Let ter s to the Editor Using Gravitational Analogies to Introduce Electric Field Theory Concepts A response I had applied similar analogies1 in my physics classes for a few years however at one point I decided to modify the way I introduced them to students due to the following observation Although analogies were a great educational tool students seemed to be overwhelmed by being introduced to them I had the impression that students viewed these analogies as a new knowledge rather than a tool helping them comprehend new concepts This observation prompted me to look closer into current physics curriculum especially into concepts referred to as analogies in the sections on gravitation and electrostatics 2 Analyzing Table I one can notice that gravitation does not contain many detailed concepts covered in electrostatics A similar conclusion can be drawn from comparing potentials and potential energies in both chapters students felt overwhelmed because they were not exposed to concepts that seemed analogous In order to have the analogies work more effectively I came up with the following conclusions If section A is to be used as an analogy to teach section B then the section A must contain all the types of concepts that section B does Students need to practice analogy type problems in section A in order to retain the knowledge and apply it in section B Table I Forces and Fields Summary of Topics in AP Physics Gravitation and Electrostatics Gravitation Determine the force that one spherically symmetrical mass exerts on another Electrostatics Determine the force that acts between specific point charges Calculate the magnitude and direction of the force on a positive or negative test charge Calculate the net force on a collection of charges in an electric field Determine the strength of the gravitational field at a specific point outside a spherically symmetrical mass Describe the electric field of a single point charge Use vector addition to determine the electric field produced by two or more point charges How to strengthen the parallelism between Gravitation and Electrostatics I made the following modifications to strengthen the correlation I implemented additional types of problems in the section on gravity While teaching gravity I emphasized that similar concepts will be studied in the section of electrostatics This proactive approach established the foundation for correlation of the chapters and prepared the students for considering electrostatics as yet another application of already learned physics concepts Below are examples of problems for Physics 1 and AP Physics that reflect these modifications Example Two masses are placed in space where no other gravitational field exists Physics 1 K 0 m 10 kg 1 2 3 4 x m m 10 kg a Calculate the net gravitation field at the point K due to these masses b If an additional mass of 5 kg is placed at the point K calculate the gravitational force exerted on the mass due this net field Define electric field in terms of the force on a test charge 554 THE PHYSICS TEACHER Vol 46 March 2008 Letters Andrzej Sokolowski AP Physics Magnolia West High school PO Box 426 Magnolia TX 77355 Andrzejsoko yahoo com y m 30 mg 0 1 2 3 4 x m a Calculate the magnitude and direction of the net gravitational field at 0 0 b If a mass of 1 kg is placed at 0 0 calculate the magnitude and direction of the instantaneous acceleration of the mass These problems can be reassigned in the section on electrostatics with masses replaced by charges Another possible extension of this modification is asking students to predict the action of these fields electrostatic and gravitational on a combination of mass and charge Summary It is apparent that the purpose of teaching physics is not exposing students to analogies but guiding them through the content I believe that any approach that makes the subject more concise and integrated is worth trying in the classroom With the discussed modifications analogies became more meaningful to my students and furthermore their understanding of electrostatics has been deeper since then 1 2 Susan Saeli and Dan Maclsaac Using gravitational analogies to introduce elementary electric field theory concepts Phys Teach 45 104 108 Feb 2007 2006 AP Annual Conference Lake Buena Vista FL Professional Development Workshop Materials College Board THE PHYSICS TEACHER Vol 46 March 2008 Authors Response We agree and differ with Mr Sokolowski regarding the role of analogy in physics learning Yes analogies are knowledge in and of themselves apart from the examples and analogies initially demand additional student effort or cognitive overhead 1 Each classroom teacher is most familiar with the needs of his her students and the classroom curricular goals the teacher must decide when where which at what level of complexity and even with which individual student the use of analogy is appropriate Much research indicates that the use of analogy in conceptual learning is almost certainly unavoidable and we particularly disagree with Sokolowski s contention that section A must be complete before teaching section B via analogy We believe that the pedagogical power in using physically analogous situations is due to the fact that analogies are not identical situations analogies are always only approximately similar and serve to promote the development and illustration of abstract models A perfect and complete analogy would be a tautology of no pedagogical power whatsoever The processes of creating abstract models and visualizations by recognizing and mapping features between different phenomena and problems lie at the heart of how science is done and how individuals conceptually learn Moreover this procedure flows back and forth so that meaningfully learning section B inescapably reinterprets and enlarges the models constructed by students when they learned section A So it often makes sense for an instructor to introduce a new idea in section B simply due to pedagogical constraints and then map backwards into section A This is typical of how physics majors learn about Gauss law while constrained by mathematics courses first for electrostatics then later for gravitation The analogies presented in our paper are keyed to some of the most powerful unifying ideas in physics invoking and visualizing field theory geometrical symmetry and conservation laws and these powerful ideas do reflect physics content that is usually at least implicitly part of introductory physics Thus these
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