How do people use information from others to solve complex problems? Prior work has addressed this question by placing people in social learning situations where the problems they were asked to solve required varying degrees of exploration. This past work uncovered important interactions between groups' "connectivity" and the problem's…

Exploratory learning environments (ELEs) promote a view of learning that encourages students to construct and/or explore models and observe the effects of modifying their parameters. The freedom given to learners in this exploration context leads to a variety of learner approaches for constructing models and makes modelling of learner behavior a…

Two thousand four hundred years ago Socrates gave a remarkable lesson of geometry, perhaps the first detailed record of a pedagogical method in vivo in history [Plato. (2008). "Apologia de Socrates. Menon. Cratilo." Madrid: Alianza Editorial]. Socrates asked Meno's slave 50 questions requiring simple additions or multiplications. At the…

Reported are the results of a study which investigated the influence of certain variables within the method of individually guided discovery in mathematics. The independent variables considered were the concepts of ordered partitions and permutations, the level of consolidation or practice after discovery, and the teachers. Also considered were…

This report discusses four different types of instruction which enable learning disabled or low achieving students to learn well enough to transfer the skill to a novel situation. After asserting that generalization depends on systematic instruction, the paper describes the four procedures: (1) teacher-directed generalization; (2) direct…

This research was based on the assumption that the teaching of broadly generalizable cognitive skills should be a primary goal of education--that students can be taught to be better insight problem solvers outside of school by training in school and that they can be given the skills necessary for efficient discovery learning. The subjects were 116…

This paper reports on a study which was performed to replicate and extend the findings of Hendrix with regard to verbalization and discovery learning. College algebra classes were randomly assigned to three verbalization conditions: (1) no student verbalization of generalizations required, (2) students make written verbalization of generalization,…

Discussed are generalizations and problem solving, unsound uses of generalizations, generalization as data, and student discovery of generalizations. (CT)

Two studies investigated the effects of verbalization of discovered generalizations on the retention of those principles. (SD)

This study is one of several conducted by the authors in their investigation of the use of "higher order rules" in the solution of problems. The focus of the current experiment was determination of the compatibility of identified rules with the knowledge of average teenagers, and of the extent to which instruction in higher order rules…

The intent of this paper is to present a case study in discovery learning using a chronological, narrative history book. (Author)

Using a geoboard to find polygons with given perimeters presents a problem which refines skills and provides an opportunity to inquire and discover. (MK)