Reasoning skills in post-16 mathematics students

This PhD project will investigate reasoning skills in post-16 mathematics students, aiming to provide research-based information to support an increase in the numbers of students studying mathematics in this age group. The project will place specific focus on Core Maths, a post-16 qualification introduced in 2014 for students who scored highly in GCSE but chose not to study mathematics at AS/A level. Core Maths provides opportunities to apply mathematics to other fields, and has three key objectives: deepening competence in selecting methods and techniques; developing confidence in applying mathematics to represent and analyse authentic situations; and building skills in mathematical thinking, reasoning and communication.
There is a strong case for improving post-16 mathematics, demonstrated by the findings in a review paper on 16-18 mathematics education (Smith, 2017). The review highlights that England remains unusual among advanced countries, as mathematics is not universally studied by students beyond the age of 16: around three quarters of students with high grades in GCSE mathematics do not choose to study mathematics beyond this level. Further, findings from this report show that around 40 per cent of 19-year-old students studying STEM subjects in UK universities do not have a mathematics qualification beyond GCSE. Furthermore, this report sets forth recommendations for the Department of Education, specifically highlighting the importance of considering ways in which the Core Maths brand could be strengthened, aiming to improve awareness and take-up of the qualification. This, in combination with the continuing demand for high level quantitative skills in industry, highlights the importance of researching Core Maths from a reasoning skills perspective.
General reasoning skills are valued in many careers and degrees, and one reason for the introduction of Core Maths is that studying mathematics is thought to improve these skills. This argument is known as the 'Theory of Formal Discipline' and is utilised in policy debates to prioritise mathematics in the school curriculum. This theory was tested by Attridge and Inglis (2013), in a study comparing the development of conditional reasoning behaviour in post-compulsory mathematics and English literature students. Findings support the Theory of Formal Discipline as conditional reasoning was developed to a greater extent in mathematics students compared with the literature students. This shows how A level mathematics improves these skills, but we do not yet know whether this is the case for Core Maths.
Therefore, this project will ask:
To what extent are general and quantitative reasoning developed in Core Maths and AS/A level mathematics?
What mechanisms link mathematical learning to general and quantitative reasoning?
How can we improve general and quantitative reasoning skills?
These main research questions will be answered by working in collaboration with Mathematics in Education and Industry (MEI), an independent charity committed to improving mathematics education. MEI creates innovative resources for thousands of students/teachers and offers a range of professional development. It has developed two Core Maths and mathematics AS/A level specifications that are examined through OCR. The research findings will both contribute to theoretical development and enable MEI to better support students and teachers, demonstrating that this project has high potential for impact in both the education sector and industry.