introducing the new secondary curriculum mathematics 13 th march 2008 subject leader development...
TRANSCRIPT
Introducing the New Secondary Curriculum Mathematics
13th March 2008
Subject Leader Development Meeting
Outline
The big pictureMore about mathsProcesses in practiceProgression and planningMoving forward
What does good/effective teaching look like?
What is the impact on students?
Use the A3 sheet to:Delete statements that you don’t agree with.Use the remaining statements as prompts to answer
the questions/formulate your opinions.
The big picture
The changes in context
Aims
• to understand the need for the curriculum review• to know the cross-curricular factors impacting on
maths• to place the maths changes in the context of the
bigger picture• to have a feel for the maths PoS
Aims of NC
• Successful learners who enjoy learning, make progress and achieve
• Confident individuals who are able to live safe, healthy and fulfilling lives
• Responsible citizens who make a positive contribution to society
Stay safe Be healthy Enjoy and achieve
Achieve economic well-beingMake a positive contribution
Threads
Personal, learning & thinking skills• independent enquirers• creative thinkers• team workers• self managers• effective participators• reflective learners
Curriculum dimensions• identity & cultural diversity• healthy lifestyles• community participation• enterprise• global dimension & sustainable development• technology & the media• creativity & critical thinking
Learning across the curriculum• creativity• use of ICT• education for sustainable development• literacy• numeracy
Attitudes & attributes• determined• adaptable
• confident• risk-taking
• enterprisingKnowledge & understanding• big ideas that shape the world
Statutory entitlement
Curriculum dimensions• identity & cultural diversity• healthy lifestyles• community participation• enterprise• global dimension & sustainable development• technology & the media• creativity & critical thinking
Personal, learning & thinking skills• independent enquirers• creative thinkers• team workers• self managers• effective participators• reflective learners
Learning across the curriculum• creativity• use of ICT• education for sustainable development• literacy• numeracy
New Programmes of Study
Importancewhy the subject
matters
Importance of Mathematics
• Mathematical thinking (as a) habit of mind• … fundamental to national prosperity in providing tools
for understanding …• … equips pupils (with) ways to describe, analyse and
change the world• … stimulate moments of pleasure and wonder ….• … functional in maths and financially capable … can
reason, solve problems and assess risk• … creative discipline …• … transcends cultural boundaries … universal
importance• … means of solving problems … for its own sake
Concepts and Processes
Essential ideas• Competence• Creativity• Applications and
implications of mathematics
• Critical understanding
Skills and ways of thinking
• Representing• Analysing
(use reasoning, use procedures)
• Interpreting and evaluating
• Communicating and reflecting
Statutory entitlement
Essential ideas• Competence• Creativity• Applications and
implications of mathematics
• Critical understanding
Skills and ways of thinking
• Representing• Analysing
(use reasoning, use procedures)
• Interpreting and evaluating
• Communicating and reflecting
Range and content
• Number & Algebra• Geometry & Measures• Statistics
Statutory entitlement
• Number & Algebra• Geometry & Measures• Statistics
Curriculum Opportunities
• … increasing range of techniques …• … sequences of tasks … same maths in changing
contexts / different maths similar contexts (increasing demand)
• … open and closed tasks … selecting the maths …• … problems … other subjects … beyond school …• … tasks … bring together different aspects of
concepts, processes and … content• Work collaboratively as well as independently …• Become familiar with a range of resources including
ICT …
Statutory entitlement
• … increasing range of techniques …• … sequences of tasks … same maths in changing
contexts / different maths similar contexts (increasing demand)
• … open and closed tasks … selecting the maths …• … problems … other subjects … beyond school …• … tasks … bring together different aspects of
concepts, processes and … content• Work collaboratively as well as independently …• Become familiar with a range of resources including
ICT …
Website: curriculum.qca.org.uk
dvd
Subjects then
Maths
Cross-curriclinks
casestudies
Scroll down for maths in
other subjects
The wider picture in maths
FunctionalSkills
ControlledAssessments
New A levels
Assessment for Learning
more U&A in current GCSEs
New GCSEs
Assessing Pupil
Progress KS2 & KS3 single level tests
Making Good Progress
Process Skills
2 unit ASA level pilots
Timeline for change
Nowold ks3 new ks3
old ks3 old/new ks3 new ks3
old ks3 new ks3old/new ks3
single level tests single level tests pilots
old ks4 new ks4old/new ks4
GCSE1 GCSE2new GCSE
Functional SkillsF Skills pilots
old ks4 new ks4old/new ks4
Functional SkillsF Skills pilots
GCSE1 GCSE2cswk GCSE new GCSE
Now 2008/09 2009/10 2010/11 2011/12
Y7
Y8
Y9
Y10
Y11
Y12
Key messages
• Not just about maths knowledge• Not just about maths teaching• Opportunity to develop teaching• Potentially, huge gains for learners
More about maths
The language of the Key Processes
Aims
• to understand the cycle of Key processes• to look in more detail at the process statements• to develop a feel for the language• to recognise common themes with other subjects
New Programmes of Study
From your highlighted PoS, discuss on your tables• how is it different?• what is important to you?
Comparing new and old - headlinesSimilarities:• Mathematical content appears unchanged
(renewed Framework will contain the detail)• Levels largely similar (p148-152)
Differences:• Using and Applying replaced with Mathematical
processes and applications• Shape and space renamed Geometry and
measures• Handling data renamed Statistics
Our impressions
Inspirational feel
Could appear to have less content
AfL embedded
Why KS3 and KS4, not just
Secondary?
How you are learningnot just what
Emphasis on contexts relevant to real life
Looks to the future
Why is MPA (like U&A)
still separate, not integrated? Emphasis on understanding
and learner independence
Clear problem-solving cycle in processes
The cycle of key processes
Representing
InterpretingEvaluating
Use proceduresAnalysing
Use reasoning
CONTEXT
MATHEMATICS
CommunicatingReflecting
Consequences
• On your tables, there are 5 differently coloured sheets, one for each process skill
• For each skill, enter your individual interpretation of what this represents, fold the paper and then pass on round the table
• Once all five are completed, open up the sheets and discuss
• Compare your interpretations with the pupil-speak cycle
The cycle in pupil-speak
Key messages
Key Processes • need to be a focal part of some lessons• need to be visited over a period of time• need to be explicitly shared with pupils, so they
understand HOW they are learning
Consider your pre-task
• Select the process statements from your pack which best describe what your pupils experienced during their lesson.
• Now look more closely at the process statements you have selected. Try to think about which ones best describe what the pupils actually learnt.
For example, if you had to use one or two as learning outcomes, which ones would they be?
• Annotate your lesson plan accordingly.
Categorising process skills
Representing
InterpretingEvaluating
Use proceduresAnalysing
Use reasoning
CommunicatingReflecting
QCA interpretation
Representing
Use reasoning
Analysing
Use procedures
make connections within mathematics
visualise & work with dynamic
images
use knowledge of related problems
explore the effects of varying values & look for invariance and covariance
reason inductively & deduce
make & begin to justify conjectures and generalisations, considering
special cases & counter-examples
work logically towards results & solutions, recognising the impact of
constraints & assumptions
appreciate that there are a number of different techniques that can be
used to analyse a situation
take account of feedback & learn from mistakes
identify & classify patterns
Concepts and Processes
Key messages
• Statements may not appear to exclusively belong to one heading
• Looking for coverage of the process statements over time, not of the 5 headings
• Statements are clearer when in the context of an activity/lesson
• Teacher aim/pupil response/context affect how statements match headings
• Common themes are present throughout all the PoS
Processes in practice
Analysing activities
Aims of this session
• to look at process skills in the context of a familiar rich task
• to know ways to incorporate process skills into the curriculum
Role play time
• One group leader• One observer• Rest participating
On the 100 square cycle:• Which process statements did you experience?• Can you reach agreement as a group?
Key messages
• Not re-inventing the wheel: adapting the scheme of work
• Need to provide opportunities to cover all process statements (rich tasks are a rich source!)
• Teacher aim/pupil response/context affect how statements match headings – so may need to be prescriptive to ensure coverage by all staff
Progression and planning
Implications for schemes of work
Aims
• to be aware of the Process objectives• to link these with Range and content objectives• to consider how to link process skills with your
schemes of work• to be aware of effective teaching and learning
strategies• to have mechanisms to audit schemes of work for
the process skills and the strategies• to share the implications with partner schools
Linking objectives to levels
Year 7
Year 8
Year 9
Year 10
Year 11
revision of level 4, but mainly level 5
consolidation of level 5, moving into level 6
mainly level 6, some level 7
mainly level 7/grade C, some level 8/grade B
mainly level 8/grade B
Lines of Progression
• Level 4 at KS2 to grade B at GCSE• Progression in Process skills from Year 7 – 11• Progression in subject skills across the five years• Further exemplification in the Secondary
Framework- available summer 2008• Electronic!
Progression in process skills
Increase the challenge & build progression by
• increasing the complexity of the application, e.g. non-routine, multi-step problems, extended enquiries
• reducing the familiarity of the context, e.g. new context in mathematics, contexts drawn from other subjects, other aspects of pupils’ lives
• increasing the technical demand of the mathematics required, e.g. more advanced concepts, more difficult procedures
• increasing the degree of independence and autonomy in problem solving and investigation
Functional Skills!
Increase the challenge & build progression by
• increasing the complexity of the application, e.g. non-routine, multi-step problems, extended enquiries
• reducing the familiarity of the context, e.g. new context in mathematics, contexts drawn from other subjects, other aspects of pupils’ lives
• increasing the technical demand of the mathematics required, e.g. more advanced concepts, more difficult procedures
• increasing the degree of independence and autonomy in problem solving and investigation
Objectives for the 100 square task• Choose objectives for the hundred square task• Discuss where you would put this activity in your
scheme of work• What level would pupils be working at?
• Repeat for the pre-task
The 100 Square Task: objectives
A• Generalise in simple cases by
working logically• Understand the significance
of a counter-example• Relate findings to the original
context• Use letter symbols to
represent unknown numbers or variables
• Simplify linear algebraic expressions by collecting like terms
B• Draw simple conclusions
and explain reasoning• Compare and evaluate
approaches• Communicate own findings
effectively• Make correct use of tables
Effective Learning and Teaching
The basic principles – Effective Learning:
• Pupils learn about and learn through the key mathematical processes
• Pupils work collaboratively & engage in mathematical talk
• Pupils work on sequences of tasks• Pupils select the mathematics to use• Pupils tackle relevant contexts beyond the
mathematics classroom• Pupils are exposed to the historical & cultural roots
of mathematics
Effective Learning and Teaching
The basic principles – Effective Teaching:
• Build on the knowledge pupils bring to a sequence of lessons
• Expose & discuss common misconceptions• Develop effective questioning• Use cooperative small-group work• Emphasise methods rather than answers• Use rich collaborative tasks• Create connections between mathematical topics• Use technology in appropriate ways
Implications for maths teams and pyramids
Questions to ask of each other and colleagues in schools:
• What are we trying to achieve?• How do we organise learning?• How well are we achieving our aims?
….and for each, when will any actions occur?
Implications
Transition
Functional Skills
Lessons
Pupil voiceExisting SoW
Non-maths aspects
Assessments
Progression for sets
Cascading to staff
Staffing Implications
Activities
Areas to consider:
Key messages
• Need to use the Lines of progression to audit scheme of work
• Need to plan for 2 levels of progress per key stage• Effective teaching and learning underpins the
curriculum and supports the shift from U&A to processes
• Need to plan how to move forward within your school and with your pyramid
Moving forward
Next steps
Aims
• to sketch out timings for action• to identify your next steps with regard to:
dissemination within the maths team and school
your curriculumwith your pyramid
2 unit ASA level pilots
Timeline for change
Nowold ks3 new ks3
old ks3 old/new ks3 new ks3
old ks3 new ks3old/new ks3
single level tests single level tests pilots
old ks4 new ks4old/new ks4
GCSE1 GCSE2new GCSE
Functional SkillsF Skills pilots
old ks4 new ks4old/new ks4
Functional SkillsF Skills pilots
GCSE1 GCSE2cswk GCSE new GCSE
Now 2008/09 2009/10 2010/11 2011/12
Y7
Y8
Y9
Y10
Y11
Y12
edulink.networcs.net
Dates for your diary
Next SLDM (Introducing the new Framework): 26th June Book through Inset Office
Workshop (Opportunity for planning time):2nd July 12:00 to 4:00 FinstallReturn confirmation when email received
What does it mean to you?