I have just completed my second year at LSE studying Economics, in which I obtained a first. I achieved 3A*s at A Levels in Mathematics, Economics, Chemistry, and an A at AS Level in Further Mathematics and Biology. I get along easily with all types of people and can be extremely supportive and understanding, and love to help people feel a bit better about their learning! I would structure lessons for maths around the problem areas and gaps of knowledge for the student, structured with types of worked examples for each subtopic which can possibly be asked in the exam, and then encouraging the pupil to apply this to questions independently, with prompts when needed. I would encourage the pupil to challenge themselves, as this is what worked for me when learning Maths; prompting and proper explanation of methods allows a true understanding of how the maths really works, and allows the student to apply different techniques learnt in different areas of Maths.
Previously, I have tutored 4 students over summer holidays. All of them showed significant improvements in their understanding. I found what worked best is providing a brief summary of the topic, and then focusing on exam style questions ranging in difficulty to ensure that the student is ready for all types of questions.