The integration of History in the educational practice can lead to the development of a series of activities exploiting genetic "moments" of the history of Mathematics. Utilizing genetic ideas that developed during the 14th century (Merton College, N. Oresme), activities are developed and mathematical models for solving problems related to uniform…

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…

In two experiments, 216 college students learned a mathematical procedure and returned for a test either one or four weeks later. In Experiment 1, performance on the four-week test was virtually doubled when students distributed 10 practice problems across two sessions instead of massing the same 10 problems in one session. This finding suggests…

This book endeavors to show elementary teachers how to integrate mathematics, science, and technology in a cooperative learning environment. The reason for detailing this approach is to help students become creative and critical thinkers. Throughout the text there are numerous inquiry-based, thematic activities specifically designed to promote…

This book addresses questions of multiple representations in human reasoning and learning. Computational approaches to learning with multiple representations are introduced, and the role of multiple representations in teaching is discussed. The following chapters are included in Part I: Multiple Representations in Learning Concepts form Physics…

This paper summarizes and extends a study of SES (socioeconomic status) related differences in a mathematics classroom aligned with current U.S. reforms. Qualitative analyses compared the lower- and higher-SES students' experiences with whole-class discussion and contextualized, open-ended mathematics problems. The higher-SES students tended to…

This teacher's guide, with accompanying videotape, presents an episode of the NASA SCI Files. In this episode, one of the tree house detectives has had an accident and cannot get into the tree house. Using problem-based learning, the rest of the gang investigates the world of simple machines and physical science and "pull" together to…

This paper describes a models and modeling framework that has been applied to various areas in teaching, learning and problem solving. It examines the implications of that framework on metacognition and higher order thinking during everyday problem-solving situations that required teams of students to produce complex solutions in approximately 1-2…

This paper describes the approaches taken at a middle school to improve student problem solving ability and test results for the Indiana Statewide Testing for Educational Progress (ISTEP) mathematics tests. The focus was on grade 6. In 1996, 35% of the 437 students in grade 6 did not master the mathematics problem solving skill. A committee of…

MathWings is the mathematics program of the Success for All Foundation, a non-profit organization that develops and disseminates school reform programs originally developed at Johns Hopkins University. MathWings, based on NCTM standards, emphasizes the use of cooperative learning, problem solving, and metacognitive strategies to help all children …

Presented are a series of word problems which give students the opportunity to use or develop problem solving skills. The problems are open-ended, with possible answers included. (JP)

Discusses models in inquiry and of instruction based on critical Fallibilistic philosophy, developed by Karl R. Popper, which holds that all knowledge grows by conjecture and refutation. Classroom applications of strategies which result from the model are presented. (JP)

Outlines a guided discovery activity for ascertaining the conditions which allow for the correct tracing of networks. (JP)