HoDoMS - Heads of Departments of Mathematical Sciences

Heads of Department of Mathematical Sciences

The teaching and learning environment: AS/A levels, Benchmarking, National Qualifications Framework, Credits the implications for mathematics.

Charles M. Goldie (University of Sussex), Chair of HoDoMS (Heads of Departments of Mathematical Sciences in the UK)

Notes of talk given at CPAM, 22nd May 2002, UCL

I. Pre-university

A-Level before 2001:

2000/01: new AS Levels, followed by A2 (A-Level) at end of year 2.

Summer 2001:

2001/02: more resit/sit opportunities,



II. University

January 2001:

March 2002:

Issues, gaps:

To address these issues the Council for the Mathematical Sciences set up a small working party in the summer of 2001, under the chairmanship of Professor Peter Saunders (KCL). The Council for the Mathematical Sciences (CMS) is composed of the Presidents of the IMA, LMS and RSS with their Executive Secretaries. The working party included representatives of these societies, and myself as Chair of HoDoMS. We drafted two Briefing Papers, The Future of the MMath and The MSc and the QAA Framework for Qualifications. After consultation and revision these were adopted by the CMS and published on the web at


by courtesy of the LTSN MSOR Network, Birmingham. The Briefing Papers relate in the main to the Framework for EWNI, as that for Scotland is significantly different.

Future QAA Subject Review

The QAA's new model for subject review was finally published in outline, after much back tracking, in March 2002 (see http://www.qaa.ac.uk/). It will essentially be internal review with external members being included in the internal panels. However there will be Institutional Audits which will include discipline audit trails drilling down into 4-6 subject areas in an audit visit.

Review documentation will include the Framework for HE Qualifications, the MSOR Benchmark, other published material such as Codes of Practice, and no doubt the familiar forest of internal paper. Given that no benchmark is in prospect for the MMath, nor for MSc degrees in our subject area, the aim of the CMS in commissioning and adopting the two Briefing Papers referred to above was to provide appropriate material for review teams to help interpret the official documentation for the cases of these particular qualifications.

The MMath

I use the term MMath to refer to the MMath itself, MSci degrees in MSOR, and rare variants such as MMathStat. The key passage in the Framework for EWNI is the following:

Within an overall programme, the learning outcomes required for a degree are unlikely to be achieved in less than the equivalent of one academic year's full-time study, which addresses those outcomes directly. For example, an extended undergraduate programme might have units of Masters level credit equivalent to study over one half of an academic year. That is unlikely to be sufficient to enable a student to match fully the expectations of the Masters degree descriptor, in which case an Honours degree would be the appropriate award for successful completion of the programme. Achievement of the full Masters outcomes would be needed for the award of a Masters degree.

One implication of this is that there should be no difference in level between the most advanced parts of an MMath, and an MSc. The former concludes at Master's level while the latter by definition is at that level, but they are different degrees: the MMath final year (assuming that the Master's level material is all in that year) is an academic year in length while the MSc is a calendar year. The usual quantification of these in credits is 120 for an academic year as against 180, half as much again, for the calendar year. Given that the two degrees conclude at the same level, it is rational on resource grounds to provide common modules at M (Master's) level for the MMath final-year students and the MSc students, in departments that offer both qualifications.

The passage quoted above states unequivocally that half an academic years study at Level M is not enough for an MMath. However it is generally accepted that an MSc degree may include a limited amount of credit, typically 30, at Level 3 (final-year Honours BSc level; terminology varies). See the MSc Briefing Paper for details. On proportionality grounds the MMath final year should therefore also allow some credit at Level 3, as otherwise the MMath final-year students will have to choose all their modules to be Level M ones whereas the MSc students will be allowed some Level 3 modules, an anomalous situation. The MMath Briefing Paper takes the view that 90 credits at Level M suffices for attaining the full Master's level outcomes in an MMath degree, leaving up to 30 credits allowed at Level 3 in the MMath final year, assuming all the Level M credits are taken in that year.

A model by which an MMath final year, and a 1-year MSc, can be resourced side-by-side, using common taught modules, might be as in the following table. To avoid confusion, Level 3 modules are denoted B (for BSc level); thus 12B denotes a 12-credit Level 3 modules, while 18M denotes an 18-credit Level M module. The teaching pattern is assumed to be 2 terms, with 12-credit modules taught in the Autumn Term and 18-credit modules taught in the Spring/Summer Terms. It is easy to adapt this to an equal-semester pattern, with 15-credit modules: just add 3 to all the 12s, and subtract 3 from all the 18s!



Year 4 MMath




2 12M



3 12M

Spring +


2 18M


3 18M

Summer vac



60M Project

Credit total





Year total




To avoid doubts over whether Level M modules are indeed at that level it would seem best to distinguish them carefully from Level 3 modules, and avoid dual-level modules and similar devices. For the same reason it would seem inadvisable to allow Honours BSc students to take any Level M modules as a matter of routine. Permitting the best BSc students to take some Level M modules by special permission would be unobjectionable, however.

The MSc

The Briefing Paper for the MSc takes pains to delineate the notion of a conversion MSc, and insists that inclusion of some elementary material can be consistent with Master's level outcomes, if appropriately laid on:

Even if a masters programme includes some elementary material, this is taught in a way that assumes that the students are advanced and experienced learners. For example, while mathematics graduates taking an MSc in statistics may well cover some material that is also included in many undergraduate statistics programmes, it will be in a module that has been designed for students with the additional mathematical sophistication and maturity that they possess. They will not normally take the same module as the undergraduates; if they do, that would be included in the 25% of [Level M] material that masters students are permitted to take.

Qualifications Descriptors

The Framework for HE Qualifications contains descriptors for honours BSc degrees and MSc degrees that are over-ambitious for our highly developed and technical subject area. For instance, the Framework requires that, among other things, a graduate with an honours degree should be able to describe and comment upon particular aspects of current research, or equivalent advanced scholarship, in the discipline, that he should have an appreciation of the uncertainty, ambiguity and limits of knowledge, and that he should be able to make use of scholarly reviews and primary sources (e.g. refereed research articles and/or original materials appropriate to the discipline). Someone with a masters degree should be able to evaluate critically current research and advanced scholarship in the discipline. As concerns honours BSc level, the Benchmark is much more measured, limited and realistic over the level that can be achieved, and in future Subject or Institutional Reviews it would clearly be appropriate to rely on the subject-specific characterisation of the Benchmark in preference to the generic statements in the Framework. This issue is dealt with at greater length in the two Briefing Papers.


The Credit Consortia are associations that facilitate middle-level administrators in HE liaising over credit transfer, mutual recognition of credit, and so on. Their acronyms are SEEC, NUCCAT, NICATS and CQFW, the first standing for Southern England Consortium for Credit Accumulation and Transfer, and the others with similar expansions. The QAA's Framework for HE Qualifications in the version for England, Wales and Northern Ireland does not include any recommendations on credits. However the Credit Consortia have produced such recommendations, specifying minimum amounts of Level M credit for MMath and MSc degrees. For the MSc these are consistent with the position adopted by the CMS in the MSc Briefing Paper, and indeed with the earlier Harris Report, Review of Postgraduate Education (1996), which commanded general agreement and support. However for the MMath the recommendation is for 120 credits at Level M, equivalent to the whole final academic year, and as argued above this is disproportionately high.

It is for individual HE institutions to take whatever account of the Credit Consortia recommendations they feel appropriate. The recommendations of the Consortia are not binding in any way, even on their member institutions. It should be noted that HE institutions do not have to join these bodies and a substantial proportion choose not do so.