Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

It is generally believed that students should use multiple representations in solving certain physics problems, and earlier work in PER has begun to outline how experts and novices differ in their use of multiple representations. In this study, we build on this foundation by interviewing expert and novice physicists as they solve two types of…

The theoretical perspective outlined here offers an alternative to explanations of knowledge transfer that posit its source in the construction and application of abstract, context-independent knowledge structures. A case study analysis of an undergraduate student's attempt to solve a series of problems related to an elementary statistical…

PROJECTTUTOR is an intelligent tutoring system that enhances conventional classroom instruction by teaching problem solving in project planning. The domain knowledge covered by the expert module is divided into three functions. Structural analysis, identifies the activities that make up the project, time analysis, computes the earliest and latest…

This paper examines students' mathematics learning in a social context as two versions of an instructional sequence designed to facilitate students' development of a conceptual foundation for place-value numeration are enacted in two third grade classrooms. The same instructional sequence is used in each classroom with the regular classroom…