1. Charlie Gilderdale University of Cambridge December2014 Mathematics Workshop 2: Teachers as creative, reflective professionals Inspiring teaching, Inspiring learning

2. Build a community of mathematicians By: Creating a safe environment for learners to ask questions Providing opportunities for collaborative work Valuing a variety of approaches Encouraging critical and logical reasoning

3. Opposite vertices If I give you a line, can you tell me straight away if that line could be: the side of a square? the diagonal of a square? If such squares CAN be drawn, can you find an efficient method for drawing them?

4. Triangles in a Square Here is a triangle drawn on a 5 by 5 dotty grid square by joining the top-right-hand dot to one dot on the left hand side of the square, and one dot on the bottom side of the square

5. What questions can we ask? Triangles in a Square Triangles in a Square

6. Mind Reader? http://www.flashlightcreative.net/swf/mindreader/ Choose any two digit number, add together both digits and then subtract the total from your original number…

7. Now look up your answer on the chart and find the relevant symbol. Now concentrate on the symbol…

8. Mind Reader?

11. How do we follow this up? Always a Multiple? http://nrich.maths.org/7208

12. What’s Possible? Give me a whole number…

13. Why might a teacher choose to use these activities?

14. Alan Wigley’s Challenging Model (an alternative to the path-smoothing model) Leads to better learning – learning is an active process Engages the learner – learners have to make sense of what is offered Pupils see each other as a first resort for help and support Scope for pupil choice and opportunities for creative responses provide motivation

15. Tilted Squares Can you find a quick and easy method to work out the areas of tilted squares?

16. What can we offer learners? Low threshold, high ceiling tasks Opportunities to exhibit their thinking and refine their understanding A conjecturing culture where it is OK to make mistakes A careful use of guiding questions and prompts Opportunities to practice skills in an engaging way: HOTS not MOTS Frequent opportunities for talk (about maths) Teachers who model mathematical behaviour Teachers who emphasise mathematical behaviours that they wish to promote

17. Enriching mathematics website www.nrich.maths.org The NRICH Project aims to enrich the mathematical experiences of all learners by providing free resources designed to develop subject knowledge and problem-solving skills. Enriching the Secondary curriculum http://nrich.maths.org/11244

18. Think of a topic you’ve just taught, or are about to teach, and look for opportunities to reverse the questions look at/for alternative methods seek all possibilities greater generality (what if…?)

19. The next steps Two weeks with the students or it’s lost…… Think big, start small Think far, start near to home A challenge shared is more fun What, how, when, with whom?

20. Learn more! Getting in touch with Cambridge is easy Email us at info@cie.org.uk or telephone +44 (0) 1223 553554 www.cie.org.uk