Arush Panwalkar

The aim of my lessons is to emphasise derivation, proof and logic to arrive at the theorems and formulae provided, rather than simply stating them and using them for the purposes of computation. Arriving at intuitive arguments, however, is not a skill I would ever pass up on, as it allowed me and many of my peers to understand topics like combinatorics, for which much of the formal proof actually required extensive computation.

Once informed of a particular topic for a lesson to be dedicated to, my first instinct as a tutor would be to look at small cases of the topic to develop an intuition, before attempting to construct either a logical or intuitive argument for the general case. Derivations would be done almost in full, but without straying into topics which are beyond the scope of the syllabus, unless they greatly assist with improving the student's understanding of the topic at hand. Finally, a few practice problems would be employed which would vary in difficulty; one of the most important methods of improving problem solving is to solve problems which are substantially more difficult than those found on the papers—for example, solving questions from STEP or TMUA can massively assist with problem solving in further maths or normal A-level maths respectively.

The most important thing I would encourage students to do is to consume mathematics for fun. Watch mathematics videos, read mathematics books, join mathematics problem-solving clubs, et cetera. Engaging with mathematical content will always improve one's own problem solving skills, and could even stifle a mathematics phobia!