Transcript (Presentation title here)

Mathematics Subject Leader Network Meeting
June 2012
Programme
Session 1
Update on recent developments in mathematics including
Mathematics: Made to Measure, draft KS1 and 2 programmes of
study
Session 2
Sharing good practice
Rob Apperley and Ross Currie
Session 3
Teaching percentages
Objectives
• To have a clear understanding of the latest national and regional
developments.
• To consider the recommendations outlined in the recent Ofsted
report ‘Mathematics: Made to Measure’
• To share good practice from Dudley schools and consider how they
can be integrated into schemes of work
• To consider the progression in teaching percentages and address
some of the main issues and misconceptions in this topic
Starter
SESSION 1:
Update on recent developments in
mathematics
Assessment
• KS2 SATs
• L6 test
• GCSE
Y6 SAT questions
Paper A 2012
Level 6
Paper 1 Calculator not allowed
Level 6
Paper 2 Calculator allowed
2012 Level 6 test
• Try these questions with your current Level 6 pupils, what is their
response?
• What is your plan for your L6 learners when they come to you in Y7?
GCSE Edexcel - Higher
QWC 4 marks
GCSE AQA Foundation Paper 2 Q22*
5 marks
Mathematics: made to measure
Recommendations: Ofsted will:
•
•
produce support materials to help schools identify
and remedy weaknesses in mathematics.
raise ambition for the mathematics education of all
pupils by placing greater emphasis in school
inspection on:
 how effectively schools tackle inconsistency
in the quality of mathematics teaching
 how well teaching fosters understanding
 pupils’ skills in solving problems
 challenging extensive use of early and
repeated entry to GCSE examinations.
Mathematics: made to measure
Recommendations
The DfE should:
• ensure end-of-key-stage assessments, and GCSE
and AS/A-level examinations require pupils to solve
familiar and unfamiliar problems and demonstrate
fluency and accuracy in recalling and using essential
knowledge and mathematical methods
• raise ambition for more-able pupils, in particular
expecting those pupils who attained Level 5 at Key
Stage 2 to gain A* or A grades at GCSE
• research the uptake, retention and success rates in
AS and A-level mathematics and further mathematics
by pupils attending schools with and without sixthform provision.
Mathematics: made to measure
Recommendations
Schools should:
• tackle in-school inconsistency of teaching, making more good or outstanding, so
that every pupil receives a good mathematics education
• increase the emphasis on problem solving across the mathematics curriculum
• develop the expertise of staff:
• in choosing teaching approaches and activities that foster pupils’ deeper
understanding, including through the use of practical resources, visual
images and information and communication technology
• in checking and probing pupils’ understanding during the lesson, and
adapting teaching accordingly
•
in understanding the progression in strands of mathematics over time, so
that they know the key knowledge and skills that underpin each stage of
learning
• ensuring policies and guidance are backed up by professional development
for staff to aid consistency and effective implementation
• sharpen the mathematical focus of monitoring and data analysis by senior and
subject leaders and use the information gathered to improve teaching and the
curriculum.
Mathematics: made to measure
Recommendations
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.
Mathematics: made to measure
• Consider the recommendation on your sheet
and write down:
• What you are presently doing to address the
issue
• What you could be doing to address the issue
• Read through the comments already made and
add any thoughts of your own
Draft Primary National Curriculum
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•
•
•
Published in draft June 2012
Consultation through NCETM and ACME portals
PoS is split into KS1, Lower/Upper KS2
Yearly programme with no levels mentioned
Draft Primary National Curriculum
Headlines:
• Add, subtract, multiply and divide fractions (consistent with
expectations in the high-performing education jurisdictions of
Singapore and Hong Kong)
• By age nine, pupils should know their times tables up to 12x12. (in
line with expectations in the high-performing jurisdiction of
Massachusetts).
• By age seven, pupils should know “number bonds” up to 20. These
are simple addition and subtraction facts that pupils should be able
to recognise and use instantly (eg 9+9=18 or 16-7=9).
Other notable changes
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•
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Move to vertical methods for written calculations in Year 2
Roman numerals (Y5)
Binary (Y6)
More formalised algebra in Y6 (e.g. using algebra to solve
perimeter/angle problems)
• Slimming down of Data Handling
Good Education for All
Key Changes
• require ‘outstanding’ schools to have ‘outstanding’ teaching
• define an acceptable standard of education as being ‘good’
• replace the current ‘satisfactory’ judgement with ‘requires improvement’ where
schools are not inadequate but are not yet providing a good standard of
education
• replace the ‘notice to improve’ category with ‘serious weaknesses’
• introduce earlier full re-inspection of schools judged as ‘requires improvement’
• usually limit the number of times schools can be deemed to ‘require
improvement’ to two consecutive inspections before they are judged
‘inadequate’ and deemed to require ‘special measures’
• shorten the notice we give of an inspection
• request that schools provide anonymised information of the outcomes of the
most recent performance management of all teachers
Parent View
http://parentview.ofsted.gov.uk/
New Teachers’ Standards
• Replace the existing core
standards
• Come into effect Sept 2012
• Apply to all teachers
Mathematics CPD
E-Newsletter – Mathematics
https://education.staffordshire.gov.
uk/enewsletter/subscribe.aspx
How might today have impact in
our settings?
• Improved liaison with feeder primary schools, with a particular focus
on Level 6 pupils
• Issues and recommendations from ‘Mathematics: made to measure’
addressed and actions implemented for further development
• New Teacher Standards implemented from September 2012
Customer Negotiated Support
Half Day
(up to 3 hrs)
Whole Day
(up to 6 hrs)
£195 *
£395 *
Mathematics Network Meeting
for Subject Leaders
2012/13 Network Meetings:
• 6 December 2012 – whole day
• 21 March 2013 – half day
• 27 June 2013 – whole day
The ET Secondary Mathematics team contact details are:
[email protected] 07791 032373
[email protected] 07966 328815
Progression in teaching percentages
Objective:
• To consider the strategies that can used for
assessing pupils,
developing group work,
developing problem solving
through the progression in teaching percentages
Mathematics: made to measure
At Key Stage 4 and in the sixth form, schemes of work were rarely
adapted to the particular circumstances of the school and its pupils. They
were often simply the schemes provided by awarding bodies or in
conjunction with textbooks. Other schemes of work were little more than
a list of topics. Specific weaknesses included:
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•
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lack of agreement among teachers in the same school or guidance in the schemes
of work about the preferred ways of tackling particular topics, or the depth of
treatment expected for different groups
little clarity about how concepts were to be introduced and linked to ensure the
development of understanding
common schemes of work being provided for entire year groups, with no guidance to
teachers about what was expected in each set
few opportunities for pupils to develop their skills in using and applying mathematics
or, where using and applying activities were included in the scheme, no guidance on
how pupils should develop skills progressively over time
For Starters….
Which would you rather have…?
18% of £25
or
25% of £18
Show that these two amounts are equal.
Developing a chain of reasoning
0.18 x 25
18% and 0.18 are equivalent
25 x 0.18
Multiplication is commutative
18% of 25
25% of 18
0.25 and 25% are equivalent
2.5 x 1.8
0.25 x 18
Scaling up and scaling down
Scaling up and scaling down
Developing styles of
assessment
•practise and to learn from
each other;
•develop a sense of empathy
and to
understand other views;
Developing group work
Why are we doing this?
Developing PLTS
•Independent enquirers
•Creative thinkers
•Reflective learners
•Team workers
•Self managers
•Effective participators
Developing problem solving
Pupils can look at a problem, decide on the
most appropriate strategy, make links to
similar problems and then persevere to find
a solution
Teaching percentages… what are
the key ideas?
• Create a mind map for the teaching of percentages across KS3 and 4
 Include any related, linked topics
 Is there a key idea that underpins other topics?
Scaling up, down
Proportional reasoning
Reverse %
% as a multiplier
Compound interest
% increase, decrease
Percentages
F, D, P equivalence
Place value
% of an amount
Mental methods
Calculator methods
Choosing an appropriate strategy
% in context
Where do pupils stumble?
• Definition of percent
• F, D, P equivalence (unless ½, ¼, ¾ , 1/10)
 ‘looks different but means the same’
 place value is not secure, e.g. 0.1 and 0.01
 Concept of fractions is not secure
• When to use a mental strategy and when to use a calculator
• Use of the calculator – when does this come in?
• Application of strategies to a word problem or unfamiliar context
Misconceptions
• Percent means ‘out of 100’
• Percentages are never greater than 100%
• If 1/10 = 10%, then 1/5 = 5% and 1/20 = 20%
• An increase of 50% followed by a decrease in 50% takes us back to
the original value.
Misconceptions
• Use the % key on the calculator
• Applying half learned rules without understanding
Wayne bought an engagement ring for Tracy.
The total cost of the ring was £420 plus VAT at 17%.
Work out the cost of the ring.
Activity 1
Clouding the
Picture
Adding 7 to the
numerator and 8 to
the denominator
each time
What else do you know about 7/8?
Activity 2
Sort this set of number cards and arrange them
to make three correct calculations
Activity 3
All numbers in the first column have been increased by the same
percentage to give the results shown in the second column. A
given letter stands for the same numeral every time it appears in
that column. Work out the percentage change.
Activity 4
Place pairs of Percentages cards between each pair of Money
cards to show the correct percentage increase or decrease. Pairs
may be horizontal, vertical or diagonal.
Activity 5
Looking at Progression
Consider:
• the milestones along the path of progression for percentages
• the related skills that are needed to be able to ‘do’ percentages
Assign levels or grades to this progression with appropriate
examples
Where does problem solving fit into this progression?
GCSE Percentage Questions
These questions are taken from 2010 GCSE
specifications
 Try the questions
 Identify where these questions fit
into the progression
• What are the implications for ..?
 Teaching and learning
 Assessment
Looking at Progression
Create additional resources that would help to teach
or assess the key milestones identified in your
progression