Towards universal participation in post-16 mathematics: lessons from high performing countriesJeremy Hodgen, Rachel Marks & David Pepper, King’s College London

15 January 2013

Context

• Is the UK an outlier?– Uniquely low participation rates post-16

• The wider agenda– ACME: A new advanced level qualification?– Wolf: GCSE

• Previous initiatives – FSMQs and AS Use of Mathematics– Curriculum 2000

Recommendations

• All students should be enabled to study post-16 maths at an appropriate level

• GCSE Mathematics should remain compulsory until grade C achieved

• One new advanced mathematics pathway aimed at those who have achieved a grade C

• Encourage a greater breadth in students’ post-16 programmes

Research Questions

• What factors drive participation in upper secondary mathematics?

• What is the content and level of upper secondary mathematics provision and how does it vary across different general and vocational routes?

Methodology

1. Academic literature search

2. Compilation of detailed country profiles– Country profiles & national experts

3. Review and synthesis of available data

The Countries Surveyed

• Hong Kong• Singapore• New Zealand• USA (Massachusetts) • Germany (Rhineland-Palatinate)• Scotland• England

Caveats and limitations

• Educational systems are culturally very different– Upper secondary / Vocational– Policy concerns often very different

• Policy in small systems may be more straightforward

• Data produced differently and for different purposes

‘How Far Can We Learn Anything of Practical Value from the Study of Foreign Systems of

Education?’

‘In studying foreign systems of Education we should not forget that the things outside the schools matter even more than the things inside the schools, and govern and interpret the things inside.’

Sir Michael Sadler, 1900

‘How Far Can We Learn Anything of Practical Value from the Study of Foreign Systems of

Education?’

‘We cannot wander at pleasure among the educational systems of the world, like a child strolling through a garden, and pick off a flower from one bush and some leaves from another, and then expect that if we stick what we have gathered into the soil at home, we shall have a living plant.’

Sir Michael Sadler, 1900

Participation in upper secondary mathematics education

Participation in upper secondary mathematics education

Participation in upper secondary mathematics education

Participation in upper secondary mathematics education

Participation in upper secondary mathematics education

Participation in upper secondary mathematics education

Participation in upper secondary mathematics education

Compulsion?

• The countries where maths is compulsory have near-universal participation in maths, but not the highest rate of participation in advanced maths

• New Zealand & Singapore achieve very high participation in maths and the highest levels of participation in advanced maths

New Zealand: Pathways

• Basic ‘Level 1’ Numeracy (and Literacy) required

• Two ‘different’ subjects at advanced level– Mathematics with calculus / with statistics

• Mathematics with statistics– A distinct and separate subject– Small ‘bite-sized’ units– Respected and valued by HE / employers– Strong links to the school curriculum

Singapore: Breadth

• Academic / pre-university system – A-level(reformed to give more local control)– Contrasting subject required in the academic /

pre-university route

• Flexibility and choice through polytechnics / ‘vocational’ routes

• An ‘extended duration’ O-level course is available

• BUT reduction in Further Maths

Hong Kong: A cautionary tale?

• Reform of the entire secondary / tertiary educational system– HKDSE to replace A-levels– Upper secondary education to 17 not 18– Mathematics compulsory (but not only

mathematics)

• BUT advanced mathematics participation fallen slightly– Not required by all numerate HE courses

Breadth, pathways and choice

• Compulsion is not sufficient – Encourage breadth – Provide appropriate and valued pathways– Mathematics is never the only compulsory

subject

Factors and incentives

• Attainment more important than attitudes & aspirations

• Information, advice and guidance poorly understood

Factors and incentives

• Attainment more important than attitudes & aspirations

• Information, advice and guidance poorly understood

BUT • The strongest incentive for students to

study advanced mathematics is that they are required to do so to progress to higher education and employment

Policy

• What can be learned from smaller, “successful” systems?– Success of a qualification depends on a range

of factors• Wide availability• Respected by and required by HE / Employers• Valued by schools / colleges

– Relatively long timescales for implementation

Risks

• Teacher supply• The “FSMQ” problem

– Availability and take-up– Respect and value by HE / Employers

• Vocational routes• Dangers of stratification

Recommendations: What

• All students should be enabled to study post-16 maths at an appropriate level

• GCSE Mathematics should remain compulsory until grade C achieved

• One new advanced mathematics pathway aimed at those who have achieved a grade C

• Encourage a greater breadth in students’ post-16 programmes

Recommendations: How

• Encourage breadth of study• Any new qualification / pathway needs to

be attractive to and valued by:– Students– Schools / Colleges– HE / Employers

• Enable HE / employers to require maths• Implement over an extended time period• Research: teacher supply, IAG, vocational