Fifty years of A‐level mathematics: have standards changed?

Abstract

OfqualAdvanced-level (A-level) mathematics is a high-profile qualification taken by many school leavers in England, Wales, Northern Ireland and around the world as preparation for university study. Concern has been expressed in these countries that standards in A-level mathematics have declined over time, and that school leavers enter university or the workplace lacking the required mathematical knowledge and skills. The situation in England, Wales and Northern Ireland reflects more general international concerns about decreasing educational standards. However, evidence to support this concern has been of limited scope, rarely subjected to peer-review and of questionable validity. Our study overcame the limitations of previous research into standards over time by applying a comparative judgement technique that enabled the direct comparison of mathematical performance across different examinations. Furthermore, unlike previous research, all examination questions were retypeset and candidate responses rewritten to reduce bias arising from surface cues. Using this technique, mathematics experts judged A-level scripts from the 1960s, 1990s and the 2010s. We report that the experts believed current A-level mathematics standards to have declined since the 1960s, although there was no evidence that they believed standards have declined since the 1990s. We contrast our findings with those from previous comparison studies and consider implications for future research into standards over time.

Comparative judgement in education research

“…Variants of CJ, including forced-choice and ranking methods, have arisen in fields including marketing (Grashuis and Magnier 2018), environmental science (Hanley, Wright, and Adamowicz 1998) and health (Soekhai et al 2019). Within education, CJ-based methods were introduced to investigate the relative difficulty of examination papers (Jones et al 2016). Senior examiners judge pairs of scripts from different examination papers in terms of 'difficulty', and the outcomes are used to determine whether standards vary over time or across examination boards.…”

“…For example, a common application of CJ is to construct a scale of students' attainment based on different test questions (e.g. Jones et al 2016). This affordance of CJ methods means that we can equate independent measurement scales that were constructed at different times using different types of objects.…”

Mathematicians’ Assessments of the Explanatory Value of Proofs

“…It has also been applied in mathema.cs, to assess students' understanding of calculus, sta.s.cs, and algebra (Bisson, Gilmore, Inglis & Jones, 2016;Jones et al, 2019) and their problem-solving skills (Jones & Inglis, 2015). CJ methods have even been successfully used to assess nebulous constructs such as who is "the be`er mathema.cian", as part of a project to track examina.on standards across .me (Jones, Wheadon, Humphries & Inglis, 2016). The commonality across such studies is using CJ to assess constructs -such as explanatorinessabout which experts are expected to have an intui.ve understanding, but which they may not be able to fully ar.culate, or use to make reliable absolute judgements (Polli`, 2012).…”

Mathematics in the disciplines at the transition to university

“…Since 1951, advanced or A level awards have been the main university entrance qualifications taken by young people age 18 in England. Although the qualifications have evolved in style, and the numbers taking them have increased dramatically over the last 66 years, they have remained remarkably resilient to change, albeit with some questioning the maintenance of standards over time (Jones et al, 2016). In the early years, these qualifications were designed for those in selective grammar schools and were set by several small, regional matriculation boards, often linked to local universities.…”