Discusses the benefits of discovery learning, as opposed to a direct, lecture method, and offers 10 discovery strategies, such as playing 20 questions, using the Socratic method, and problem solving. (JC)

Two studies were conducted to obtain information about the metacognitive environment of the preschool child and the impact of parent-child communication on problem solving. Children working with parents showed improvement on several problem-solving measures, but children working alone also improved, solely as a result of practice. (Author/PP)

Describes a game used in precalculus that builds interest and confidence in the uses of inverse functions. The game is preceded by a worksheet that enables students to discover that f(x) and f-1(x) are mirror images of the line y=x. (DDR)

Consideration of a definite integral in an advanced calculus class led to a great deal of mathematical thinking and to the joy of discovery. Graphing calculators allowed students to investigate quick solutions which should be regarded as stepping stones to additional investigation and rigorous proof. With slight modifications to their proofs,…

The article discusses the classic problem: "Given an equilateral triangle and a point P inside the triangle, what is the sum of the distances from P to the three sides?" The problem is used to illustrate the generative nature of problem-posing using the heuristic "What happens if...?" (PK)

Proposes the use of conceptualization, exploration, and higher-level problem solving in differential equations courses as a replacement for some of the traditional material that can now be delegated to the computer. (MKR)

An open-ended data-analysis activity, prompted by a Royal Mail advertisement, explores the claim that the real cost of first class postage has fallen below the inflation rate. The activity provides realistic exercises in both arithmetic and statistical indices, and in logical interpretation of, and deduction from, the data. (JJK)

This article presents a rationale for emphasizing discovery instruction over guided instruction in teaching cane travel skills to people with severe visual impairments. Discovery instruction is seen to facilitate the use of intrinsic feedback in developing perceptual-cognitive skills as well as promoting problem solving, retention, and transfer of…

Presents an analysis of the question in the title which involves a discussion of fractions, number theory, and probability through modeling, exploring, and other mathematical connections. (MKR)

Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

The author discusses changes that the Texas Division for Blind Services made in its vocational rehabilitation program to increase competitive employment opportunities for vocational rehabilitation consumers who are blind and visually impaired. P. R. Warren, B. S. Cavenaugh, and M. J. Giesen (2004) reported that, nationwide, a higher proportion of…

Open-ended learning environments (OELEs) provide contexts to support exploration, experimentation, and problem-solving. This paper creates a context for understanding the issues and challenges associated with the design and development of OELEs. Discussion first centers on characteristics of OELEs which differ from traditional learning…

From a science perspective, inquiry-oriented instruction engages students in the investigative nature of science. Inquiry involves activity and skills, but the focus is on the active search for knowledge or understanding to satisfy a curiosity. This digest further describes the distinguishing features of inquiry-oriented science instruction and…

This document is a collection of reports presented at a programable calculator symposium held in Seattle, Washington, in April, 1980, as part of the annual meeting of the National Council of Teachers of Mathematics (NCTM). The session was designed to review whether the programable calculator has a place in the school mathematics program, in light…

This curriculum guide, part of a series of science units, stresses concept-learning through the discovery approach and child-centered activities. It is intended that the unit will be studied in depth by grades 3, 4, 5, and 6. Kindergarten pupils will study the unit in less detail. "Our Useful Rocks" is studied in the kindergarten,…