Comparing the Standard of GCSE with That of the National CurriculumAuthor(s): Adam WoodSource: Mathematics in School, Vol. 18, No. 5 (Nov., 1989), p. 22Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30216368 .

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Compar"g9 the Standard of

GCSE with that of the

NATIONAL CURRIC

by Adam Wood, Mathematics Adviser, Dudley

The relationship between the levels in the National Cur- riculum and the grades at GCSE is not clear at present. Figure 1, extracted from the TGAT report, shows that the average attainment at 16 + in the National Curriculum is intended to be Level 6. This would match exactly with the definition of the former CSE Grade 4, now equivalent to GCSE Grade F. The diagram also shows Grades A to F against Levels 10 to 7.

One independent way of making a comparison is to match questions from GCSE papers with the National Curriculum statements and examples. Such an investigation was under- taken for a mathematics examination that had Grades E, F and G available. There was no coursework component.

The two written papers were of the "fill-in" type and contained short answer questions only. There was a detailed mark scheme on the papers showing that 125 marks out of 200 were allocated in ones and twos. Some comparisons were particularly easy because the question mirrored the text of the national Curriculum but some parts of questions tested more than one skill. The process revealed some interesting gaps in the National Curriculum, for example, there is no requirement to calculate differences between times, and the requirement to calculate elementary areas hinges on a single example in Attainment Target 6. The results of the com- parison are shown in Table 1.

10

9 CSE I [grades

8 A to F

6 Levels

5

4 I a /'

2 '

7 8 9 10 11 12 13 14 15 16

Age (years)

Fig. 1 The Sequence of pupil achievement of Levels in the National Curriculum between ages 7 and 16 (from the TGAT report, paragraph 104).

22

Table 1 Distribution of Marks for Two GCSE Mathema- tics Papers Across the Levels in the Attainment Targets of the National Curriculum

National Curriculum Levels 2 3 4 5 6 7 Total

AT 1 5 5 10 AT 2 1 5 18 5 1 30 AT 3 18 7 16 6 47 AT 4 2 6 8 AT 5 1 3 4 AT 6 8 2 10 AT 7 3 3 AT 8 8 1 12 13 34

Total PC 1 1 32 33 55 22 3 146

AT 9 5 2 7 AT 10 3 10 2 3 18 AT 11 1 4 5 AT 12 3 5 6 14 AT 13 4 3 7 AT 14 1 2 2

Total PC 2 0 11 21 19 3 0 54

Totals 1 43 54 74 25 3 200

To use this analysis to compare GCSE Grades with National Curriculum Levels requires an interpretation of the phrase, "has mastered the understanding and com- petence required for Level x". One possible view of future standards is to expect a child to achieve a success rate of 70 per cent to attain a Level. On this basis, and on the assumption of a 90 per cent success rate on earlier Levels, the marks obtained on these examination papers by children who have attained various Levels of the National Curriculum might be:

Paper 1 Paper 2 Total (100) (100) (200)

Level 3 21 10 31 Level 4 43 35 78

Level5 70 71 141

Level 6 85 87 172

From this table, it is reasonable to judge that a child that has attained Level 4 in the National Curriculum would not quite obtain a Grade G at GCSE but that a child that has attained Level 5 would be very close to obtaining a Grade E. However this analysis is based only on the mathematical skills required. Both papers were very wordy, running to a total of 35 pages, and it is possible that candidates were constrained by their inability to read some questions.

The questions analysed weighted the two Profile Com-

ponents in the ratio 75:25 rather than in the ratio 60:40 required by the National Curriculum. It is possible that

pupils at this level may find shape, space and data handling easier than number and algebra so measured standards might rise in the future without any real change.

However, it must not be forgotten that about 30 per cent of the school population does not at present obtain Grade G in mathematics, so the analysis does suggest that the spread of ability could be wider than that given in the documents accompanying Statutory Orders. If the standard required for Grade F, the grade expected of the average child, really is below Level 5, then the range of achievement at 16 + might well be from Level 1 to Level 10.

Whether the contents of Levels 1 to 4 will allow the development of satisfactory courses for the lower attainers remains to be seen.

Mathematics in School, November 1989

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