I am happy to teach mathematics at all levels, including 11+, Key Stage 3, GCSE, A Level and later professional mathematics related topics such as actuarial exams.

Learn more about Fei

• When did you develop an interest in your chosen field and in private tutoring?

  My interest in mathematics began during my school years. I was attracted to the clarity of the subject: an answer is not simply a matter of opinion; it can be tested, justified and proved. As I progressed, I became increasingly interested in how mathematical ideas connect. A relatively simple equation, graph or probability model can reveal a much deeper structure.
  
  This interest eventually led me to complete both an MSc and a PhD in Actuarial Mathematics and then qualify as a UK actuary. Actuarial mathematics was particularly appealing because it combines theoretical mathematics with real-world uncertainty, finance, risk and decision-making. During my PhD, I also taught undergraduate statistics, which gave me some of my earliest formal teaching experience.
  
  My journey into private tutoring developed more gradually. Around 2016, I began helping my elder daughter prepare for the 11+ examinations. I later supported my younger daughter in the same way. Teaching my own children showed me that knowing mathematics and teaching mathematics are two different skills. A tutor must understand how the student is thinking, where the misunderstanding begins and how to explain an idea in a way that makes sense to that particular learner.
  
  From 2023, I began teaching other students more extensively, and tutoring eventually became my full-time profession. I have now worked with more than 100 students and currently support over 60 regular students in the UK and internationally.

• Tell us more about the subject you teach, the topics you like to discuss with students—and possibly those you like a little less.

  I teach mathematics across a very wide range of levels, from primary-school arithmetic and entrance examinations to GCSE, IGCSE, A Level, Further Mathematics, IB Mathematics and university admissions tests such as TMUA, ESAT, MAT and STEP.
  
  One reason I enjoy mathematics is that it is not really a collection of unrelated topics. Algebra supports coordinate geometry; functions lead naturally into calculus; trigonometry connects geometry and algebra; probability develops into statistics and mathematical modelling. I enjoy helping students see these relationships.
  
  I particularly like teaching algebra, functions, quadratics, calculus, probability and statistics. Algebra is especially important because it is the language underlying so much of secondary and advanced mathematics. Calculus is fascinating because it allows us to describe change, motion, growth and optimisation. Probability and statistics are also close to my actuarial background, and they provide excellent opportunities to discuss how mathematics is used to make decisions under uncertainty.
  
  I also enjoy unfamiliar problem-solving questions and mathematical competition problems. These encourage students to experiment, recognise patterns and construct arguments instead of immediately searching for a memorised formula.
  
  I would not say that I dislike any particular topic. However, I am less enthusiastic when mathematics is presented as a list of mechanical procedures without explanation. Repetitive calculation is sometimes necessary—it builds fluency, accuracy and confidence—but it should be a foundation for mathematical thinking rather than a replacement for it. My aim is for students to understand not only what to do, but why the method works and how to recognise when it should be used.

• Did you have any role models or a teacher who inspired you?

  Rather than identifying one single role model, I would say that I was influenced by several teachers and lecturers at different stages of my education.
  
  The most inspiring teachers were not necessarily those who demonstrated the most advanced mathematics. They were the people who could take a difficult idea, identify its essential structure and explain it clearly. They showed that genuine mathematical ability is not about making a subject look complicated. It is about making complicated ideas understandable without removing their depth.
  
  I was also influenced by teachers who cared about the reasoning behind an answer. They did not simply ask, “What is the answer?” They wanted to know, “Why is this true?”, “Can you justify it?” and “Is there another way to approach the problem?” Those questions have strongly influenced my own teaching.
  
  My academic and actuarial training also provided important role models. Mathematics at that level requires patience, intellectual honesty and a willingness to check one’s assumptions. A strong mathematician must be prepared to discover that an initial approach is wrong and then start again.
  
  Interestingly, my students have also become a source of inspiration. Students regularly find alternative methods or ask questions that make me examine a familiar topic from a new perspective. Teaching reminds me that mathematics is not simply knowledge passed from tutor to student; it is often a shared process of investigation.

• What qualities are required to be a good tutor?

  Strong subject knowledge is essential, but it is only the starting point. A tutor may understand a subject perfectly and still struggle to communicate it effectively.
  
  A good tutor first needs to be observant. Two students can produce the same incorrect answer for entirely different reasons. One may have misunderstood the concept, another may have made an arithmetic error, and a third may have misread the question. The tutor must diagnose the cause instead of simply correcting the final answer.
  
  Patience is equally important. Students need to feel safe enough to make mistakes and ask questions. At the same time, patience does not mean lowering expectations. A good tutor should be encouraging while still expecting careful reasoning, accurate work and genuine effort.
  
  Adaptability is another essential quality. Some students respond well to diagrams and visual explanations; others prefer algebraic arguments, worked examples or practical applications. An explanation that works for one student may not work for another.
  
  I also believe that a good tutor should be structured and consistent. Lessons should form part of a coherent learning plan. Homework should be purposeful, completed by hand where appropriate, marked carefully and followed by constructive feedback. Progress comes from a continuous cycle of explanation, practice, feedback and correction.
  
  Finally, a tutor should aim to make the student increasingly independent. The goal is not for the student to rely permanently on the tutor. It is to help the student develop the confidence and judgement to choose methods, identify errors and solve unfamiliar problems independently.

• Provide a valuable anecdote related to your subject or your days at school.

  One of the most valuable lessons in my teaching career came not from a formal classroom but from helping my elder daughter prepare for the 11+.
  
  At first, I sometimes assumed that if she could follow my explanation and complete a question with guidance, she had mastered the topic. However, when she encountered a similar problem independently later, it could still feel completely unfamiliar. I realised that understanding an explanation during a lesson is not the same as being able to reproduce the reasoning independently.
  
  That experience changed my approach to tutoring. I began to separate learning into stages. First, I explain and model the idea. Next, the student completes a similar question with some guidance. Finally, the student attempts new questions independently and writes out the full reasoning. Only at that final stage can we properly judge whether the knowledge has become secure.
  
  This is why I place considerable importance on handwritten homework, marking and feedback. A student saying “I understand” is encouraging, but independent written work provides much stronger evidence. Mistakes are not simply failures; they are information. They show us exactly what needs to be revisited.
  
  The experience also taught me that the clearest explanation is not always the most sophisticated one. A tutor must begin from where the student is, not from where the tutor wishes the student to be.

• What difficulties or challenges have you faced, or do you still face, in your subject?

  One of the central challenges in mathematics is the transition from concrete calculation to abstract reasoning. At an early level, students work with visible quantities and familiar operations. Later, they encounter algebraic symbols, functions, proofs, limits and models of uncertainty. The mathematics becomes more powerful, but also less immediately tangible.
  
  In my own advanced study of actuarial mathematics, an important challenge was learning to balance theory with application. A mathematical model can be elegant, but a real-world problem may involve incomplete information, uncertain assumptions and practical limitations. This taught me to ask not only whether a calculation is correct, but also whether the model and assumptions are appropriate.
  
  As a tutor, the continuing challenge is that every student is different. Some have significant knowledge gaps; some understand the theory but struggle with exam questions; others calculate accurately but find unfamiliar problems difficult. Some students have strong mathematical ability but lack confidence, while international students may understand the mathematics yet struggle with the language of worded questions.
  
  There is also a constant balance between covering the curriculum and developing genuine understanding. Examination deadlines are real, but moving too quickly can leave weaknesses that create greater difficulties later.
  
  These challenges are part of what makes tutoring rewarding. Mathematics may be fixed, but the best way to communicate it is never completely fixed. I am continually refining explanations, examples, questions and feedback to meet the needs of individual students.

• Do you have a particular passion? Is it teaching in general, an element of the subject or something completely different?

  My main passion is helping people see mathematics as a connected and logical subject rather than a collection of formulas to memorise.
  
  I particularly enjoy the moment when a student moves from saying, “I know which formula to use,” to saying, “I understand why this works.” That change is important because it gives the student knowledge that can be transferred to unfamiliar problems.
  
  I am also passionate about mathematical communication. A solution should not only be correct; it should be organised, readable and logically justified. This is especially important in examinations, university admissions tests and more advanced mathematics, where the quality of reasoning matters as much as the final result.
  
  Another passion is creating structured learning materials. I enjoy analysing a student’s work, identifying recurring weaknesses and designing questions that address those weaknesses progressively. Good practice should not be a random collection of exercises. It should have a purpose: developing a particular skill, correcting a misconception or preparing the student for the next stage.
  
  More broadly, I enjoy exploring the stories and ideas behind mathematics. Concepts such as zero, infinity, probability and mathematical proof have rich historical and philosophical dimensions. These discussions can help students appreciate that mathematics is a living intellectual subject, not merely an examination requirement.

• What makes you a Superprof—besides answering these interview questions?

  I bring together three different perspectives: that of a mathematician, a qualified actuary and an experienced private tutor.
  
  My MSc and PhD in Actuarial Mathematics provide a strong academic foundation, while my experience as a UK-qualified actuary allows me to show how mathematics is applied to real decisions involving finance, risk and uncertainty. Teaching undergraduate statistics during my doctoral studies gave me experience of explaining advanced ideas, and private tutoring has taught me how to adapt those explanations to students of very different ages and abilities.
  
  I have supported more than 100 students across a wide range of curricula and examinations, from primary entrance tests to GCSE, A Level, Further Mathematics, IB and university admissions. Nevertheless, I do not believe that experience should lead to a one-size-fits-all approach. Every new student begins with an assessment of current understanding, learning habits, goals and knowledge gaps.
  
  I also provide more than the lesson itself. I set purposeful work, review handwritten solutions, give constructive feedback and monitor progress over time. I want students and parents to understand what is going well, what needs attention and what the next steps should be.
  
  Most importantly, I combine high expectations with patience. I want my students to achieve strong results, but also to become more accurate, confident and independent mathematical thinkers. If that combination makes me a Superprof, I am very happy to accept the title!