Three tiers for passing
The criteria are not intended to set out the material to be assessed in GCSE mathematics. This is already laid down in the key stage 4 programme of study of the 1995 mathematics Order. The Order was produced after wide consultation during the review of the national curriculum, and was endorsed by the Joint Mathematics Council, among others, as being "based on a full and rounded view of the curriculum". Since GCSE syllabuses must match the Order, it is fair to say they will have an equally sound foundation.
The criteria themselves lay down only the required framework for arriving at the agreed maths content. This includes the tier structure for GCSE maths examinations. Tiers are needed because it is not possible to set single examination papers which enable students to demonstrate their capabilities across the full range of grades from A* to G. There are three tiers in maths: Foundation, which covers grades G-D; Intermediate for grades E-B; and Higher for grades C-A*.
To ensure that teachers and candidates are clear about what is to be covered by each tier, the criteria require that each new syllabus lists the content to be assessed by the examinations. These lists, to be agreed between the examining bodies and SCAA, will ensure comparability of demand across syllabuses, appropriate assessment for candidates who will take mathematics no further, and suitably demanding papers for high attainers. The criteria include descriptions for grades A,C and F, which reflect the content addressed by each tier.
The new structure includes narrower tiers than at present. There is a two-grade overlap between foundation and intermediate, and between intermediate and higher tiers. This overlap should enable maths teachers to make confident entry decisions. For example, a pupil reasonably sure of a grade B should enter the higher tier, with an opportunity for an A if things go better than expected, or a C if they go worse. Alternatively, a pupil who is expected to be on the borderline between grade B and grade C should be entered for the intermediate tier since there would appear to be no realistic chance of a grade A.
Foundation papers will include some of the "civic arithmetic" identified in List 1 of the 1985 GCSE criteria for maths. Higher papers will set demanding standards, including searching questions on algebra and geometry which will challenge high attainers.
All GCSE examinations must relate firmly to the key stage 4 programme of study, with questions in different tiers pitched at the appropriate level of demand. Many topics lend themselves to examination at various levels. Take the topic of direct and inverse proportion, for example: Foundation papers may include elementary examples of this, such as: if a rectangle with one side 4cm long is equal in area to another rectangle with sides of lengths 6cm and 8cm, what is its other side length? On the other hand, grade A performance would require the candidate to show a comprehensive and high level grasp of the concept of proportion as in: An object is moving in a straight line. Its speed, v ms-1, is inversely proportional to the square-root of its displacement, x, from a fixed point. When v = 1, x = 4m. Find the speed of the object when it is 9m from the fixed point.
The GCSE criteria and the programme of study serve different purposes. Taken together, they are designed to form the basis of first-rate syllabuses and qualifications. SCAA is determined that the GCSE should promote improved standards in mathematics and will work with the examining groups to that end.
Richard Browne is professional officer for maths at SCAA.