Our research into Further Maths

Why Further Maths?

Advanced mathematics qualifications are a vital requirement for studying STEM degrees at university and for the wider economy. Most STEM degree entries require good Maths grades at A-level, and some courses, such as Maths, Physics and Engineering at Imperial College London and other selective universities, may require or prefer good results in A-level Further Maths. Performing well at Further Maths is also known to ease the transition from A-level into a range of STEM degree courses, setting up students to succeed.

Unequal participation in A-level Further Maths

However, participation and attainment in A-level Maths qualifications are both unequal. From earlier research, it is clear that students’ school/college attended, gender, ethnicity and social class impacts upon participation. Not all students are given equal opportunities to access high-level mathematics qualifications and subsequently high-status commercial, technological and scientific careers.

The main questions that were explored

1. Why do students who are interested in STEM subjects choose to/not to study Maths and Further Maths A-levels? What are the main factors that encourage students’ progression to advanced maths?
2. What are students’ views, experiences and perceptions of studying maths at advanced levels, including A-levels and university (potentially in the future)?
3. What are participants’ perceptions of useful strategies which could support raising students’ GCSE attainment and facilitate progression to Further Maths A-level, particularly for those from disadvantaged backgrounds and/or underrepresented groups?

The main focus of the study was conducting focus groups with 62 Year 10-13 students from 22 state schools/colleges in 2022. We also spoke to four maths teachers to provide some additional information for our study. We attempted to reach a range of schools and participants from different regions and different contexts, especially students from backgrounds under-represented at Imperial College London. We have also linked data collected with the external data source, the Higher Education Access Tracker (HEAT) database, which provides additional information on participants based on students’ postcodes and schools. 70% of the students were from the Greater London area, and 82% of the student lived at home postcodes in high levels of deprivation. The majority of students were from Black and Minority Ethnic (BAME) backgrounds.

Ethics approval for the project was gained from the College. All participants have been assigned pseudonyms.

The findings from the study confirms certain patterns from existing literature and provides further insights on certain issues.

Why Further Maths?

Reasons for choosing Further Maths

• A requirement or preferred choice for their university course
• Benefits to their Maths A-level and/or future study
• Appreciation of complex maths

"I knew I wanted to do Engineering at university, and I know it’s very Maths-heavy. So, I thought, it wasn’t required for any of the unis I was looking at. But I thought, if I was studying that, I would be really good at the normal Maths which is required. And if when I get there, even if I don’t get an A*, the stuff I’ve learnt for that will be helpful in the actual uni course itself." - Tim (Year 13) 

Reasons for not choosing Further Maths

• Not meeting the course requirement
• Course unavailability
• Competing demands or wanting more options
• Negative perception and reputation of Further Maths
• Workload
• Gender related issues, including gender imbalance in further maths classrooms, confidence and cultural issues

"No, I never thought about doing it. Honestly, I kind of thought it was in the name, Further Maths, I don’t know, it was too much for me. And I felt like a lot of the people that do it, I’m not as motivated as them. And I feel like they’re, I don’t know, because I got an Eight as well, so I was like, I feel like loads of people who do Further Maths only get 9s, so I was like, it’s kind of out of the picture for me as well." - Melis (Year 12)

Reasons for dropping Further Maths

• Managing workload
• Decision made by the school when students are perceived as not able to get top grades

"I feel like people drop Further Maths because you do Maths, the whole of A-level Maths in one year. So, then the second year, if you drop Further Maths, you can just relax on that Maths side and concentrate on the other two subjects that you’ll have." - Christina (Year 12)

"They [people who don’t do Further Maths] might see a couple of integral signs and someone who hasn’t seen an integral sign before in their life, they go oh, what is this? And then, they might think, you must be a genius. You work on this all the time. But once you get introduced to it, it’s kind of second nature to you." - Jedrick (Year 13)

We would like to use the conceptual tools of ‘Further Maths capital’ and ‘Further Maths habitus’ to help us to better understand uptake of Further Maths and to find ways to remove or lessen the barriers to participation. What kind of resources or ‘capital’ would support students to choose and succeed in A-level Further Maths? How can we support students to feel like Further Maths is an option for them?

The use of these concepts is an extension of the concept of Science capital (Archer et al., 2015) and also recent Further Maths research (Boylan et al., 2016). The idea of Further Maths capital provides a way to understand and organise all the Maths and Further Maths-related resources that a person may have or can develop. From this study, we identified some shared clusters of attitudes and dispositions among Further Maths A-level students, which we interpreted as signalling a potential form of Further Maths habitus.

Here are our project findings and some recommendations, particularly relevant to university and outreach perspectives:

• Prior/GCSE attainment is a strong predictor for participation in Further Maths A-level and future attainment.
  Recommendation: Support to raise prior/GCSE maths attainment to give more students the option to choose Further Maths. This is particularly the case for socially/economically disadvantaged pupils with high prior attainment levels, where achieving a top grade at GCSE could greatly affect their chance of progressing to Further Maths.

• The prospect of studying Further Maths is not positively perceived or well understood by many, and some high attaining students might view it as too challenging.
  Recommendation: Most students do not have access to GCSE Further Maths or Statistics courses. Further Maths taster sessions or more information about studying Further Maths A-levels would be useful to help students to make informed decisions – students can evaluate their interest in the topics they would meet at A-level and to experience the challenge and success with this material in order to reduce the perceived risk of committing to a difficult A-level subject.

• There is a gender bias with fewer girls taking Further Maths.     
  Recommendation: Foster inclusive teaching and learning to help tackle gender and other bias in maths and STEM in general (e.g. meaningful representation of women and girls and people from other underrepresented groups in curricula, educators, and role models); support students in developing a more accurate match between performance and maths self-concept.
  
  
• Students from schools/colleges with fewer resources receive no or limited support on choosing A-levels and future pathways, as well as preparing for university applications and additional subject specific exams for selective universities.           
  Recommendation: Provide more information on the potential benefits of studying Further Maths, including the transferability of the qualifications and high-level mathematical skills, to students and parents to aid them to make more informed decisions; raise awareness of subject requirements for the application process and expected mathematical knowledge required in different STEM degree courses. Upskill teachers and careers advisors particularly in 11 to 16 schools where knowledge about Further Maths and the progression routes it unlocks may be limited.
  
  
• Students from schools with a strong maths culture and larger A-level Maths and Further Maths cohorts are more likely to choose and succeed in the subject.
  Recommendation: Support schools and teachers to increase the organisational Further Maths Capital at school level to improve access (i.e. more support for teacher CPD to enable more offerings of Further Mathematics, more funding to support more provision of Further Maths in lower participation areas).
  
  
• There is heavy gatekeeping at school/college on who can take and continue Further Maths; the Further Maths results are more skewed than other subjects.
  Recommendation: Facilitate conversations with schools and teachers to challenge the less helpful discourse around aspirations, emphasising the importance of high expectations for young people and from their teachers. School/college and university to examine their current highly selective policies and practices relating to Further Maths and higher education admissions.