The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

Using mathematics as an example, the nature of the confusion between "knowledge" and "coming to know" is elucidated. The range of curriculum choices available to structuralists once the distinction is clarified is larger, and teaching a body of knowledge and teaching by discovery are compatible. (Author/MLF)

Students often fail to apply knowledge and skills learned in one context to other situations. Although the implicit assumption in educational practice has been that transfer takes care of itself, a knowledge of the mechanisms of transfer can enable educators to help their students integrate general and local knowledge. (TE)

Analyses of 42 mothers' summary descriptions of their child relationship problems revealed that multistressed mothers produced less complex reports than singularly distressed mothers. Findings suggested that multistressed mothers do not engage their kinfolk and friends in problem-solving discussions, nor do the listeners encourage such…

This is a qualitative study of 22 9th graders performing generalizations on a task involving linear patterns. Our research questions were: What enables/hinders students' abilities to generalize a linear pattern? What strategies do successful students use to develop an explicit generalization? How do students make use of visual and numerical cues…

This research report presents a study of the work of agronomy majors in which an extension of linear models to non-linear contexts can be observed. By linear models we mean the model y=a.x+b, some particular representations of direct proportionality and the diagram for the rule of three. Its presence and persistence in different types of problems…

Investigated was student inability to understand mathematics across concepts, focusing on the processes by which students solve problems. In-depth clinical interviews were used with students during ninth-grade general mathematics. Mathematical abilities investigated were information gathering, generalization, reversibility, flexibility, and…

Examines the generalizability of the Problem Solving Inventory (PSI) through research with Black South African samples. The estimates of the factor structure as well as other reliability and validity estimates provided strong support for the generalizability of the PSI to South African Black college students. The results also provided partial…

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.…

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

Discusses the impact of computer programing instruction on cognitive skills and suggests two mechanisms of transfer--low road, from practice, and high road, from generalization. Previous research that tried to measure transfer from programing is reviewed, six categories in which transfer might occur are presented, and 71 references are provided.…

The reasons people most often give for the failures of U.S. schools involve poverty, racial inequality, and a host of social problems. This paper argues that even if all these conditions were remedied, the schools would not produce many more people with the ability to think than they do today. Teachers, who are usually able to think, do not know…

The author sauggests that present inquiry methods are often missing their goal and offers a technique to engage students in creative inquiry. (Author)

Study explored how analog type and format and learner's prior knowledge would affect transfer outside of an experimental setting, examining the relationship between the analog's contextual elements and high school freshmen's performance on a science problem. Some students spontaneously applied structural elements on the analog to the solution. (SM)

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.)