HGSMaths.com
The purpose of our curriculum is to build, within each student, a rich, interconnected schema of mathematical knowledge that enables increasingly sophisticated mathematical thinking.
Mathematics is one of humanity’s greatest intellectual achievements. It underpins modern science, engineering, technology and economics and is also a discipline of profound intellectual value. As a cumulative discipline, each generation builds upon the discoveries of those who came before, allowing us to stand on the shoulders of giants. Through the study of mathematics, students inherit this remarkable body of knowledge and encounter the abstraction, structure and elegance that make mathematics a uniquely powerful way of understanding the world.
At HGS, our ambition is for every student to become the best mathematician they can be. We believe that students think mathematically because of what they know. Our carefully sequenced curriculum ensures that each new idea builds securely upon prior learning, strengthening and extending each student’s mathematical schema.
As each student’s mathematical schema develops, so too does their capacity to think mathematically. Procedural fluency and conceptual understanding develop together, enabling students to reason with precision and apply secure knowledge to unfamiliar and challenging problems. We believe that genuine problem solving is the application of secure knowledge to novel situations.
By the time they leave HGS, our students appreciate the power, coherence and elegance of mathematics and are equipped to think mathematically with confidence and independence. High standards of attainment are the consequence, not the purpose, of this curriculum.
Our curriculum in practice
Our curriculum is deliberately sequenced so that new ideas build securely on what students already know and prepare them for the mathematics they will meet later. Students do not accelerate through content without firm understanding; progression is based on learning, not simply on coverage.
The curriculum is supported by bespoke booklets written in-house. These are used instead of textbooks because our resources are designed to serve our curriculum, rather than requiring our curriculum to follow a published textbook. The booklets contain explanations, example pairs and knowledge organisers, while separate task booklets provide structured independent practice.
Examples are carefully chosen to expose mathematical structure. Through variation, intelligent sequencing, non-examples and misconception-aware questions, students are helped to notice patterns, make connections and develop secure understanding before moving to independent practice.
We define mastery as fluency: the knowledge and skill that remain when attention is elsewhere. Retrieval practice and regular review are therefore built into the curriculum so that students retain what they have learned and can use it flexibly in future mathematics.
Courses
All students follow the same core curriculum from Years 7 to 11, culminating in the Higher Tier Edexcel GCSE Mathematics qualification. As a selective grammar school, we believe all students should have access to the full breadth and challenge of the Higher Tier course. This ambition is reflected in student outcomes, with all students achieving at least Grade 4 and the overwhelming majority achieving significantly higher grades. Whilst Grade 4 represents the national standard pass, our ambition is for every student to achieve at least Grade 7.
Alongside GCSE Mathematics, approximately 60 students each year study the AQA Level 2 Certificate in Further Mathematics. This qualification provides additional challenge and introduces students to mathematical ideas that support progression to Advanced Level study.
In the Sixth Form, students may study either A-Level Mathematics or A-Level Further Mathematics. All students taking Further Mathematics also complete A-Level Mathematics. We follow the Edexcel specifications, with Further Mathematics students studying the Further Pure 1 and Further Pure 2 options.
Unlike many schools, Further Mathematics is taught as a discrete class rather than alongside an A-Level Mathematics teaching group. This allows us to sequence the curriculum specifically for Further Mathematics students, introduce key ideas at the optimal point and teach the two qualifications as one coherent programme.
Whilst the content of these qualifications is largely prescribed at A-Level, the way in which the curriculum is delivered at HGS is distinctive. We operate a booklet-based curriculum designed specifically for our students and their needs. Rather than following a textbook sequence, we carefully organise content to support long-term mathematical understanding and progression. For example, many pure topics are taught before applied units so that students have the mathematical foundations required to access the material successfully. We also prioritise key topics such as integration at an earlier stage due to their central importance across the A-Level curriculum.
In Further Mathematics, topics required for the TMUA are introduced early in the course to support students applying for mathematically demanding university courses. Carefully selected example problem pairs, DrFrost fluency practice, retrieval practice, and bespoke departmental resources combine to create a curriculum tailored to HGS students rather than one dictated by a published textbook.
A-Level Mathematics is the most popular subject at HGS, while A-Level Further Mathematics continues to grow in popularity. Outcomes at GCSE and A-Level are consistently exceptional and reflect both the ambition of the curriculum and the commitment of our students.
Results
All numbers given, unless otherwise stated, are percentages.
GCSE Maths
| year | 2022 | 2023 | 2024 | 2025 |
| 9 to 8 | 61 | 42 | 51 | 53 |
| 9 to 7 | 82 | 70 | 76 | 72 |
| 9 to 4 | 100 | 100 | 100 | 99 |
GCSE Further Maths
| year | 2025 |
| 9 to 8 | 80 |
| 9 to 7 | 95 |
| 9 to 6 | 100 |
A-Level Maths
| year | 2022 | 2023 | 2024 | 2025 |
| A*/A | 36 | 38 | 51 | 53 |
| A*-B | 64 | 48 | 64 | 69 |
| A*-E | 100 | 99 | 100 | 100 |
A-Level Further Maths
| year | 2023 | 2024 | 2025 | |||
| A*/A | 100 | 92 | 100 | 73 | 100 | 71 |
| A*-B | 100 | 100 | 100 | 91 | 100 | 100 |
| A*-E | 100 | 100 | 100 | 100 | 100 | 100 |
Assessment
Assessment is an integral part of teaching and learning in mathematics. We use different forms of assessment for different purposes and are careful not to conflate them. Formative assessment is used to inform teaching, while summative assessment provides an overview of what students have learned. Each assessment is designed with a clear purpose so that the information it provides can be used appropriately.
Formative assessment takes place continually in every lesson and is at the heart of our teaching. Through techniques such as deep probing cold-call questioning, mini-whiteboards, entrance tickets and short quizzes, teachers gain immediate insight into students’ understanding. This enables misconceptions to be identified quickly, teaching to be adapted in real time, and students to receive the support or challenge they need. Formative assessment is not an addition to teaching; it is a fundamental part of it.
Alongside this, students complete summative assessments at key points throughout the year. Unit assessments are administered only when students are ready, ensuring that assessment reflects secure learning rather than simple coverage of content. In Years 7 to 11, these include end-of-year assessments that draw on cumulative knowledge, reflecting the hierarchical nature of mathematics, as well as in-class assessments on recently studied units. In Years 12 and 13, the assessment programme aligns with the school’s wider assessment calendar. These assessments provide a broad picture of students’ attainment and progress, supporting reporting and enabling informed academic decisions.
Homework
Homework is a necessity for deep learning. To become successful mathematicians, students must consolidate their learning beyond the classroom. We set homework to strengthen retrieval, consolidate recently taught material and develop fluency. Learning is a permanent change in long-term memory, and carefully designed homework provides the thinking and practice needed to bring about that change.
In Years 7 to 11, students are set two homework tasks each week using the DrFrost platform. In Years 12 and 13, students are set homework after every lesson. As DrFrost does not provide comprehensive coverage of A-Level Mathematics, Sixth Form homework may consist of either DrFrost Key Skills tasks or carefully selected questions from the course textbook.
As the purpose of homework is to promote learning rather than simply complete tasks, students will often be assessed on homework content during subsequent lessons. These in-class checks enable teachers to verify understanding, reinforce retrieval and ensure that homework has achieved its intended purpose, regardless of how it was completed.
Enrichment
Our enrichment programme is designed to foster a lifelong appreciation of mathematics, expose students to ideas beyond the taught curriculum and inspire them to continue studying mathematics beyond school. Enrichment is not reserved for the most able; we believe every student should have the opportunity to engage with mathematics beyond the classroom.
The UKMT Maths Challenges are central to our enrichment programme. We encourage all students to participate, with entry numbers and success continuing to grow. Students regularly qualify for follow-on rounds, supported by weekly preparation sessions, classroom guidance and problem-solving activities using UKMT resources.
Beyond competitions, we maintain strong links with former students, local universities and industry. Students benefit from university visits, visiting speakers and opportunities to explore where mathematics can lead beyond school. The success of our enrichment programme is reflected in the high numbers of students choosing A-Level Mathematics and Further Mathematics, and in the significant proportion who go on to study mathematics and related subjects at university.
Staffing
Head of Maths – Mr G Dhillow
Second in Maths – Mr B Bansal
Associate Vice-Assistant to the Deputy Strategic Teaching and Learning Lead in Mathematics Curriculum, pedagogy and excellence – Mr P Alexander
Ms. P To
Ms. Sohal
Mr Mian
Mr Sangar
Ms. Lin Fellows
Mr Campbell
Mr Kafai
HGSMaths
Our mathematics website, HGSMaths.com, is a central part of the way we teach and learn mathematics. Rather than simply supporting lessons, it mirrors the curriculum taught in school, giving students access to almost everything they use in the classroom.
Every booklet used in lessons is available on the website alongside lesson resources, worked examples, practice questions, revision materials and enrichment activities. In effect, almost everything a student needs to succeed in mathematics can be found in one place. Whether a student has missed a lesson, wants to consolidate new learning, is preparing for an assessment or wishes to explore mathematics beyond the curriculum, they can quickly find the resources they need.
The website has been developed over many years and is exceptionally comprehensive. Every topic taught from Year 7 through to A Level and Further Mathematics is supported by a carefully organised collection of high-quality resources. Students can revisit previous learning, work independently outside the classroom and access additional practice whenever they need it. For many topics, the website contains far more material than could ever be covered in lessons alone, allowing students to deepen their understanding and challenge themselves at their own pace.
Students make extensive use of the website throughout their time in the department, and it is consistently praised by both students and parents for the breadth of its content, its organisation and the ease with which resources can be found. It has become an integral part of mathematics teaching and learning at the school, ensuring that every student has access to the support, practice and enrichment they need, whenever and wherever they choose to learn.