A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…

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…

Relativistic hydrodynamics is essential to our current understanding of nucleus-nucleus collisions at ultrarelativistic energies (current experiments at the Relativistic Heavy Ion Collider, forthcoming experiments at the CERN Large Hadron Collider). This is an introduction to relativistic hydrodynamics for graduate students. It includes a detailed…

We present a study of the ascending vertical motion of a self-propelled body under a uniform gravitational field suffering the action of two different types of air friction forces: linear on the velocity, which is valid for slowly moving bodies, and quadratic on the velocity. We study the special case where the thrust force is a decreasing…

Viewing challenging behavior as the result of lagging skills (kids do well if they can) rather than as poor motivation (kids do well if they want to) has significant ramifications for how adults interact with kids with behavioral challenges and try to help them. A wide range of lagging skills can set the stage for challenging behavior. Challenging…

We solve for the motion of an object with initial velocity v[subscript 0] and subject only to the combined drag of forces linear and quadratic in the velocity. This problem was treated briefly by Newton, after he developed a theoretical argument for the quadratic term, which we now know is characteristic of turbulent flow. Linear drag introduces a…

This study investigated quantitative and qualitative changes in mental rotation performance and solution strategies with a focus on sex differences. German children (N = 519) completed the Mental Rotations Test (MRT) in the 5th and 6th grades (interval: one year; age range at time 1: 10-11 years). Boys on average outperformed girls on both…

It is interesting to note how technology has changed the way that people communicate with one another. Several of the major historical developments of communication are: (1) language; (2) alphabet; and (3) writing. These early forms of communication enabled humans to go beyond verbal and symbolic communication and on to such technologies as the…

We measured what students perceive physicists to believe about physics and solving physics problems and how those perceptions differ from the students' personal beliefs. In this study, we used a modified version of the Colorado Learning Attitudes about Science Survey which asked students to respond to each statement with both their personal belief…

In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to cope up with students' conviction based only on…

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are…

Relations were examined between epistemic profiles, regulation of cognition, and mathematics problem solving. Two hundred sixty-eight students were sampled from undergraduate mathematics and statistics courses. Students completed inventories reflecting their epistemic profiles and learning strategies, and were profiled as rational, empirical, or…

The aim of this study was to investigate the strategies used by third graders in solving the 81 elementary subtractions that are the inverses of the one-digit additions with addends from 1 to 9 recently studied by Barrouillet and Lepine. Although the pattern of relationship between individual differences in working memory, on the one hand, and…

Under the backdrop of the investigation of rational functions and their respective curved asymptotes, the reader is invited to experience the mathematical process alongside the authors and observe the application of the NCTM Process Standards and the use of multiple representations in the investigation and solution of a problem. (Contains 9…

This article explores the use of classroom video as a tool for fostering productive discussions about teaching and learning. The setting for our research is a 2-year mathematics professional development program, based on the Problem-Solving Cycle model. This model relies on video from the teachers' own classrooms and emphasizes creating a…