This study investigates the nature of student errors in the context of problem solving and Dynamic Math Environments. This led to the development of the Problem Solving Action Identification Framework; this framework captures and defines all activities and errors associated with problem solving in a dynamic math environment. Found are three…

The impact of touch-screen technology on spatial cognitive skills as related to molecular geometries was assessed through 102 one-on-one interviews with undergraduate students. Participants were provided with either printed 2D ball-and-stick images of molecules or manipulable projections of 3D molecular structures on an iPad. Following a brief…

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…

This study examines the specificity of information provided by structural assessment of knowledge (SAK). SAK is a technique which uses the Pathfinder scaling algorithm to transform ratings of concept relatedness into network representations (PFnets) of individuals' knowledge. Inferences about individuals' overall domain knowledge based on the…

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…

Genetic algorithms (GAs) are a problem solving strategy that uses stochastic search. Since their introduction (Holland, 1975), GAs have proven to be particularly useful for solving problems that are "intractable" using classical methods. The language of genetic algorithms (GAs) is heavily laced with biological metaphors from evolutionary…

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…

Advances in computers and multimedia technology have changed traditional methods for learning and skills training. Online learning continues to play a major success of any academic program. Such learning can personalize learning needs for students, it can provide an environment where virtual reality techniques are used to create interactive…