Helping Students Organize And Retrieve Their Understanding Of Dynamics-猫眼课题宝

帮助学生组织和检索他们对动力学的理解

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2003

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G. Ellis;Warren Turner

在物理入门课程中，面对大量的信息，学生往往难以吸收概念，也难以看清全局。因此，他们可能很难将他们的知识转移到新的环境中。在本文中，我们提出了一个概念框架，我们已经开发的教学和应用动态在中学和大学水平。在这个框架中，运动的原因与使用牛顿定律和脉冲/动量关系的运动描述图形相关。该框架可容纳平移和旋转、多维和时变力。除了介绍该框架，我们还描述了教师和学生如何在课堂上使用它作为以学习者为中心的课程的一部分，并提供了一个电梯活动作为例子。最后，我们包括学生对这种方法的反应。大多数介绍性的物理文本投入10个或更多的章节涉及到动力学的主题，包括先决条件的技能，如矢量操作，运动学，牛顿定律，冲量关系和应用动力学到各种各样的情况。因此，许多学生不明白动力学的概念是如何相互关联的，这并不奇怪。缺乏对知识结构的深刻理解，学生可能会把精力集中在学习过程中处理方程来解决问题。如果是这样的话，他们将无法获得对主题的概念性理解，也无法将他们的知识转移到他们经验中狭窄和理想化的领域之外。美国国家研究委员会（NRC）总结了各种各样的研究，说明专家和新手在解决物理问题的方式上是如何不同的。NRC指出，“专家们通常会提到适用于该问题的主要原则或法律，以及如何应用它们。”相比之下，值得注意的是，“……有能力的初学者很少提及物理学中的主要原理和定律；相反，他们通常会描述他们将使用哪些方程以及如何处理这些方程……专家们的思维似乎是围绕着物理学中的大概念组织起来的，比如牛顿第二定律及其应用，而新手往往认为解决物理问题就是记忆、回忆和操纵方程来得到答案。”NRC引用的Chi的工作与我们的论文特别相关。NRC写道：“在表示斜面的图式时，新手的图式主要包含斜面的表面特征。相比之下，专家的图式立即将斜面的运动与物理定律和2003年美国工程教育学会年会暨博览会论文集联系起来版权2003，美国工程教育学会P . 832.1法律适用的条件。”此外，基于Larkin和Chi等人的工作，NRC指出，“专家似乎拥有一种有效的知识组织，在相关元素之间具有有意义的关系，这些关系聚集在由潜在概念和原则支配的相关单元中……在这张专业知识的图片中，‘了解更多’意味着在记忆中有更多的概念块，定义每个卡盘的更多关系或特征，块之间有更多的相互关系，以及检索相关卡盘的有效方法和将这些信息单元应用于解决问题的过程。”考虑到结构化知识对学习物理过程的重要性，那么问题就是如何最有效地帮助学生组织知识。我们将描述一个简单的概念框架，以帮助学习和应用动力学及其在以学习者为中心的课程中的使用。我们开发的动态概念框架如图1所示。在这个框架中，运动通过牛顿第二定律和冲量-动量关系与它的原因联系起来。通过框架右侧的位置、速度和加速度来量化运动。这些变量通过图形和微积分关系联系起来。我们认为图形化的方法与基于微积分的方法相结合（或在以后的时间里）对于学习运动学是最有效的，因为图形化的分析可以让学生在直接使用基本原理的同时将运动可视化。这种方法还充分利用了实验室技术的进步，包括使用运动检测器（用于测量、查看和操纵具有恒定或时变加速度的运动图形的理想工具）和视频分析的实时数据收集。Ellis和Turner给出了这种方法在运动学学习中的细节和实例应用。虽然描述运动的变量之间的图形和微积分关系是框架右侧的基本特征，但左侧描述了影响运动的力和扭矩。在这里，我们强调了自由体图，以及如何使用它来找到物体上的合力和扭矩。因此，该框架说明了识别力、构造自由体图和添加这些力的必要性。在图的中间是牛顿第二定律和把两边联系起来的冲量。根据我们的经验，如果没有适当的指导，学生们会把这两种关系看作是两种完全不同的方法，适用于完全不同的情况。例如，学生可能会觉得冲量法适用于碰撞问题，牛顿第二定律适用于电梯问题。将这两种观点直观地表示为运动及其原因之间的关系，说明了它们的相似性。我们还向学生展示了牛顿第二定律和脉冲动量在数学上是如何相互关联的（在动力学框架上两个概念之间用箭头表示）。版权所有2003，American Society for Engineering Education P . 832.2 Fnet = ma τnet = Iα W = mg自由体图斜率或导数r或θ

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

Helping Students Organize And Retrieve Their Understanding Of Dynamics

帮助学生组织和检索他们对动力学的理解

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