Although, I do not have formal teaching qualification and I only started offering private tuition at the beginning of 2015, I have tutored a range of tutees from Common Entrance Exam level to adult learner including teenage CGSE students for both Mathematics and Statistics. However, my casual "teaching" roles go back to 1973, post graduation. I taught maths to several children of friends as well as adult friends and colleagues need to obtain better qualification. My research positions included teaching / lecturing roles at all levels from work experience pupils up to senior clinicians as well as giving guest lectures on B Sc and M Sc courses in physiology. I found particular pleasure explaining to children and parents the purpose of the tests / research and the "mathematics" behind the analysis and interpretation of the results. In my own time, I helped several long term inpatients with school work in science and others with projects related to the maths and biology of their respiratory problems.
As George Orwell never said “All tutees are not the same but some are more different than others”. I have a variety of approaches, depending on factors such as (i) whether the tutee needs teaching or revision; (ii) the number of lessons they can fit in before the exam; (iii) their strengths and weaknesses as well as their interests; (iv) the length of the sessions 45-90 mins and (v) the work they are willing / keen to do between sessions. However, there are aspects that are common to all tutees; I spend as long as necessary to clarify import issue such as (i) which board, level and paper they will be sitting; (ii) the text book they use and which parts of the syllabus have been covered and whether any need revising or explaining and (iii) wherever possible, obtaining suggestions and feedback from their teachers including where marks had been lost in recent exams.
Other aspects of my approach include (i) the tutee attempting appropriate questions / papers from other boards to make them “think outside the box” and be more prepared for questions that do not fit the usual mode; (ii) e-mailing questions or papers in advance of session to allow adequate time for preparation; (iii) feeding back how sessions have gone and suggestions for change either after the session and / or by e-mail; (iv) moving up and down the difficulty ladder depending on the progress; (v) working on exam technique and teaching how to not misinterpret questions, sometimes, badly written; (vi) offering to prepare for difficult topics in advance to ensure the tutee gets the most out of upcoming school lessons and (vii) using examples from everyday life to demonstrate the use and usefulness of maths and statistics in everyday life.
Additionally, I make extensive use of marking schemes and examiners reports to discuss how the tutee may have obtained the correct answer but lost marks or lost time by providing too much details and this has been very successful and interesting for the tutees.