An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (MP)

An example of a lesson involving calculators that focused on calculator use is given. An examination of the traditional algorithm by the students led to student-directed investigations. (MP)

Describes activities in a mathematics class for six-year-olds. The article makes several points, including: working independently is very absorbing; investigative work is as important as algorithms; and children working in groups can achieve more than even the brightest child working alone. (PK)

Alternative algorithms, "tricks," and shortcuts are viewed as ideally suited for inclusion in a systematic program of practice because of their motivational effect and the mental stimulation involved in discovering why they work. (MP)

Suggestions are given for having students write or modify computer programs for listing prime positive integers and continued fractions, to help them discover mathematical concepts. Sample programs are included. (MNS)

Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability…