Hi, I'm Dr. Xin. I'm a private Maths and Science tutor in Manchester with 7 years of teaching experience, working with GCSE, A-Level and university level students. I hold a PhD in Materials Science and Engineering from the University of Manchester, and alongside GCSE and A-Level teaching I regularly teach university level mathematics, including calculus, linear algebra, probability, statistics, mechanics and mathematical modelling.

My approach is to find exactly where a student's understanding breaks down, often a specific gap in algebra, problem interpretation or exam technique rather than general difficulty with maths. I break problems down step by step, get students explaining their own thinking, and build exam technique alongside content, with personalised notes and homework between lessons.

This summer I'm taking on:

• Students who want to bridge the gap before September, moving up a year group or catching up on specific topics
• Students preparing for the Mathematical Challenge over the next couple of months
• University level students working through calculus, linear algebra, mechanics and related modules

I have taught students across a wide range of levels and exam boards, including GCSE, IGCSE, A-Level, Further Maths, university entrance preparation, and undergraduate mathematics modules.

My experience includes:

• GCSE & IGCSE Maths and Science
• A-Level Maths, Further Maths, Physics, and Mechanics
• University-level Mathematics and Engineering topics
• 11+ and secondary school entrance preparation

A large part of my teaching focuses on identifying exactly where a student’s understanding begins to break down. In many cases, the issue is not simply “difficulty with maths”, but specific gaps in reasoning, algebraic fluency, problem interpretation, or exam technique that gradually compound over time.

Because of this, I place a strong emphasis on targeted practice and carefully structured explanations tailored to each student individually. Rather than relying on repetitive drilling alone, I aim to help students recognise patterns, understand the logic behind methods, and develop the confidence to approach unfamiliar problems independently.

I also provide personalised lesson notes, homework, and detailed feedback outside lesson time where needed, so students can continue building understanding between lessons in a clear and organised way.

My teaching approach is highly adaptive and centred around how each student thinks and learns.

Rather than focusing purely on memorising methods, I try to help students understand the logic behind the mathematics. Once students begin to see patterns and connections clearly, difficult topics often become much less intimidating.

In lessons, I usually break problems down step by step and encourage students to explain their thinking aloud. This helps identify gaps in understanding early and builds genuine confidence over time.

I also place a strong emphasis on exam technique and problem-solving under pressure, especially for GCSE and A-Level students. Many students know more than they think they do — they simply need clearer structure, better habits, and more confidence in their own reasoning.

Above all, I want lessons to feel supportive rather than stressful. Mathematics is not something to fear, but a beautifully logical language waiting to be understood step by step.