In today's class I will be observed by another member of my PGCHE group.
Today's class is the first on integration, treating it as the reverse process to differentiation. I have been thinking a lot about this session since the introduction to differentiation class, in which I feel I failed quite dramatically to get over the deep concepts and the students went away with a toolbox they don't understand. I do not know if this is a problem. People use computers but have no idea how they work; similarly cars. Does it matter if I give someone a mathematical tool to apply to scientific problems in their area and they don't understand how that tool is derived? From the notes I have been given to teach from there are several areas where a rule or technique is derived and I have generally skipped over this as they do not need to know the mathematical proof in order to apply the technique. But we feel Calculus is an area where the application requires some understanding of the deep meaning.
So I will be trying to get across concepts of infinity. I will do this using Xeno's paradox of Achilles and the tortoise and a bouncing ball, which I have been carrying in my pocket and occasionally bouncing for just this purpose for the last few weeks.
