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A Level Mathematics Courses as a Foundation for Degree Studies A Level Mathematics Courses as a Foundation for Degree Studies A teacher’s perspective

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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 presentation

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Exam 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

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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

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Overview of Changes to Maths A Levels The first core for A Level Mathematics was introduced from 1983; it contained only pure mathematics and was intended to form 40% of the syllabus. It led to overly large syllabuses which led to a decline in the numbers of learners taking mathematics;. With the introduction of Curriculum 2000 (in which the norm is that in the first year learners take four GCE subjects rather than three), the core was again revised, this proved too demanding and was followed by a reduction of one-fifth in the numbers taking A GCE in Mathematics. In response to this drastic fall, Since 2004, there has been a substantial and continuing growth in numbers taking A GCE Mathematics (and proportionately an even greater growth in the numbers taking A GCE Further Mathematics). The first core for A Level Mathematics was introduced from 1983; it contained only pure mathematics and was intended to form 40% of the syllabus. It led to overly large syllabuses which led to a decline in the numbers of learners taking mathematics; a smaller revised core was introduced in With the introduction of Curriculum 2000 (in which the norm is that in the first year learners take four GCE subjects rather than three), the core was again revised, this proved too demanding and was followed by a reduction of one-fifth in the numbers taking A GCE in 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 growth in numbers taking A GCE Mathematics (and proportionately an even greater growth in the numbers taking A GCE Further Mathematics). Taken from ACME Position Statement on Qualifications in Mathematics at Level 3 from 2011 February 2009

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Modularisation Introduction of Discrete/Decision Maths Minor changes to content of modules at various stages

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Changes 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 3 _part_of_the_A_Level_curriculum_Final_Report_Dec_07%201%20.pdf

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Focus on Increasing Uptake of Further Maths in Schools and Colleges: Further Maths Network Further Maths Networks (DfES funded, with centres managed by MEI) set up in Importantly facilitated teaching of Further Maths by external tutors and coordinated teaching of Maths at different schools. 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.

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Further 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.

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YearAll Subjects All Maths Subjects %Further Maths n/a n/a n/a Taken from ACME Position Statement on Qualifications in Mathematics at Level 3 from 2011 February 2009 A Level GCE Entries

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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 reviews Media opinion Teachers’ views Context: Encouraging more pupils to take Maths to a higher level, whilst a wider range of A Level subjects are now on offer; some of which are not as academically demanding

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Changes to Course Content InequalitiesCombining D1/C4 SeriesSums 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)

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Coordinate systems INow in FP2 Requires C4 Coordinate systems IINow in FP2 (except polar coordinates in FP1) Requires C4 Complex numbersMost in FP1 Linear algebra (using matrices) Not in FP1 or FP2 Integration (standard forms and reduction formulae) Requires C4 integration Now in FP2 VectorsExtension of C4 Numerical methodsFor solving differential equations Requires C4 ProofNot in FP1 or FP2 P4: AS module in Further Maths prior to 2004 (Edexcel)

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Q1145,4,5 Q2151,5,5,4 Q3162,3,9,2 Q4153,5,3,4 Q133Q285,3 Q333 Q433 Q573,4 Q655 Q774,3 Q8185,2,3,6,2 Q9181,3,7,7 OCR MEI P2 June 2001 (marks per question) OCR MEI C3 June 2009 (marks per question)

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OCR MEI June 2001 P3 OCR MEI June 2009 C4

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Difficulties 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

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Assessment 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%)

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QCA/Ofqual Reviews : Decline in algebraic manipulation skills Increase in structuring of questions No increase in reasoning/problem solving : Greater consistency across awarding bodies, but greater variety of routes Questions more ‘accessible’ but greater degree of structuring Increased exam time led to greater thoroughness, but also greater predictability : Greater consistency across awarding bodies, number of possible routes became more consistent C1 helped address gap between GCSE and A Level C4 provided more rigorous assessment Still over structuring of questions Limited coverage of AO2

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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

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Broader educational factors which might affect the 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 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

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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 materials Teachers have little control of availability of these resources Throughout secondary schools; strong emphasis on achieving target grades

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New 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.

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Changes in allocation of unit grades to A Level Maths and Further Maths _MAR08_SUBJ.PDF#gce_math

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Changes 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

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More details of possible changes QCDA Draft subject criteria for new mathematics A Levels 4 Maths A Levels proposed (AQA): A Level Maths A Level Further Maths A Level Use of Maths A Level Use of Statistics

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Changes 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:Smith Report 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

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Maths A Levels: A variable and changing foundation for degree studies Diversity in units studied, especially with Further Maths Base line is C1-C4; diagnostic testing Different styles of teaching and learning across schools Independent 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.

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