What are the common mistakes and misconceptions students make in a first year calculus course?
What can I do to prevent/rectify them?
Context: Soon I will be doing some calculus lecturing. As this is the first time I've been entrusted with this responsibility, I've been thinking a lot about what I can do beyond regurgitating the material. I've had some experience doing tutorials (I imagine this would be equivalent to what a T.A. does in the U.S.) but lecturing is different as I will be introducing the material as opposed to reinforcing it. Obviously becoming a good (or even average) lecturer takes time and experience, and can not be obtained via a single answer to any question I could possibly ask here. Instead, I chose to ask the questions above.
I asked the first question because I don't think I can accurately answer it myself until I've taught the course at least once - I'd rather be able to address these issues the first time around. The second question is more general. There are many well-known mistakes students make when first learning mathematics, but they are well-known because they occur frequently and continue to do so over time. The fact that these mistakes/misconceptions continue to occur means that these particular issues haven't been resolved.
The topics that will be covered in the course are:
- Differential Equations (separable, linear second order constant coefficients)
- Applications of Calculus (volume of revolution)
- Limits (not including $\epsilon - \delta$ definition)
- Taylor Series
I know that this post may be too general/not suitable for this site. If this is the case, I apologise.