1. “Working towards Mastery”
KS2 to 3 Arithmetic Development Programme
Day 1: Session 1
Adwick Conference Centre 30 Jan 2015

2. Learning from each other; locally, nationally & internationally
Helping teachers to develop
as reflective practitioners

3. Aims and Priorities
With respect to developing and consolidating non-calculator arithmetic skills. Arrange the cards into some sort of order of importance
Hand out the sort cards and ask for thoughts – this is just to provoke a discussion and focus attention to thoughts around developing non-calculator arithmetic skills
9.35 – 9.45

4. Lessons learned from Shanghai et al
Resolute belief that fluency comes about through a balance conceptual understanding & procedural “mastery”
Reflected in the new national curriculum
The 2014 national curriculum for mathematics has been designed to raise standards in maths, with the aim that the large majority of pupils will achieve mastery of the subject.
Start 9.45

5. Conceptual Understanding
Procedural Fluency
Conceptual Understanding
Talk about how there needs to be a balance of the two, but more so than this, the two need to be integrated.
Many schools are doing either one or the other well but few are doing both, this is the challenge.
(procedural fluency – can do the methods, Conceptual understanding – understands what they are doing)
Mastery 5

6. Mathematics programmes of study state that:
All pupils should become fluent in the fundamentals of mathematics, including…
.. varied and frequent practice, so that pupils develop conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems.

7. Sally knows all her tables up to 12 x 12 When asked what is 13 x 4
Sally knows all her tables up to 12 x 12 When asked what is 13 x 4? She looks blank Does she have fluency and understanding?
Fluency as knows times tables, but no understanding as cannot apply

8. The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. When to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage.

9. Does this represent fluency and understanding?
Not sure?! Perhaps we need to ask the pupil further questions to see whether it is an error, or lack of understanding!

10. Pupils who grasp concepts rapidly should be challenged through rich and sophisticated problems before any acceleration through new content.
Those pupils who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

11. 1256 apples are divided among 6 shopkeepers.
How many will each shopkeeper get?
How many apples will be left?
Understanding - as divide means share between the 6 people
No signs of fluency

12. For many schools and teachers the shift to this ‘mastery curriculum’ will be a significant one. It will require new approaches to lesson design, teaching, use of resources and support for pupils. Certain principles and features characterise this approach:

13. Teachers reinforce an expectation that all pupils are capable of achieving high standards in mathematics.
The large majority of pupils progress through the curriculum content at the same pace.
Teaching is underpinned by methodical curriculum design…..

14. Teaching is supported by carefully crafted lessons and resources to foster deep conceptual and procedural knowledge. Differentiation is achieved by emphasising deep knowledge and through individual support and intervention.

15. Practice and consolidation play a central role
Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts in tandem.

16. Teachers use precise questioning in class…
… to test conceptual and procedural knowledge,
and assess pupils regularly to identify those requiring intervention so that all pupils keep up.

17. Challenge for this Programme
To what extent does the “Rainbow” strategy…
address the concepts as well as the skills, we are trying to develop?
employ successful conceptual development strategies such as;
“variation” , “pictorial” and extending “deeper”?
cater for a primary learning environment?
How can we adapt the strategies and resources to make up any shortfalls?
End 10.15

18. “Development of Rainbow”
KS2 to 3 Arithmetic Development Programme
Day 1: Session 1b
Adwick Conference Centre 30 Jan 2015

19. How it all started
Regular practice of a variety of basic arithmetic skills
Differentiated to cater for different levels
What are the strengths and benefits (WWW)?
What changes would you make (EBI)?
Which of the “cards” does this strategy address?
Give examples of homework sheets A Red to UV (Top halves only) to look at consider – www/ebi
Would this be appropriate for y5/6?
What changes would you make?
Stress for the time being DON’T worry about linking in to Nat Curric we will discuss this later
BUT does it address the cards? – well few but key element is how its used as a resource

20. Addressing the “can’t do” questions
Full lessons became “short bursts” addressing issues that arose from the homework sheets
Mini-whiteboards were used widely
Randomised spreadsheet developed into an invaluable resource
Explain that teachers found they were to start with doing loads of lessons aimed at addressing misconcepts
Clear that prior number skills were not embedded deeply – FLUENCY
The preferred method was to do small bursts focussing on specific single skills rather than long dreary lessons AND we still had a curriculum to teach
Give demo of mini whiteboard lesson & use of randomised spreadsheets ENIGAMI??

21. This is NOT part of Rainbow
 
11011
+ 1101
IV x VI -
If ¾ of boys can do this question but only 2/3 of girls can, how many more in a class of 36 can do the question if the ratio of boys to girls is 2:1 rather than 1:2 ?

22. Routine of starters Mixed Practice Focused Learning Focused Practice
Main
Lesson
Main
Lesson
Main
Lesson
Main
Lesson
Main
Lesson
Homework
Sheets
This soon became a pattern of practice – focus – practice
Point out then that there were two sets of learning going on
Topic Homework

23. Routine of starters Identify an issue Deal with issue Practice
Mixed Practice
Focused Learning
Focused Practice
Focused Practice
Mixed Practice
Identify an issue
Deal with issue
Practice
Return to mixed
Demonstrate the mixed challenges
How to use a specific question in teaching using whiteboards
Cut & paste to make practice sheets
Back to mixed questions

24. Resource Development Mixed starter “challenges” Bank of questions
Cut & paste facility

25. Review so far
Which of the “cards” are being addressed and how well? Which aren’t yet? What adaptations need to be made to cater for the Primary scenario?
So part way through this development of rainbow – before a break consider the sort cards & questions above

26. “Progress, Practice and Feedback”
KS2 to 3 Arithmetic Development Programme
Day 1: Session 2
Adwick Conference Centre 30 Jan 2015

27. Emphasis on presentation
Written homework became an opportunity to focus on development of communication skills
Mini-whiteboard work focused on “quicker response”
Multi-step, worded questions and extensions
Explain how this was an accidental benefit of the sheets
But linked in with the growing strategy of best/rough appropriate type of work depending on situation
Plus a way for more able students to develop whilst still practicing techniques they can do (MASTERY)
Extensions were an optional extra stolen from UKMT but served a purpose – see next slide

28. Building an expectation of independence
“Have a go” culture
Checking answers with a calculator
What to do when you get it wrong or stuck
Other issues arose that weren’t necessarily intended but were important especially in attitudes to learning.
Rules – answer all questions, expectation ask if stuck OR use a support resource eg youtube video
Answers should be calculated (which then raises calculator sessions may need to be included)
Extensions were optional and difficult to mark: Arose the problem starter every 2 weeks?
TASK – What Rules would you lay down to your classes – How can you make this work?

29. Individualised follow up
Specific focus for individual pupils to practice
Expectation of responsibility incl. self checking
Support resources
Most recently has been the development of individualised follow up
Replacing the Topic hmwk – but requiring students to “do dome work on..”
Resources required – questions to have a go at..
Random? Make them up? Spreadsheet access? PDF hundreds of Q’s ? Grouped targeted practice?
Back to expectation of self checking and DIRT time , own progress chart of objectives?
VLE show example
What realistically can be expected of Primary?

30. Feedback & Intervention
Focussing on an issue together as a class
Individual or small group teaching
Whole class practice
Differentiated practice
Mentored support
Individual support resources
Problems of mixed ability vs setted groups – How many colours can be accommodated
What is realistically practical?
Have some work photocopied for consideration – my Y7?
Consider the rules already thought about what Routine/rules would you like to work towards – This will take time but have a vision!

31. Which level? Strands , broad levels & the National Curriculum
Pre-tests
Directed differentiation or pupil choice
Targets & expected levels
Progress tests & assessment without levels
Show NCETM , explain about colours , strands, progress tests , raise issues of directed or choice.
All open to schools to taken on OR adapt as they see fit and what’s most appropriate for their students

34. Describe pre-test, Show tracker , tests , explain that a colour needs to be completed
Expected colours ? Working towards – so not there straight away – issues of different levels
Is it so bad that some more advanced students do , either below or independently?

35. What are the expectations?
How does this fit into new national curriculum?
How & when do you go from level to level?

36. “Working towards Mastery”
KS2 to 3 Arithmetic Development Programme
Day 1: Session 3
Adwick Conference Centre 30 Jan 2015

37. Variation, Pictorial, Deeper
Required Resource Development
More varied styles of same question focus
Pictorial addition to randomised practice, videos & teacher explanations
Extension problems to be more focused on skills at that colour/level
These are my thoughts to bring in a more mastery approach -

38. Variation Can we design different questions around a theme?
Give examples of one type – discussion sheet then / or ratios
Get them to pick one aspect / question type and design variation

39. Pictorial
Consider a shift towards “Bar” diagrams IF your school is heading that way What manipulatives do you use? Do you want to link?
Show the fraction example I’ve designed explain possible avenues eg video explanations, links to “teaching” spreadsheets
“practice” spreadsheets , at the lower levels as techniques are emerging?

40. Deepening Understanding
Conceptual understanding
Language & communication
Mathematical thinking
First two somewhat addressed by a) diagrams b) emphasis of clear communication
But extension questions
What is better UKMT, nrich or multi-step worded questions in context?
Give some examples and ask them to consider what they feel is most appropriate at the bottom and how they would incorporate this into their weekly/fortnightly routine & expectations

41. Next steps Try out materials Ideas and suggestions for amendments
Issues to discuss next time we meet?
Resources in action
Best practice
Required developments

42. “Which is the better fit
“Which is the better fit a round peg in a square hole or a square peg in a round hole?”