Accreditation of degree programs
Mathematics is the most universal of disciplines. What first year undergraduates learn in their mathematics courses in Britain or America is, by and large, what our first year students here learn. Australian honours students easily slot into graduate programs all around the world.
A consequence of this is that most mathematicians have some shared idea of what a Mathematics Degree 'is'. The mathematics programs across Australia reflect this in the significant degree of uniformity between them.
One might ask therefore, why we should bother with an accreditation program at all. There are two main arguments for this process:
- Public certification.
- Defence of standards.
The Australian Higher Education system contains a wide variety of institutions. Although there are, from time to time, some attempts from the Federal Government at quality assurance, this usually consists of checking that the institutions are engaged in some sort of assurance process. Discipline level quality assurance processes are clearly beyond the expertise of the government agencies. In the professional disciplines there is a long tradition of accreditation by the professional societies and it seems likely that where these processes are in place, the government will regard having undergone a review by such a society as fulfilling the appropriate quality assurance requirements. Apart from the professional disciplines, many of our sister organisations in FASTS are involved in these activities. One of the main aims of the Australian Institute of Physics is `setting and supporting professional standards and qualifications in physics' whereas the Australian Institute of Biology gives as one of its activities `the development of strategy and procedures for the professional accreditation of biologists and biological courses.'
In developing a strong accreditation system, the Society aims to have a say in the teaching of mathematics at Australian universities, while providing a procedure for enabling these institutions to satisfy their quality assurance requirements.
A significant impetus for the interest in quality assurance measures has been the great change in the Higher Education system over the past two decades. New entrants to the system, pressure to keep up pass rates and a drift away from interest in mathematics as a major area of study have all put standards under threat. A Society led accreditation procedure is one way of defending our disciplines by applying some pressure in the opposite direction.
Of particular importance here is the training of the next generation of high school teachers. Many students are already being taught mathematics by insufficiently qualified teachers, and there is certainly a great deal of current pressure to redefine what a suitable mathematics background is for the teaching of secondary mathematics. The provision of an accreditation scheme is one way of promoting the Society's view of what should be required in this area.
School of Mathematics
University of New South Wales
- Glossary of terms
- Overview of the Accreditation Process
- The Accreditation Standards
- Details of the Review Process
As different institutions use conflicting terminology we list here some of the words used in this document with their interpretation:
- (degree) program
- a course of study leading to the award of a degree
- an individual subject offering being a component of a degree program
- the organisational unit(s) of the university responsible for the provision of mathematics teaching
- head of department
- the person responsible for the management and leadership of the department. In cases where there is more than one organisational unit, it is expected that the university concerned will nominated the head of one of these units as the main contact for the review.
The Australian Mathematical Society provides an accreditation procedure for programs leading to a degree in Mathematics (or the Mathematical Sciences) at Australian Universities. Accreditation, which is undertaken at the request of the institution concerned, requires a review of each program by a committee of the Society. The level of detail and feedback for these reviews can be varied according to the needs of each institution. At the core of each review however is a comparison of the degree programs with a set of standards agreed by the Council of the Society. Accreditation will be awarded for a fixed period, usually of five years.
The initial assessment will usually be carried out by a single suitably chosen academic. This Assessor will have a minimum of 10 years service in Australian universities with a wide range of teaching experience. The Assessor will provide a report on his/her findings to both the university and also to the Society's Review Committee. This report should include a recommendation as to whether Accreditation should be granted to the degree program(s) under consideration.
The Review Committee will contain three or four members with perhaps one representative from outside the university system. The role of the Review Committee is:
- To help choosing an Assessor.
- To ensure that a diligent job has been done by the Assessor.
- To providing a degree of continuity and consistency in the process.
- To make the final decision on Accreditation (possibly after further consultation with the Assessor.
Accreditation should take place with respect to agreed standards for the various degrees. On the other hand, one needs to recognise that most mathematics undergraduate programs are undertaken as part of generalist degrees such as BSc or BA, and so it would be inappropriate to be too prescriptive about the structure of a degree. We should not define a mathematics degree as something that looks like the program at UNSW or the University of Melbourne.
The criteria listed below define a core set of characteristics for each of the common types of degrees available. The importance of each of the criteria will obviously depend on the nature and focus of the degree. Programs which do not meet these criteria, whilst not being deemed ineligible for accreditation, would need to explain how the program makes up for the omissions.
In all cases, the physical facilities should be appropriate to allow the academic program to proceed successfully. Apart from the use of appropriate teaching rooms, this would include the provision of suitable computing and library resources.
3 year pass degree.
This is typically a generalist Arts or Science degree. Graduates are expected to have developed a reasonable level of specialist knowledge. An average graduate should be able to apply standard mathematical techniques with some direction, but will not necessarily be capable of significant independent mathematical work.
The syllabus will be assessed with regard to both its depth and breadth.
- A significant proportion of the degree must be in mathematics. Traditionally this has consisted of, minimally, 25% of first year, 33% of second year and 50% of third year studies being in mathematics. Perturbations of this model are acceptable, although it is unlikely that a program would be approved in which less than one third of the total degree was in mathematics, or in which there is insufficient advanced content. Both the mathematics and non-mathematics sections of the degree should be of a suitable intellectual level.
- Programs should include first and second year courses in
- Calculus in one and several variables;
- Matrices and linear algebra.
- A typical program should contain a broad range of standard topics from across mathematics. All students should be required to see a certain amount of most, if not all, of:
- Differential equations;
- Discrete mathematics;
- Complex variables;
- The use of computers in mathematics.
- Students should have some exposure to the ideas of proof and to axiomatic systems.
- Students should have some exposure to the use of mathematics in applications.
Additional notes on the interpretation of these criteria is given below.
- Most staff should have postgraduate qualifications in mathematics.
- Within the context of the institution and the chosen delivery methods, teaching should be undertaken with care and professionalism.
- The assessment methods should enable independent monitoring of student achievement.
- There should be processes for monitoring the quality of teaching.
- Students should be able to obtain additional assistance, if necessary, outside of their timetabled classes.
- Should be able to demonstrate high levels of numeracy and problem solving.
- Should be able to communicate technical information effectively.
- Should be comfortable with the use of information technology.
- Should have sufficient mathematical training to comfortably teach all of secondary school mathematics.
4 year Honours degree
The Honours degree is a qualification with greater depth and breadth than the pass degree. This degree typically develops a wider range of skills (such as research and report writing) than the pass degree. The Honours degree is a certification of a high level of skill in undergraduate mathematics. As well as providing preparation for postgraduate study, the Honours degree should provide suitable training for graduates in order that they may apply the mathematics they have seen with a certain degree of independence.
- Entry to the Honours year should require more than satisfying the minimal conditions for the pass degree. Most of the third year should be taken in mathematics or a cognate discipline.
- The final year should usually comprise a combination of advanced courses and a supervised research project.
- The topics covered will depend on the area of specialisation, but should be at a high enough level, and cover a broad enough range, to meet the broader objectives described above.
- The requirements in terms of qualifications and experience are higher than for the provision of a pass degree.
- Students attaining the equivalent of Honours Class IIA (or equivalent) should be sufficiently prepared to undertake postgraduate study. A grade of Honours Class I should be a clear indication of suitability to attempt a PhD. Convincing evidence of this would be the success of past graduates in postgraduate programs at other universities.
- Graduates should have superior skills in the areas of numeracy and problem solving. They should be capable of presenting technical information in either written or verbal form with limited supervision.
Joint degrees: The standards for these degrees should be substantially the same as those for the Pass and Honours degrees considered above.
At present the Society has only accredited undergraduate programs. In the event of an institution requesting accreditation for higher degrees, the Society will need to develop suitable criteria for these degrees as well.
Masters degrees by coursework: The standard for these degrees should be at least equal to that of the final year of the Honours degree considered above.
Research degrees: The criteria here should be that the department possesses sufficient research experience to suitably supervise students across a range of topics, and that standards are moderated by the use of external examiners for theses.
Ideally, all students graduating from the program being reviewed should meet at least a minimal amount of each of the topics listed under items 3, 4 and 5. For example, students should
- See that some important real-world systems can be modelled by differential equations and that there are standard techniques for solving some classes of equations.
- See the notion of a random variable and understand about its mean and variance.
- Be exposed to one or more mathematical computer packages or languages.
- Know what a theorem is!
The criteria in items 3, 4 and 5 should not be viewed a set of independent topics to be ticked off. As an analogy, one might declare that a cake recipe should usually contain eggs, butter, sugar and flour. Clearly not every combination of these ingredients makes a decent cake, and one can find good cakes recipes that omit one or more of the ingredients. The important thing here is that each graduate should have seen a range of subject areas and should have seen some subject areas in depth. Of course, the depth and breadth requirements might be satisfied by different students within a program in different ways. A student concentrating on Pure Mathematics should almost certainly have done a reasonable first course on complex functions, and have seen abstract systems like vector spaces and groups. A student concentrating on Applied Mathematics may see little in the way of formal axiom driven proofs, but would presumably need to have seen more differential equations that one gets in a `standard' first year calculus course.
- Requests for accreditation and review should be sent to the Society's Secretary, usually from the requesting university's administration.
- In consultation with the Review Committee, the Society will appoint an Assessor. The role of the Assessor is to gather the information necessary for the review and to write a report and recommendation for the Review Committee.
- Before the review commences the Assessor should reach agreement with the university under review regarding the scope of the review and the fees to be paid to the Assessor. It is likely that different types of review will be requested by different institutions:
- A simple accreditation check with limited feedback to the university.
- An accreditation review with a detailed report of strengths and weaknesses observed. (We expect that this would be the standard type of review.)
- An accreditation review with an in-depth examination of the teaching program and a report with recommendations for future changes. (It is recommended that the cost of a standard review should cover the Assessors expenses (travel, accommodation etc as required), recovery of costs for administrative assistance if required, and a per diem for the Assessor. As a guide, a standard review should require 3 or 4 days work by the Assessor, depending on the size of the mathematics programs.)
- Agreement should also be reached as to an appropriate timetable.
Conduct of the Review:
The initial phase of the review will require that the university requesting accreditation supply certain information (listed below) to the Assessor. This will be followed by a Site Visit, which would usually be conducted in a single day.
Provision of information:
- The Assessor should undertake a preliminary examination of the program being reviewed by consulting the appropriate handbooks and web pages.
- The Assessor should consult with the Head of Department concerned regarding any timing issues and request a summary of each of the degree programs being assessed. This should include
- A statement of the objectives of the program.
- A statement of the requirements for the award of the degree being assessed.
- A summary of how the program meets the appropriate accreditation standards listed earlier in this document. Where the program does not meet the stated standards, argument will need to be made as to how the program makes up for these omissions.
- A description of a typical program of study leading to the award of the degree.
- The handbook entries of all units in mathematics and statistics, as well as any other units that may form a compulsory part of the degree. This should include a summary of the content of each course, as well as an indication of contact hours. A textbook list should also be included.
- A description of the teaching methods employed, especially where these differ from the traditional lecture/tutorial pattern.
- Details of student numbers, including the number of graduates produced each year, and average class sizes.
- A list of staff involved in teaching the mathematics component of the degree, together with their qualifications.
- It is expected that much of the information being requested would be supplied as photocopies of pages from handbooks and other documents.
- In requesting the summary, the Assessor may also indicate areas of interest or concern that may need to be addressed and invite the Head of Department to provide more information on these matters.
- The list of items in (2) above does not preclude the Head of Department from including any other information that they may consider relevant to the review. In particular, the Head of Department may wish to draw attention to any unusual aspects of their degree program.
The Site Visit will usually include:
- A meeting with the Head of Department (or a nominee). At this meeting the Assessor should raise any issues arising from his/her examination of the information already provided.
- Examination of assessment tasks and student responses, especially for core courses. This would include written examinations, assignments and Honours theses as appropriate.
- Discussions with other members of the academic staff.
- Discussions with students.
- Examination of some of the physical facilities of the university, such as lecture theatres, computing facilities, libraries and so forth.
Following the site visit, the Assessor will produce a draft report listing the information obtained in the review, strengths and weaknesses observed in the program and recommendations for accreditation. In the first instance this document should be provided to the department involved for their comment.
After receiving feedback from the department, the assessor will forward a final report to the Review Committee. In cases where the department disagrees with some of the findings, the head of department should be invited to submit a succinct rejoinder to accompany the report.
The Review Committee will make a decision as to whether to grant accreditation to the program(s) as soon as practical after the submission of the final report. Accreditation may be granted at the following levels:
- Full accreditation, meaning that all mathematics graduates from the program will have completed a degree that meets the Society's standards.
- Limited accreditation, meaning that while some students may graduate with degrees which do not meet the Society's standards, a substantial proportion of the mathematics graduates do in fact complete a satisfactory program.
Once the Review Committee has made the decision on accreditation and approved the final report, this report is formally presented to university's administration.
The Society will not publicly release the final report, but will keep copies for further reference and comparison. The university will be free to make the contents of the final report publicly available (although the Society would expect that great care would be taken to avoid selective misleading quotations from the report). The Society will announce successful accreditations in its publications.
If the requesting university wishes to challenge the decision of the Review Committee, they should make a written submission to the Chair of the Review Committee. The appeal will be considered by the President and Secretary of the Society, and the Chair of the Review Committee, who may:
- Deny the appeal;
- Request that the Review Committee reassess the case with the additional information provided by the university, or;
- Appoint an independent Assessor to provide a new report.