A Level Mathematics A Level Mathematics Courses as a Foundation Courses as a Foundation

for Degree Studiesfor Degree Studies

A teacher’s perspective

Current Maths A Levels

Brief outline of changes over last

25 years!

Further Maths Networks

Have Maths A Levels got easier or have standards risen?

Broader educational factors

Future changes

Summary

Outline of presentationOutline of presentation

Exam BoardsExam Boards AQA

Edexcel OCR

WJEC

All courses are modular; different schools impose different levels of ‘modularisation’

Subject Criteria set by QCDA (Core material for A Level Maths only)

Regulated by Ofqual

AS Levels and A2 Levels in:• Maths (C1, C2, C3, C4 + 2 applied)• Pure Maths (C1, C2, C3, C4 + 2FP)• Further Maths (FP1, FP2 + 4 other)

Modules available:C1-4, S1-6, M1-5, D1-2, NM(2), FP (3)

Other Maths AS/A Levels:• Use of Maths• Statistics

Overview of Changes to Maths A LevelsOverview of Changes to Maths A Levels

The first core for A Level Mathematics was introduced from The first core for A Level Mathematics was introduced from 1983; it contained only pure mathematics and was 1983; it contained only pure mathematics and was intended to form 40% of the syllabus. It led to overly large intended to form 40% of the syllabus. It led to overly large syllabuses which led to a decline in the numbers of syllabuses which led to a decline in the numbers of learners taking mathematics; learners taking mathematics; a smaller revised core was introduced in 1995. With the introduction of Curriculum . With the introduction of Curriculum 2000 (in which the norm is that in the first year learners 2000 (in which the norm is that in the first year learners take four GCE subjects rather than three), the core was take four GCE subjects rather than three), the core was again revised, this proved too demanding and was followed again revised, this proved too demanding and was followed by a reduction of one-fifth in the numbers taking A GCE in by a reduction of one-fifth in the numbers taking A GCE in Mathematics. In response to this drastic fall, Mathematics. In response to this drastic fall, a revised core was introduced in 2004 which spread the existing pure content over four units instead of three and reduced the number of applied units from three to two. Since 2004, there has been a substantial and continuing Since 2004, there has been a substantial and continuing growth in numbers taking A GCE Mathematics (and growth in numbers taking A GCE Mathematics (and proportionately an even greater growth in the numbers proportionately an even greater growth in the numbers taking A GCE Further Mathematics).taking A GCE Further Mathematics).

Taken fromTaken fromACME Position Statement on Qualifications in Mathematics at Level 3 from 2011 February 2009ACME Position Statement on Qualifications in Mathematics at Level 3 from 2011 February 2009

ModularisationModularisation

Introduction of Discrete/Decision MathsIntroduction of Discrete/Decision Maths

Minor changes to content of modules at Minor changes to content of modules at various stagesvarious stages

Changes to Further MathsChanges to Further Maths

Prior to 2004 AS in Further Maths had to include a compulsory unit Pure Maths 4, which required as a pre-requisite A Level Core Maths; AS FM could only begin after A Level Maths had been completed.

From 2004, the ‘replacement’ compulsory FP1 module was designed to be taught alongside the new AS Core Maths content.

Broader content Allowed, individual schools, to teach A Level Maths and Further

Maths students together for the A Level Core Maths component. Affected course content of the full A Level in Further Maths.

See MSOR Connections Aug 2004, Vol 4 No 3http://www.furthermaths.org.uk/manager_area/files/Offering_further_mathematics_as_part_of_the_A_Level_curriculum_Final_Report_Dec_07%201%20.pdf

Focus on Increasing Uptake of Further Focus on Increasing Uptake of Further Maths in Schools and Colleges: Maths in Schools and Colleges:

Further Maths NetworkFurther Maths Network

Further Maths Networks (DfES funded, with centres managed by MEI) set up in 2004. Importantly facilitated teaching of Further Maths by external tutors and coordinated teaching of Maths at different schools.

http://www.fmnetwork.org.uk/

The FMSP has three strands:

Student Support - helping to provide access to Further Mathematics tuition for all students.

Teachers' Professional Development - enabling more teachers to teach Further Mathematics and Level 3 mathematics within diplomas.

Communications and Marketing - promoting mathematics and raising awareness of the benefits of studying mathematics beyond GCSE.

Further Maths A LevelFurther Maths A Level

Students may not have choice over which modules to study

Students may be taught in mixed ability groups

Lessons may not be timetabled in normal hours. May have to travel to different centre to ‘share teachers’; may have reduced contact hours.

Year All Subjects

All Maths Subjects

% Further Maths

1989 661591 84744 12.8 n/a

1994 732974 64919 8.9 n/a

1999 783692 69945 8.9 n/a

2004 766247 58508 7.6 5720

2006 805698 63252 7.9 7270

2008 827737 73684 8.9 9091

Taken from ACME Position Statement on Qualifications in Mathematics at Level 3 from 2011 February 2009

A Level GCE EntriesA Level GCE Entries

Have Maths A Levels got Easier?Have Maths A Levels got Easier?

My perceptions: Some changes to the course content Structure of exam papers/mark distribution Predictable questions More scaffolding More limited algebraic solutions, less requirement to solve problems One quarter of the Core Maths material is higher level GCSE material Retake culture Teachers better able to ‘teach to exams’

Research evidence/QCDA reviewsMedia opinion

Teachers’ views

Context: Encouraging more pupils to take Maths to a higher level, whilst awider range of A Level subjects are now on offer; some of which are not as

academically demanding

Changes to Course ContentChanges to Course Content

Inequalities Combining D1/C4

Series Sums of finite series

Complex numbers

Numerical solution of equations

Iteration formula, linear interpolation, interval bisection, Newton-Raphson

First order differential equations

Requires C4 differentiation

Second order differential equation

Extension to C4

Polar coordinates

FP1: AS module for Further Maths post 2004 (Edexcel)

Coordinate systems I Now in FP2

Requires C4

Coordinate systems II Now in FP2 (except polar coordinates in FP1) Requires C4

Complex numbers Most in FP1

Linear algebra (using matrices)

Not in FP1 or FP2

Integration (standard forms and reduction formulae)

Requires C4 integration

Now in FP2

Vectors Extension of C4

Numerical methods For solving differential equations

Requires C4

Proof Not in FP1 or FP2

P4: AS module in Further Maths prior to 2004 (Edexcel)

Q1Q1 1414 5,4,55,4,5

Q2Q2 1515 1,5,5,41,5,5,4

Q3Q3 1616 2,3,9,22,3,9,2

Q4Q4 1515 3,5,3,43,5,3,4

Q1Q1 33 33

Q2Q2 88 5,35,3

Q3Q3 33 33

Q4Q4 33 33

Q5Q5 77 3,43,4

Q6Q6 55 55

Q7Q7 77 4,34,3

Q8Q8 1818 5,2,3,6,25,2,3,6,2

Q9Q9 1818 1,3,7,71,3,7,7

OCR MEI P2 June 2001(marks per question)

OCR MEI C3 June 2009(marks per question)

OCR MEI June 2001 P3

OCR MEI June 2009 C4

Difficulties comparing questionsDifficulties comparing questions

Changes to unit structure/content Context of mark scheme and grade boundaries

is missing Same topic but level of difficulty may depend on

question position Question may be set to meet a different

Assessment Objective

Assessment ObjectivesAssessment Objectives AO1: Recall, select and use mathematical knowledge, concepts and

techniques in a variety of contexts. (30%) AO2: Construct rigorous mathematical arguments and proofs through

use of precise statements, logical deduction and inference, including ..extended arguments ..to substantive problems in unstructured form. (30%)

AO3: Use of standard mathematical models to represent real world situations.. discuss assumptions and refinements of models. (10%)

AO4: Comprehend translations of common realistic contexts into mathematics, use of results and calculations to make predictions. (5%)

AO5: Use of contemporary calculator technology and other permitted resources accurately and efficiently. Understand limitations and, give appropriate accuracy. (5%)

QCA/Ofqual ReviewsQCA/Ofqual Reviews1995-1998: Decline in algebraic manipulation skillsIncrease in structuring of questionsNo increase in reasoning/problem solving

1998-2004: Greater consistency across awarding bodies, but greater variety of

routesQuestions more ‘accessible’ but greater degree of structuringIncreased exam time led to greater thoroughness, but also greater

predictability

2004-2007:Greater consistency across awarding bodies, number of possible

routes became more consistentC1 helped address gap between GCSE and A LevelC4 provided more rigorous assessmentStill over structuring of questionsLimited coverage of AO2

Have standards risen?Have standards risen?

Increased use of interactive and ICT based resources e.g. autograph/omingraph for visualizing transformations, polynomials and trigonometric functions etc

Greater access to web resources e.g. mei.org

Extended teaching: revision courses, tutors

Improved diagnostic assessment and target setting

Improved teaching through CPD

Broader educational factors which might affect the Broader educational factors which might affect the depth/breadth of Mathematical Studies?depth/breadth of Mathematical Studies?

Throughout secondary school an increased number of subjects are being covered or are available e.g. ICT, citizenship, RE often compulsory

More able pupils expected to extend in all areas (G and T agenda); some take 12-14 GCSEs

In year 12, pupils take 4/5 subjects. Common to take a mix of subjects (e.g. humanities and sciences)

Increased focus on e.g. target setting days, enrichment activities, leadership activities

Most courses are modular, time out of main teaching, increased focus on exam practice, overall examination times have increased

Wide variety of teaching styles across schools, increasing emphasis on team working and use of ICT and other interactive resources/activities; perhaps less independent study

Maths lessons generally more tutorial based than lecture based; difference in year12/13 between Science and Maths in this respect

Greater access to: Past exam papers

Solutions Mark schemes/exemplar materialsTeachers have little control of availability of these resources

Throughout secondary schools; strong emphasis on achieving target grades

New A* GradeNew A* Grade

The A* grade will be awarded to candidates who have achieved:

An A grade overall in their A Level, and 90 per cent of the maximum uniform marks (UMS) on the aggregate of their A2 units.

It should also be noted that the percentage of A* grades is likely to vary from subject to subject, as does the percentage of A grades awarded each year. The new grade is not being awarded to a set percentage of the total candidates or a set percentage of those who achieve an A grade – it will strictly be awarded according to the rules set out above.

Changes in allocation of unit Changes in allocation of unit grades to A Level Maths and grades to A Level Maths and

Further MathsFurther Maths

http://store.aqa.org.uk/admin/library/EU34_MAR08_SUBJ.PDF#gce_math

Changes likely from 2012Changes likely from 2012 2 units at AS Level and 2 units at A2 Level for A

Level Maths (no change FM)

33-40% Applications (A Level Maths)

No decision as yet re content of ‘Applications’

Fixed content for Further Pure AS and A Level

The style of some questions, particularly at A2, may be different to the current examinations to incorporate 'stretch and challenge' and the inclusion of 'proof' and unstructured problem-solving questions

More details of possible changesMore details of possible changes

QCDA Draft subject criteria for new mathematics A Levels http://www.qcda.gov.uk/qualifications/3971.aspx

4 Maths A Levels proposed (AQA):

A Level Maths A Level Further Maths A Level Use of Maths A Level Use of Statistics

http://web.aqa.org.uk/qual/gcse/maths_cp_project_gce.php

Changes to GCSE MathsChanges to GCSE Maths Why is GCSE Maths changing?

In 2004 the Smith Report identified ‘a crisis in the teaching and learning of Mathematics in England’ and found that the current GCSE Maths curriculum and qualifications framework:

• fails to meet the mathematical needs of learners • fails to fulfill the expectations of higher education and employers • fails to motivate sufficient numbers of young people to continue with

Maths study post-16. AQA

Main changes:

• Inclusion of functional elements • More emphasis on selecting appropriate technique, problem solving and communicating arguments• Less scaffolding• Double Maths GCSE: Methods in Mathematics; Applications in Mathematics

Maths A Levels: A variable and changing Maths A Levels: A variable and changing foundation for degree studiesfoundation for degree studies

Diversity in units studied, especially with Further MathsBase line is C1-C4; diagnostic testing

Different styles of teaching and learning across schoolsIndependent problem solving skills need to be developed (any substantive changes in schools will take many years to reach undergraduate entry)

Future changes likely to address, at least in principle, ‘problem solving aspect’. In reality unlikely to affect grades, if numbers taking A Level Maths to be maintained, alongside diverse range of alternatives.

Has a lack of ‘depth’ in Mathematics been compensated for by other skills?In the longer term do students who struggle with Maths content early on in the course, perform worse overall, in terms of degree level or subsequent progress.

Differences depending on type of school attended.