What separates me from a good tutor is what's beyond the standard teaching approach of explaining theory and attempting problems. The techniques I've accumulated over the years, as a student and as a tutor, may sound simple but make a great deal of difference if applied correctly and consistently. Here are a few of those techniques that have proven successful in previous students, and a description of what my lessons are like.

Ask leading questions; allow the student to do the work themselves. When they get stuck, don't save them, but rather, give them a leg up and allow them to make the connection themselves (as they would do when stuck in an exam). For example, what integration techniques have you been equipped with so far that may fit here? Write down all the formulas you can recall on this topic, which of these apply to the question at hand? Write down the information you're giving in an algebraic form, does the question seem less daunting now? Do you recall the simpler derivation of a complicated formula? Or even as simple as asking what the student is thinking when they get stuck, encouraging them to verbalise their thought process which also bolsters their self-reflection, and reinforces their ability to be creative in their solution.

Throw in critical questions; even when they have the right answer, throw them off so they don't think you only ask such leading questions to correct them, but rather, to encourage them to naturally be critical of their own solution. For example, under what conditions does this assumption not hold? Are your solutions exhaustive? Or even asking the student to justify why their answer, is right whether it is or isn't, allowing them to recognise their own mistakes when they're wrong, and rigorously defend their solutions when they're right.

Encourage mathematical fluency; develop a general understanding of concepts rather than just surface-level memorisation of solutions for specific types of questions, without any real comprehension of why a method works or how to extend it to slightly different questions. This can be done by throwing in small custom questions to fill in gaps of knowledge before proper complete questions, visualising concepts, deriving concepts from first principles, providing an overarching intuitive explanation, suggesting alternative methodologies, and so on.

How to prepare for exams. Timed past papers under exam conditions, so the real deal is not the first time you're subjected to such high-pressure conditions. How to utilise short-term and long-term memory. What to brute-force memorise and what to deeply understand to efficiently designate your revision resources. How to design and implement a revision plan, including how to conservatively estimate how long different topics will take to revise for each student so that we're left with sufficient time before exams to be ready in the event of unforeseen complications.

And finally, good protocols in an exam. For example, how to interpret what examiners are looking for, how to pick up extra marks when you're completely lost, how to pace yourself and when to cut your losses and pick up marks elsewhere.

These are all factors I constantly consider during my time with students, both for individual lessons as well as over an extended study program.