1. DEVELOPING FLUENCY, PROBLEM SOLVING AND REASONING KS1 Presented by Mark Hattersley - mark@totallymaths.co.ukmark@totallymaths.co.uk

3. 2 MINUTE TASK What is important?

4. WHAT IS FLUENCY? Your thoughts…

5. How fluent you are is measured by how flexible you are. Dr Yeap Ban Har International benchmark for Fluency is about a minute for a computation at age related.

6. mark@totallymaths.co.uk

7. PROMOTING FLUENCY - NRICH Pairs of numbers Totality Strike it out

8. BREAK

10. Play to 37

11. WHAT PROBLEM SOLVING SKILLS DID YOU USE?

12. Problem solving is something that a pupil becomes involved in when (s)he has to do some extra exploration in order to find a solution Problem solving may not involve problem solving for the more able as they might instantly produce a solution Bernard Bagnall, Nrich

13. A problem is something that you probably will not immediately see how to tackle or which once started will challenge your thinking Jennifer Pigott, Nrich

14. DEVELOPING PROBLEM SOLVING

15. WEAKNESSES IN TEACHING PROBLEM SOLVING

16. THINGS TO CONSIDER… Discuss with one another What is the role of the teacher during problem solving? What would a problem solving lesson objective look like? How do you teach problem solving?

20. TOOLS FOR PROBLEM SOLVING Drawing a Diagram Drawing a Table Acting it Out or Using Concrete Material Guessing and Checking Creating an Organised List Looking for a Pattern

21. NRICH – 11082 4 stages Stage 1: Getting started Stage 2: Working on the problem Stage 3: Going further Stage 4: Concluding

22. CONSIDER How to encourage skills of enquiry, independence and perseverance for problem solving … Stuck pupils - encourage perseverance Draw conclusions Encourage children to get started Make positive interventions – encourage perseverance

23. REFLECT BACK ON … How would you now use play to 37 with your class?

25. Your turn - choose a problem. Discuss the strategies you are using.

26. Two digit targets The Brown Family One of Thirty-six Growing garlic

27. WHAT IS REASONING? Reasoning is the use of logical thinking to make sense of a situation or idea. Annenberg Learner Mathematical reasoning is not something that students walk into your classroom knowing how to do… it is a process that must be learned whilst you are teaching the content Ball and Bass

28. NRICH – FIVE STEP PROGRESSION 1. Describing – tells what they did 2. Explaining – offers some reasons for what they did (may be incorrect) 3. Convincing – confident that their chain of reasoning is correct. May not be correct but argument has more coherence. May use ‘I reckon’ or ‘without doubt’

29. 4. Justifying – a correct logical argument with a complete chain of reasoning. Uses words such as ‘because’, therefore’, ‘and so’… 5. Proving – a watertight argument that is mathematically sound, often based on generalisations

30. HAVE A GO…

31. Reasoning Mat What if… This worked so... I can see a pattern... I tried … This didn’t work so... I noticed that... I decided to......... because........ I wondered why…

32. REASONING QUICK WINS – 10 REASONING STARTERS Shoot CrocodilesNasty!

33. IMPROVING REASONING : ANALYSING ALTERNATIVE APPROACHES NRICH MALCOLM SWAN In mathematic lessons the attention is given to answer getting NOT improving the quality of the reasoning tackle it twice approach In pairs have a go Review where you get to, look at other’s approaches Tackle it again

37. REASONING

38. HMI BETTER MATHS 31/01/14 DAILY… DOING AND UNDOING Progression through a few questions (get harder) Then try a missing term Then no terms, just the answer Have you found several possibilities? Have you found all the possibilities? How do you know?

40. WHAT ABOUT MORE ABLE?

41. HOW WILL CHILDREN’S PROGRESS BE MEASURED? WHAT DO WE KNOW? Released last year for key stage 1 and key stage 2 Sample questions released June 2014 Sample tests released June 2015

42. PLENARY