This study investigated how students reason about the partial derivative and the directional derivative of a multivariable function at a given point, using different graphical representations for the function in the problem statement. Questions were formulated to be as isomorphic as possible in both mathematics and physics contexts and were given…

Physics experts and students commonly use a variety of representations when working with partial derivatives, including symbols, graphs, and words. One especially powerful representation is the contour graph. In open-ended problem-solving interviews with nine upper-division physics students, we asked students to determine derivatives from contour…

Previous studies have identified physics students' difficulties with graph slope and area under a graph in different contexts. In this study we compared physics and nonphysics (psychology) students' understanding of graphs; i.e., we evaluated the effects of concept (graph slope vs area under graph), type of question (qualitative vs quantitative),…

Cross-grade studies are valuable for the development of sequential curriculum. However such studies are time and resource intensive and fail to provide a clear representation to integrate different levels of representational complexity. Lin (Lin, 2006; Lin & Chiu, 2006; Lin, Chiu, & Hsu, 2006) proposed a cladistics approach in conceptual…

The aims of this cross-grade study were (1) to determine the level of understanding of energy concepts of students at different academic grades and the differences in understanding between these grades and (2) to analyse the conceptual development of these students. Two hundred and forty-three students at 3 different levels (high school,…

This book looks at how teachers implement national math and science standards in their classrooms. Teacher-authored chapters provide insights into how children think and reason as they pose questions, collect data, and build data models to answer their questions. While the spotlight is primarily on student understanding and its development over…

Focuses on images of energy that may help to construct key scientific concepts. Analyzes interpretations given by students of documents containing images evoking ideas that are seldom visually explained within a theoretical semiotic frame. Confirms the utility of this frame and suggests some abilities needed for students to correctly interpret…

This study uses the context of the weather to explore the development of students' intuitive ideas of variation from pre-Grade 1 to Grade 9. Three aspects of understanding these intuitions associated with variation are explored in individual videotaped interviews with 73 students: explanations, suggestions of data, and graphing. The development of…

Clinical interviews were conducted with 25 seventh- and eighth-grade students to determine: (1) the extent to which they could produce correct graphical representations of familiar situations; (2) to what extent they could infer relationships from graphs; (3) what are the most commonly held graphing misconceptions and how stable they are; and (4)…

Two microcomputer-based laboratories, the motion detector and the sound detector, are discussed in terms of their affects upon the facilitation of an understanding of graphs and their ability to aid in the development of conceptual understanding from graphical analysis. The author relates experiences in using these labs with high school students…

An approach to teaching electrochemical driving force that helps students comprehend the forces that govern ion flux across biological membranes and sets the stage for more elaborate analysis of biochemical signals is presented. Background information and two sample problems and answers are included. (KR)

When comparing performances across four versions of Computer as Lab Partner curriculum, increases in understanding were found when students predicted outcomes and reconciled results, and students used a heat-flow model of thermodynamics to integrate their experimental results. Argued is that curriculum must explicitly motivate students to…

Graphs of objects in motion are frequently used in introductory high school or college physics courses since they offer a valuable alternative to verbal and algebraic descriptions by offering students another way of manipulating the developing concepts. If graphs are to be a valuable tool for students, then the level of the students' graphing…

This paper discussed the use of structured observations as a research strategy in two recently completed studies that investigated students thought processes and behaviors in a microcomputer-based laboratory (MBL) environment and in other instrument-based laboratory environments. In the first study, students' behaviors and thought processes were…

The main purpose of this symposium was to find new ideas and resources for the evaluation and improvement of physics education on all levels. The papers included in this document are entitled: (1) "Quality of Physics Teaching Through Building Models and Advancing Research Skills"; (2) "Evaluation of Physics Education in Terms of Its…