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whitepapers:narratives:dq 2012/05/02 11:50 whitepapers:narratives:dq 2013/06/25 14:12 current
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===== Example of Small Group Conversation about Geometric and Algebraic Representations of a Physical Quantity ===== ===== Example of Small Group Conversation about Geometric and Algebraic Representations of a Physical Quantity =====
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This video clip starts at 54:42 and ends at 58:17 in the video 071026Ph422Grp6.mov This video clip starts at 54:42 and ends at 58:17 in the video 071026Ph422Grp6.mov
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 +//This interpretative narrative is based upon a video of the class session and discussions with the instructor and the director of the Physics Paradigms Program, Corinne Manogue, and Len Cerny, a doctoral student.  A postdoc, Elizabeth Gire, interacts with a small group in the video. In writing the narrative, Emily van Zee drew upon her research in the tradition of ethnography of communication (Hymes, 1972; Philipsen & Coutu, 2004; van Zee & Minstrell, 1997a,b), a discipline that studies cultures through the language phenomena observed.  This interpretative narrative presents an example of students growing into participants in the culture of “thinking like a physicist.”//
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This narrative presents an example of a small group of three students working together on a large whiteboard on which they have written a complex algebraic expression.  One of them draws a geometric representation of a relevant physical quantity and the others try to understand what this drawing means and how it relates to the algebraic expression they have written and the physical quantity it represents. This narrative presents an example of a small group of three students working together on a large whiteboard on which they have written a complex algebraic expression.  One of them draws a geometric representation of a relevant physical quantity and the others try to understand what this drawing means and how it relates to the algebraic expression they have written and the physical quantity it represents.
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The students are thinking about how to write a formula for the current density, $J$, of a ring of charge $Q$ and radius $R$ that is spinning with period $T$.  The students are thinking about how to write a formula for the current density, $J$, of a ring of charge $Q$ and radius $R$ that is spinning with period $T$. 
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The algebraic expression they have written for the current density $J$ is: The algebraic expression they have written for the current density $J$ is:
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Other people in the group believe that the symbol d should be reserved for things that are differentials in the precise mathematical sense. $dQ$ is not the differential of anything and so they do not want that written down.  This particularly rears its ugly head with the switch over to thermodynamics and the students need to distinguish between things that are exact differentials like $dU$ for the internal energy versus things that are not exact differentials like FIXME d(slash)Q or d(slash)W or the heat or the work.  This distinction is so important that the d(slash) symbol has been developed.  Her personal view in these slightly lower level courses has been to emphasize that what one is chopping up is always physical space and that one then adds up some physical quantity on that little chopped up piece so that in this case she would always write $Q$ = integral of $\lambda Rd\phi$.  She has been on the fence about using $dQ$ explicitly because she has always felt like it would help some people and make it worse for other people.  So this is a video clip where one student is spontaneously using $dQ$ probably because it has been used by either his high school or intro course teachers, it is a common symbol, and it totally confuses one of the other students in this group.  Now we have some actual evidence about what happens to students around this question. Other people in the group believe that the symbol d should be reserved for things that are differentials in the precise mathematical sense. $dQ$ is not the differential of anything and so they do not want that written down.  This particularly rears its ugly head with the switch over to thermodynamics and the students need to distinguish between things that are exact differentials like $dU$ for the internal energy versus things that are not exact differentials like FIXME d(slash)Q or d(slash)W or the heat or the work.  This distinction is so important that the d(slash) symbol has been developed.  Her personal view in these slightly lower level courses has been to emphasize that what one is chopping up is always physical space and that one then adds up some physical quantity on that little chopped up piece so that in this case she would always write $Q$ = integral of $\lambda Rd\phi$.  She has been on the fence about using $dQ$ explicitly because she has always felt like it would help some people and make it worse for other people.  So this is a video clip where one student is spontaneously using $dQ$ probably because it has been used by either his high school or intro course teachers, it is a common symbol, and it totally confuses one of the other students in this group.  Now we have some actual evidence about what happens to students around this question.
 +**References**
T. J. Bing, Ph.D. thesis, University of Maryland, 2008, http://www.physics.umd.edu/perg/dissertations/Bing/ T. J. Bing, Ph.D. thesis, University of Maryland, 2008, http://www.physics.umd.edu/perg/dissertations/Bing/
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 +Hymes, D. (1972).  Models for the interaction of language and social life.  In J. Gumperz & D. Hymes (Eds.), Directions in sociolinguistics: The ethnography of communication  (pp. 35-71).  New York: Holt, Rinehart & Winston.
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 +Philipsen, G. & Coutu, L. (2004). The Ethnography of Speaking. In K. L. Fitch & R. E. Sanders (Eds.), Handbook of language and social interaction (pp.l 355-380.  Mahwah, NJ: Lawrence Erlbaum.
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 +van Zee, E. H. & Minstrell, J. (1997a).  Reflective discourse: Developing shared understandings in a high school physics classroom.  International Journal of Science Education, 19, 209-228.
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 +van Zee, E. H. & Minstrell, J. (1997b).  Using questioning to guide student thinking.  The Journal of the Learning Sciences, 6, 229-271.
 +

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