1. Confident mathematicians A view from Ofsted
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Confident mathematicians A view from Ofsted
Jane Jones HMI, National lead for mathematics
8 July 2016
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2. Aims To: explore what it means to be a ‘confident mathematician’
consider Ofsted’s findings about good/weaker practice in mathematics and priorities for improvement
bust some myths about inspection.
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3. We want confident mathematicians …
… who are the confident mathematicians that we want?
Pupils Teachers Subject leaders Senior leaders TAs Parents Adults the world over … … in work and life
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4. … what inspires confidence in mathematics?
Two questions for you …
… what inspires confidence in mathematics?
… how would you describe a confident mathematician?
Discuss!
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5. What inspires confidence in mathematics?
Someone who:
believes in a learner and helps her/him develop belief in herself/himself and mathematics
encourages perseverance
enables learning from mistakes, and understanding that those mistakes are part of learning mathematics
challenges thinking
makes a learner unafraid to tackle new ideas/problems.
Some mathematics that:
sparks excitement
leads to a sense of satisfaction/achievement …

6. A confident mathematician …
is able to:
recall knowledge, carry out methods proficiently, and understand concepts, structures and relationships
reason mathematically
solve problems.
These are the aims of the mathematics national curriculum. The aims of GCSE and post-16 mathematics, and the Early Learning Goals are similar to the NC aims.
All/nearly all pupils should be able to learn mathematics sufficiently well that it can be built on securely – mastery.
Some pupils (the ‘rapid graspers’) need challenge through greater depth. Others need extra support/intervention.
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7. Challenge through depth
Qs from UKMT junior challenge
pi day

8. Opportunities The new National Curriculum (including the new GCSE):
captures, in its aims, the best mathematical education for all pupils
represents greater ambition for all pupils, especially the lower attainers (and pupils in receipt of Pupil Premium)
emphasises depth over acceleration
lets us think afresh about progression, the wider aims and conceptual links. The programmes of study, accompanying guidance (primary) and ‘working mathematically’ (sec) offer much more, potentially, than lists of content
provides a context for teachers and schools to learn from each other and together (including through Maths Hubs).

9. 2014/15 inspection findings – primary
New NC seen as more demanding. All schools visited implementing it as expected.
Many teachers and subject leaders lack awareness of the aims of the NC, and concentrate on delivering the content. Problem solving tends to focus on the four operations, often using very similar word problems.
The best informed teachers and subject leaders
know the aims and give increased emphasis to reasoning and problem solving across the mathematics curriculum
use practical apparatus and images to support pupils’ conceptual understanding.
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10. 2014/15 inspection findings – secondary
Wide variation in emphasis given to the new NC, which is not always seen as more demanding than the old NC. (Academies/free schools do not have to follow the NC.)
Many schools’ principal focus is the new GCSE (which is based on the national curriculum). Too many schools do not seem to realise that getting KS3 right should boost performance at GCSE. Few schools see secondary mathematics as a 5-year journey (or even 7-year).
Improving emphasis on problem solving, especially a feature of the stronger practice.
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11. Priorities for improvement
Priorities common to the primary and secondary phases:
a better awareness of the NC aims and expectations
the development of mathematical reasoning across the mathematics curriculum
deepening learning of pupils who grasp ideas quickly.
Some examples of very strong teaching but teaching overall remains variable within and between schools:
The best builds concepts from first principles, develops reasoning (through discussion, questioning, careful choice of tasks/exercises/problems), and provides challenge.
The weaker continues to teach methods like recipes with lack of attention to reasoning and problem solving.

12. 2014/15 inspection findings – CPD
Wide variability in the CPD provided for primary staff. The best reflects a grasp of the challenges, including:
development of the NC aims, emphasising reasoning and problem-solving across the mathematics curriculum
ensuring pupils understand calculation strategies and make links between different methods and operations
how to challenge and deepen the more able, a.k.a. the ‘rapid graspers’
strengthening teachers’ subject knowledge.
Little CPD on the NC provided for secondary staff. More have attended training on the new GCSE.
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13. Today’s conference Teachers also need to be confident mathematicians.
Today, you have taken part in a range of inspiring keynote talks and workshops, including on:
mastery
subject knowledge
professional development activities
reasoning
problem solving
sixth-form mathematics.
You are completely in tune with the developments suggested by Ofsted’s findings!
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14. A puzzle for you
+ + = 30
+ + = 22
– = 0
+ + = ?

15. A topical ‘real-life’ puzzle for you
Without any set going to a tiebreak, what is the greatest number of consecutive points a tennis player can lose and still recover to win a best-of-five-sets match?
The photo is of John Isner and Nicholas Mahut at Wimbledon in 2010.
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16. Problems and puzzles
Problems do not have to be set in real-life contexts. Beware pseudo contexts.
Providing a range of puzzles and other problems helps pupils to reason strategically to:
find possible ways into solving a problem
sequence an unfolding solution to a problem
use recording to help their thinking about the next step.
It is particularly important that teachers and teaching assistants stress such reasoning, rather than just checking whether the final answer is correct.
All pupils need to learn how to solve problems – not just the high attainers or fastest workers.
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17. Teaching problem solving ... do:
06/10/2017
Teaching problem solving ... do:
set problems as part of learning in all topics for all pupils
vary the ways in which you pose problems
try to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations
make sure you discuss with pupils alternative approaches to help develop their reasoning. If relevant, consider why one approach/solution might be more elegant than another
ensure that problems for high attainers/‘rapid graspers’ involve more demanding reasoning and problem-solving skills and not just harder numbers.
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18. Developing reasoning: primes & factors
Find the number, given the following 10 clues:
it’s less than 100
it’s one more than a multiple of 3
exactly one of its digits is a prime
if you reverse the digits, you get a prime
it’s not a multiple of 5
it’s not prime
it has exactly 4 factors
it’s not square
the sum of its digits is prime
if you multiply it by 5, the answer is greater than 100
Which clues were the most useful, which the least? Why?
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19. Reasoning
Reasoning is integral to the development of conceptual understanding and problem-solving skills.
Inspection findings:
Of the three NC aims, it is the least well developed.
Not all classrooms have a positive ethos that encourages learning from mistakes.
Teachers do not exploit opportunities to model thinking.
Tasks are not used well enough to develop reasoning.
Talk often focuses on the ‘how’ rather than the ‘why’, ‘why not’, and ‘what if’ in:
teachers’ explanations and questions
pupils’ responses.
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20. Mathematics and Inspection
A question for you …
… what do you think inspectors expect to see in relation to mathematics teaching?
… would it be different where schools are teaching for mastery?
Discuss!
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21. Ofsted expects …
… teachers to use their subject and pedagogical expertise to provide high quality teaching and curricular experiences in order to secure the best possible learning and outcomes for their pupils.
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22. Characteristics of teaching for mastery (Taken from Developing mastery in mathematics NCETM)
An expectation that all pupils can and will achieve.
The large majority of pupils progress through the curriculum content at the same pace. Differentiation emphasises deep knowledge and individual support/intervention.
Teaching is underpinned by methodical curriculum design, with units of work that focus in depth on key topics. Lessons and resources are crafted carefully to foster deep conceptual and procedural knowledge.
Practice and consolidation play a central role. Well-designed variation builds proficiency and understanding of underlying mathematical concepts in tandem.
Teachers use precise questioning to check conceptual and procedural knowledge. They assess in lessons to identify who requires intervention so that all pupils keep up.
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23. What Ofsted says on inspecting maths
Look at the extract on inspecting the impact of the teaching of mathematics, taken from the School Inspection Handbook.
With a partner, consider which points might align with high quality teaching and learning in mathematics at your school.
Are any points in conflict with the characteristics of mastery?
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24. Myth-busting
Ofsted does not have a preference for particular teaching styles, assessment systems (including marking and feedback), or ways of planning the curriculum.
Guidance on these and other aspects can be found at:
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25. Good practice in teachers’ marking
Is manageable as well as useful. Careful selection of work set in lessons and for homework can support teachers’ better assessment of what pupils understand and can do and thereby better inform subsequent teaching.
Concentrates on important mathematical aspects, such as misconceptions and recurring errors. Prompts/comments help pupils to see where they have gone wrong, point the way forward, enable pupils to think again and self-correct.
Includes use of ‘what if …?’ and/or ‘try this …’ as ways to challenge pupils and/or check they understand.
Might contribute to whole-school literacy through emphasis on mathematical reasoning, correct mathematical present- ation and accurate use of mathematical language/symbols.
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26. With a partner, discuss this question, the pupil’s answer, and the teacher’s comment.
Marty’s pizza is bigger than Luis’s pizza.
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27. Opportunities for developing reasoning
Under what mathematical circumstances is the:
teacher correct?
pupil correct?
How much bigger than Luis’s pizza would Marty’s pizza have to be for the pupil’s answer to be completely correct?
Marty’s pizza is bigger than Luis’s pizza.
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28. Reasoning with images
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29. Transition: a national priority
Ofsted’s report, Key Stage 3: the wasted years? identifies the particular concern of secondary pupils repeating primary mathematics work. Of Year 7 pupils surveyed, 39% said that in mathematics they were doing the same work as in primary school most or all of the time.
In the context of the new NC, readiness for the next stage is important at all transition points within a school as well as between schools.
Two factors that influence the effectiveness of transition are:
the pupil’s mathematical readiness for the next (key) stage
the teacher knowing and building on the pupil’s prior learning in mathematics.
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30. … how next-stage ready are your pupils?
Pause for thought …
… how next-stage ready are your pupils?
… do you pass on information about pupils’ curricular experiences and achievement in problem-solving and reasoning?
… how well do you use information from the previous teacher?
Discuss!
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31. Answer to the tennis problem
76 points. 
You start by winning 5 games and getting to 40-love in the sixth game of the first set. (Could also be the second or third set, with you winning up to that point.)
Your opponent then needs 5 points to win that game, and 6 more games (24 points) to win the first set 7-5. Then 24 points to win the second set 6-0 and then another 23 points to be at 5 games and 40-love in the third set.