Mindful of the fact I had released the coursework I was prepared for the fact that attendance might jump this week and fill the room with students wanting to ask questions about the coursework material. However, if we don't introduce the concept of differentiation this week we will be running to catch up all through Calculus, which is a terrible place to lose them. My strategy was to go through this weeks material and field questions on the coursework afterwards.
3 students attended. The same 3 as last week.
Anyway, I had to get across to them what is going on when we differentiate a function. This is not a simple concept and involves ideas of infinitely small distances, etc. It is further complicated by the fact that knowledge of what happens in differentiation is not needed at all to get through the exam. We like to imagine that it is important for the students to have a look under the hood, as it were, and get some feel for what is really going on when they apply this ubiquitous technique. However, in the same way that we don't feel compelled to take a computer apart before we use one students outside of pure mathematics are not particularly keen to do so. Still, I know it is important to de-mystify the mathematics; understanding makes a technique better remembered. Also a sense of how differentiation works and what it does will be useful when we learn integration in a few weeks time.
The reality of the situation was that I was pretty ill and kept losing my place and having to refer to my notes. I found the situation fairly frustrating as I know this explanation quite well and had revised it prior to class. I tried to break down the derivation into manageable parts and take the students through it slowly and carefully. At the end I showed them the formula that is needed for differentiating any polynomial function. I realised up until then that they were thinking they would need to derive differentiation as a concept to answer every question, as this was what I had done so far. When they realised all they needed to do what apply a simple formula they became much more comfortable with the technique. Polynomial functions draw on the material from previous weeks and was back in the comfort zone. I really feel I could have done better here, and a clear head would have gone a fair way towards this.
I explained for a bit, they did some questions, then I took them through the next part on the board and they finished with some more questions. They left early, but the closest to 2 hours we have been so far.
