Valio Ivanov

Above all, a true mastery of a topic in Maths is rooted in a concrete understanding of the fundamentals and theory behind it. I believe this aspect of the subject is placed at a lesser emphasis at a school level and while excessive rigour is unnecessary, many students are often puzzled on why they learn a topic in the first place. At the beginning of a lesson I would place a short emphasis on this to make sure that the student is comfortable with the ideas of the material that they're studying and if not, clear up any gaps in knowledge or common misconceptions. By doing this, I believe that it sparks a greater interest to continue learning a topic and explore its applications.

If there are any other particular topics or specific questions that a student feels unsure on, I would emphasise crystallising these ideas and perhaps offering different angles, perspectives or visualisations of an already familiar problem as everyone has a different form of presentation that lets them see certain ideas more clearly. I would be sure to provide plenty of examples along the way and where appropriate comment on any interesting remarks or real world applications as that is how I would say I feel most engaged myself. The key in all of this is back and forth communication that helps the student better engage with the subject as opposed to passively taking or reading over notes in class.

Finally, I would look at a few particular and hand selected problems that I feel are most appropriate regarding the topic and see if we can hopefully apply our discussion to some standard or perhaps occasionally more advanced exam style questions. Along the way I would be sure to point potential errors, identify neater methods and generally discuss a model answer in accordance with an exam board mark scheme. Finally at the end of the session, I would be happy to provide any further resources, videos or practise questions that might be of interest.