The social studies curriculum travels through time and space and is bigger on the inside than it is on the outside. To an outsider, the social studies curriculum is a single line on a program of studies, 45 minutes of a student's school day. Those on the inside, however, know that the field covers history, geography, civics, economics, and much…

Self-advocacy, self-management, self-regulation, and self-knowledge are complex terms, often considered forms of self-determination. Whatever term you may use, helping young adults with intellectual disability (ID) make authentic decisions about their own goals and behaviors often results in passive agreement. Even though advancing…

Students often view mathematics as a set of unrelated facts and procedures and fail to make the connections between and among related topics. One role of a teacher is to help students understand that mathematics is an interrelated discipline. Another role is to assist students in the scaffolding of their knowledge so that they can make connections…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

The NCTM calls for the use of rich tasks that encourage students to apply their own reasoning to problem situations. When students work through algebraic generalization tasks, their reasoning often elicits a variety of strategies (Lannin 2003; Stacey 1989; Swafford and Langrall 2000). Challenges for teachers include facilitating student awareness…

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…

This note contains material to be presented to students in a first course in differential equations immediately after they have completed studying first-order differential equations and their applications. The purpose of presenting this material is four-fold: to review definitions studied previously; to provide a historical context which cites the…

Discusses the process of generalization. Illustrates the process by generalizing the classic problem of how a farmer can get a fox, a goose, and a bag of corn across a river in a boat that is large enough only for him and one of the three items. (MDH)

This study of 75 gifted students in grades 6-8 found that the group receiving Creative Problem Solving training with transfer strategies infused had a higher percentage of students applying the strategies to problems out of the context of the training sessions, compared to control group students and students receiving traditional training.…

The paper describes four categories of experience that help elementary students with learning disabilities in a writing process classroom. They are: (1) a sense of a community of learners, (2) control of one's writing, (3) collaborative and independent problem solving, (4) opportunities for generalization and transfer of learning. (Author/DB)

Research relevant to improving instruction for learning disabled students with mathematical problem solving deficits is reviewed. Using a cognitive-metacognitive framework, techniques for teaching both specific and comprehensive mathematical problem solving strategies as well as techniques to enhance strategy generalization are presented.…

This article describes ways in which students develop schemas as they generalize and formalize patterns when solving related algebraic problems that involve size, shape, growth, and change. (Contains 7 figures and 3 tables.)

Gifted students in grades 6-8 were divided into two experimental groups, one receiving traditional creative problem-solving training and the other receiving creative problem-solving with transfer strategies infused; there was also a control group receiving training in various memory tasks, analogical skills, and logic exercises. After the…

Two individuals with severe mental retardation, participants in a supported employment program, were taught to use self-instruction in combination with multiple exemplar training to solve work-related problems. Use of the combined strategy resulted in generalization of self-instruction statements and correct responses to untrained problem…

Investigates the question concerning the maximum number of lines of symmetry possessed by irregular polygons. Gives examples to illustrate and justify the generalization that the number of lines of symmetry equals the largest proper divisor of the number of sides. Suggests related classroom activities. (MDH)