I identify what drives the individual, asking what their hobbies and goals are. I then relate the mathematical content of the subject, and if disposed, some of the funnier bits of mathematics to engage their interest in a subject classically seen as dispassionate and dull.

Once their motivation increases, I cover the syllabus at a speed suitable to them. I take the 70/30 approach, of 70% doing and 30% reading at every stage in order to learn and affirm their knowledge and understanding.
Honesty is a tutor's greatest asset, allowing us to determine the students strengths and areas to work more upon. I engender a non-judgemental, supportive and confidence building atmosphere to allow the student to shine and ask for more support where it is needed.

Through this approach of appealing to their passions and providing a confidence boosting space, I have successfully engaged and improved the scores of students, from year 8's to university level mathematicians.

In addition to the core syllabus, maths must be fun and interesting. I encourage students to seek out odd examples of maths applied every day (once prompting an unruly year 10 to investigate mortality statistics in her own time, after she asked a joking question) and to go beyond the rigmarole of learning, into the expanse of exploration that culminates into a real drive for success.

For individual lessons this entails a debrief of last week's work, introducing the new content through related or relatable concepts, working through several questions together and then setting them some work for the lesson. The last ten minutes are to talk about the fun side of maths, encouraging them to research odd or intriguing questions in their own time while leaving a positive psychological marker at the end of every lesson, impressing that joy can be found within numbers. Homework will then reinforce the learned topic and covered at the next lesson in order to identify strengths and weaknesses in their understanding and in the approach taken to teach it so far.