Discusses two students' discovery that both of their answers to a computation for E in a chemical reaction in electrochemistry were correct, that there was not a unique answer, and that the textbook had presented only one of the possible answers to the problem. (MKR)

Pullout pages provide suggestions for teaching elementary students at all levels about the wonders of human ingenuity. The suggestions help students see that great ideas come from the need to solve real-life problems and that one great idea leads to another, so current inventions help predict future inventions. (SM)

Three worksheets are provided to help secondary students explore relationships among the areas of a variety of similar figures constructed on the sides of right triangles. The activity is extended to include the relationship among the lengths of the sides of the right triangle. Included are several student worksheets. (DC)

A one-to-one teaching session with a student is described and analyzed in an attempt to communicate how student attempts at discovery in mathematics can be thwarted by teachers who do not allow room for creativity. (MP)

The ecological issues of pollution, overpopulation, and conservation can be explained in the classroom through the use of creative play, problem solving, and discovery methods among groups of young children. Activities for teaching the topics of air, water, land, and noise pollution; overpopulation; and conservation are suggested. (DG)

A problem-solving approach is developed for secondary or college students to estimate the number of piano tuners in a large city. The answer and method are analyzed for appropriateness. Four similar problems are suggested. (DC)

Describes an extended investigation of polygons and polyhedra which was conducted in response to a challenge posed in Focus, a newsletter from the Mathematical Association of America (MAA). Students were challenged to construct a polyhedron with faces that measure more than 13 inches to a side. Outlines the process, including the questions posed…

A new core curriculum at Newmann College (Pennsylvania) aims to provide liberal learning through cross-disciplinary instruction without destroying the identity of specific content areas. The Collaborative Probing Model (CPM) provides a basis for the kind of creative self-control that will lead to flexible work within and between disciplines. This…

Describes grade-appropriate weekly activities designed to appeal directly to students by giving them open-ended questions. Activities may be worked on individually, in pairs, or in small groups. This particular set of activities focuses on stories from literature involving measurement, earning money, marketing a product, and setting up a…

A mult tile is a set of polygons each of which can be dissected into smaller polygons similar to the original set of polygons. Using a recursive LOGO method that requires solutions to various geometry and trigonometry problems, dissections of mult tiles are carried out repeatedly to produce tile patterns. (MDH)

A mathematics teacher shares a family discussion about Pythagorean triples as her child discovers new ideas about generating a triple. This idea can be useful for introducing students to the Pythagorean theorem. Observes that middle school students tend not to share creative insights in spite of supportive families and teachers. Presents…

Presents an alternate form of assignment, called "Special Problems," that incorporates writing in journals into the mathematics classroom. The method requires students to provide process narratives to accompany selected homework exercises. Allows the teacher to monitor the student's thought processes and development. (MDH)

Reports on a pilot study that examined use by sixth-grade students in Costa Rica of a mathematical microworld written in LOGO. The investigation had three phases: (1) open exploration of the microworld; (2) group discussion and sharing of hypotheses; and (3) guided discovery and problem solving. (Contains 11 references.) (SLW)

The Invent America program addresses the need to provide K-8 students with opportunities to learn critical and creative thinking skills through the process of inventing. Students apply problem-solving skills as they turn their own creative ideas into inventions. It is an effort to integrate the curriculum, help students synthesize knowledge, and…

This review features new examples of using the computer relative to college-level mathematics to enhance pedagogy, solve problems, and model real-life situations. Included is a LOGO program that can be used to create and to stimulate subsequent investigations of spirolaterals, those figures generated by repeatedly drawing basic loops. (JJK)