Students who enjoy mathematics and who plan to study AS/A level Mathematics in year 12 should have the opportunity to consider studying AS/A level Further Mathematics.

Similarly, students in year 12 who decide they want to study for a degree in a mathematically-rich subject area such as engineering, science, computing, finance/economics, and mathematics itself, should also have the opportunity of AS Further Mathematics in year 13.

Schools and colleges can help provide information and raise awareness about the benefits of studying A level Further Mathematics. The FMSPW can support schools and colleges to promote the uptake of Further Mathematics.

Advantages of Studying Further Mathematics

- Why Offer Further Mathematics
- Supporting A Level Mathematics And Other Subjects
- Progression To University (And Beyond)
- Supporting More Able Students
- Retaining Able Students
- Raising The Profile Of Mathematics In The School/College
- Case Studies

Students need to be made aware of the advantages that studying Further Mathematics can give them.

The following are some successful strategies used by schools/colleges to generate interest and enthusiasm, and boost recruitment for Further Mathematics.

- Displays highlighting careers making use of Mathematics and Further Mathematics. Please see our Careers page for more information.
- Providing information about degree courses in mathematically-rich subjects where Further Mathematics is essential or highly desirable. Please see our Universities section for more information about entry requirement.
- Extending and enriching the GCSE Mathematics curriculum. For example, offering
*Level 3 Additional Mathematics*alongside the study of GCSE Mathematics introduces students to more advanced topics and helps to build their confidence and enthusiasm for mathematics. - Organising and/or attending enrichment events and activities helps to generate interest in mathematics and provides students with information about careers and progression to university.

Your local FMSPW Area Coordinator organises enrichment events for students designed to promote the study of Mathematics and Further Mathematics post-GCSE. If your school is registered with the FMSPW then you will receive information about these events. It may also be possible to arrange for someone to come to your school/college to speak to your students. Please contact your local FMSPW Area Coordinator if you would like to discuss this.

**Why offer Further Mathematics?**

A level Further Mathematics has consistently been one of the fastest growing A level subjects over the last 11 years.

Further Mathematics is **not** just for the top A level Mathematics students. AS Further Mathematics is accessible to many students capable of passing A level Mathematics.

There are many very good reasons to offer Further Mathematics.

**Supporting A level Mathematics and other subjects**

- Studying Further Mathematics helps students to achieve their best possible A level Mathematics grade, by consolidating and reinforcing their standard A level Mathematics work.
- The additional applied units studied by A and AS level Further Mathematics students support the study of other A levels. For example, advanced statistical techniques that are used in Geography and Psychology and mechanics topics in Physics.

##### Progression to University (and beyond)

- Students taking A or AS Further Mathematics are better prepared for the transition to mathematically-rich university courses.
- Some leading university courses include Further Mathematics in their offers for places as a requirement, by not offering Further Mathematics you could prevent your students from applying to these courses. Other Universities lower the offer required for students who have studied Further Mathematics. See the Universities section for further details on entry requirements for higher education.
- Studying AS Further Mathematics in year 13 is an excellent option for students who wish to pursue a degree in a STEM subject. As well as introducing them to new topics that they will find useful for their degree course, it is likely to improve their A level Mathematics grade.

##### Supporting more able students

- Overwhelmingly, students taking Further Mathematics find it to be an enjoyable, rewarding, stimulating and empowering experience.
- For more able A level Mathematics students it enables them to distinguish themselves as able mathematicians both for university applications and in the employment market.
- For students who enjoy mathematics, it provides a challenge and a chance to explore new and/or more sophisticated mathematical concepts.

##### Retaining able students

- High achieving GCSE students may be tempted to change school/college for their AS/A levels if your school does not offer them the opportunity to study Further Mathematics.
- Increasingly, Russell Group Universities are requiring Further Mathematics or making lower offers for students taking it. Therefore, by offering Further Mathematics, schools can improve their destination statistics.

##### Raising the profile of Mathematics in the school/college

- Offering Further Mathematics raises the profile of Mathematics across all year groups and often has a positive impact on performance in mathematics across the whole school.
- You may find it easier to attract and retain well-qualified, enthusiastic teachers.
- Further Mathematics students can be excellent ambassadors for mathematics throughout the school and in some cases act as mentors, supporting younger students.

##### Case Studies

In 2015 UCL’s Institute of Education undertook research into the wider benefits of introducing A level Further Mathematics. The IoE looked at 4 institutions that had recently established Further Mathematics with support from the FMSPW. The report outlines the factors which were important in the successful implementation of the curriculum changes. The researchers found evidence of changes to teacher identity and confidence, departmental identity and changes to pedagogy not just for A level but lower down the school.

#### Making the case for Further Mathematics

- To Students And Their Parents
- To Senior Leaders
- Further Mathematics Can Be Provided In Cost-Effective Ways With Support From The FMSPW
- Who Should Study Further Mathematics?

This information and these resources are provided to support mathematics departments in making the case for A level Further Mathematics provision in their institution.

**To Students and Their Parents**

Studying Further Mathematics:

- is likely to increase their enjoyment of mathematics and improve their grade in A level Mathematics;
- broadens their mathematical skills and promotes deeper mathematical thinking;
- helps ensure a successful progression to mathematics-based subjects at university;
- is a requirement for entry to prestigious mathematics-based courses at leading universities and improves their chances of an offer at many others;
- is a way to make their university application stand out;
- is not just for students who want to become engineers or physicists.

Any student applying to study a science, technology, engineering, or other mathematics-related degree, such as economics, should consider taking Further Mathematics to at least AS level. **AS level in Further Mathematics is accessible to lots of students.** There is some useful information on our HE & Careers page on careers, degrees and apprenticeships open to students who have studied A/AS level Further Mathematics.

*Those students who had studied Further Mathematics to A or AS level standard reported coping better with the mathematical content of the degree, and as such perceived that they required less additional support throughout their studies.* Mind the Gap report 2010 – Institute of Physics

**To Senior Leaders**

- The number of students taking A level Further Mathematics has increased each year for 13 years;
- Further Mathematics is one of the facilitating subjects as described by the Russell Group and the DfE;
- A school/college that does not offer Further Mathematics is restricting the opportunities of some students wishing to apply for Mathematics, Physics and Engineering degrees at more prestigious universities;
- High achieving GCSE students may move to another school/college in order to study Further Mathematics;
- Further Mathematics is often taken as a 4th A level subject.
- AS Further Mathematics is a useful option and is accessible to most A level Mathematics students;
- The opportunity to teach Further Mathematics is useful in the recruitment and retention of enthusiastic and well-qualified mathematics teachers;
- The experience of teachers and the FMSPW in providing tuition to students in Further Mathematics also shows that taking Further Mathematics can have a significant positive impact on A level Mathematics performance;
- “Students who take both maths and further maths achieve substantially higher grades in their maths than comparable students who take maths alone” is the conclusion of ALIS, the Advanced Level Information System;

**Further Mathematics can be provided in cost-effective ways with support from the FMSPW**

- The FMSPW provides a free Scheme of Work, Flipped Classroom Videos and Revision Videos (for access to these, register with the FMSPW) as well as free teaching materials through the Integral Online Resources.
- Schools and colleges can access high-quality, professional learning through the FMSPW to develop A level Mathematics and Further Mathematics teaching and learning.
- FMSPW Area Coordinators offer free advice and support to teachers.
- The FMSPW helps schools and colleges to work together to offer Further Mathematics and provides direct tuition, either face-to-face or online.

**Who Should Study Further Mathematics?**

Further Mathematics is a suitable course for many more students than just for the top A level Mathematics students.

AS level Further Mathematics is accessible to any student capable of passing A level Mathematics. Any student planning to take a degree with significant mathematical content will benefit enormously from taking AS Further Mathematics. New ideas such as complex numbers and matrices occur in the first year of many undergraduate STEM degree courses. Studying these at A level together with two more applied modules will help students get off to a good start with their degree studies.

In Wales 2017 around 14% of all A level Mathematics students also took A level Further Mathematics. So it is likely that if you have students taking A level Mathematics then a small number of these would also benefit from studying Further Mathematics to at least AS level.

#### Encouraging Girls

- Girls’ Participation In A Level Mathematics And Further Mathematics
- Research Evidence Into Factors Affecting Girls’ Participation In Advanced Level Mathematics
- Successful Strategies For Girls’ Participation In Mathematics: Case Studies
- Recommended Strategies For Promoting Greater Gender Balance In Advanced Level Mathematics
- Teacher Resources
- Enrichment And Extension
- Links

##### Girls’ participation in A Level Mathematics and Further Mathematics

The number of students taking A levels in Mathematics and Further Mathematics in the UK has risen considerably over the last ten years.

In 2016, Mathematics was the fifth most popular A level amongst girls, behind English, Biology, History and Art whilst it was the most popular subject taken by boys. The participation rates at AS level were the same with Mathematics being the most popular subject taken by both boys and girls. The proportion of students taking Mathematics (AS/A level) who are girls is around 40% with the corresponding figure being 30% for Further Mathematics (AS/A level). The Further Mathematics Support Programme Wales promotes participation in Advanced level Mathematics to all students who would benefit from taking the qualifications, especially girls.

##### Research evidence into factors affecting girls’ participation in Advanced Level Mathematics

The UCL Institute of Education (IOE) produced a literature review of recent national and international findings on gender participation and performance in post-compulsory mathematics.

Prior attainment in mathematics was found to be the most significant factor in progressing to A level, but boys were more likely to continue to A level than girls with the same GCSE grade. This disparity becomes much more pronounced for students with A or B grades, suggesting that girls may see good, but not excellent, grades as a barrier to progress.

Students were more likely to choose mathematics if it was their highest grade at GCSE. With girls attaining more A/A* grades across the full range of GCSE subjects, their positioning as ‘all-rounders’ may negatively affect their uptake of A level Mathematics. Enjoyment was more likely to be cited by girls than boys as a reason for STEM related choices.

Girls have been found to have lower mathematics self-concept than boys of the same ability; this is of concern because research shows the degree of match between task performance and self-concept is linked to intention to continue with mathematics. Students were found to be aware of the stereotypical images of mathematicians, but they still used them. Female students were also sometimes distanced by presentation of images of highly successful, attractive female mathematicians, meaning the images had the reverse effect to that intended. A lack of awareness of the utility of mathematics affected students of both genders.

Advice and encouragement to continue with mathematics from a teacher or family member was found to be important; and this could mediate the effect of lower mathematics self-concept for girls in particular. Research evidence acknowledges the importance of socio-economic factors and the impact of ‘science capital’. Students who had formed an opinion against pursuing mathematics and science in the future by age 10 were highly unlikely to change their minds by the age of 14.

##### Successful strategies for girls’ participation in mathematics: Case Studies

From October 2014, the UCL Institute of Education worked with the FMSP (now AMSP) in England to produce five case studies of schools and colleges that are making an impact on improving girls’ participation in Advanced level Mathematics.

Through analysis of data, teacher and student focus groups and lesson bservations, researchers have examined strategies that have contributed to effective change in the take-up of A level Mathematics and Further Mathematics.

Senior leaders: The support of senior leaders is seen as crucial in guiding the development of a clear whole-school culture which promotes participation in post-16 mathematics by girls and supporting an appropriate curriculum within the mathematics department. For example, three of the case study schools prepare students for Level 2 qualification in Additional Mathematics, which offers students an insight into what is involved in A level Mathematics. This is beneficial to girls who report that they feel more confident in progressing to A level having been exposed to more challenging mathematics during Key Stage 4.

Careers advice should start early and illustrate the utility of mathematics across a range of disciplines. At one school, students have researched possible university courses by Year 11 and noted that mathematics was necessary for a range of careers including the armed forces and sports science. At one College, mathematics is valued as a currency that keeps options open and is a gateway to specific careers, including optometry, medicine, food nutrition, youth work, forensic science and physics. Wall displays highlight the importance of mathematics. At a Further Education College, personal careers advice for new and prospective students emphasises pathways in which mathematics is an essential companion or a central subject.

Teachers: The role of mathematics teachers in supporting girls and getting to know them individually is valued by female students. They like teaching strategies that provide opportunities for checking understanding with friends and quiet conversations with the teacher. Teachers in the three mixed schools described the importance of directing questions to girls in class. In several of the schools, the mathematics department’s ‘open door’ policy was seen as crucial in building girls’ confidence.

Influence of family: In the case study girls’ participation is seen to be assisted by strong family appreciation of the value of mathematics and the role of hard work. Family support for the study of mathematics was particularly high in non-white British ethnic groups. Students in the Further Education College were dismissive of negative cultural messages amongst some young people, such as it being ‘smart to dumb down’.

Motivation: The messages about `participation in Further Mathematics focused n motivation rather than simply focusing on the cleverest group of students in the year group.

##### Recommended strategies for promoting greater gender balance in Advanced Level Mathematics

Strategies that senior leaders and heads of mathematics departments could implement to promote greater gender balance in the uptake of A level Mathematics and Further Mathematics:

Consider the gender balance in previous A level cohorts. Use the JCQ data to identify the relative participation rate of girls against the national picture, in Wales and the UK and similar schools in Wales if the data is available. Look for trends in progression from Year 11 classes and/or feeder schools.

Identify and support girls in Year 10/11 who show the potential and/or interest in mathematics to progress to post-16 study. Analyse the proportion of girls and boys with an A or A* in GCSE Mathematics who progress to study mathematics to at least AS level.

Introduce more mathematics topics and qualifications alongside GCSE for students expected to get a grade B or above. Girls value the opportunity to evaluate their interest in the topics they might meet at A level and how they might cope with the more demanding material.

Throughout years 7 to 11, develop a schoolwide culture in which girls aspire to study mathematics to A level.

Teachers should embed advice about how mathematics is used in real life contexts into lessons to make students aware of the utility of the subject.

Teachers should provide students, especially female students, with regular positive feedback on their progress and ability. Praise resilience, discussion and careful work, and support female students in developing a more accurate match between task performance and mathematics self-concept. Avoid presenting A level Mathematics as a ‘specialist’ subject – emphasise the general benefits of studying the subject. Present a clear message to staff interviewing and enrolling students to A level courses about the possible barriers that may need to be broken down when recruiting girls to post-16 mathematics courses and provide clear information about the importance of A level Mathematics and Further Mathematics qualifications.

Engage with parents/carers about the importance of promoting a positive message to both boys and girls about progressing to study mathematics post-16.

Provide clear messages to students, and girls in particular, about the wide range of careers and degree courses for which post-16 study of mathematics would be beneficial. Invite current or previous female A level Mathematics students to speak to younger students about the importance of mathematics in their degree course or future employment, both in STEM and non-STEM fields.

##### Teacher Resources

The FMSPW are keen to identify opportunities where the mathematics occuring within other subjects can be demonstrated to students. Research indicates that girls are more likely than boys to take A level Mathematics alongside non-STEM A level subjects and so identifying the mathematics that occurs within Business Studies, Psychology, Geography and other fields is important.

##### Enrichment and Extension

On the AMSP Supporting your students’ transition to advanced maths page, please scroll down to the **Find ways to encourage girls** section.

##### Links

The Institute of Physics (IoP) 2013 Closing Doors report investigated progression to A level in Mathematics, Physics, Economics, English, Psychology, Biology and Economics. The report recommends that school leaders reflect on their own statistical data relating to progression and gender and put in place whole school measures to counter gender-stereotyping.

2014 saw the first female winner of the Fields Medal for outstanding achievement in mathematics. Maryam Mirzakhani was recognised for work in the field of complex geometry.

The Programme for International Student Assessment (PISA) study on gender and the learning of mathematics was published in 2014. It calls on educators and parents to make a concerted effort to challenge and eliminate gender stereotypes and bolster girls’ self- belief. A facebook page about Women in Maths has been launched and has over 8000 followers.

A set of Women in Maths careers videos produced by the University of Nottingham feature women discussing their work in mathematics and how it relates to other subjects such as Biology. They also talk about what other career options they had when they were younger and why they are glad they chose mathematics.

Good Housekeeping magazine published a campaign to encourage girls to study mathematics. Three leading advertising agencies were asked to produce an advert that would make girls think differently about maths. See the October 2014 edition for full details – which advert do your female students prefer?

Director of ‘Maths Inspiration’ Rob Eastaway uses his blog to discuss interesting findings from a practical experiment with upper primary boys and girls relating to classroom preferences for mathematical activity. Do the same preferences apply in sixth form mathematics classrooms?