The purpose of this paper is to open lines of thinking about discovery learning not tried before. This effort is a strident attempt to establish new insights and outlooks that will improve the language, theory, and practices connected with this teaching method. (Author/MK)

Describes physiological, affective, and cognitive mechanisms by which didactic and discovery methods appear to work, as revealed by research literature. The optimal instructional method depends on the instructional objective, the educator's skills, and the nature of the students. Suggests more use of discovery methods. (69 references) (Author/MKR)

Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)

Proposes that problem scenarios are activities that give students opportunities to employ mathematics across the curriculum by asking them to define problems, identify information needed and potential sources of data, and make related conjectures. Discusses an example of a scenario involving transportation. (MDH)

Reports development and results of the Kramer Project, a two-year study of the implementation of a problem-solving, activity-based mathematics program in the elementary grades. Describes the mathematical content covered, participating teachers, instructional materials employed, inservice teacher training provided, and academic achievement gains of…

Provides a rationale for a learning environment in science classrooms that integrates science, mathematics, and technology while solving authentic problems. Describes activities that can be used in such an environment and presents data regarding students' attitudes toward the described activities. (MDH)