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)

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)

Argues that not just composition teachers, but all faculty members have the responsibility to encourage good student writing by stressing the importance of effective writing in their own fields. (MM)

Research shows that hands-on science education is more effective than a textbook and lecture approach. This suggests that the "new curriculum" introduced in science classes in the seventies was more effective than was thought. (JM)

Alternative identification and instructional procedures are discussed. Instructors are warned against assuming an equivalence between the quantity of mathematical work a child demonstrates and the quality of that child's thinking. A need to integrate qualitative information is seen. Two types of activities for gifted pupils are detailed. (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)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

Several methods of numerical mappings other than the usual cartesian coordinate system are considered. Some examples using parallel axes representation, which are seen to lead to aesthetically pleasing or interesting configurations, are presented. Exercises with alternative representations can stimulate pupil imagination and exploration in…

LOGO (a computer language) is designed to provide an environment in which learners determine a problem to solve, make choices, experiment, try out solutions, and build on what they already know. Student activities using LOGO and the teacher's role in a LOGO classroom are discussed. (JN)

Results of two studies using the Esper paradigm to determine development of rule application and discovery are reported. Subjects learned and generalized when rule and structure were provided, but there was little evidence of rule discovery. Manipulations of memory and attention facilitated learning, but only attention facilitated rule discovery.…

Discusses the need for a sustained and systematic effort toward establishing a theoretical framework for educational simulations, proposes the adaptation of models borrowed from the natural and applied sciences, and describes three simulations based on such a model adapted using Brunerian learning theory. Sixteen references are listed. (LLS)

The teacher's role in promoting student creativity is that of risk-taker and facilitator. As a risk-taker, the teacher is a fellow learner in the search for knowledge. As a facilitator, the teacher provides the opportunity and the environment within which creative thinking flourishes. (SK)

Investigates the exploratory behavior of young children as it relates to individual differences in curiosity, the novelty of the objects explored, and the interactive style employed by an adult experimenter. (Author/MP)

Worksheets designed to aid in the instruction of graphing on the Cartesian coordinate system are presented. Finding areas and perimeters of polygons the pupils graph are the intended lesson topics. (MP)

An outline model of a student-presented mathematics club program on non-Euclidean geometries is discussed. The suggested instructor approach is to assign four students to research and collectively present this material to club members. (MP)