This paper discusses recent research on cognition and its implications for mathematics education. Learning as a generative process, structural organization, processing of information, processes and structures, individual differences, brain research, higher-order processes, motivation, and delay-retention effects are discussed. (MS)

A special topics elective course is described. The rationale and organization are discussed and examples of course content and student achievement are presented. (MP)

An approach is presented that is based on modifying the standard axiomatic system found in high school geometry books. Such changes start with the introduction of a side-angle-side (SAS) postulate for similar triangles. It is shown how the new system can prove existence and uniqueness of parallel lines. (MP)

The first idea discusses the use of Pascal's triangle to discover the total number of gifts presented during the 12 days of Christmas. The second idea looks at an approach to viewing L'Hospital's rule that is geared toward helping beginning calculus students develop a feeling as to why it works. (MP)

An exploration approach with calculators that promotes student investigation and development of mathematical processes and concepts is highlighted. The presentation helps to highlight the enormous potential of calculators to facilitate new and imaginative approaches to certain areas of number work, and shows how student interest is promoted. (MP)

It is viewed understandable that many teachers consider fractions one of the most difficult mathematical topics to teach. School experiences need careful planning to include sequential activities which develop accurate concepts, and concepts are thought best developed by activities which move along the concrete-to-abstract continuum. (MP)

An approach to teaching geometry is promoted that allows students to decide for themselves what they could prove from given information. Such an approach allows pupil involvement in the personal process of discovering mathematical ideas and formulating problems. It is noted these methods will not work for all. (MP)

The unmarked protractor appears to have been ignored in considerations of construction tools other than the standard straightedge and compass. Some geometric problems are presented which are designed to be done using only the unmarked protractor. They are thought to provide challenges to better students. (MP)