554 THE PHYSICS TEACHER ◆ Vol. 46, March 2008Lettersto the EditorUsing Gravitational Analogies to Introduce Electric Field Theory Concepts – A responseI 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 obser-vation:Although analogies were a great educational tool, students seemed to be overwhelmed by being intro-duced to them. I had the impres-sion 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.2Analyzing Table I, one can notice that gravitation does not contain many detailed concepts covered in electrostatics. A similar conclusion can be drawn from comparing poten-tials 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 anal-ogy-type problems in section A in order to retain the knowledge and apply it in section B.How to strengthen the parallel-ism between Gravitation and Electrostatics? I made the following modifica-tions to strengthen the correlation:• I implemented additional types of problems in the section on grav-ity.• While teaching gravity, I empha-sized that similar concepts will be studied in the section of electro-statics.This proactive approach estab-lished 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.ExampleTwo masses are placed in space where no other gravitational field exists.(Physics 1)a. Calculate the net gravitation field at the point K due to these mass-es.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.Gravitation Electrostatics• Determine the force that one spherically symmetrical mass exerts on another.• Determine the force that acts between specific point charges. • Calculate the magnitude and direction of the force on a posi-tive or negative test charge.• Calculate the net force on a col-lection of charges in an electric field.• Determine the strength of the gravitational field at a specific point outside a spherically sym-metrical 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. • Define electric field in terms of the force on a test charge.Table I. Forces and Fields; Summary of Topics in AP Physics Gravitation and Electrostatics.K0 1234x,m = 10 kg = 10 kgmmTHE PHYSICS TEACHER ◆ Vol. 46, March 2008 555Letters(AP Physics)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 modifica-tion is asking students to predict the action of these fields (electrostatic and gravitational) on a combination of mass and charge. SummaryIt is apparent that the purpose of teaching physics is not exposing stu-dents to analogies but guiding them through the content. I believe that any approach that makes the sub-ject more concise and integrated is worth trying in the classroom. With the discussed modifications, analo-gies became more meaningful to my students and furthermore, their un-derstanding of electrostatics has been deeper since then. 1. Susan Saeli and Dan Maclsaac, “Us-ing gravitational analogies to intro-duce elementary electric field theory concepts,” Phys. Teach. 45, 104–108 (Feb. 2007).2. 2006 AP Annual Conference, Lake Buena Vista, FL, Professional Devel-opment Workshop Materials, College Board.Andrzej SokolowskiMagnolia West High schoolPO Box 426Magnolia, TX [email protected]’ ResponseWe 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 ad-ditional student effort or cognitive overhead.1 Each classroom teacher is most familiar with the needs of his/her students and the classroom cur-ricular 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 learn-ing 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 iden-tical situations; analogies are always only approximately similar and serve to promote the development and illustration of abstract models. A per-fect 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 sci-ence 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 sec-tion 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
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