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…

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 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…

This paper has two goals. The first is to present a model of the acquisition of a concept image of function. Theories describing the objectification of function are outlined through two different but related paths, and both stem from the conception of function as a process. The first path to objectification involves the generalization of the…

This paper suggests that the mathematics teacher needs to do much reading and studying of important trends in improving the mathematics curriculum. Recommendations are made for what teachers need to look for in research studies in mathematics in order to help them recognize what would make for a quality study. Collaborative and individualized…

Over the past 10 years, national conferences and committees investigating the state of American mathematics education have advocated an increased emphasis on problem solving and mathematical modeling situations in the secondary school curriculum. However, little effort has been made to prepare secondary school teachers to use mathematical modeling…

Autonomous Learning Behavior (ALB) as mediators between internal and external influences and performance on high level cognitive tasks was proposed as a possible explanation for gender-related differences in mathematics. This study developed a measure of ALB by drawing on teachers' working knowledge and the literature on problem-solving, including…

This document addresses the need to provide problem-solving materials for teachers of mathematics in the upper elementary grades. The activities are designed to: help teachers emphasize problem-solving techniques, develop positive attitudes toward mathematics and problem solving, provide problems that could be used whenever free time exists,…

A 2-year study of mathematics performance of sixth-grade students was conducted to: (1) determine the extent to which previously reported sex differences in California data exist and influence student response; (2) examine the predominant successful and unsuccessful strategies used by sixth-grade students in solving story problems; (3) discover to…

The purpose of this study is to contribute to an understanding of how errors could be employed in mathematics instruction so that the students use them constructively in support of their learning of mathematics. A teaching experiment was designed to create an ideal context in which the pedagogical approach to errors as springboards could be…

Some recent research findings with implications for improving mathematics instruction are reviewed in this report. The focus is on two topics: computation, in particular subtraction and estimation, and problem solving. Findings about each are listed, with references for each cited study included. Effective algorithms and strategies used by…

This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…

The document opens with an editorial comment discussing the role of mathematics in teaching and learning. Then, 13 reports related to mathematics education are abstracted and analyzed. Three of the reports deal with problem solving, and another three look at aspects of cognitive development. There are two each on mathematics instruction,…

This document presents a first approximation for a model for student performance in solving linear equations. First, characteristics of a model of student performance for solving linear equations is discussed. It is noted that there is a need for some theoretical structure to support and organize the bits and pieces of information provided by…