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Stretch and Challenge in GCE Mathematics

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Stretch and Challenge in GCE Mathematics

Stretch and Challenge in GCE Mathematics Draft 5 22 January 2006

    0 Executive Summary

    The take-up of the AEA has been disappointing and a review of provision for the most able is timely. Bringing the provision back under the GCE title is likely to increase visibility and may serve to increase take-up. Whilst having commonality of purpose, the form it takes in each subject will need to be sensitive to the nature of the subject. There is a consensus that in GCE mathematics that stretch and challenge can best be provided by a separate paper than by attempting to attach material to unit examinations.

    The introduction of Curriculum 2000 led to a severe fall in numbers taking GCE Mathematics which were stabilising after long-term decline. Changes introduced in 2004 are seeking to encourage more students to take the subject; it is hoped that over time Mathematics will be perceived as accessible to a wider range of students. It is vital that any changes designed to stretch and challenge the most able do not undermine attempts to ensure a higher proportion of the workforce have studied mathematics at Level 3. There is a grave danger that modifications to GCE unit examinations might well have such negative effects.

    GCE mathematics examinations are designed to provide a robust test of candidates competence in

    the subject matter whilst the AEA has provided a test of thinking in more depth so giving a better indication of candidates’ flair for the subject. GCE papers require a fluency in the core techniques of the subject, something that involves the efficient and consistent use of time; such skills are necessary but not sufficient prerequisites for success in pursuing the subject at degree level. The higher level skills also desired need more sophisticated questions such as are found on AEA papers, these require more time for reflection and developing a response. It is difficult to see how such questions could be incorporated into a GCE unit examination.

    In a unit-based approach to providing stretch and challenge, candidates are likely to have to make choices which involve an element of risk either in their choice of questions or in their use of time. As a result candidates who are risk-adverse are less likely to attempt the material giving access to the new grades. This is likely to discriminate against girls and candidates from centres which lack a history of success at this level.

    Since GCE mathematics specifications contain many units, a unit-based approach would be expensive to implement and likely to lead to increased examination costs. Separate papers, one per GCE qualification, which might be common across specifications, would be cheaper to implement. The money saved could be used more usefully to promote up-take and to provide support for students preparing for the additional assessments either within their centres or by distance-learning. This paper contains an outline of present provision (summarised in Section 1 with further detail in Appendix A), some remarks on the White Paper (in Section 2 with extracts from key documents in Appendix B), a discussion of possible models for including stretch and challenge in GCE (in Section 3) and a list of recommendations (in Section 4).

    1 Present Provision

    The following relevant qualifications exist:

     ASGCE and AGCE Mathematics,

     ASGCE and AGCE Further Mathematics,

     Additional Award in ASGCE and AGCE Further Mathematics,

     ASGCE and AGCE Pure Mathematics,

     AEA Mathematics,

     STEP Mathematics 1, 2 and 3.

    Their distinctive features are discussed briefly below and in more detail in Appendix A.

    New specifications for GCE mathematics were introduced for first teaching in 2004 and it is expected that the revisions resulting from the work on Post-14 Mathematics Pathways will be introduced in 2010, with mathematics retaining its present 3 + 3 unit structure in 2008 given the then impending further reforms. There are six specifications (each with its own rules of combination): AQA, CEA, Edexcel, MEI (administered by OCR), OCR and WJEC. The

    specifications provide considerable choice of units, especially in applied mathematics, with many units not tied to particular qualifications. Where a candidate seeks simultaneous certification for AGCE Mathematics and GCE Further Mathematics, the awarding body optimises (in accordance with the rules of combination) the candidate’s results, units only being allocated to particular

    qualifications at the result stage. Uniquely, AGCE Mathematics may contain 3 or 4 AS units, the number depending on the student’s choice of applied mathematics units. GCE Further Mathematics

    qualifications may contain fewer than 3 AS units, and in some specifications this is also the case for GCE Pure Mathematics.

    Whilst GCE provides a test of competence, the AEA gives candidates the opportunity to demonstrate a flair for mathematics. AEA Mathematics is conducted by Edexcel only, an economical arrangement which also avoids having issues of comparability between awarding bodies. It is a 3-hour paper set on content of the pure core (so accessible regardless of GCE specification). It provides candidates with an opportunity to demonstrate the ability to answer unstructured questions and build sustained chains of reasoning in a way not available within the short GCE unit examinations. There are about 1000 entries a year for AEA Mathematics. Although outside the National Qualifications Framework, STEP, which is conducted by OCR, has an entry of the same order of magnitude as that of the AEA. It is used in offers by the Universities of Cambridge, Oxford and Warwick, and is also taken by some other candidates who relish the challenge that the papers provide. (STEP was withdrawn in other subjects when the AEA was introduced.)

    2 The White Paper and its Implementation

    The White Paper, 1419 Education and Skills, was published on 23 February 2005. It contained

    proposals to replace the AEA by optional harder questions in A Level papers as well as other measures to help stretch and differentiate between the most able. On 14 December 2005 an Implementation Plan for the White paper was published. Some extracts from these documents and from the minutes of a recent QCA Board meeting are given in Appendix B.

    There are widespread doubts about the practicality of implementing the proposal in the White Paper and considerable apprehension at possible negative side effects. There is a consensus in mathematics that moving stretch into units would be detrimental. At this level candidates need time to develop approaches to answering questions, drawing together ideas from across the subject, so as to create sustained arguments; this cannot be achieved in a short section tacked on to another examination. There is likely to be a backwash into standard provision which will nourish the perception that GCE mathematics is inaccessible for ordinary students and so lead to a drop in uptake, so nullifying the 2004 reforms.

    As yet, there is little in the public domain about what form practical implementation might take. The next section considers some possible models. The term unit-based is used where the extra

    assessment is incorporated in the assessment for particular units and the term qualification-based

    where the assessment, while being within the GCE qualification is not attached to particular units. 3 Possible Models

    Unlike AEA which was available in only a small number of GCE subjects, the new provision is to be available in all GCE subjects (and beyond). So this means there needs to be provision for AGCE Mathematics, AGCE Further Mathematics and AGCE Pure Mathematics. (Provision might also

    have to be made for the Additional Award in AGCE Further Mathematics but, given that there were only 31 entries in 2005 and the maximum under Curriculum 2000 has been 48, it would be hoped that separate provision for this award could be avoided.) This approach will inevitably be more expensive, both in terms of human and financial resources, with tasks likely to have to be repeated for different specifications and units. Also it is clear, given the broad range of qualifications which are to incorporate stretch and challenge, that a variety of approaches will need to be adopted. The wording of the White Paper seems to envisage incorporation of additional material into the written examination for A2 units. It is unclear whether all units would need to be adapted or just some (perhaps the A2 units or just those A2 units containing a synoptic element would need to incorporate this additional stretch and challenge. Although the consistent reference in the White Paper and its Implementation Plan to ‘A level’ suggests that it is envisaged that only A2 units

    would be affected.

    Mathematics has suffered a substantial drop in take-up; it is vital that any measures introduced to provide stretch and challenge for the highest achievers do not damage the experience of the majority of students, either in their examinations or in their learning preparatory to them. If numbers are to recover then the new candidates are likely to come from those beyond the clever core [QCA, enquiry into the take-up of GCE mathematics, 2005]. A major influence on student subject choice is informal feedback from previous students. Whilst some students will pursue courses in mathematics for progression reasons, the strongest influence is positive prior experiences in the subject (this is particularly the case for girls who are already underrepresented among those

    studying mathematics) [Allan, MSc thesis, 2005]. To ensure continuation from ASGCE to AGCE Mathematics (and into Further Mathematics) it is particularly important to ensure that students feel comfortable with the mathematics they encounter in AS units. It will be important that extension provision is structured in such a way that teachers do not feel pressured into presenting extension material in their teaching to all candidates, regardless of suitability; great care will need to be taken to avoid such a situation if all candidates are to be presented with the extension material in the examination, rather than just those for whom it is suitable.

    The proposed reform is in response to the poor take-up of AEA and is meant to increase the number of students undergoing assessment at this level. There is grave danger that it may have the opposite effect, if there is an element of putting the basic result at risk in opting to tackle the optional section. This will not only affect risk-adverse students but also those who are taught in risk-adverse settings such as less confident or successful departments who will be inclined to encourage their candidates to play safe.

    3.1 Unit-based approaches

    The variety of routes to AGCE Mathematics, let alone AGCE Further Mathematics, might make attaching the extension assessment to units seem the most straightforward, but on closer consideration it can be seen to be impractical. It would not seem appropriate to attach such extension to AS units, but if all (and only) A2 units carried it then a problem could arise as AGCE Mathematics can include 3 or 2 A2 units which would create inequity in candidates’ opportunities to demonstrate high achievement. Thus for AGCE Mathematics there seem only the following options for a unit-based approach: all units (AS and A2) contain extension material, all A2 units and all applied AS units contain extension material, or only units C3 and C4 (or just one of these, presumably C4) contain extension material and the first two applied units in a strand do not. For those candidates also taking AGCE Further Mathematics (which there is a Government-funded initiative to promote), C3 and C4 may well be taken before the end of the course. Such students whilst having developed the ability to tackle standard A-level questions successfully, may well not have achieved the level of mathematical maturity needed for the more sophisticated AEA-type material by that point in the course and so be placed at a disadvantage.

    If attaching extension material to AS units is to be avoided (on grounds of maturity and to avoid an excessive burden of assessment), this leaves only the last option. What consequences does this have

    for extension provision for AGCE Further Mathematics. As provision in the first two applied units has already been excluded, and many will not include any applied units beyond the second, on grounds of equity, no applied units can include any stretch and challenge. In most specifications (all except CEA and even for CEA this might be varied on special application), the number of pure units is not fixed. The only unit one can guarantee that a candidate sits is FP1, but in some specifications this is an AS unit which may well have been taken in the lower sixth. In some specifications FP2 would also be compulsory, but where it is not there is no mutually exclusive alternative which means that (if candidates are to have parity of access to extension) only FP1 could carry extension material, an undesirable outcome given it might be an AS unit. So either specification structures would need to be changed (which we understand is not the intention) or candidates wishing to attempt extension material would have a specially limited choice of units, if that was the case then it is likely many candidates would be excluded from access to extension material as they would not have access to the unit required combinations (or if they are late developers they might already be committed to unsuitable unit combinations).

    This seems to lead to the conclusion that, regardless of considerations of educational desirability, it is impractical to implement a unit-based approach for extension in AGCE Further Mathematics, without changing specification structures or inserting AEA-type material in AS units. Nevertheless, some unit-based approaches are considered below.

    3.2.1 Models which rely on differentiation by response

    An approach would be to leave the question papers unchanged but to extend the marking schemes. For example, an essay that was marked out of 25 with marks from 0 to 5 on each of five strands, might have the top band in each strand divided to give 5, 6 or 7, so each strand would now be marked from 0 to 7. Such an approach would fail to incorporate specific and identifiable material, yet might be viable in subjects where differentiation is primarily by response rather than task: for example, where an essay has to be written in response to a brief title or an artefact produced in response to a written stimulus (in the latter case it is difficult to imagine any other unit-based approach being practical).

    There is also the issue of compensation. At present (in the example given), the maximum any strand can contribute is 5, so a candidate might score (to give an extreme case) 5 + 5 + 5 + 2 + 2 = 19 which would be likely to produce a B grade but could in the model given get 7 + 7 + 7 + 2 + 2 = 25 which would be likely to produce an A grade (and might even qualify for one of the extended grades) or another might perhaps score 7 +7 + 7 + 0 + 0 = 21 which would be likely to get an A grade (previously a C) despite very poor performance on two strands. Although allowing the extra marks to provide compensation would be administratively simple, it might be considered pedagogically undesirable as candidates could just concentrate on some strands and give little attention to others. Also, the increased diversity in how candidates achieved particular mark totals would make it harder to set grade boundaries reliably. An alternative would be to treat the sixth and seventh marks (in the example) as bonus marks which did not contribute to the total for grades E to A and were only considered (either on their own or by addition to the existing total) once the candidate had reached the threshold for an A grade. Such an approach would increase administrative complexity and there would be a question of how reliably markers could implement such a scheme (a past scheme involving bonus marks was abandoned because of difficulties in this regard).

    3.2.2 Models where candidates undertake additional material

    Another approach is to append additional material to the end of the paper. Candidates who tackle this material might be given no extra time, they might be given extra time but their work on the ordinary material would be collected at the end of normal time, all their work might be collected at the end of the extra time, or the extension section questions might only be made available to candidates at the end of normal time. Any approach involving extra time is likely to have consequences for timetabling.

    The third of these is open to abuse in that by making a nominal attempt at the extension section a candidate can gain extra time for the ordinary material, so this third option effectively becomes the first. The second option would overcome the problem of the diversion of time, but might prove difficult to achieve in practice as it requires candidates to be disciplined about where they write their answers, and practical experience would suggest that this is unrealistic, also it would be difficult to ensure centres responded in a uniform way to candidates who failed to observe the requirement. This second option would only be practical if candidates wrote their answers on the question paper (to reduce the risk of answers being written in the wrong book).

    The first and second options share the problem that candidates are encouraged to rush the normal material (with possible mistakes and loss of marks). The examination’s ability to assess the candidate’s mathematical prowess is confounded by the factor of the candidate’s skill in judging how to allocate time between the sections, as well as making it a speed test. (Any candidate needs to allocate time sensibly but the introduction of the additional section moves the judgement from common sense to gamesmanship.) Included in that gamesmanship is the candidate’s attitude to risk

    which raises issues of equal opportunities, especially gender.

    This leaves the fourth option, which is effectively a separate paper. If following C4, it could be like the present AEA in style if not length. In seeking to achieve stretch and challenge in mathematics, one wishes to develop in students the ability to link ideas together (both within and across topics), to select approaches (rather than be told them or have them obviously telegraphed), and to develop ingenuity and persistence in problem-solving. These things need time: time to think, candidates may well spend 80% of their time thinking rather than writing; time to try out more than one approach, if needs be. This tends to militate against short assessments where candidates would need to be able to get quickly into writing their answers to a question. Any extra time for extension material would prevent two units happening in the same half-day session, so if this approach was adopted there would be 90 minutes left (except for MEI C4) in the session. It would be better to have one unit with a 90-minute extension than two units with 45-minute extensions, if one is to develop and reward the desired characteristics in candidates; a 30-minute extension would be unlikely to provide opportunity for suitable material. (The one-hour comprehension paper in the MEI C4 unit or the extension for the MEI C4 might be timetabled separately (say with C3).) Nevertheless, even a 90-minute duration would give a very narrow basis (in terms of product on the page) on which to make an award.

    3.2.3 Models where candidates undertake alternative material

    An approach might be to provide alternative sections of normal and extension material which candidates choose between, these would probably follow a common section on normal material undertaken by all candidates. Immediately candidates are called upon to make choice like this (especially under examination conditions), issues of risk-averseness arise along with the associated equal-opportunities issues alluded to above. It is quite likely that many candidates will under-perform with such an approach. For example, an ambitious A/B borderline candidate may struggle with the extension option but have been able to put in a sound performance on the normal option. A weak candidate may not recognise the more appropriate section to attempt and achieve little (experience with papers containing alternative sections where candidates attempt sections for which it is clear that they have not been prepared is sufficiently common to suggest that this will be a real issue). Examiners will be faced with trying to set unit grade thresholds where candidates have gained their marks by alternative routes; this will reduce the reliability of assessment and consequently public confidence in the GCE.

    If candidates’ scripts are to contain a comparable amount of product, candidates undertaking the extension section will need to be given longer than those taking the normal alternative. Unless candidates have to opt in advance (which might make it easier to manage the issue of candidates attempting inappropriate sections), this would be very difficult to manage in examination rooms.

3.3 Qualification-based approaches

    A qualification-based approach is one in which the extension assessment, while lying within GCE, is not attached to a particular unit. It is less in the spirit of the White Paper but could be accommodated within its objectives. The AEA has been disappointing in its take-up and some re-launch of extension provision is needed. There is also a lack of equity in that access to it is only available in some subjects.

    Nevertheless, the three-hour paper provides the opportunity for candidates to demonstrate higher-level skills and traits which it is difficult to achieve in a short paper. Candidates can demonstrate the ability to draw ideas together from across mathematics, to develop sustained arguments and to solve problems to which the solution is not immediately obvious. A qualification-based extension assessment also enables the ordinary GCE units, and their teaching, to be protected from undesirable side effects which might result from a unit-based approach. Also, the AEA in Mathematics has proved popular, relative to other AEAs, so it would be desirable to continue its good features. The prevailing view in the mathematics education community is that extension provision will best be achieved in mathematics by developing an assessment instrument which has largely the feel of the present AEA.

    A major possible weakness of a qualification-based approach (which may also exist in unit-based approaches) is that it requires a decision to enter in advance. It will be important that strong steps are taken to promote entry whatever approach is adopted but all the more so with a qualification-based approach in order to overcome the inertia against commitment to enter. The steps taken need not only to raise awareness and demand but also to assist centres in meeting that demand. Some centres will be confident that they are able to provide good support for extension candidates but other may feel the need for support. External support can more readily be given where there is greater commonality in the extension assessments. It is unlikely it would be practical or viable to make distance-learning provision available for unit-based assessments across all specifications. The timing of the assessment within the examination season is likely to have an effect on take-up and will need to be judged carefully. It should be sufficiently late that candidates are not inhibited from entry because of worries about preparation for it interfering with revision for GCE units. Nevertheless it should not be so late in the season, that candidates (at least those taking the most likely combinations of GCE subjects) would have a prolonged period after the end of their GCE units waiting for the assessment while their friends were already indulging in post-examination relaxation.

    On the other hand, it is likely to lead to a more efficient provision and fewer candidates attempting inappropriate material. Teachers will be able to guide students appropriately in making their entry choices and be clear which students they are helping to prepare for the extension assessments. Centres will be able to plan their use of examination staff and rooms efficiently. Awarding bodies will be able to allocate scarce examining staff more efficiently and be able to draw on a wider pool of possible markers (as it will not be necessary for all markers to be able to cope with the extension material). As marks for the extension material will not need to be aggregated with other marks, the reliability of the present assessments is not undermined.

    The present AEA makes national provision at the cost of preparing one three-hour examination with no choice of question. Unit-based provision would have to be unit specific and so specification specific. This will increase costs, and may undermine the viability of some units with small entries and lead to a reduction in the number of sessions at which units are offered. A qualification-based approach would make it easy for a common paper to be taken by candidates regardless of their AGCE Mathematics specification; this might also be possible for AGCE Further Mathematics. If a common paper was adopted then HEIs (and other users) would have the incentive of enhanced comparability of applicants which would be likely to lead them to make more ready use of it. Although outside the NQF, the existence of STEP (which at present has a comparable number of entries to AEA) needs to be taken into account when planning extension provision in mathematics.

It is unlikely that a unit-based approach would command the confidence of those HEIs which

    currently use STEP.

    4 Recommendations

    4.1 Whatever approach is adopted in providing extension material in mathematics, an over-riding consideration must be that it in no way diminishes the experience of the bulk of candidates or

    discourages students from taking-up or continuing with GCE mathematics.

    4.2 For many candidates in mathematics, GCE Further Mathematics provides an important element of stretch and challenge. The measures adopted should not lead to a diminution in the take-up of ASGCE and AGCE Further Mathematics.

    4.3 So that candidates are best able to demonstrate their response to stretch and challenge in mathematics, separate qualification-based (rather than unit-based) assessments containing suitable material should be introduced for AGCE Mathematics and AGCE Further Mathematics (and for the

    other AGCE qualifications if they are retained). Consideration should be given to whether these assessments could be common across specifications.

    4.4 Candidates should receive a (standardised) score for their performances in extension assessments on their Statements of Results, although it would not contribute to the grade awarded (and appear on their certificates) unless an A grade had been achieved in the normal assessment, so that all attempting the extension assessment would have some evidence of their performance in it. 4.5 The extension assessment for AGCE Mathematics should be a three-hour written paper addressing the common core content of C1 to C4; it would be sat in a different half-day session from the normal GCE units. It would stand apart from the normal GCE units.

    4.6 The extension assessment for AGCE Further Mathematics should be a three-hour written paper it would be sat in different half-day session from the normal GCE units; candidates would have a choice of questions. If a common paper was set, the content would be organised in such a way that for each major topic area would be such that a candidate who had studied the topic beyond any

    specification’s FP1 would be able to access the material; knowledge of the content of C1 to C4

    would be assumed and some questions might just be sophisticated questions on that material. (This approach gives an advantage to candidates taking more FP units as is desired by some higher

    education institutions but with sufficient choice should allow all candidates to demonstrate their

    abilities.) It would stand alone from the normal GCE units.

    4.7 Steps should be taken to encourage candidates to enter for these assessments and to encourage centres to support such entries, through funding and performance indicators. Inspection procedures should report whether all appropriate students have satisfactory access to extension provision. Encouragement should also be given to HEIs to include extension grades in their offers, where

    appropriate.

    4.8 To give candidates greater equality of opportunity between centres, the work of the National Further Mathematics Network should be extended to include helping centres prepare candidates for the extension assessments, this will be particularly important to provide equity of access for

    candidates in less confident or successful departments. To enable this to happen, funding should be provided to the NFMN, centrally or through centres.

    4.9 Funding should be made available (in England, through the LSC) to meet the cost of entry and teaching so that those students with the potential to excel are able to demonstrate their abilities. (For budget purposes we would envisage (at current costs) annual entries rising over five years from the current AEA level of 1000 to 8000 for Mathematics and 2000 for Further Mathematics, at ?150 per entry: ?30 for examination entry fee, ?10 for costs in administering the examination, ?110 for the additional teaching and resource costs (this being half the cost of distance-learning for a GCE unit with the NFMN).)

Appendix A Details of Present Provision

    A.1 Present AGCE Structures

    At present there are six specifications, one from each awarding body and a specification devised by

    the Mathematics in Education and Industry Schools Project which is administered by OCR. Units

    are provided in pure mathematics Core and Further Pure and applied mathematics Decision (not available from CEA and WJEC), Mechanics, Numerical(available only from MEI) and

    Statistics. All units are worth a maximum of 100 UMS points and have timed examinations which

    are 90 minutes long (except for MEI C4 (which includes a one-hour comprehension paper) and the

    computer-based DC and NC units which last 150 minutes, and for AQA units where the optional

    coursework is undertaken when the length is then 75 minutes). Coursework is required in MEI C3,

    DE and NM, and optional in AQA M1, M2, S1 and S2. Candidates may offer more than the

    minimum number of units and, subject to the rules of combination, their results are optimised

    automatically.

    A.1.1 Pure Mathematics for AGCE Mathematics

    In all specifications, the units C1 to C4 are compulsory and contain the core content (with some

    small additions which vary between specifications).

    A.1.2 Applied Mathematics for AGCE Mathematics

    1121Two units are required from D1, D2, DC, M1, M2, S1 and S2 (AS units are in italics, not 2available from CEA and WJEC, available only from MEI). The content of units varies between

    specifications.

    A.1.3 Pure Mathematics for AGCE Further Mathematics

    AQACEAEdexcelMEIOCRWJEC

    FP3FP3FP3

    FP2FP3FP4FP2FP3FP2FP3FP2FP2FP2

    DE

    FP1FP1

    C4C4C4C4C4C4

    FP1FP1FP1FP1

    C3C3C3C3C3C3

    C2C2C2C2C2C2

    C1C1C1C1C1C1

Units in italics are AS units, other units are A2 units. Units in bold are compulsory, other units are

    optional but where units are joined by double horizontal lines then one of those units must be taken.

    The content included in the FP units varies both individually and in total between the specifications;

    the MEI specification has a separate unit in Differential Equations. It is understood that Edexcel is

    considering changing to a structure like that of OCR for its pure units.

    A.1.4 Applied Mathematics for AGCE Further Mathematics Two or three units (depending on the number of pure units taken) further to those undertaken for

    AGCE Mathematics are required, drawn from:

    AQA D1 D2 M1 M2 M3 M4 M5 S1 S2 S3 S4 CEA M1 M2 M3 M4 S1 S2 Edexcel D1 D2 M1 M2 M3 M4 S1 S2 S3 MEI D1 D2 DC M1 M2 M3 M4 NM NC S1 S2 S3 S4 OCR D1 D2 M1 M2 M3 M4 S1 S2 S3 S4 WJEC M1 M2 M3 S1 S2 S3 The content of units varies between specifications.

    A.1.5 Additional Qualification in AGCE Further Mathematics

    In the MEI specification, a second additional qualification in AGCE Further Mathematics is

    available for candidates offering at least 18 units.

    A.1.6 AGCE Pure Mathematics

    This qualification which has a small entry, 201 in summer 2005, makes use of the units created for

    GCE Mathematics and Further Mathematics; it may not be taken alongside them. It is not available

    from CEA except by special application.

    A.2 Advanced Extension Award in Mathematics and STEP This three-hour paper is set on the GCE core (C1 to C4); when the AEA was being devised it was

    found impractical to include applied mathematics in a way that was fair to candidates taking all

    specifications. Until recently this qualification carried no UCAS points, a Distinction now receives

    40 points and a Merit 20 points (a grade A at GCE is worth 120 points, reducing by 20 points per

    grade to 40 points for a grade E). For each subject, only one awarding body conducts the AEA; for

    Mathematics it is Edexcel. It is intended for about the top 10% of the candidature or the top half of

    those achieving A grades (in mathematics there is a considerable discrepancy between these two

    descriptions). Some candidates who might take this paper take instead or additionally one or more

    of the Sixth Term Examinations Papers Mathematics 1, Mathematics 2 and Mathematics 3

    conducted by OCR; STEP is not included in the UCAS tariff but has been used in offers by some

    universities, including Cambridge, Oxford and Warwick. STEP includes mechanics and statistics as

    well as pure mathematics.

    Entries for Special Paper (to 2001) and AEA (from 2002)

     1990 1993 1996 1999 2001 2002 2005

    Mathematics 2094 1157 * * 461 968 1000

    % of AGCE Mathematics 3.1 2.0 * * 0.8 2.1 1.9

    Further Mathematics 194 121 30 last offered 1998 (27 candidates)

    % of AGCE Further Mathematics 3.4 2.6 0.6 all subjects 6936 9305

    % of AGCE all subjects 1.0 1.2

    1996 was the first year in which Special Papers were free-standing, prior to that they were attached

    to particular syllabuses (although not all syllabuses had them, CEA did not offer Special Paper at

    all). AEA is only available in a limited number of subjects, some new subjects were introduced in

    2005. (*Figures for OCR from 1994 to 1999 for Mathematics and 1994 to 1995 for Further

    Mathematics are incomplete; in 2000 OCR accounted for about 70% of the total (533) entries for

    Mathematics Special paper.) For comparison the figures for STEP are given below.

Entries for STEP (to 1994 / from 1995)

     1990 1993 1996 1999 2001 2002 2005

    Mathematics / Mathematics 1 511 414 155 476 470 347 353

    Further Maths A / Mathematics 2 296 236 422 530 635 508 565

    Further Maths B / Mathematics 3 245 109 296 355 396 364 430

    total 1052 759 873 1361 1501 1219 1348

    Many candidates sitting STEP take two papers.

    Appendix B The White Paper and its Implementation

    B.1 The White Paper

    The White Paper, 1419 Education and Skills, was published on 23 February 2005. It can be downloaded from http://www.dfes.gov.uk/publications/14-19educationandskills/. The following

    extracts are taken from the White Paper.

    Strengthening GCSEs and A levels (page 7, Executive Summary, section 13): ‘At A level we will:

    ? increase stretch for the most able by introducing optional harder questions into separate sections

    at the end of A level papers;

    ? introduce an ‘extended project’ to stretch all young people and test a wider range of higher-level

    skills;

    ? enable the most able teenagers to take HE modules while in the sixth form;

    ? ensure that universities have more information on which to make judgements about candidates

    by ensuring that they have access to the grades achieved by young people in individual modules

    by 2006. We will also support those universities who wish to have marks as well as grades [The

    DfES’s publication, Secondary Teachers, Number 37, March 2005 states ‘Universities will be given students’ exact marks for all AS and, later, A2 units’.]; and

    ? reduce the assessment burden at A level by reducing the numbers of assessments in an A level

    from 6 to 4 but without reducing the standard or changing the overall content of A levels.’

    The first point is expanded on page 63:

    ‘8.14. In 2004, around 3.5% of the age cohort achieved 3 or more A grades at A level. We believe

    that there is more that we can do to stretch and challenge our brightest students. We also want to

    help universities to differentiate between the highest performing candidates.

    8.15. First, we want more stretch within A levels. Because we make it a priority to preserve A level

    as a qualification, with consistent standards over time, we will take a slightly different route to that

    proposed by the Working Group. We will seek the introduction of a new section in A level papers

    covering AEA material. We will ask QCA to consider the best means of doing this across all A

    levels, so that increased stretch and challenge are available to all students in all types of institution,

    and scholarship can flourish.’

    B.2 Implementation Plan

    On 14 December, the DfES published the 1419 Education and Skills Implementation Plan which

    can be found at http://www.dfes.gov.uk/publications/14-19implementationplan/docs/14-

    19%20Implementation.pdf. The following extract is taken from the Implementation Plan (pages 37

    and 38).

     ‘2.27 We intend that whatever route young people are on, they will be challenged to achieve their

    best. In KS3, that will include greater space in the curriculum for young people to be stretched and

    more scope for acceleration through the Key Stages. At KS4, it will include more opportunities to

    accelerate and to take advanced level qualifications. AS level qualifications taken by students in

    KS4 are now fully recognised in performance tables.

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