Executive Summary
The disruption to our national examination system caused by the pandemic prompted MEI to consider the effectiveness of mathematics curricula and assessments at KS4 and KS5.
This position paper details our analysis of England’s current systems of curriculum and assessment, with proposals for how they might be improved.
We believe these proposals can help more young people to master the mathematics they need to meet their aspirations for further study and employment, and equip them to use and understand mathematics and statistics with confidence in all aspects of their lives.
Key points relating to each section are summarised below. Detailed proposals are given within each section of the paper.
1. Accrediting Qualifications
There is a lack of coherence between the intended curriculum of the current GCSE and A Level mathematics qualifications and the curriculum as it is implemented in schools and colleges. The result is that students’ mathematics education has not improved to the extent intended by the most recent qualification reforms. At AS and A Level, not all subject criteria are being met, particularly those relating to the analysis of data and statistics, and the use of technology to help analyse and solve quantitative problems.
An expert curriculum and assessment body for mathematics should be established with the aim of ensuring coherence across curricula, teaching, professional development and assessment. A long-term planning and development process is needed to ensure that teaching and learning resources, professional development and assessments are designed to enable the curriculum to be implemented as intended.
2. Mathematics to age 16
Mathematics is vitally important for future work, study and economic well-being. It is by nature a subject where each level of understanding is dependent on a secure foundation of earlier study, meaning that each assessment requires a suitable level of challenge if it is to provide useful information about what students know, understand and can do.
In GCSE Mathematics, thresholds for lower grades are too low. Students awarded lower grades, including grades 4 and 5 on the higher tier, are not given a proper opportunity to demonstrate what they know, understand and can do. This is demotivating for students and
means grades do not give a clear indication of the mathematics a student has mastered.
There are potential benefits from including an element of teacher assessment in mathematics alongside external examinations.
The content of foundation tier GCSE Mathematics has a large overlap with what would reasonably be considered ‘essential maths’. Students need to achieve mastery of this to form a solid foundation for further study of mathematics, and to use basic mathematics in everyday life. Consequently, we propose that all students should take a GCSE focused on essential maths when ready, prior to a further GCSE based on content for progression to A level Mathematics.
Well-designed assessment could enable many more students to master ‘essential maths’ and also improve students’ attitudes to mathematics.
3. 16 to 18 mathematics
We want to move to a position where all students are keen to continue with mathematics post-16 and can make an informed choice of the best pathway to meet their needs and aspirations.
We face a persistent problem that most students who achieve grade 3 in GCSE Mathematics at age 16 do not go on to achieve a grade 4 by age 18, and the proportion of students who achieve below grade 3 gaining a grade 4 by age 18 is extremely low.
In considering ‘essential maths’, an expert curriculum and assessment body should review whether a single assessment model is suitable for all young people up to the age of 18 sitting the examination when ready, or whether a different assessment model should be designed for the assessment of ‘essential maths’ for post-16 students.
At level 3, Core Maths is now available in 30% of schools and colleges that offer A level Mathematics. This represents significant progress, but there are still large numbers of young people who cannot access these qualifications.
It is important that students have the option to study either Core Maths or AS Mathematics. Action is required to ensure schools and colleges routinely offer AS Mathematics and that it is the norm for 16 to18 institutions offering level 3 courses to offer a Core Maths qualification. Appropriate funding support should be available to allow this.
Grade boundaries for A level Mathematics in 2019 examinations were too low across the whole range of grades. Ofqual should work with the exam boards to check that suitable target grade boundaries for AS and A level Mathematics are included in each Assessment Strategy and should hold the exam boards accountable for achieving grade boundaries close to these.
4. Technology in mathematics assessment
The use of digital technology is now central to many applications of mathematics. Using technology in the assessment of mathematics allows direct assessment of contemporary approaches to solving mathematical problems, including the use of software to model and analyse data and geometry.
Engagement with the large data sets in AS and A level Mathematics falls short of the intentions expressed in the AS and A level Mathematics specifications. Implementation of the more general requirement for technology to permeate the study of AS and A level mathematics also falls short of the intentions in the specifications.
There are significant opportunities to assess the use of technology and appropriate software to help solve mathematical problems. There should be government support for trialling the use of technology and software in mathematics assessments at A level to bring such assessments up to date.
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