Introducing the New Secondary Curriculum Mathematics 13 th March 2008 Subject Leader Development Meeting

Outline The big picture More about maths Processes in practice Progression and planning Moving 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 safeBe healthyEnjoy and achieve Achieve economic well-being Make 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 enterprising Knowledge & 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 Importance why 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- curric links case studies Scroll down for maths in other subjects

The wider picture in maths Functional Skills Controlled Assessments 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 Now old ks3new ks3 old ks3old/new ks3new ks3 old ks3new ks3old/new ks3 single level tests single level tests pilots old ks4 new ks4 old/new ks4 GCSE1 GCSE2 new GCSE Functional Skills F Skills pilots old ks4 new ks4 old/new ks4 Functional Skills F Skills pilots GCSE1 GCSE2 cswk GCSEnew GCSE Now2008/092009/102010/112011/12 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 - headlines Similarities : Mathematical content appears unchanged (renewed Framework will contain the detail) Levels largely similar (p ) 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 learning not 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 Interpreting Evaluating Use procedures Analysing Use reasoning CONTEXTCONTEXT MATHEMATICSMATHEMATICS Communicating Reflecting

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 Interpreting Evaluating Use procedures Analysing Use reasoning Communicating Reflecting

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 voice Existing 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 curriculum with your pyramid

2 unit ASA level pilots Timeline for change Now old ks3new ks3 old ks3old/new ks3new ks3 old ks3new ks3old/new ks3 single level tests single level tests pilots old ks4 new ks4 old/new ks4 GCSE1 GCSE2 new GCSE Functional Skills F Skills pilots old ks4 new ks4 old/new ks4 Functional Skills F Skills pilots GCSE1 GCSE2 cswk GCSEnew GCSE Now2008/092009/102010/112011/12 Y7 Y8 Y9 Y10 Y11 Y12

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Dates for your diary Next SLDM (Introducing the new Framework): 26 th June Book through Inset Office Workshop(Opportunity for planning time): 2 nd July12:00 to 4:00Finstall Return confirmation when received

What does it mean to you?