The Renewed Frameworks For Mathematics

The Renewed Frameworks for Mathematics Effective September 2008

New curriculum aims from QCA  

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Motivating and engaging Gain relevant skills for education, employment and life Assessment supports teaching Curriculum meets needs of learners Smooth progression Encourages access to higher education

New Frameworks have common format. 

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Importance statement: why it matters Key Concepts: big ideas that underpin each subject Key Processes: essential skills for each subject Range and content: what to teach Curriculum opportunities

Mathematics Key Concepts 

Competence:   

Apply suitable maths Communicate effectively Select appropriate tools and methods

Mathematics Key Concepts 

Creativity 

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Combine previous experiences to construct new knowledge Use knowledge to solve new problems Pose questions and develop arguments

Mathematics Key Concepts 

Applications and implications of maths   

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Know that maths is rigorous Know that maths is a tool Recognise historical and cultural roots of maths Engage in maths as an interesting activity

Mathematics Key Concepts 

Critical Understanding 

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Maths is abstract and therefore can be used to model Recognise limitations and scope of model

Key Processes (what we’re all calling MPAs or Mathematical Processes and Applications)  

Representing Analysing  

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Use mathematical reasoning Use appropriate mathematical processes

Interpret and Evaluate Communicate and reflect

Range and Content (Still called ATs but new names)    

MPA (AT1) Number and Algebra (AT2) Geometry and Measures (AT3) Statistics (AT4)

Curriculum Opportunities 

Opportunities to enhance and enrich learning, including making links with other subjects and the wider curriculum.

Quick Summary Is what students have to know different? Is the new curriculum at odds with what we want students to achieve from maths? Is it prescriptive about how concepts have to be taught? Does it provide opportunities for teachers to deliver content in the way they want?

No

No

No

Yes

Cause for anxiety 

Understandable that anxiety creeps in – students still have to know all the things that they used to have to know but there is the expectation that there will be a real change in the emphasis of how maths is taught – one which will develop students into learners who can use their maths to solve problems. So how do we fit it all in?

Why it makes me feel Why it makes me feel ok anxious It is in tune with why I teach maths and what I love about maths.

I think I have got to be doing it all now.

Don’t panic. It is expected that the changes in the emphasis of teaching will be introduced during 2008 and 2009 to Y7 (Y8 might be a good idea too) and that this will continue as they move through years 8 and 9.

2008/09

Y7

Y8

Y9

Y10

2009/10

2010/11

new KS3

old or new KS3

new KS3

old or new KS3

new KS3

Functional skills GCSE 1 and/or GCSE 2

Starting points for the new curriculum 

Every child matters agenda     

Enjoy and achieve: creativity, solutions Be healthy: numeric data Stay safe: understand risk Economic well-being: interpreting Make a positive contribution: empowered to contribute by being logical

Starting points for the new curriculum 

Personal Learning and Thinking Skills:      

Independent enquirers Creative thinkers Team workers Self managers Effective participators Reflective learners

Assessment 

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New diploma process will assess these skills (first 5 piloted from Sept 2008) Functional skills are integral part of this, qualifications in own right also. APP resources for maths awaited in Spring (trialling in Foundation subjects now) In the classroom and at other “nonstatutory” times schools are encouraged to develop a range of approaches that can be used to develop learning.

How it might look in the classroom 

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Still seeing students making progress in their learning Some lessons might be very explicitly about developing the MPA skills Some lessons might develop these skills implicitly, it might be a good idea to make these explicit later!

• Representing

MPAs

– Recognise problem as one that can apply maths to, breaking it down & using appropriate words, symbols and diagrams

• Analysing (Reasoning) – Generalising, logical working, explaining reasoning, taking feedback and adapting approach.

• Analysing (Mathematical processes) – Doing the maths by appropriate and accurate means

• Interpreting and evaluating – Relate finding to original context, justify methods and conclusions and compare approaches.

• Communicating and reflecting

– Effectively communicate own results, recognise other equivalent approaches. •Some descriptions seem to overlap to me – don’t think it really matters.

4 possible models for the inclusion of an MPA rich task into a unit of work Start of task

A

B

C

D

End of task

Teach the syllabus and the mathematical content required for the NC in the main part. Introduce some elements of MPA into teaching through specifically aiming at a particular objective or skill set in part of a lesson. MPA rich starter to make learners aware of context and necessity for learning upcoming skills.

Teach the syllabus and content required for the unit of work.

Teach the syllabus and content required for the unit of work

Re-visit the initial prompt and ask students if they are now better equipped to approach the problem Deliver an MPA 'Rich' Task which will draw on the skills learnt enabling the students to apply their new knowledge. Assess students learning by observing the conversation and approaches used to engage with the activities

•Deliver an extended MPA 'Rich' Task covering a range of skills and knowledge. •Stop students and teach as problems and gaps in knowledge arise

Mathematical content lesson

MPA rich activity

Level of risk

Low

Low/ Med

Med/ High

High

Key web references for information 

There are two main sources to refer to: www.curriculum.qca.org.uk and www.standards.dcsf.gov.uk as detailed below.

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http://curriculum.qca.org.uk/key-stages-3-and-4/subjects/mathematics/index.aspx (page for KS3 and KS4 PoS) then on right hand side there is a box to click on for: How mathematics links to Aims (this is key aims of learning maths) Personal development (this is how maths contributes to the five ECM aims) PLTS (this is how maths contributes to the six PLTS headings) Functional skills (links Functional skills to KS3 PoS)

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http://curriculum.qca.org.uk/key-stages-3-and-4/skills/plts/index.aspx (click on Download PLTS Framework for overview of PLTS non subject specific) http://curriculum.qca.org.uk/key-stages-3-and-4/personaldevelopment/index.aspx (brief overview of ECM aims) http://www.standards.dcsf.gov.uk/secondary/framework/maths/fwsm particularly the 5 sections from the left hand side under Framework for Secondary Mathematics include: 

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Overview: gives summary of the 5 strands. Can then link to Overview which shows each AT split into Y7 to 11 and Extension Framework learning objectives: General information and link to APP assessment guidelines which is a 2 page levelling grid Introduction to Learning Objectives: The “Revision to objectives in y7, 8 and 9” links to AT for KS3 PoS breaking down each AT into levels. The “Objectives in Y10 and 11” gives info on making 2 levels progress in KS4 and on right hand side gives link to Key Process Maps i.e. the PDF spider documents for the MPAs. Supplement of examples: click on AT to get document showing supplement of examples (old Framework folder I believe) Mathematics Learning Objectives: in the main body the “maths overview and learning objectives” gives