If you haven’t already noticed, Mathematics and Further Mathematics AS and A levels in England have changed!

Ok, so first teaching of these reformed qualifications didn’t start until September 2017. There are quite a few changes from the old qualifications, so here’s a brief guide to what you need to know: what’s the same, what’s different, and what’s new.

A detailed account of the rationale for and details of the reforms can be found here. And just in case you were wondering, these reforms haven’t just sprung up overnight – the journey has a been a long, and sometimes torturous one, starting as long ago as 2010.

There had been some concern in higher education institutions/universities about the preparedness of students for undergraduate study across many subjects, but especially so for disciplines that depended on Mathematics and Further Mathematics AS and A levels.

The mathematics reforms have taken longest of all to be introduced, partly because GCSE Mathematics has also undergone major reform and is now more challenging, ambitious and rigorous. The first awards for the new GCSEs were in the summer of 2017, preparing students much better for the new AS and A levels.

These are the eight key areas to pay attention to:

**Linearity**. All A levels are now ‘linear’ meaning that the final grade achieved is based solely on the (typically three) papers taken at the end of the two-year course of study, and assessing the *whole* of the Subject Content.

**Decoupled**. AS continues, but the results from an AS will not contribute to the A level grade.

**Synoptic**. With both AS and A levels being linear, each qualification is intended to be synoptic, with any examination question being able to draw from across the *whole* of the content.

**100% prescribed content, including mechanics and statistics for Mathematics**. The content of Mathematics A level (and AS) is now fully prescribed, and so is the same for anyone taking this qualification. Much more emphasis is placed on how mathematical ideas are interconnected and how mathematics can be applied: to model situations mathematically using algebra and other representations; to help make sense of data; to understand the physical world; and to solve problems in a variety of contexts.

**Use of data in statistics**. A significant change in the reformed AS and A levels is the requirement that students work with large data sets, using technology such as spreadsheets or specialist statistical packages, interpreting real data presented in summary or graphical form, and using data to investigate questions arising in real contexts.

**Overarching Themes**. A fundamental part of the reforms is the introduction of the three Overarching Themes: OT1 Mathematical argument, language and proof; OT2 Mathematical problem solving; OT3 Mathematical modelling. These themes will apply to the *whole* of the detailed content, along with associated mathematical thinking and understanding.

**Use of technology**. The use of technology, in particular mathematical and statistical graphing tools and spreadsheets, will permeate the study of AS and A level Mathematics and Further Mathematics.

**Further Mathematics**. The structure of Further Mathematics has changed significantly. Broadly speaking, 50% of A level Further Mathematics is compulsory comprising ‘pure’ mathematics - as well as building on algebra and calculus introduced in A level Mathematics, the A level Further Mathematics core content includes: proof, complex numbers, matrices, vectors, hyperbolic functions, and differential equations, all fundamental mathematical ideas with wide applications in mathematics, engineering, physical sciences and computing. The non-core content includes different options that enables students to specialise in areas of mathematics that are particularly relevant to their interests and future aspirations, e.g. further mechanics, statistics, calculus, and discrete mathematics, varying according to the specification offered by an exam board.

AS Further Mathematics has been designed to be co-taught with A level Further Mathematics as a separate qualification and which can be taught alongside AS or A level Mathematics. The AS broadens and reinforces the content of AS and A level Mathematics, and includes complex numbers and matrices. There is a compulsory element of ‘pure’ mathematics, and component of ‘pure’ mathematics with some optionality, with further options along the lines of the full A level.

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**OUT**:

- modules; accumulating marks on modules over the course of two years; resits to improve final grades
- SIX different A levels in Mathematics with four ‘core’ modules and six different combinations of applications modules
- students performing routine calculations in examinations to determine summary statistics for artificial datasets
- Further Mathematics AS and A levels with no common/compulsory content, and a large number of combinations of different modules that could be put together to form the qualification

**IN**:

- a two-year course of study far more coherent with more meaningful examination questions to match
- for AS and A levels in Mathematics the two main applications of the core (pure) mathematics at this level: mechanics and statistics replace six optional combinations. Far more detail is provided for the content so that teachers and students know exactly what should be studied. Both changes are vital for higher education – students will be able to build on the whole of the A level content with a high degree of confidence
- for statistics, an emphasis on understanding and interpretation in meaningful, real contexts
- a clear focus on understanding coherence and progression in mathematics, and how different areas of mathematics are connected
- use of mathematical knowledge to make logical and reasoned decisions in solving problems both within pure mathematics and in a variety of contexts, and communicate the mathematical rationale for these decisions clearly
- a common core of Further Mathematics AS and A levels

We now have AS and A levels that should be so much more enjoyable to study and teach.

By Paul Glaister, Department of Mathematics and Statistics, University of Reading, Reading, UK. Email: p.glaister@reading.ac.uk