Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

A generalization of a well-known result for the arctangent function poses a number of interesting questions concerning the existence of integer solutions of related problems.

The concept of school curriculum in science and mathematics is discussed and related to the structures of the disciplines and theory developments. Recent epistemological studies on theory dynamics (Kuhn, Sneed) are put into context with the understanding of learning processes. (Author/MK)

A simple enumeration problem from some research on problem solving is used to illustrate the contention that conjecture and proof have a central place in mathematics teaching. (Author/TG)