Discusses the rationale and use of problem fields which are sets of related and/or connected open-ended problem-solving tasks within mathematics instruction. Polygons with matchsticks and the number triangle are two examples of problem fields presented along with variations in conditions that promote other matchstick puzzles. (11 references) (JJK)

Indicates that utilizing calculators to introduce algebraic concepts in a prealgebra course provides students with a solid foundation for the study of college mathematics. Pedagogical criteria emphasized the difference between exact and approximate results, appropriate use of the calculator in problem solving, the role of estimation in…

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Presents three stories from mathematics history that can be integrated into classroom teaching: (1) the account of how Eratosthenes measured the circumference of the earth to discuss the concept of units in measurement, (2) ideas from Archimedes, Vite, and Descartes to introduce pi, and (3) the discovery of the Cardanic formula as an example of…

Discusses historian Henry Adams' disillusionment with the educational system and with his own teaching. Suggests improving history instruction by involving students more actively in learning. Proposes incorporating interactive learning strategies including (1) interactive lectures; (2) questioning; (3) small groups; (4) critical thinking and…

Discussion of technological innovations in education focuses on the potentials of the microcomputer as a classroom instructional method. Programing, computer literacy, software applications, and problem solving are suggested as ways to incorporate computers into the curriculum, and examples of applications of computers in elementary and secondary…

The "Thinking Actively in a Social Context" (TASC) project, currently underway with African-American high school pupils and teachers in KwaZulu/Natal schools (South Africa), stresses the systematic development of thinking and problem-solving skills. The program has been very successful with relatively high achieving students but requires…

Discusses instructional uses for the "Carmen Sandiego" software series to encourage interest in geography. Suggests "Carmen" be incorporated into the curriculum by teacher-directed grouping that adds teacher instruction into cooperative and competitive arenas, curriculum integration linking diverse specialties, and isolated…

Instructional strategies are presented that illustrate ways of developing students' understanding of nonnumerical notation that are compatible with a constructivist stance. The concepts of using letters to represent a range of values and those used to represent unknowns are discussed. (KR)

Discusses the limitations in the explain-practice and active learning methods of teaching mathematics. Proposes that problem-centered learning is a teaching method that encourages student reflection, and presents examples demonstrating that encouraging reflection results in greater mathematics achievement. (MDH)

Presents two teaching ideas. The first helps students identify and correct their own mistakes. A checklist of common mistakes is filled out by students after quizzes and tests and examined for error patterns. The second develops the formula to determine the payments necessary to pay off a loan over a required period of time. (MDH)

Proposes a novel method of introducing and promoting the topic of geometric sequences through the problem of calculating the number of games necessary to determine the winner of a single elimination tournament in which two, three, or more teams compete at a time. (MDH)

The Patient-Oriented Problem-Solving System, a cooperative learning model, was implemented in a second year immunology course at the Oregon Health Sciences University School of Dentistry, to correlate basic and clinical sciences information about Acquired Immune Deficiency Syndrome. Student enthusiasm and learning were substantial. (MSE)

This article discusses empowering thinking skills such as brainstorming, problem solving, analysis; comparison/contrast and how to cultivate these abilities in gifted children. Examples are given of ways for teachers to model thinking skills for students. The response of a student to the ideas of the article is included. (PB)

The use of calculators in helping students to construct their own learning is discussed. Two games which illustrate this concept are presented. The features of a constructivist lesson which uses calculators are listed. (CW)