Better mathematics keynote spring 2015

Better mathematics conference
Keynote: understanding ways forward
Jane Jones HMI,
National lead for Mathematics
Spring 2015

Aims of keynote session
To be better informed about:
 important weaknesses nationally in provision and
outcomes in mathematics
 key features of good practice and effective ways schools
have overcome weaknesses.
To sharpen your expertise in identifying:
 key weaknesses in mathematics in your school
 priorities to drive improvement.
Better mathematics conference keynote 2015

Keynote content
 National figures for attainment and progress in mathematics
 Findings from our triennial report, Mathematics: made to
measure, highlighting good practice and key concerns
nationally
 Short activities to help convey main points (for example,
about problem solving and conceptual understanding)
 Opportunities for you to reflect on implications for your
school and to prioritise areas for improvement
During the session, please do not hesitate to speak about the
activities to supporting HMI. If you have further questions,
please note them down on paper and hand to HMI.

Keynote sections
Achievement
Teaching
Curriculum
Leadership and management
Planning ways forward in your school
The information booklet contains text from the principal slides,
in particular the national findings and key concerns.

Achievement

Attainment
Attainment has risen:
at GCSE grades A*-C, due to a strong emphasis by schools
at AS/A level with a huge increase in uptake.
In primary schools, attainment has:
risen in the EYFS with calculation weakest; 2013 new ELGs
stalled then recent rise at L2+ at KS1; declining trend at L3+
stalled then recent rise at L4+ at KS2; rise at L5+.
Key concern
1.Although attainment is generally rising, pupils are not made to
think hard enough for themselves. Pupils of all ages do too little
problem solving and application of mathematics.

A problem for you to solve
The animals represent values.
Which value could be found first, next and last, and why?
Which value cannot be found second and why?

Early Years Foundation Stage
The Early Learning Goals that were introduced in
September 2012 represent substantially higher expectations
than previously.
Problem solving is an explicit part of each Early Learning Goal.
(It used to be just one of eight points from which children had
to meet any six to reach the age-related expectation.)

Progress (2013 figures; 2011 in brackets)
88% (82%) of pupils made the expected 2 levels of progress
KS1→KS2 but:
70% of L2c reach L4 compared with 91% of L2b; (58% cf 86%
in 2011).
70% (62%) of pupils made the expected 3 levels of progress
KS2→KS4 but:
58% of L4c reached grade C; (48% in 2011)
still only 29% of low attaining pupils made expected progress;
(30% in 2011)
over 31000 pupils who attained L5 at primary school got no
better than grade C at GCSE; 2700+ got grade D or lower.

Gaps in attainment and progress
(2013 in black; 2011 M2M figures in blue)
 Overall, 9% of pupils did not reach L2 at age 7, 15% did not
reach L4 at age 11, and 30% of the cohort did not reach
grade C at GCSE; (cf 10%, 20% and 36% in 2011).
 FSM pupils did much worse than their peers on attainment
and progress, the gaps generally widening with key stage.
The gaps are still there!
Attainment FSM (%) Non-FSM (%)
KS1 L2+
L3+
85 (81)
12 (9)
94 (92)
27 (23)
KS2 L4+
L5+
77 (67)
27 (19)
88 (83)
47 (38)
GCSE C
A*/A
53 (42)
8 (6)
77 (68)
22 (21)
Expected
progress
FSM
(%)
Non-
FSM (%)
KS1-2 84 (75) 90 (84)
KS2-4 54 (45) 76 (67)

Think for a moment …
How well do your FSM pupils, and others
supported by the Pupil Premium, achieve?
To think about back at school …
When do they start to lose ground?

Achievement – key concerns
2. The percentage of pupils meeting expected standards falls
at successive key stages. Reaching the expected level in
one key stage does not ensure meeting it at the next. This
is often due to a focus on meeting thresholds rather than
securing essential foundations for the next stage.
3. FSM pupils do far worse than their peers at all key stages,
most markedly at Key Stage 4.
4. Low attainers are not helped soon enough to catch up,
particularly in the EYFS and Key Stage 1. No improvement
in the proportion making expected progress KS2→KS4.
5. High attainers not challenged enough from EYFS onwards.
6. Potential high attainers are being lost to AS/A level – the
big uptake has come mainly from pupils with GCSE A*/A .

Achievement
Highlight any of the national key concerns that
are also a concern in your school.

Teaching

Teaching – Ofsted’s findings
The best teaching develops conceptual understanding
alongside pupils’ fluent recall of knowledge and confidence in
problem solving.
In highly effective practice, teachers get ‘inside pupils’ heads’.
They find out how pupils think by observing pupils closely,
listening carefully to what they say, and asking questions to
probe and extend their understanding, then adapting teaching
accordingly.
Too much teaching concentrates on the acquisition of
disparate skills that enable pupils to pass tests and
examinations but do not equip them for the next stage of
education, work and life.

Teaching examples
Problem solving
The animal puzzle is an example of problem solving. Problems
may, or may not, involve realistic contexts.
Conceptual understanding
The questions on the next slide illustrate the importance of
understanding concepts within fractions in:
 setting firm foundations for future work in fractions,
algebra and proportional reasoning
 avoiding developing misconceptions.

Understanding fractions
A question for you: what is a fraction?
Questions for pupils:
1. What fraction is shaded?
2a. What does ¼ mean?
2b. Tell me a fraction that is bigger than ¼
3a. How do you work out one quarter of something?
3b. Can you work it out another way?

Aims of the National Curriculum
The three aims, summarised below, are consistent with
Ofsted’s findings on effective teaching and learning.
Become fluent in the fundamentals of mathematics,
so that pupils develop conceptual understanding and the
ability to recall and apply knowledge rapidly and accurately
Reason mathematically
Solve problems
The next slide gives an example of why conceptual
understanding is intrinsic to fluency.

Fluency using conceptual understanding
 Understanding that multiplication is commutative, so
8 x 6 = 48 and 6 x 8 = 48 (also 48 = 6 x 8, 48 = 8 x 6)
 Understanding that the inverse relationship between
multiplication and division leads to equivalent statements,
such as 8 = 48 ÷ 6 and 48 ÷ 8 = 6
 Knowing division is not commutative, so 8 ≠ 6 ÷ 48
 Deriving related facts, for example:
 80 x 6 = 480, 6 = 480 ÷ 80 and 0.8 x 0.6 = 0.48
 8 x 6 = 48 so 16 x 3 = 48

Teaching – findings (Made to measure)
 Wide variation between key stages and sets, especially in
Key Stage 4 with high sets receiving twice as much good
teaching as low sets, where 14% is inadequate.
 Weakest teaching in Key Stage 3 (38% good or better and
12% inadequate).
 Strongest teaching in the EYFS and Years 5 and 6 with
around three quarters good or outstanding. Weaker in Key
Stage 1 (particularly Year 1) than in Key Stage 2.
 Wide in-school variation causes uneven progress and gaps
in achievement, even in good and outstanding schools.
Stronger staff are often deployed to key examination or test
classes. Leaders appear to accept that other pupils may
need to make up ground in the future.

In-school variation in 151 schools
 half had at least one lesson with inadequate teaching
 only two had consistently good or better teaching
Distribution of teaching grades in secondary school lessons
0
2
4
6
8
10
12
14
Each bar represents a different school
Numberoflessonsateachgrade
1
2
3
4

Changes to the inspection of teaching
 From September 2014, inspectors will not grade the quality
of teaching in individual lessons.
 In evaluating the overall quality of teaching in a school (or in
the subject for a mathematics inspection), inspectors will
consider strengths and weaknesses of teaching observed
across a broad range of lessons and other activities, placed
in the context of other evidence of pupils’ learning and
progress over time.
 The judgement on leadership and management will include
use of performance management and effectiveness of
strategies to improve teaching, including account taken of
the Teachers’ Standards.

What choices do you make about staff
deployment in your school?
To think about back at school …
How do you pinpoint and tackle
specific weaknesses in teaching
(including temporary, part-time
and non-specialist staff)?

Teaching – key concerns
7. Wide in-school variation in teaching quality.
8. Conceptual understanding and problem solving are
underemphasised.
a. Too often, teaching approaches focus on how, without
understanding why, so that pupils have insecure
foundations on which to build future learning.
b. Many pupils spend too long working on straightforward
questions, with problems located at the ends of exercises
or set as extension tasks, so that not all tackle them.
7. Circulating to check and probe each pupil’s understanding
throughout the lesson and adapting teaching accordingly
are not strong enough.

Teaching

Curriculum

Curriculum
Key differences and inequalities extend beyond the teaching:
they are rooted in the curriculum and the ways in which
schools promote or hamper progression in the learning of
mathematics.
Progression is different from progress.
 Progress is the gain that pupils make in terms of
knowledge, skills and understanding between one point in
time and another.
 Progression describes the journey in the development of
concepts and skills along a strand within mathematics,
drawing upon other strands and feeding into them as
needed.

Practical, mental and written methods
 The photo shows a pupil
using practical equipment
to help her understand the
written method of column
addition.
 The extract shows how
mental partitioning with
jottings links to the process
of column addition. Y3
pupils in this lesson were
encouraged to see and
discuss the connection.

Curriculum findings (Made to measure)
 The degree of emphasis on problem solving and
conceptual understanding is a key discriminator between
good and weaker provision.
 Planning in primary is usually based on National Strategy
materials. It is detailed, but tends to lose the big picture of
progression in strands of mathematics.
 In secondary, planning and schemes of work are commonly
based on particular examination specifications.
 Pupils’ curricular experiences are inconsistent and depend
too much on the teacher they have and the set/class they
are in.

Variation in use of ICT
All teachers should follow the school’s agreed approaches with
ICT to help develop pupils’ conceptual understanding.

Curriculum – key concerns
10.Problem solving is not emphasised enough in the curriculum.
11.Teachers are not clear enough about progression, so
teaching is fragmented and does not link concepts.
12.Pupils’ curricular experiences are inconsistent because:
a. teachers lack guidance and support on building
conceptual understanding and progression over time
b. teachers’ subject knowledge and pedagogic skills
(subject expertise) vary. They are not enhanced enough
through subject-specific professional development and
guidance. Less experienced/non-specialist/temporary
staff do not receive the specific guidance and support
they need.

The importance of subject expertise
Subject knowledge and pedagogic skills underpin the
development of:
conceptual understanding, knowledge and skills to build
fluency and accuracy
problem solving and reasoning
progression and links.
Subject knowledge and pedagogic skills are necessary for:
anticipating, spotting and overcoming misconceptions
observing, listening, questioning to assess learning and adapt
teaching.

GCSE entry findings (Made to measure)
 In 2011/12, nearly 90% of schools entered some or all
pupils early for GCSE. Nationally, over half of the cohort
took GCSE early, with many pupils resitting it.
 Teaching commonly focuses on the next exam and includes
much practice on exam-style questions. This approach relies
on pupils’ recall of disparate facts and methods.
 Higher sets are not always given enough time on hard topics
e.g. algebra, geometry, graphs – needed for AS/A level.
 Best practice for higher attainers is taking GCSE alongside
additional qualifications at the end of Y11.
A current concern (2014) is the use of multiple GCSE entry
using different awarding bodies.

GCSE entry patterns – key concern
13.Choices about GCSE entry and qualification pathways can
limit pupils’ achievement and/or drive short-termism in
teaching approaches:
a. pupils entered early for GCSE generally attain less well
after resits than do those entered only once at the end of
Year 11, and few pupils who gain GCSE grade A early
go on to resit with the aim of improving their grade
b. teaching focuses on exams, relying on pupils’ short-term
memory, rather than on progression and development of
understanding
c. pupils are less well prepared for their future studies in
mathematics and other subjects, including resitting
GCSE post-16.

Curriculum

Leadership and management findings
Stronger management practices, particularly in secondary:
 monitoring of teaching (e.g. learning walk, work scrutiny)
 use of data to track progress and for intervention
 use of performance management to drive higher
examination results.
Key concern
14.Monitoring tends to focus on generic features rather than on
pinpointing subject-specific weaknesses or inconsistencies. It
is not used strategically to improve teaching, learning or the
curriculum.

Why does your school do work scrutiny?

The potential of work scrutiny
To check and improve:
teaching approaches, including development of conceptual
understanding
depth and breadth of work set and tackled
levels of challenge
problem solving
pupils’ understanding and misconceptions
assessment and its impact on understanding.
To look back over time and across year groups at:
progression through concepts for pupils of different abilities
how well pupils have overcome any earlier misconceptions
balance and depth of coverage of the scheme of work,
including using and applying mathematics.

Work scrutiny
What does this extract suggest about how well:
the pupil understands the
topic (collecting like terms)
the exercise provides
breadth and depth
of challenge
the marking identifies
misconceptions and
develops the pupil’s
understanding?
The commentary on this extract shown in the next slides is
also provided in the information pack for the workshops.

Work scrutiny – understanding
 The pupil adds like terms correctly but makes an error with
subtraction.
 The exercise has too many
straightforward questions on
addition before subtractions
start. This makes it too
narrow and unchallenging to
develop understanding of
the whole topic.
 Such narrowness prevents
the teacher from checking
the extent of the pupil’s
understanding.

Work scrutiny – teacher’s comments
 The teacher’s comment ‘only
1 wrong’ misses the pupil’s
difficulty with subtraction
shown by the wrong answer
to Q8 and incomplete Q9.
 It is likely that the pupil left
the signs unmoved when
rearranging
3j – 4k + 2j + k to get
3j – 2j + 4k + k
 The comment does not help
the pupil to overcome this
misconception.

Work scrutiny and lesson observation
 The top priority to bear in mind when scrutinising work is
‘Are the pupils doing the right work and do they understand
it?’
 Thinking back to the extract, the pupil was not doing ‘the
right work’. The questions lacked breadth, did not develop
understanding fully, and included no problems. Improving
these is more important than improving marking.
 The skills you have just used in scrutinising the extract of
work are equally applicable when observing lessons.
 A key additional element when observing lessons is seeing
how well teachers check and deepen each pupil’s
understanding. Does the teacher move round the class
observing and listening to pupils to check their progress?

In your school, what is the relative emphasis on
improving:
the quality of work pupils are given in order to
promote their understanding
marking?

Work scrutiny – assessment policy
 In accordance with the school’s policy, the teacher has
provided a ‘next step’.
 ‘Equations’ is not a
‘next step’ to help the
pupil improve in this topic.
Understanding subtraction
is needed first.
 Working with brackets,
constant terms and powers
would give fuller breadth of
the topic.

 Whole-school policies may not work well for mathematics.
For example, an assessment policy might expect teachers
to:
 assign an attainment grade to each piece of marked work
 mark one substantial piece of work periodically
 refer to the lesson objective when marking
 identify ‘next steps’ to help pupils improve their work.
 Best practice ensures that policies can be customised for
mathematics in ways that reflect its distinctive nature and
thereby promote good teaching and learning.
Key concern
15.Some whole-school policies do not work well for
mathematics.Better mathematics conference keynote 2015

How mathematically friendly are your
whole-school policies?

 Enabling teachers to work together (e.g. on a calculation
policy or guidance on progression in algebra) supports
consistency and improvement. However, teachers usually
share ideas and good practice informally, rather than record
them in guidance, schemes of work, or policies.
Key concern
16.Because sharing of good practice and provision of guidance
are usually informal, only those who are involved can
benefit. Not capturing these informal interactions in writing
means that teachers who miss out or join the school later
cannot benefit from them.

Use of assessment data – findings
 Primary schools have improved their use of assessment
information to provide more focused and timely intervention.
The best schools:
 pick up quickly on misconceptions, difficulties and gaps
 intervene speedily to overcome them so that pupils do
not fall behind.
 In secondary schools, interventions have tended to
concentrate on practising topics for GCSE examinations.
Schools use assessment data to identify key groups of
pupils, particularly at the grade C/D borderline.

Use of assessment data – key
concerns
17.Despite increasingly sophisticated tracking and analyses
that identify pupils who are underachieving and topics/gaps
where difficulties arise, schools rarely use such assessment
information to improve teaching or the curriculum.
18.Intervention, particularly for lower attainers, is not early
enough to overcome gaps and build a firm foundation for
future learning. Gaps arising from misconceptions,
absence, changing teaching group or school are not
systematically identified or narrowed.
19.Secondary schools rarely use intervention to overcome
gaps in pupils’ understanding, particularly in Key Stage 3,
choosing instead to focus on examination preparation.

Planning ways forward in your school

Integrated planning for improvement
Good
quality
teaching
and learning
Meaningful
curriculum
experiences and
qualifications
Insightful,
rigorous
leadership
and
management
Good
achievement
with conceptual
understanding

Do the priorities in your mathematics
improvement plan include all three of the
areas:
teaching and learning
curriculum
leadership and management?

Recommendations for schools
 The national key concerns gave rise to recommendations
for schools that were published in Mathematics: made to
measure.
 Look at these recommendations in the information booklet.
 Highlight any that your school would find helpful in its
improvement planning.

Recommendations for schools –
summary
 Tackle in-school inconsistency of teaching.
 Increase the emphasis on problem solving.
 Develop the expertise of staff:
 in fostering pupils’ deeper understanding
 in checking and probing pupils’ understanding during the
lesson, and adapting teaching accordingly
 in understanding the progression in strands of
mathematics
 ensuring policies and guidance are backed up by
professional development.
 Sharpen the mathematical focus of monitoring and analysis,
and use findings to improve teaching and the curriculum.

Recommendations for schools
In addition, primary schools should refocus attention on:
improving pupils’ progress from the Early Years Foundation
Stage through to Year 2 to increase the attainment of the most
able
acting early to secure the essential knowledge and skills of
the least able.
In addition, secondary schools should:
ensure examination and curricular policies meet all pupils’
best interests, stopping reliance on the use of resit
examinations, and securing good depth and breadth of study at
the higher tier GCSE.

Do the priorities in your mathematics
improvement plan include the
recommendations you highlighted?

In summary
You have identified three sets of areas for improvement in
mathematics in your school:
 the key concerns you highlighted
 the recommendations for schools you highlighted
 your school’s mathematics improvement plan.
The next activity involves using these three sources to help
you select one short-term priority and one long-term priority for
which you can start to devise actions today.
Planning actions for your priorities

Ideas for priorities and actions
Short-term priorities:
raise attainment by the end of reception to ensure all pupils
are well prepared for Key Stage 1
raise attainment at GCSE grades A*/A by improving
qualification pathways and transition from KS3 to GCSE.
Long-term priority:
ensure teaching focuses on conceptual development
Planning involves thinking about:
where to start (e.g. calculation/ Y7)
agreeing approaches, including professional development
monitoring through the subject leader checking that
conceptual approaches are being planned and used well
evaluating through subject discussions with pupils to check
their understanding.

Select one short-term priority and one long-term priority for
which you can start to devise actions during this session.
To inform your selection, refer to:
 the key concerns you highlighted
 the recommendations for schools you highlighted
 your school’s mathematics improvement plan.
For each priority, specify precisely:
 the actions you will take, including coaching and targeted
professional development, and how you will monitor their
quality, providing support and challenge as needed
 what you expect the impact of successful actions to look
like and by when, and how you will evaluate this.
Planning actions for your priorities

Further planning
When you are back at school, you may find it helpful to:
look in detail at your school’s information/data to explore
whether other areas of national concern might also be priorities
for your school
continue to work together on your improvement plan for
mathematics.
We hope you have found this morning useful. If you have any
further questions or points you wish to raise, please speak with
one of the HMI during the lunch break.

Better mathematics keynote spring 2015

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