In traditional advanced mathematics lectures the instructor usually provides definitions, theorems, and proofs on the board rather quickly. The students often cannot make sense of these during the lecture as they are busy writing. In order to gain an understanding of the content, an intensive post-class processing on the basis of their notes would…

This case study investigates the effectiveness of a lecture in advanced mathematics. We video recorded a lecture delivered by an experienced professor. Using video recall, we then interviewed the professor to determine the content he intended to convey and we analyzed his lecture to see if and how this content was conveyed. We also interviewed six…

This study aims to evaluate the consistency of teaching content with teaching approaches in calculus on the basis of lecturers' views. In this sense, the structures of the examples given in two commonly used calculus textbooks, both in traditional and reform classrooms, are compared. The content analysis findings show that the examples in both…

The purpose of this study was to investigate how intelligent tutoring system ALEKS, which was implemented in remedial Basic Algebra courses, affected students' success in subsequent lecture courses and how former ALEKS students and instructors in lecture courses perceived ALEKS learning environment. ALEKS courses were delivered in emporium style:…

The author became aware that there are hundreds of retired teachers in the community who want to continue to learn, or at least to have their intellect stimulated. Some join clubs or read books or do crosswords or even surf the net when they retire, but these folks wanted to be stimulated with some mathematics. The author was initially surprised…

According to "Standards of Excellence in Teaching Mathematics in Australian Schools," excellent teachers of mathematics need to create "an environment that maximises students' learning opportunities"; so that they can encourage self-directed learning, "model mathematical thinking and reasoning," and provide…