This article focuses on the ways in which four eighth-grade girls, each with varying levels of algebraic understanding, share ideas, debate, and gradually move toward generalizations inherent in the "Painted Cube" problem. The intent of this article is to examine how students move to progressive formalization and to provide insights into the ways…

Many students with disabilities continue to struggle with understanding what mathematics means. They memorize basic facts or step-by-step mathematical procedures without understanding the underlying concepts related to the problems. Thus, instruction designed to help students understand the meaning of the mathematics that they are learning in…

Among the 12 documents selected for this annotated bibliography of documents and journal articles in the ERIC database is an expert's argument that the brain's multipath and multimodal capacities are ignored by educators. Another writer fears that the "back-to-basics" movement may have eclipsed the prominence earlier accorded to thinking…

How secondary social studies teachers can teach concepts through the skills of categorizing and generalizing is discussed. (RM)

Describes a method of teaching the order of mathematical operations based upon the psychological theory of conceptual generalization. (MDH)

Identifies an induced incorrect generalization as a generative cause for the formation of misconception. Analyzes students' protocol of an exploratory learning experiment about the laws of reflection of light. Suggests recommendations for textbook, teaching, and practical work. (Author/YP)

Presents a method that connects the area formulas for triangles, rectangles, parallelograms, and trapezoids by focusing on the relationships between the bases and heights of each figure. Transformations allow figures to be reconceptualized to establish a general concept of area that can be applied to other figures. (MDH)

Discusses issues and problems concerning concept development among students in elementary social studies programs. Suggests good teaching uses analogies and metaphors to facilitate learning. Recommends illustrating key concepts through myths, fables, and parables. Argues that using stories that show how things work allows students to apply the…

Contends social studies is an exciting, relevant aspect of the curriculum, but it is often presented in a mundane and dated fashion. Reviews research on instructional processes and recommends teaching generalizations based on concepts grounded in fact. (CFR)

Asserts that teaching concept formation and generalization development are central to any social studies program. Presents a classroom activity designed to teach geographic concepts to middle school students. Includes four figures and instructional procedures to be used in the activity. (CFR)

Presents an activity in which students develop their own theorem involving the relationship between the triangles determined by the squares constructed on the sides of any triangle. Provides a set of four reproducible worksheets, directions on their use, worksheet answers, and suggestions for follow-up activities. (MDH)

This study tested the effectiveness of having fifth-grade students generate their own examples of selected concepts on energy. Hypotheses were that subjects would perform better on sections of a test related to definitions and recognition of exemplars of the concepts for which they found their own examples than on sections related to comparible…

Presents a method for improving reading comprehension through direct instruction of inductive reasoning. Students gather clues to personality of characters as play progresses and from these arrive at an overall generalization concerning the complexities of the character. (SRT)

Describes 20 trade books to aid teachers in the development of social studies concepts. Suggests ways to use these books to extend lesson units by emphasizing formation of concepts and generalizations, integrating social sciences, clarifying values, achieving objectives, and maintaining of objectivity in discussing societal conflict. (KO)

Defines a generalization as "a descriptive statement of broad application indicating a relationship between two or more concepts." Argues that successful teaching about generalizations can only occur when students understand the relationship between concepts and facts. Discusses four issues and four approaches related to teaching…