Back when I was an undergrad, the maths classes I attended could be broadly classified into two types – general and small classes. The latter are mainly algebra and topology classes which attract an enrolment of less than 15. The former are large classes, usually essential modules or courses that are thought to be easy. I never had much problem with those large classes. The reason being I was among the top end of the cohort and the lecturer needed to “dumb down” in order to cater to everybody. Even Lebesgue integration was never too intimidating. On the other hand, I had a lot of trouble with the group theory and topology and I often wondered during those days why I signed up.
In those big classes, there was one particular lecturer who was very well liked in general and always won awards. I didn’t like him because I felt he was “playing” to the audience, dumbing down too much, oversimplifying and very hand-holding.
Fast forward to the present. As a lecturer, I have this dilemma. The class is huge and the ability of the students diverse. As much as I want to teach rigourously, I find myself guilty of “dumbing down”, to the extent that one particular student commented that I should be replaced. Retribution, I guess. I’m still not sure how to find the right balance, considering that only 10% of the cohort may eventually end up graduating as math majors. How do you teach rigour without at the same time putting off the rest of the 90%, or worse still, extending the bad impression that they may have about mathematics.