7.1 How USMs are determined in Mathematics

Analysis of marks

There are two parts to the BA examinations: Part A and Part B

Part A
At the end of the Part A Examination, a candidate will be awarded a University Standardised Mark (USM) for each of the four papers.  The USMs awarded will be carried forward into a classification as described below.

Part B
The Board of Examiners for Part B will assign USMs for each paper taken in Part B and and may scale the raw marks to arrive at the USMs reported to candidates.  

The examiners may choose to scale marks where in their academic judgement:

  • a paper was more difficult or easier than in previous years, and/or
  • a paper has generated a spread of marks which are not a fair reflection of student performance on the University's standard scale for the expression of agreed final marks, i.e. the marks do not reflect the qualitative marks descriptors.

Such scaling is used to ensure that all papers are fairly and equally rewarded.

When scaling the raw marks on a paper the examiners will consider the following:

  • the total sum of the marks for all questions on the paper, subject to the rules above on numbers of questions answered;
  • the relative difficulty of the paper compared to the other Part B papers;
  • the report submitted by the examiner or assessor who set and marked the paper.

Examiners will use their academic judgement to ensure that appropriate USMs are awarded and may use further statistics to check that the marks assigned fairly reflect the students' performances on a paper.  Examiners may also review a sample of papers either side of the classification borderlines to ensure that the outcome of scaling is consistent with the qualitative marks descriptors.

The USMs awarded to a candidate for the papers offered in Part B will be carried forward into a classification as described below.

Marking of Mathematics Examinations

All mathematics examinations are marked by a single assessor or examiner according to a pre-agreed mark scheme which is strictly adhered to.  The examination scripts are then checked by an independent checker to ensure that all work has been marked, and that the marks have been correctly totalled and recorded. Please see the qualitative descriptors of the bands of marks awarded to examination answers. 

The Part B extended essays are independently double-marked, normally by the project supervisor and one other assessor.  The two marks are then reconciled to give the overall mark awarded.  The reconciliation of marks is overseen by the examiners and follows the department's reconciliation procedure (see https://www.maths.ox.ac.uk/members/students/undergraduate-courses/teaching-and-learning/projects/extracurricular-projects).

The BO1.1 examination and essays are independently double-marked, normally by the course lecturer and one other assessor.  The two marks are then reconciled to give the overall mark awarded.  The reconciliation of marks is overseen by the examiners and follows the department's reconciliation procedure (see https://www.maths.ox.ac.uk/members/students/undergraduate-courses/teaching-and-learning/projects/extracurricular-projects).

Please see the qualitative descriptors of the bands of marks awarded to examination answers and extended essays/projects.

Further information on the setting and marking of mathematics papers is given in the appendices to the Examination Conventions in Mathematics available online https://www.maths.ox.ac.uk/members/students/undergraduate-courses/examinations-assessments/examination-conventions

Marking schemes and Model Solutions

Assessors setting questions should be asked to provide complete model solutions indicating everything that a candidate would be expected to write to answer the question fully.  The model solutions and marking scheme need to be sufficiently clear and comprehensive to be meaningful to an external examiner.  

The model solution for each question should be accompanied by a marking scheme out of 25.  The marking scheme should aim to ensure that the following qualitative criteria hold (see also the class descriptors given below):

20--25 marks: A completely, or almost completely, correct answer, showing excellent understanding of the concepts and skill in carrying through the arguments and/or calculations; minor slips or omissions only.

13--19 marks:  A good though not complete answer, showing understanding of the concepts and competence in handling the arguments and/or calculations, and some evidence of problem-solving ability. Such an answer might consist of an excellent answer to a substantial part of the question, or a good answer to the whole question which nevertheless shows some flaws in calculation or in understanding or in both.

7--12 marks: Standard material has been substantially and correctly answered with some possible minor progress on to other parts of the question.

0--6 marks: Some progress has been made with elementary, accessible material.

Assessors should classify the parts of each question under the headings: 

  • B1: bookwork material: explicitly seen before;
  • B2: routine material, easily synthesized from material explicitly seen before;
  • S: similar to material seen before;
  • N: new, demanding good command of concepts and/or methods.

Coursework

The examiners should pay careful attention to what candidates have been told about the assessment of coursework in the Examination Regulations and the Course Handbook.  All coursework is independently marked by at least two assessors.  The examiners will oversee the reconciliation of marks, following the established reconciliation procedure (http://www.maths.ox.ac.uk/members/teaching-staff/information-supervisors-undergraduate-projects).  If reconciliation is not possible, an additional marker should be appointed.

Projects and extended essays will be be assessed with reference to the following qualitative descriptors.

For BSP Projects

90--100:  Work of potentially publishable standard, as evidenced by originality or insight. The work should show depth and accuracy, and should have a clear focus.  It is likely to go beyond the normal level for part B.  The standard one sees in winners of one of the examination prizes.
80--89: Work in this range will be at the level of a strong candidate for a DPhil applicant.  The project will be an easy choice as a winner of a college essay prize. It will have depth, accuracy and a clear focus. It will show a strong command of material at least at the level of part B.  It is likely to contain original material, which may take the form of new mathematical propositions, new examples, or new calculations, for example.
70--79: The work submitted is of a generally high order, with depth, clarity and accuracy, but may have minor errors in content and/or deficiencies in presentation. It may contain original material, at least in the sense of new examples or calculations.
60--69: The candidate shows a good grasp of their subject, but without the command and clarity required for first class marks. Presentation, referencing and bibliography should be good, and the mathematics should have no more than minor errors.
50--59: The work shows an adequate grasp of the subject, but is likely to be marred by having material at too low a level, by serious or frequent errors, a high proportion of indiscriminate information, or poor presentation and references.
40--49: The candidate shows reasonable understanding of parts of the basic material, but reveals an inadequate competence with others.  The material may be at too low a level.  There are likely  to be high levels of error or irrelevance, muddled or superficial ideas, or very poor writing style. 
30--39: The candidate shows some limited grasp of at least part of the material.
0--29: Little evidence of understanding of the topic. The work is likely to show major misunderstanding and confusion.

For BOE and BO1.1 extended essays

70--100: The candidate shows clear focus on the question, with precise and accurate details (mathematical and other), imaginative selection of examples and appropriate selection and quality (rather than quantity) of sources, and cogent argument, supported by evidence.

Within this band the following finer gradations may be helpful:
90--100: Work of publishable quality.
80--89: Demonstrates originality of content or insight.  Work at  the upper end of this range could be publishable after minor improvements. Would be an appropriate entry for a national or university prize.
70--79: Work of high or very high quality, but perhaps lacking the originality that would be expected of publishable work. Might be a good candidate, for example, for a college prize.

60--69 Work that addresses the given topic, with solid command of factual content, reasonable range of examples and sources, coherent argument and analysis, and correct referencing and bibliography.


(Essays at the lower end of this range may lack some of these qualities or show them only intermittently.)
50--59: Work with some use of facts, sources, and arguments, but marred by one of more of a failure to address the topic, serious or frequent errors of fact, a high proportion of indiscriminate information, speculation or unsupported argument, and incomplete or inaccurate referencing.
40--49:  The candidate shows some knowledge of the topic but the work is marred by several of the following:-high levels of error or irrelevance, muddled or superficial ideas, incoherent or non-existent argument, incompetent use of sources, or very poor writing style.
30--39:  The work demonstrates a little knowledge of the topic but no coherent argument.
0--29: The work demonstrates almost no knowledge of the topic.


Qualitative description of examination performance in Mathematics

The average USM ranges used in the classifications reflect the following general Qualitative Class Descriptors agreed by the Teaching Committee:

First Class: the candidate shows excellent skills in reasoning, deductive logic and problem-solving. They demonstrate an excellent knowledge of the material, and can use that in unfamiliar contexts.

Upper Second Class: the candidate shows good or very good skills in reasoning, deductive logic and problem-solving. They demonstrate a good or very good  knowledge of much of the material.

Lower Second Class: the candidate shows adequate basic skills in reasoning, deductive logic and problem-solving. They demonstrate a sound knowledge of much of the material.

Third Class: the candidate shows reasonable understanding of at least part of the basic material and some skills in reasoning, deductive logic and problem-solving.

Pass: the candidate shows some limited grasp of at least part of the basic material.

[Note that the aggregation rules in some circumstances allow a stronger performance on some papers to compensate for a weaker performance on others.]

Fail: little evidence of competence in the topics examined; the work is likely to show major misunderstanding and confusion, coupled with inaccurate calculations; the answers to questions attempted are likely to be fragmentary only.