Measures of success
This year, however, he had additional "evidence" on which to draw, that is the rise in the number of candidates entered for modular A-levels. His comment that they were "not worth the paper they are written on" was countered by most of the quality press, including The TES.
However, from the Government there was an implied agreement with his views. In the same week as the A-level results were announced Lord Henley, junior education minister, was interviewed on the Today programme on BBC Radio 4. He stated that the School Curriculum and Assessment Authority was looking at Sir Ron Dearing's review of 16 to 19 qualifications and had already accepted its recommendation that candidates should only be able to resit each module once.
I have yet to see this particular point in print or see any research evidence to support the view that the ability to resit leads to lower standards.
As those of us who have taken GCSE mathematics resit classes for year 12 students will testify, it does not get any easier second time around. Although some students seem to see gaining the qualification as some sort of long-service award - "I have taken it three times; they have got to give it to me this time!" - this is not the case.
Are people who pass their driving test at the third attempt better or worse drivers than those who pass first time? Do people fail because they were ill-prepared, entered too early or because they had a run of bad luck?
While one must beware of employing this type of analogy, it may help to focus the thoughts of those who should know better. It may even encourage them to look to see what evidence is available from examination boards.
There are fewer grades N and E awarded through modular courses, candidates decide when to "cash in" their modules for a final grade and are unlikely to do so if they are going to fail.
Modules have a "shelf life" of five years and so allow for such flexibility. Many students may decide to opt for an AS grade, which requires half the number of modules of a full A-level.
I have looked at the grades attained by students in mathematics A-level in 1994 and 1995 as held on the A-Level Information System (ALIS) database. I have compared the achievements of students with similar academic qualifications at GCSE level who have then followed either a modular or linear route to accreditation in A-level maths.
ALIS was established at the University of Newcastle upon Tyne in 1983 and is now based at the University of Durham. It initially provided information concerning value added, attitude and process to schools and colleges in the Tyneside area. Since 1990 it has expanded significantly and now covers institutions in England, Wales and Northern Ireland. For this research, data from 342 institutions was accessed to produce information on more than 6,700 students who were awarded a grade in A-level mathematics. More than 500 of those followed a modular course.
The academic quality of the students following A-level mathematics courses was similar when judged by their average GCSE results. This has been shown in the ALIS project to be the best indicator of success in A-level. The grades are coded A=7, B=6, C=5, to U=0. Modular course students had an average GCSE grade of 6.00 (sd=.71) while non-modular students average score was 6.05 (sd=. 71).
Average GCSE grade (1994) Average GCSE Male Female Modular 5.90 6.22 Linear 5.93 6.28 Despite the similarity between the previous attainment of students, their final grade attained in A-level mathematics is different. Those following a non-modular course had a mean score of 5.52 (sd=3.74) while those following the modular course scored 6.52 (sd=2.71). The grades are coded A=10, B=8, C=6, D=4, E=2, N=0 and U=-2.
Final A-level grade (1994) A-level grade Male Female Modular 6.53 6.52 Linear 5.44 5.69 This would appear to imply that, for students of equal prior achievement, measured by their average GCSE score, following an A-level course with modular assessment allows them to gain a result half a grade higher than if they had followed a non-modular course.
It is not quite as simple as that. A more subtle measure is required to assess the real effect on attainment by a modular approach to assessment.
A more sensible approach is to look at the residuals of the data. Residuals are calculated, as part of the ALIS data, by finding the difference between the actual A-level grade attained and the grade that was predicted based on a student's GCSE results.
A positive residual means that a student attained a higher grade than expected at A-level whereas a negative residual means that they did not do as well as expected. The grades are allocated a numerical value, that is from A=10, B=8, C=6 to N=0, U=-2.
Hence a residual of +2 means that a student attained a whole grade more than hisher previous attainment predicted. So, using this criteria, what effect does the ability to follow a modular course appear to have on attainment in A-level maths?
A-level residuals (1994) Residuals Male Female Modular 1.35 0.51 Linear 0.17 -0.48 It would appear from this research into the data from A-levels attained in 1994 that female candidates did slightly better than expected in modular A-level and slightly worse in linear A-level.
Male candidates did better than predicted. The differences between the residuals for modular and non- modular courses indicate that candidates improve their result by half a grade. A similar pattern emerged when looking at the 1995 data. This time three specific modular courses were studied.
Perhaps the biggest surprise of this relatively small-scale research is that, on average, students only improve their grade by a half. This despite the flexibility of being able to resit modules, include coursework (in some options), use graphical calculators and take more than the required number of modules in order to "cash in" the best.
For A-level grades awarded this year, SCAA rules made it necessary for students to attain 30 per cent of their marks in the examination taken at the end of the course. Rather like the decision to limit the amount that coursework can contribute to maths at GCSE level, this ruling appears to have been led more by dogma than by research evidence.
Let us stop this constant denigrating of our young mathematicians and start using our time, energy and resources to discover ways of further developing and assessing their mathematical knowledge and understanding.
Sally Taverner is a lecturer in the department of education at the University of Newcastle upon Tyne.