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?