and Digital Technology used in mathematics teaching

27. Start by choosing one of the Principles for the effective teaching of mathematics, focus on that and embed it in your practice.