Skip to Content.

Celtic KnotThe School of Mathematics
Internal Website

Official Course Documentation

In This Section

This document refers to the official course information appearing in DRPS and the form used to prepare this which is presented to Board of Studies in the event of changes or when a new course is proposed.

It is important that all courses have correct information along these lines under the specified headings.

Basic principles

  • The DRPS information for a course should be at a reasonably high level and not, except where necessary by University regulations, contain a lot of information that would need to change if for example a new lecturer takes over and shifts the emphasis a little and changes what is covered at the margins.
  • Lecturers should produce more information than is in DRPS for students at the start of each instance (the university term for a particular delivery) of the course. For instance, details of assessment (format of exam, dates and weightings of in-course assessments, etc) would certainly need to be included and in most cases some further expansion of the syllabus and learning outcomes would be appropriate.
  • Most users of DRPS do not know the mathematics in the course they are looking at and so information setting the context for the course, such as what it follows on from and what it leads to, is important. On the other hand, academic colleagues here and elsewhere may want to know what is in the course (e.g. to advise visiting students) and so it is reasonable that the syllabus particularly is addressed partly to them.

Below, we consider relevant fields in DRPS entries in order.

Summary

The summary is designed to be a brief entry (probably a single paragraph) highlighting the most important information: what is the field of study; what does it follow in from or lead to; how is it taught and assessed.

Course description

This is an opportunity to explain more about the course and where it sits in the mathematical landscape in general and in our programmes in particular. It is to some extent an advertisement for the course. Here you should explain if there is anything innovative about the course, if it involves skills such as programming, and generally indicate how it is taught.

Syllabus

In the University's database, syllabus is a separate entry, but in DRPS it is added to the end of the course description. A fully detailed syllabus has a number of disadvantages: they require continual updating and if that does not happen they become out of date; if followed rigorously they can lead to material being presented in a rush at the end of the course; questions arise as to whether we may teach and examine something not on the syllabus; if numbers of lectures for a topic as delivered (or the order) disagrees with the syllabus, then we might be liable to an appeal.

A major point about syllabuses is that they are a reference point for follow-on courses. Given that such follow-ons may be one or even two years later, in reality a topic which has been covered in a rush in the last lecture with a tacit admission that it will not be examined is unlikely to remain in students' memories. If lectures in later courses are going to assume students "know" everything specified in a detailed syllabus for a previous course, then much of the class will be rapidly lost.

For these reasons, the syllabus entry should specify the general areas of study and list ideas, methods and results that should feature sufficiently pervasively that a diligent student could be expected to retain some understanding of them. Typically this might lead to a syllabus of 3-6 items, each of which is a few words or a couple of sentences at most. It should be assumed that the ordering is subject to change and precise allocations of topics to particular lectures or weeks, or to the numbers of these should be avoided unless there is a strong reason such as interaction with another simultaneous class. (It may be appropriate for syllabus in some PGT courses to be more tightly specified.)

Pre-requisites etc

An accurate listing of pre-requisites is important: students are understandably concerned if they discover half way through a course that the lecturer is assuming previous knowledge they have not studied, even if ultimately it seems to us that it is of limited usefulness.

It should not be assumed for example that "because this is a year 4 course students must have done core third year courses": joint degree students, visiting students and students in other Schools considering taking an "outside" course should be considered. Similarly unnecessary pre-requisites should not be introduced for reasons such as forcing a course to be taken in a given year.

If a working knowledge of the content of another course is likely to be necessary for many students to do well in the class, make it a pre-requisite: do not expect, hope or assume that students can just pick it up with some extra reading (which is something that can be rather harder for them than we imagine). If we err on the side of caution we can still allow unqualified students to take the course, but we ensure that they get suitable advice before committing themselves.

Courses in Year 1 and in PGT for instance will not normally have pre-requisites which can be specified in terms of other UoE courses. In that case use the "Other requirements" heading under "Entry Requirements", particularly if there are skills needed (eg computing) that students may not have.

A co-requisite is a course that must be taken concurrently with the course at issue. Note that one should not have a concurrent course as a pre-requisite.

Pre-requisites can be "recommended" rather than "compulsory". It is suggested that use of this possibility is avoided, certainly unless one explains carefully to students what it means in the case at hand (e.g. does it mean a couple of hours extra reading is needed or might it be a couple of weeks of study). Remember that we can always allow students to take a course for which they do not have pre-requisites via the concession mechanism.

We have in the past been very reluctant to specify pre-requisite for courses and in some cases this may be the desire not to discourage students from taking the course. Consequently we have for example high-level UG courses with no pre-requisties, which does not make any sense at all in a subject that we are forever saying is particularly hierarchical. There is a potential vicious cycle here because low numbers in course X will discourage us from making it a pre-requisite for course Y. But not making X a pre-requisite for anything is likely to cause it to have lower numbers.

Pre-requisite information for visiting students is also asked for. It is suggested that the wording: "Required knowledge may be deduced from the course descriptions and syllabuses of the pre-requisite University for Edinburgh courses listed above." is entered by default unless course creators decide on something more informative.

Learning Outcomes

In brief, a syllabus tells you what to expect in the lectures for a course but the learning outcomes try and indicate the nature of the exam or other assessments. In more detail, a learning outcome is something assessable and achievable that students are taught to do during the course and assessed on. There should be a verb (or possibly two) that indicate what is to be done and preferably a statement of the standard which is expected to be reached and there may be something about the conditions under which it is to be done. Courses are allowed no more than five learning outcomes and therefore the intention is that these are at a high level. Everything assessed in the course should fall under the headings of the learning outcomes. The following are examples.

  1. Use the calculational methods and algorithms studied in the course appropriately and accurately to solve standard problems without explicit prompting.
  2. State accurately and prove in good mathematical style the principal theoretical results of the course without access to notes or other resources.
  3. Use the results and methods of the course to solve unseen problems related to or extending examples studied.
  4. Work cooperatively and constructively in a group on complex problem solving tasks extending the lectured material.

Note that all four outcomes have consequences in terms of what should be assessed. (A) means that one is expecting students, for example, to spot the need for Gaussian elimination and carry it out. If the last three words were removed, it suggests that students may only be expected to carry it out when directly instructed to. (B) implies a closed-book exam and that in at least some assessments significant attention is going to be paid to writing style. (C) tells us that the solving of unseen problems is going to be required. One could strengthen it with wording suggesting that the problems might substantially extend seen examples, or weaken it by further emphasising the similarity to such. (D) tells us that there is group work, and if taken literally it will be assessed (although one could argue that conventional hand-ins could do that if students are encouraged to work cooperatively) and it could even imply that individuals contributions to their group's cohesion and functioning will be considered. (If one is not going to assess anything that addresses the latter points, then it would be sensible to replace "cooperatively and constructively" with "effectively".)

In traditional Mathematics course design, we were very explicit about the syllabus - the topics to be covered. We were very implicit about the nature of performance required to achieve a satisfactory outcome in the course. We had an idea about what was appropriate for different levels of course in different areas of mathematics: perhaps we were agreed that a year one course might be somewhat less rigorous and that a lot of marks could be obtained by following standard procedures in more or less well-rehearsed situations; probably we believed that more advanced pure mathematics courses were more challenging in that proving unseen results was required or substantial theoretical bookwork was reproduced - or maybe both. Whatever the case, we did not necessarily articulate to ourselves or explain to students what we were imagining nor did we have some sort of map as to how we were developing these sorts of "mathematical maturity" through our programmes.

We have syllabuses because, among other reasons, it is better if lecturers of following courses know what we hope students have previously learned. The idea of Learning Outcomes is to make explicit those levels of performance and so give the lecturer of a following course a guide to what students can be expected to do as opposed to wwhat they have been told. It is surely important to know whether students have, for example, previously demonstrated competence in proving straightforward results from the axioms in abstract algebra (a possible Learning Outcome).

In general, the cognitive challenge of a Learning Outcome is usually identified by placing it in a "taxonomy". A very popular example is Bloom's Taxonomy which has six levels but they are not always easy to interpret in a mathematical setting. A possible, more manageable tool for mathematics is the MathKIT taxonomy which has just three levels: (K) Knowledge/routine skills; (I) Interpretation/Internalisation/Insight; (T) Transfer and Translate. This taxonomy is meant to represent the often expressed desire that students should: "know the material" (K); "understand it" (I) and "be able to use it" (T). Like learning outcomes themselves, there is ambiguity and the classification will depend on context. One can use MathKIT also at the level of individual items of assessment. For example, on the topic of equivalence relations and classes one might decide: asking for the definition is K; verifying an example is K/I depending on how standard it is; providing an example with certain properties is I and using the idea in an involved, novel context such as quotient groups is T.

Examples

  • The LO map is an attempt to write some fairly generic Learning Outcomes for courses at each level, loosely classified under the MathKIT headings. The intention is that the LOs on similar skills become more demanding as one goes up the years. They are written with courses in Pure Mathematics and to some extent in Mathematical Methods in mind and will need adapting for other areas.
  • The DRPS entries of the courses Mathematics for the Natural Sciences 1a and Symmetry and Geometry both have updated course information including Learning Outcomes.

The intention is not that the School will import the examples provided wholesale without some consideration. For many courses they might not even make sense. Rather, setting some Learning Outcomes is an opportunity to think about what it is we hope students can do at the end of the course that they could not do when they started. Hopefully, the examples might provide some inspiration for that process.

Last direct edit: 16:06, Tuesday 29 August 2017, by Toby Bailey. (Feedback? Please contact the page owners)

This page can be read by: Public access, unrestricted (or: Specified users, but only if server config requested). [Help ?]
(This access control information does not currently work correctly for new changes, although the access controls are still applied correctly.
(On TODO list to fix at some point..))