Presentation on theme: "Outline of presentation"— Presentation transcript:
1 A Level Mathematics Courses as a Foundation for Degree Studies A teacher’s perspective
2 Outline of presentation Current Maths A LevelsBrief outline of changes over last25 years!Further Maths NetworksHave Maths A Levels got easier or have standards risen?Broader educational factorsFuture changesSummary
3 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
5 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; 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 fromACME Position Statement on Qualifications in Mathematics at Level 3 from 2011 February 2009
6 Introduction of Discrete/Decision Maths ModularisationIntroduction of Discrete/Decision MathsMinor changes to content of modules at various stages
7 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 contentAllowed, 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
8 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 byexternal tutors and coordinated teaching of Maths at different schools.The FMSP has three strands:Student Support - helping to provide access to Further Mathematicstuition for all students.Teachers' Professional Development - enabling more teachers toteach Further Mathematics and Level 3 mathematics within diplomas.Communications and Marketing - promoting mathematics and raisingawareness of the benefits of studying mathematics beyond GCSE.
9 Further Maths A LevelStudents may not have choice over which modules to studyStudents may be taught in mixed ability groupsLessons may not be timetabled in normal hours. May have to travel to different centre to ‘share teachers’; may have reduced contact hours.
10 A Level GCE Entries Year All Subjects All Maths Subjects % Further Maths19896615918474412.8n/a1994732974649198.91999783692699452004766247585087.657202006805698632527.972702008827737736849091Taken from ACME Position Statement on Qualificationsin Mathematics at Level 3 from 2011 February 2009
11 Have Maths A Levels got Easier? Research evidence/QCDA reviewsMedia opinionTeachers’ viewsMy perceptions:Some changes to the course contentStructure of exam papers/mark distributionPredictable questionsMore scaffoldingMore limited algebraic solutions, less requirement to solve problemsOne quarter of the Core Maths material is higher level GCSE materialRetake cultureTeachers better able to ‘teach to exams’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 asacademically demanding
12 Changes to Course Content FP1: AS module for Further Maths post 2004 (Edexcel)InequalitiesCombining D1/C4SeriesSums of finite seriesComplex numbersNumerical solution of equationsIteration formula, linear interpolation, interval bisection, Newton-RaphsonFirst order differential equationsRequires C4 differentiationSecond order differential equationExtension to C4Polar coordinates
13 P4: AS module in Further Maths prior to 2004 (Edexcel) Coordinate systems INow in FP2Requires C4Coordinate systems IINow in FP2 (except polar coordinates in FP1) Requires C4Complex numbersMost in FP1Linear algebra(using matrices)Not in FP1 or FP2Integration(standard forms and reduction formulae)Requires C4 integrationVectorsExtension of C4Numerical methodsFor solving differential equationsProof
14 OCR MEI C3 June 2009(marks per question)OCR MEI P2 June 2001(marks per question)Q13Q285,3Q3Q4Q573,4Q65Q74,3Q8185,2,3,6,2Q91,3,7,7Q1145,4,5Q2151,5,5,4Q3162,3,9,2Q43,5,3,4
16 Difficulties comparing questions Changes to unit structure/contentContext of mark scheme and grade boundaries is missingSame topic but level of difficulty may depend on question positionQuestion may be set to meet a different Assessment Objective
17 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%)
18 QCA/Ofqual Reviews 1995-1998: Decline in algebraic manipulation skills Increase in structuring of questionsNo increase in reasoning/problem solving: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: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
19 Have standards risen?Increased use of interactive and ICT based resources e.g. autograph/omingraph for visualizing transformations, polynomials and trigonometric functions etcGreater access to web resources e.g. mei.orgExtended teaching: revision courses, tutorsImproved diagnostic assessment and target settingImproved teaching through CPD
20 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 compulsoryMore able pupils expected to extend in all areas (G and T agenda); some take GCSEsIn 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
21 Most courses are modular, time out of main teaching, increased Most courses are modular, time out of main teaching, increased focus on exam practice, overall examination times have increasedWide variety of teaching styles across schools, increasing emphasis on team working and use of ICT and other interactive resources/activities; perhaps less independent studyMaths lessons generally more tutorial based than lecture based; difference in year12/13 between Science and Maths in this respectGreater access to:Past exam papersSolutionsMark schemes/exemplar materialsTeachers have little control of availability of these resourcesThroughout secondary schools; strong emphasis on achieving target grades
22 New A* GradeThe 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.
23 Changes in allocation of unit grades to A Level Maths and Further Maths
24 Changes likely from 20122 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 LevelThe 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
25 More details of possible changes QCDA Draft subject criteria for new mathematics A Levels4 Maths A Levels proposed (AQA):A Level MathsA Level Further MathsA Level Use of MathsA Level Use of Statistics
26 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:fails to meet the mathematical needs of learnersfails to fulfill the expectations of higher education and employersfails to motivate sufficient numbers of young people to continue with Maths study post-16. AQAMain changes:Inclusion of functional elementsMore emphasis on selecting appropriate technique, problemsolving and communicating argumentsLess scaffoldingDouble Maths GCSE: Methods in Mathematics; Applications inMathematics
27 Maths A Levels: A variable and changing foundation for degree studies Diversity in units studied, especially with Further MathsBase line is C1-C4; diagnostic testingDifferent 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.