In every day conversations, the UK weather is by far the safest bet for non-controversial small-talk. This is because the variability and relative unpredictability of UK weather easily ensures that you can find loads of points of agreement with your fellow conversationalist. Within engineering education we also have another favourite topic for small talk – this is the A Level mathematics qualifications. This is because, until recently, it was relatively easy to find something within the A Level mathematics qualifications that any two members of the engineering academic community could agree to mourn about. This is all about to change, however. A Level mathematics has recently undergone a complete transformation, and the refurbished qualifications are already being delivered in schools, with the first batch of A level graduates expected to start their university studies in September 2019.
Why the A Level mathematics qualifications had to be redesigned
Over the past thirty years or so, there have been wide ranging complaints about the quality and perceived shortcomings of A level mathematics. Michael Gove, the then Secretary for Education, adequately summarised these shortcomings in a letter that he wrote to the Chief Executive Office of Qualifications and Examinations Regulation [DfE, 2013]:
- A level mathematics fails to provide the solid foundation that students need to prepare them for degree-level study and for vocational education
- A level mathematics students lack the deep understanding and/or the necessary skills to make connections between mathematics topics, and between mathematics and other subjects
- Assessment practice in A level mathematics is overly structured and encourages a formulaic approach to mathematical thinking instead of using more open-ended questions that require advanced problem-solving.
- Universities have had to adapt their teaching approaches to include remedial mathematics tuition for underprepared first year undergraduates.
A survey of mathematics departments within universities also revealed the following shortcomings [ALCAB, 2014]:
- The mathematical thinking of the most able students is not developed.
- The distinction between A and A* grades, i.e. the top most grades, seems to be based on the avoidance of careless slips rather than genuine mathematical ability.
- It is not clear what applied mathematics students have learnt.
- Current statistics provision tends to focus on routine calculations at the expense of interpretation and understanding.
Purpose of the new A Level Mathematics
According to the Department for Education, the primary purpose of the new A level mathematics qualifications is to [DfE, 2016]:
- Build from GCSE level mathematics and introduce calculus and its applications
- Emphasise how mathematical ideas are interconnected and how mathematics can be applied to model situations mathematically using algebra and other representations
- Helping students to make sense of data
- Helping students to understand the physical world and to solve problems in a variety of contexts, including social sciences and business
- Preparing students for further study and employment in a wide range of disciplines involving the use of mathematics.
Structure of the new A Level Mathematics qualifications
With the exception of further mathematics, all students studying A level mathematics now have to cover statistics and mechanics in addition to pure mathematics [Ofqual, 2016a]. This now provides universities with certainty as to the exact nature and level of mathematics covered by A level mathematics graduates.
In addition, students are now also expected to demonstrate the following overarching knowledge and skills across the entire content detailed in the A Level mathematics specification [DfE, 2016]:
- Mathematical argument, language and proof
- Mathematical problem solving
- Mathematical modelling.
Ofqual has also provided guidance on mathematical problem solving, modelling and the use of large data sets in statistics. This guidance also includes advice on assessing these key aspects, together with example questions [Ofqual, 2016c].
The new A Level Mathematics objectives and assessment format
The new A level mathematics qualifications have been specifically designed to deliver the following objectives [Ofqual, 2015]:
- Using and applying standard techniques: The new qualifications seek to ensure that learners are able to select and correctly carry out routine procedures, and to accurately recall facts, terminology and definitions.
- Reasoning, interpreting and communicating mathematically: Learners should be able to construct rigorous mathematical arguments (including proofs), make deductions and inferences, assess the validity of mathematical arguments, explain their reasoning and use mathematical language correctly.
- Solving problems within mathematics and in other contexts: Learners should be able to translate problems in mathematical and non-mathematical contexts into mathematical processes, interpret solutions in the context of a problem, and, where appropriate, evaluate their accuracy and limitations. Learners should also be able to translate situations in context into mathematical models. They should also be able to use mathematical models, evaluate the outcomes of modelling in context, recognise the limitations of models and, where appropriate, explain how to refine them.
Ofqual recommends that these three objectives should be assessed in accordance with the weightings outlined in Table 1 below [Ofqual, 2016b]:
Table 1: Assessment weighting for A and AS level mathematics
|Objective||Weighting (A Levels)||Weighting (AS Levels)|
|Using and applying standard techniques||50%||60%|
|Reasoning, interpreting and communicating mathematically||25%||20%|
|Solving problems within mathematics and in other contexts||25%||20%|
The new A Level Mathematics qualifications compared to First Year Engineering Mathematics
The new A Level mathematics qualifications are closely aligned to engineering mathematics as taught in the first and second year of university. For example, the objectives of the new qualifications closely agree with the intended learning outcomes of our first year mathematical modelling and analysis course module for engineering at University College London, whereby we state that by the end of the course module, students will be able to:
- Recognise the connections between mathematics and engineering, and how mathematical ideas are embedded in engineering contexts;
- Represent real-world systems from engineering in a mathematical framework;
- Identify and draw upon a range of mathematical concepts, including Calculus, Linear Algebra and Differential Equations to analyse specific problems and identify the appropriate mathematics to realise a solution;
- Employ appropriate computer programming and modelling techniques and statistical analysis to efficiently solve and evaluate the performance of engineering systems;
- Use estimation, approximation and dimensional analysis to reduce complexity;
- Relate the behaviour of the output of mathematical models to the underlying physical or conceptual models of interest;
- Carry our engineering problem solving both collaboratively in a team and independently;
- Present and interpret mathematical results in effective and appropriate ways to varied audiences, including non-mathematical engineering audiences.
Given such close alignment, we expect that from September 2019 onwards it will be much easier for first year students to adapt to university-level teaching. This is likely to reduce the time and effort spent by academic staff in remedial mathematics teaching. Instead, we hope that academics responsible for first and second year engineering mathematics teaching will use that time to focus on bringing engineering mathematics into closer alignment with other course modules in engineering.
DfE (2013). Reform of GCE A Levels – Letter from Secretary of State to Glenys Stacey. Available at: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/278146/SoS_January_2013_ofqual_letter_alevels_v2.pdf [accessed 25 August, 2018]
ALCAB (2014). Report of the ALCAB panel on mathematics and further mathematics. The A Level Content Advisory Board. https://alevelcontent.files.wordpress.com/2014/07/alcab-report-on-mathematics-and-further-mathematics-july-2014.pdf [accessed 25 August, 2018]
DfE (2016). Content for mathematics AS and A level for teaching from 2017. Department for Education. Available at: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/516949/GCE_AS_and_A_level_subject_content_for_mathematics_with_appendices.pdf [accessed 25 August, 2018]
Ofqual . AS and A Level Mathematics and Further Mathematics: Consultation on Conditions and Guidance. Ofqual. https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/481981/as-and-a-level-mathematics-and-further-mathematics-consultation-on-conditions-and-guidance.pdf [accessed 25 August, 2018]
Ofqual [2016a]. GCE Subject Level Conditions and Requirements for Mathematics. Ofqual. https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/517726/gce-subject-level-conditions-and-requirements-for-mathematics.pdf [accessed 25 August, 2018]
Ofqual [2016b]. GCE Subject Level Guidance for Mathematics. Ofqual. https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/514465/gce-subject-level-guidance-for-mathematics.pdf [accessed 25 August, 2018]
Ofqual [2016c]. Report on Mathematical Problem Solving, Modelling and the Use of Large Data Sets in Statistics in AS/A Level Mathematics and Further Mathematics. A Level Mathematics Working Group, Ofqual. https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/481857/a-level-mathematics-working-group-report.pdf [accessed 25 August, 2018]