Helping Students Organize And Retrieve Their Understanding Of Dynamics

When confronted with the large amount of information presented in an introductory physics course, students often have difficulty assimilating the concepts and seeing the big picture. Thus they may have difficulty transferring their knowledge to new situations. In this paper we present a conceptual framework that we have developed for teaching and applying dynamics at both the secondary school and college levels. In this framework the causes of motion are graphically related to the description of motion using Newton’s laws and impulse/momentum relationships. The framework accommodates translation and rotation, multiple dimensions, and time-varying forces. In addition to presenting the framework, we describe how it is used by teachers and students in the classroom as part of a learner-centered curriculum and provide an elevator activity as an example. Finally, we include the response of students to this approach. Introduction Most introductory physics texts devote 10 or more chapters to the topics involved in dynamics, including pre-requisite skills such as vector operations, kinematics, Newton’s Laws, impulsemomentum relationships and the application of dynamics to a wide variety of situations. Thus it is not surprising that many students do not see how the concepts of dynamics are related to each other. Lacking a solid understanding of how the knowledge is structured, students may concentrate their efforts on learning processes to manipulate equations to solve problems. If this is the case, they will not gain a conceptual understanding of the subject matter, nor will they be able to transfer their knowledge to domains outside the narrow and idealized ones of their experience. The National Research Council (NRC) summarizes a variety of studies illustrating how experts and novices differ in the way that they solve physics problems. The NRC notes that, “Experts usually mentioned the major principle(s) or law(s) that were applicable to the problem, and how one could apply them.” By comparison it is noted that “...competent beginners rarely referred to major principles and laws in physics; instead, they typically described which equations they would use and how those equations would be manipulated...Experts’ thinking seems to be organized around big ideas in physics, such as Newton’s second law and how it would apply, while novices tend to perceive problem solving in physics as memorizing, recalling , and manipulating equations to get answers.” The work of Chi cited by the NRC is particularly relevant to our paper. The NRC writes, “In representing a schema for an incline plane, the novice’s schema contains primarily surface features of the incline plane. In contrast the expert’s schema immediately connects the motion of an incline plane with the laws of physics and the Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright 2003, American Society for Engineering Education P ge 832.1 conditions under which laws are applicable.” Further, based upon the work of Larkin and Chi et al., the NRC notes that, “Experts appear to possess an efficient organization of knowledge with meaningful relations among related elements clustered into related units that are governed by underlying concepts and principles...Within this picture of expertise, ‘knowing more’ means having more conceptual chunks in memory, more relations or features defining each chuck, more interrelations among the chunks, and efficient methods for retrieving related chucks and procedures for applying these informational units in problem-solving context.” Given how important structuring knowledge is to the process of learning physics, the question then is how to most effectively help students with knowledge organization. We will describe a simple conceptual framework to aid the study and application of dynamics and its use in a learner-centered curriculum. Dynamics Conceptual Framework The dynamics conceptual framework that we have developed is shown in Figure 1. In this framework, motion is related to its causes by Newton’s second law and impulse-momentum relationships. Motion is quantified by position, velocity and acceleration on the right side of the framework. These variables are related by graphical and calculus relationships. We feel that a graphical approach integrated with (or followed at a later time by) a calculus-based approach is most effective for learning kinematics, because graphical analysis allows students to visualize motion while working directly with fundamental principles. This approach also takes greater advantage of advances in laboratory technology, including real-time data collection using motion detectors (an ideal tool for measuring, viewing and manipulating motion graphs for motion with constant or time-varying acceleration) and video analysis. Details and example applications of this approach for learning kinematics are given in Ellis and Turner. While the graphical and calculus relationships among variables describing motion are the fundamental feature of the right side of the framework, the left side describes the forces and torques that affect motion. Here we highlight the free-body diagram and how it is used to find the net force and torque on an object. Thus the framework illustrates the need to identify forces, construct a free-body diagram and add these forces. In the middle of the diagram is Newton’s second law and impulse-momentum to relate the two sides. It has been our experience that, without proper guidance, students view these relationships as two completely different approaches that apply to entirely different situations. For example, students may feel that impulse-momentum is appropriate for collision problems and Newton’s Second Law is appropriate for elevator problems. Seeing both ideas represented visually as relationships between motion and its causes illustrates their similarity. We also show students how Newton’s second law and impulse-momentum are related to each other mathematically (as represented by an arrow between the two concepts on the dynamics framework). Proceedings of the 2003 American Society for Engineering Education Annual Conference & Exposition Copyright 2003, American Society for Engineering Education P ge 832.2 Fnet = ma τnet = Iα W = mg Free-Body Diagram Slope or derivative r or θ