Some implications of choice of tiering model in GCSE mathematics for inferences about what students know and can do

ABSTRACT

This study compared models of assessment structure for achieving differentiation across the range of examinee attainment in the General Certificate of Secondary Education (GCSE) examination taken by 16-year-olds in England. The focus was on the “adjacent levels” model, where papers are targeted at three specific non-overlapping ranges of grades. Examinees enter for a pair of papers at adjacent levels and receive the highest grade achieved. There is no aggregation of marks across papers. This study used simulation, based on data from a GCSE Mathematics exam, to compare the adjacent levels model with two other tiering models in terms of: (1) suitability of grade boundary locations; (2) score distributions; and (3) reliability. The adjacent levels model led to lower reliability but arguably improved two aspects of validity: the strength of the inference about what examinees with a given grade would know and be able to do; and the removal of the ambiguity about overlapping grades inherent in the current system.

KEYWORDS:

• GCSE
• tiering
• validity
• reliability
• Rasch

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. Grade E on the higher tier is a safety net for those who just fail to get a grade D, to prevent them from “falling off the bottom” and receiving a grade U. It is set half the C–D distance below grade D.

2. Ofqual (2015) states that the science subjects, mathematics, and modern foreign languages will be the only subjects to be tiered in the reformed GCSEs first taught in 2016 and 2017. Decisions for those subjects to be first taught in 2018 have not been taken at the time of writing, but none is proposed to be tiered except Statistics.

3. Even though around 25% of items were common to both tiers, common-item equating was not used to link the papers, because this gave different values for the overlapping grade boundaries to the actual values. The higher tier difficulty values for these common items were used in the bank.

4. In fact, an algorithm was written to find the final question(s) to ensure the 60-mark total was achieved; this was done once the cumulative mark total was within reach of the required maximum. (Selecting the top N questions does not guarantee a given paper total mark because questions vary in the number of marks they are worth).

5. For simplicity, the higher tier grade E on models 1 and 3 was set according to the bank scale, rather than by using the half-grade rule applied in practice (see note 1).