1. Promoting Improvement
ITE Thematic dissemination conference:
Primary mathematics
5 November 2013
Jane Jones HMI, National Lead for Mathematics
Mark Williams HMI
Angela Milner HMI, National Lead for ITE, including FE

2. Welcome, introductions and objectives
To promote improvement in the quality of initial teacher education (ITE) by:
sharing the key findings of the ITE thematic inspections of primary mathematics which took place in
identifying areas of strength and what needs to be improved
sharing expectations and good practice.
A web link to associated materials and published resources will be available on Ofsted’s website after the event.
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3. Inspection of primary mathematics ITE
In gathering evidence, inspectors:
observed
mathematics teaching by trainees and by newly qualified teachers (NQTs)
centre and school-based training sessions
held discussions with
partnership leaders responsible for mathematics
trainees and NQTs
scrutinised various documents, including
course information
trainees’ and NQTs’ folders
records of observations and discussions with trainees.
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4. The overview
21 of the 34 inspections of primary ITE included a focus on primary mathematics.
Taken together, the effectiveness of partnerships’ work in primary mathematics was weaker than the picture overall for primary ITE.
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5. Discussion point 1
Why is the effectiveness of partnerships’ work in primary mathematics weaker than the overall effectiveness?
Use

6. Key findings: trainees’ confidence
Trainees are often increasingly enthusiastic and confident about teaching mathematics as training progresses.
Discussions, debate and training sessions on mathematics and how it is best taught help them to refresh, build and deepen their knowledge of mathematics.
But trainees:
lack confidence when they have gaps in their subject knowledge, and then struggle to enthuse pupils, and to plan and teach for progression and understanding
worry about teaching different age groups, especially the EYFS and KS1 when they had had experience in KS2 only.
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7. Discussion point 2
Reflecting on your trainees’ development as teachers of mathematics, what areas of:
growth in confidence
anxiety
do they show?
What are you doing to overcome the anxieties?
Use

8. Key findings: trainees’ lesson planning
Trainees generally planned interesting lessons that take account of the skills and knowledge of different groups of pupils.
But trainees often:
catered least well for higher attainers
deployed additional adults to support low-attaining groups and/or pupils with SEN. (Some trainees recognised that this did not have to be the way they were deployed)
showed a lack of awareness of progression (including prior learning and links with future learning) in their short-term planning. This was often due to training that focused on unit plans or textbook schemes coupled with insufficient opportunities to plan longer sequences of lessons.
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9. Discussion point 3
Why do trainees cater least well for high attainers?
What are you doing to help them with this?
Use

10. Activity 1: the formula for area of a rectangle
Look at the extracts from a trainee’s Year 5 lesson plan. What do they suggest about:
a) the teaching approach
b) the trainee’s subject knowledge?

11. Activity 1: what do these extracts from a trainee’s Year 5 lesson plan suggest about: a) the teaching approach b) the teacher’s subject knowledge?
The trainee’s notes for the main part of the lesson included:
We calculate the area of rectangles using a formula Length x breadth (width). Ask a child to identify the length and the width of the shape. If the length is 5m and the width is 4m then your number sentence will be 5 x 4. Explain to children that the answer must be squared. M2
The trainee had prepared a large number of floor plans for pupils to work on. The tasks were differentiated thus:
SEN - rooms (rectangles) by counting squares
LA - rooms (regular & irregular) by counting squares/part squares
MA - regular & irregular by counting squares/part squares; then use formula for rectangles
HA - use formula L x W for regular real-life shapes
GT - use formula L x W for regular & irregular real-life shapes.
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12. And how might you expect your trainees to introduce the formula for area of a triangle?

13. Activity 2: challenging reasoning about area and developing problem solving
Look at the extracts from an NQT’s Year 6 lesson plan. What do they suggest about:
a) the teaching approach
b) the trainee’s subject knowledge?

14. Activity 2: Look at the extracts from an NQT’s Y6 lesson plan
Activity 2: Look at the extracts from an NQT’s Y6 lesson plan. What do they suggest about: a) the teaching approach b) the teacher’s subject knowledge?
The NQT’s notes for the main part of the lesson included:
Explain how to find the area of a rectangle, formula length x height = area. Work through examples on IWB. Then show football pitch and pose question: the area is 1800m2 and the length is 60m, so the width must be? Ask chn how they worked it out. Using the inverse. Chn to work through mix of questions. Then explain how to find area of triangle. Formula area = (base x height) ÷ 2.
Her notes for the plenary were: work through SATs questions involving finding the area of a rectangle or triangle.
The next lesson, she moved onto compound shapes, closing with the cm challenge of finding the yellow area cm
2cm
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15. Key findings: trainees’ teaching (1)
Improving strengths in trainees’ teaching included use of:
a range of resources and activities, including some problem solving and use of outdoors for younger pupils, that interest pupils and promote good behaviour
questioning to check learning (although not always to re-shape teaching subsequently)
mathematical vocabulary by trainees and pupils
and provision of:
opportunities for pupils to use different strategies and to share their ideas and thinking.
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16. Key findings: trainees’ teaching (2)
Key areas for development in trainees’ teaching:
although problem solving and application of mathematics in real-life contexts form part of most trainees’ training, and were observed in some lessons, trainees’ ability to plan explicitly for and assess the skills is limited
where trainees’ explanations, and tasks set, focused on ‘how’ rather than ‘why’, they did not promote or deepen pupils’ understanding; this was sometimes linked to use of the school’s textbook scheme or other resources that were repetitive rather than challenging pupils to think for themselves
ICT was rarely used as a tool for learning.
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17. Activity 3: using and applying mathematics
Look at the case study extract from the report Mathematics: made to measure.
With a partner, discuss how the NQT might be supported to improve: - the lesson planning - the learning and outcomes.

18. The case study (1)
Many teachers and trainees find difficulty in planning for, teaching and assessing UAM. In this example, all pupils might have started with square ponds so that they could build up patterns in the numbers of tiles used:
Pupils quickly notice four more tiles are needed each time the size of the pond increases by one. They also notice that there are always four corner tiles. For square pond the number of tiles required is 4 x length of side + 4 corner tiles, which can be written algebraically as 4n + 4 for an n by n pond.
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19. The case study (2)
Some of the pupils were working on the harder task in which the dimensions of the pond differed by one. So, a 3 by 4 pond for instance would require tiles along the edges, and 4 at the corners.
This aligns in the case study with the TA’s formula of L + L + W + W + 4, but which pupils had difficulty seeing for themselves.
The pupil’s jottings related to a pond of dimensions 10 by 11.
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20. Key findings: assessment in lessons
The best trainees used questioning to check learning and re-shape teaching
But other trainees:
did not spot misconceptions, and therefore could not address them, or missed opportunities to build on pupils’ responses (such as the trainee who did not make use of the Year 1 pupil’s response of ‘ninety one’ for 19)
did not challenge pupils’ thinking, especially high attaining pupils, by use of follow-up questions such as ‘what if …?’
sometimes were unclear about what the learning objective meant and therefore struggled to promote and to assess the learning, e.g. in relation to fractions.
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21. Trainees showed more awareness of misconceptions in number than in other areas of the curriculum
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22. Key findings: development of trainees’ subject knowledge
Best practice establishes a baseline of trainees’ subject knowledge, promotes and tracks its development.
In general, trainees accepted responsibility for developing their own subject knowledge through, for instance, NCETM resources.
But:
in weaker practice, recruitment information was not followed-up rigorously and subsequent audits are not used to track impact.
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23. Use Discussion point 4 Where are you on this continuum?
Does your work to audit and develop trainees’ subject knowledge include their conceptual understanding too?
In the light of the new National Curriculum, what are you doing differently this year to develop trainees’ subject knowledge?

24. Key findings: development of trainees’ understanding of progression
The best focuses on developing trainees’ understanding of:
progression in strands of mathematics (though predominantly in calculation and/or number)
teaching approaches that develop pupils’ conceptual understanding (including through models and images).
Training often includes an emphasis on misconceptions.
But:
not all trainees gain insight into early mathematics so their understanding of progression from EYFS to Y6 is insecure
trainees have few opportunities to put their understanding about progression into practice, for example in planning sequences of lessons or through scrutiny of pupils’ work over time.
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25. Activity 4: progression in subtraction
In the plastic wallet are the elements of the subtraction section of a school’s calculation policy.
It is not presented as exemplary, but has strengths.
In groups of two or three:
put the elements in the order they could be taught
identify strong features of the policy.

26. Progression in subtraction
Order in school’s policy 1
Begin to count backwards 10
Begin to partition to take away 2
Continue the count back in ones 11
Subtract 1 from two-digit number 3
Relate subtraction to taking away 12
Subtract 10 from two-digit number 4
Find one less than 13
Subtract multiples of 10 5
Count back in tens 14
Partition number to be subtracted 6
Use structured number line 15
Use empty number line to subtract 7
Use – and = for mental subtraction 16
Find difference by counting up 8
Subtraction facts to 10 and 20 17
Expanded method 9
Subtract single digit numbers 18
Standard written method
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Inspector training mathematics Spring 2013

27. Key findings: school-based mentoring
The quality of school-based training varied and was too dependent on:
the calibre of the mentor, especially in terms of the mentor’s knowledge of good practice and insight of guidance provided by her/him
the suitability of the placement, particularly in terms of the quality of practice demonstrated in the school and the relevance of the age group assigned to the trainee.
Expertise in partnership schools was not always exploited well.
Training for mentors was of inconsistent quality, frequency and uptake.
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28. Use Discussion point 5 How do you:
ensure that all mentors provide good quality training and support for trainees?
develop or refresh mentors’ subject expertise?
What about the tutors … … and the course leaders?
Use

29. Key findings: training
The best training:
models a range of high quality teaching approaches, promoting reasoning and discussion and a coherent view of the subject
is informed by current educational research and thinking, including Ofsted survey reports, and changes such as the new National Curriculum and EYFS framework.
But:
a common clear emphasis in training on problem solving was not reflected in trainees’ teaching or, too often, in the teaching within the school. Some trainees said that they had not observed teachers teaching problem solving.
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30. Training on problem solving
While many trainees are often given good opportunities to work in groups on problems and investigations, they too rarely have to devise or adapt problems for themselves.
For instance, adapting routine and repetitive questions by:
removing intermediate steps
reversing the problem
making the problem more open
asking for all possible solutions
asking why, so that pupils explain
asking directly about a mathematical relationship
or, alternatively, setting an open problem or investigation instead.
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31. Activity 5: deepening problem solving
20cm
5cm
What is the area of this rectangle?
Adapt this question to encourage pupils to think harder about how to solve it, and better develop problem solving and conceptual understanding of area of rectangle.
(The problem you devise should be based on the same 20cm by 5cm rectangle.)

32. Some problems based on 5x20 rectangle
Which square has the same area as this rectangle?
Find all the rectangles with whole-number side lengths that have the same area as this one.
How many rectangles have an area of 100cm2? Explain.
If I halve the length and double the width, what happens to the area? What if I double the length and halve the width?
Imagine doubling the length and width of the rectangle (do not draw it). Think: what will the area of the new rectangle be? Now draw it and check its area. Explain your findings.
What happens to the area and the perimeter when you cut a piece from the corner of the rectangle? Can the perimeter to be the same or larger than originally? How?
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33. Key findings: lesson observation
The best training gives due weight to observing trainees’ teaching of mathematics in school.
But:
feedback on teaching frequently did not contain enough mathematics-specific detail to promote improvement in trainees’ subject knowledge and subject-specific pedagogy
rarely was feedback followed up in a timely way into the next observation
not enough detailed knowledge was gathered on how all trainees teach mathematics, particularly on whether their focus was on ‘why’ as well as ‘how’.
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34. Activity 6: lesson observation and feedback
Look at the lesson-observation and feedback records you brought with you, and think about how lesson observation and feedback are used in your partnership.
Do they get to the heart of the matter?
Do the records:
identify the most important subject-specific aspects
promote improvement in trainees’ teaching of mathematics?

35. Lesson observation records
Example with input & impact for five key aspects contributing to progress. Cells contain prompts for recording evidence.
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36. Discussion point 6
Can you improve the effectiveness and consistency in quality of lesson observation and feedback in your partnership?
How might you go about it?
Use

37. Lesson observation in your partnership
Improvements you might make could include:
ensuring lesson-observation records take account of:
monitoring to enhance progress
conceptual understanding
problem solving
misconceptions
accuracy of language and symbols
reviewing the way lesson observation is carried out, including follow-up observations in mathematics
strengthening the mathematical attention to detail, particularly in the evaluation and development points
checking the weight given to progress in judging teaching
following up development points more effectively.
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38. Discussion point 7
What are the implications for ITE of the new National Curriculum?
Use

39. The National Curriculum for mathematics aims to ensure that all pupils:
become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems
reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
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40. Discussion point 7
What are the implications for ITE of the new National Curriculum?
Use

41. The new National Curriculum and ITE
Current areas of weakness and inconsistency in ITE that relate to the new National Curriculum and the EYFS Framework include:
a gap between the common emphasis on problem solving in training and trainees’ practice and school experiences
trainees’ insecure understanding of progression from the EYFS to Year 6, and lack of opportunity to strengthen it through practical activity
the emphasis on use of mathematical vocabulary is appropriate but goes only part way to developing pupils’ reasoning skills – more discussion around structures and relationships is required.
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42. Use Final discussion point What is your top priority?
what strengths can you build on?
what barriers must you overcome?
Use

43. Conclusion and departure
We hope you have found this conference helpful. Any questions?
Conference on-line evaluations
Web link and associated materials will be available on the Ofsted website:
We wish you a safe journey home.
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44. Promoting Improvement
ITE Thematic dissemination conference:
Primary mathematics
5 November 2013
Jane Jones HMI, National Lead for Mathematics
Mark Williams HMI
Angela Milner HMI, National Lead for ITE, including FE