Observation

Hey guys, today I got to observe James' lesson with his student Otis. During the lesson, James worked with Otis on differentiating and integrating inverse trigonometric functions, as well as using the reverse chain rule to integrate trigonometric functions. James used this lesson to focus on what the formulas were and how to identify when to use each formula is applicable (ie when to use reverse chain rule and when to use trigonometric identities to simplify the integrals).

James began by looking over the derivative and integral formulas for inverse trigonometric functions, including inverse sin(x/a), inverse cos(x/a), and inverse tan(x/a). He explained how these formulas apply to different expressions and demonstrated the steps he needed to undertake to complete the textbook examples. The lesson then moved on to integration using the reverse chain rule. James showed how to recognise whether a function came from the derivative of a chain rule or whether the function was an expansion of a trigonometric identity (ie sin2x or cos2x). He worked through examples involving different functions, explaining in which circumstances Otis would prefer simplifying the trigonometric identity over trying to break the integral.

Through out the lesson, James encourages Otis to work on these questions. Having already been accelerated to complete Maths Advanced the year before, this aided in his understanding of how the derivates and integrals work, specifically the reverse chain rule integrals. Through the questions, Otis was able to express his understanding of this, being able to complete more difficult questions as the lesson went on. This reinforced the application of the formulas in completing the integrals.

Overall, the lesson was enjoyable to observe. James explained the concepts clearly, used worked examples effectively, and provided Otis with opportunities to apply techniques that he had learnt from Advanced Maths to complete the questions. Great work James!