The goals of this four-phased study were to enhance the quality of educational experience for under-represented (rural, low income, and female) secondary students (N=628), and to increase their participation in mathematics and science courses beginning at the middle school level. Teachers (N=28) were asked to expand their pedagogical content…

This 3-week summer project was designed to (1) identify and improve the teaching capabilities of under-prepared junior high school mathematics and science teachers and (2) acquaint college and junior high school teachers with current techniques in mathematics and science at the two different levels (college and junior high) and continue…

This paper describes a study in which both collaborative action research and collaborative mathematics classroom instruction took place. The mathematics instruction consisted of the implementation of a problem-solving curriculum into seventh-grade mathematics classrooms. One problem-solving strategy per week for 10 weeks was introduced to the 4…

Recently, some employers were polled to find out which skills are most important for young people working at their first jobs to have. This guide discusses how parents can help children prepare for the work world. Employers are interested in the academic skills of young people and use job application forms and interviews to evaluate them. They…

This book addresses the subject of learning mathematics with an understanding that shares a consensus about the essential features of classrooms for understanding mathematics. By describing the essential features of classrooms that support students' mathematical understanding and by providing pictures of several classrooms that exhibit these…

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…

Metaphorical reasoning explains how people can interpret abstract representations through a complex activity and then apply them to new problems. In particular, metaphors can facilitate both conceptual understanding and problem solving by: (1) intuitively justifying mathematical operations, (2) integrating mathematical knowledge, (3) enhancing the…

The elements of statistical formulae that cause people to perceive them as difficult were studied, working from theoretical bases that involve cognitive load, motivational perception, and impasse driven learning. In a pilot study conducted to identify difficulties that novices perceive while learning statistical formulae, 22 students in an…

This study, involving 65 undergraduates at the Georgia Institute of Technology (Atlanta); explores a scheme for representing problem-solving knowledge and predicting transfer as a function of problem-solving subgoals acquired from examples. A subgoal is an unknown entity (numerical or conceptual) that needs to be found in order to achieve a higher…

This paper explores the relationship between the concept of cognitive apprenticeship and situated cognition and the social construction of knowledge. Cognitive apprenticeship is the enculturation of students into authentic practices through authentic activity and social interaction in a way similar to that which is evident--and evidently…

This booklet is the print component of a Title II-funded package designed to enhance elementary school mathematics instruction through a problem solving approach that promotes mathematics learning in an environment of inquiry, risk taking, and classroom dialogue. The other component is a 28-minute videotape in which teachers present each of the…

The concept of the mole and its relationship to chemical algebra is difficult for many high school chemistry students to master. This paper describes a study of the use of proportional reasoning when teaching mole relationships and its effect on developing critical thinking skills. The Test of Logical Thinking (TOLT) was used as a pre- and…

A project of the Center for the Study of Learning at the University of Pittsburgh, this yearbook combines the two major trends/concerns impacting the future of educational development for the next decade: knowledge and thinking. The yearbook comprises the following chapters: (1) "Toward the Thinking Curriculum: An Overview" (Lauren B.…

This program information guide describes two approaches, Cognitively Guided Instruction (CGI) and Active Mathematics Teaching (AMT), for teaching academic skills in mathematics to limited English proficient (LEP) students. CGI is based on four related teacher competencies: knowing how specific mathematical content is organized in children's minds;…

The comprehension processes of adult students solving two-step problems of comparison were studied using eye-movement experiments based on the assumption that eye fixations are synchronous with internal cognitive processes. Twenty university students each solved 24 two-step mathematical word problems of three sentences each with consistent…