April 5, 2005: Learning Goals - Summary

Matt Rissler gave a sample lecture on 'Related Rates' and did several problems involving geometry.

Suggestions:

• Make sure to carefully explain steps in unfamiliar operations such as implicit differentiation.
• To write down everything that you say. In particular, make sure that the notes presented on the board offer a complete explanation of the topic being presented.
• Offer justification for the name of the topic, which, in this case, was related rates.
• Don't do just one type of problem. In this case it was suggested that a non-geometric related problem should be presented.
• Offer an explanation of what the answer actually means in relation to the physical situation being modeled.

Chris Porter gave a sample lecture on 'Convergence of Infinite Series'.

There was a brief discussion on the merits of offering justification of the mathematical formulas being given if the justification would involve relatively advanced mathematical ideas. It was generally agreed that only a brief justification would be helpful to the students.

Prof. Qing Han said that graduate students tended to be good lecturers and so younger graduate students should ask older ones for advice on teaching.

(reported by Marc MacGonagle)