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whitepapers:narratives:ptchargeshort 2011/06/08 10:41 whitepapers:narratives:ptchargeshort 2014/07/23 16:42 current
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=====Examples of Spontaneous Use of Small White Boards===== =====Examples of Spontaneous Use of Small White Boards=====
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====Using a White Board to Clarify a Student’s Thinking [01:07:35.01] - [01:09:36.07]==== ====Using a White Board to Clarify a Student’s Thinking [01:07:35.01] - [01:09:36.07]====
-The long narrative presents what had happened when Corinne had asked the class to write on their small white boards an expression for the electrostatic potential at a particular location in space due to a point charge.  She had collected a representative set of the students’ responses and then discussed these. Several times during that discussion, she spontaneously asked students to write what they were thinking on their small white boards so that she and the other students could understand better what they were trying to say.  For example, a student offered an analogy as a way to think about potentials:+{{whitepapers:narratives:clarifystudentthinking.mov|Video Clip}} 
 + 
 +The short narrative presents what had happened when Corinne had asked the class to write on their small white boards an expression for the electrostatic potential at a particular location in space due to a point charge.  She had collected a representative set of the students’ responses and then discussed these. Several times during that discussion, she spontaneously asked students to write what they were thinking on their small white boards so that she and the other students could understand better what they were trying to say.  For example, a student offered an analogy as a way to think about potentials:
Student: Way I think about it is to relate the electric potential to the gravitational potential Student: Way I think about it is to relate the electric potential to the gravitational potential
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Corinne: Write me down your equation so I can hold it up Corinne: Write me down your equation so I can hold it up
-The student wrote W = F⋅d and then  V =  K Q1Qd/r2 from 0 to d+The student wrote $W = F\cdot d$ and then  $V =  \int K Q_1 Q_d/r^2$ from 0 to $d$
{{whitepapers:narratives:070927ph320wb_8.jpg?300 |}} {{whitepapers:narratives:070927ph320wb_8.jpg?300 |}}
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but I think that's a variant of this. but I think that's a variant of this.
-Corinne reached for and held up the white board with V = ∫E⋅ds that had been discussed earlier.+Corinne reached for and held up the white board with $V = \int E\cdot ds$ that had been discussed earlier.
Corinne: Since if there's only one thing in the universe, we can't yet be talking about forces, Corinne: Since if there's only one thing in the universe, we can't yet be talking about forces,
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By welcoming the student’s suggestion, prompting him to write out his idea on his small white board, holding up the board for the rest of the class to see, and discussing its contents, Corinne had used a student’s writing on a small white board in the midst of the discussion to help communicate the student’s thinking to the rest of the class.  Although the physics was not appropriate - his suggestion referred to forces, which could not occur with only one charge in the universe - she took care to complement the thinking - his reasoning and effort to pull relevant information from his memory.  By welcoming the student’s suggestion, prompting him to write out his idea on his small white board, holding up the board for the rest of the class to see, and discussing its contents, Corinne had used a student’s writing on a small white board in the midst of the discussion to help communicate the student’s thinking to the rest of the class.  Although the physics was not appropriate - his suggestion referred to forces, which could not occur with only one charge in the universe - she took care to complement the thinking - his reasoning and effort to pull relevant information from his memory. 
 +
====Example of Using a Small White Board to Clarify a Student’s Question [01:15:25.12]- [01:17:14.02]==== ====Example of Using a Small White Board to Clarify a Student’s Question [01:15:25.12]- [01:17:14.02]====
-After the class had come to agreement on an appropriate expression for the electrostatic potential due to a point charge, V= k Q/r, Corrine initiated a discussion about the meaning of r, what distance was it representing?  Speaking with hesitation expressed as a question, a student offered a more nuanced expression for the distance between the charge and the probe:+{{:whitepapers:narratives:sy07092704mpt1subclip2.mov|Video Clip}}
-Student: r minus r naught?+After the class had come to agreement on an appropriate expression for the electrostatic potential due to a point charge, $V= k Q/r$, Corrine initiated a discussion about the meaning of $r$, what distance was it representing? Speaking with hesitation expressed as a question, a student offered a more nuanced expression for the distance between the charge and the probe:
-Corinne: What about r minus r naught?+Student: $r$ minus $r$ naught? 
 + 
 +Corinne: What about $r$ minus $r$ naught?
Student: The distance between there and there Student: The distance between there and there
Corinne: Write me something on your white board.  Corinne: Write me something on your white board. 
-I don't know what r minus r naught means.+I don't know what $r$ minus $r$ naught means.
Corinne and the class waited and watched while the student wrote his expression on his small white board.  Then she held it up for all to see: Corinne and the class waited and watched while the student wrote his expression on his small white board.  Then she held it up for all to see:
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Corinne agreed that when a student asks about a formula, she and the student can communicate much more clearly if the student writes the formula on a small white board.  She noted that this is what professionals do when talking with each other, they write on napkins or backs of envelopes or whatever board is nearby to be sure that they understand and agree on the formula that they’re discussing. Corinne agreed that when a student asks about a formula, she and the student can communicate much more clearly if the student writes the formula on a small white board.  She noted that this is what professionals do when talking with each other, they write on napkins or backs of envelopes or whatever board is nearby to be sure that they understand and agree on the formula that they’re discussing.
-Corinne: Ah. Ok!  He's trying to write a magnitude of r minus r naught. +Corinne: Ah. Ok!  He's trying to write a magnitude of $r$ minus $r$ naught. 
-So where is r and where is r naught?+So where is $r$ and where is $r$ naught?
-Student:  r naught is at the origin +Student:  $r$ naught is at the origin
Corinne: Where is the origin? Corinne: Where is the origin?
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Corinne put down the student’s white board and while still holding up the ball representing the charge, held up the coordinate system so all could see it. She then put both the ball and the coordinate system down together on the table. Corinne put down the student’s white board and while still holding up the ball representing the charge, held up the coordinate system so all could see it. She then put both the ball and the coordinate system down together on the table.
-Corinne: Ok. So I'm going to put this charge at the origin.  +Corinne: Ok. So I'm going to put this charge at the origin.\\\\  
-\\\\Imagine it's in the center.+Imagine it's in the center.
All right.  And then? All right.  And then?
Corinne picked up the student’s white board again and held it up for the students to see. Corinne picked up the student’s white board again and held it up for the students to see.
-Student: The r is wherever you’re thinking about at the moment+Student: The $r$ is wherever you’re thinking about at the moment
Corinne walked back to the table and picked up the probe and held it high for all to see: Corinne walked back to the table and picked up the probe and held it high for all to see:
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If I put the charge at the origin, then what does that tell you about this? If I put the charge at the origin, then what does that tell you about this?
-She pointed at the r in r – r’ on the student’s white board:+She pointed at the $r$ in $r – r’$ on the student’s white board:
-Students: r naught is zero+Students: $r$ naught is zero
Corinne: Then it's just zero.  What kind of a zero? Corinne: Then it's just zero.  What kind of a zero?
It's a zero vector. It's a zero vector.
-All right.  So the zero vector minus r prime +All right.  So the zero vector minus $r$ prime
is just the vector from the origin (points to coordinate system on the table) is just the vector from the origin (points to coordinate system on the table)
to here (picks up probe). to here (picks up probe).
-In discussing this video, Corinne noted that in a discussion in which she was trying to help the students understand which is r and which is r prime, that she had mixed it up herself.  So the words “zero vector minus r prime” should have been “the zero vector minus r.”  Fortunately the rest of the discussion was correct and she hopes she did not confuse anybody too much.+In discussing this video, Corinne noted that in a discussion in which she was trying to help the students understand which is $\vec r$ and which is $\vec r'$, that she had mixed it up herself.  So the words “zero vector minus $r$ prime” should have been “the zero vector minus $r$.”  Fortunately the rest of the discussion was correct and she hopes she did not confuse anybody too much.
So yes indeed, if I put this charge at the origin (points to coordinate system), So yes indeed, if I put this charge at the origin (points to coordinate system),
-then this r here (points to white board with correct formula V = Q/4πε0r) +then this r here (points to white board with correct formula $V = Q/4πε_0 r$)
is just the distance from here (ball representing charge) is just the distance from here (ball representing charge)
to here (voltmeter probe), to here (voltmeter probe),
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During this conversation about r minus r naught, a webcam videoing group 6 shows a student sitting quietly until Corinne says “write on your white board” to the student with whom she is conversing about r minus r naught. The student shown on Webcam 6 turns to his white board in response even though the comment was not directed to him.  During this conversation about r minus r naught, a webcam videoing group 6 shows a student sitting quietly until Corinne says “write on your white board” to the student with whom she is conversing about r minus r naught. The student shown on Webcam 6 turns to his white board in response even though the comment was not directed to him. 
-Visible in the video was the student’s initial response on his white board to Corinne’s planned small white board question, what is the electro potential due to a point charge? When Corinne initially posed this question, the student had drawn a circle, put a question mark in the circle, drawn an arrow pointing to the circle, and after a long pause while thinking, finally written kQ/r2. He also added some words (that cannot be discerned on the video.)  Throughout the long discussion of the various student responses that Corinne had facilitated, he had not changed anything on his small white board.  +Visible in the video was the student’s initial response on his white board to Corinne’s planned small white board question, what is the electro potential due to a point charge? When Corinne initially posed this question, the student had drawn a circle, put a question mark in the circle, drawn an arrow pointing to the circle, and after a long pause while thinking, finally written $kQ/r^2$. He also added some words (that cannot be discerned on the video.)  Throughout the long discussion of the various student responses that Corinne had facilitated, he had not changed anything on his small white board. 
-However, now in response to Corinne’s direction to another student “write on your white board,” this student took his cloth eraser and carefully erased the 2 from the r squared. Then he also revised his drawing by extending the line to the center of the circle and labeling the line r.+However, now in response to Corinne’s direction to another student “write on your white board,” this student took his cloth eraser and carefully erased the 2 from the $r$ squared. Then he also revised his drawing by extending the line to the center of the circle and labeling the line r.
This spontaneous correction by a student on what he had written earlier on the small white board illustrates another advantage of these devices, that they can provide a prominent visual image of the focus of a discussion for each student, one that the student can revise later as needed. This spontaneous correction by a student on what he had written earlier on the small white board illustrates another advantage of these devices, that they can provide a prominent visual image of the focus of a discussion for each student, one that the student can revise later as needed.
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Corinne: So if you're really clever, you can put one at the origin Corinne: So if you're really clever, you can put one at the origin
-and you can put the other one along the x axis +and you can put the other one along the $x$ axis
(picks up coordinate system) (picks up coordinate system)
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(points to board) (points to board)
-But do I have to put my probe also on the x axis somewhere between them?+But do I have to put my probe also on the $x$ axis somewhere between them?
Student B: Well I Student B: Well I
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A student’s spontaneous and unexpected contribution prompted this interaction among the instructor and several students.  The student had used the resource of a small white board to express what she was thinking by sketching a diagram, the sketch made her thinking visually available to the instructor who leaned over to see what the student was drawing, the student was able to offer her thinking via the small white board to the instructor who then was able to convey and discuss the student’s ideas with the whole group; several members of the whole group then contributed to the conversation, and made explicit the connection between the current discussion and the activity in which the students had participated earlier in the session. A student’s spontaneous and unexpected contribution prompted this interaction among the instructor and several students.  The student had used the resource of a small white board to express what she was thinking by sketching a diagram, the sketch made her thinking visually available to the instructor who leaned over to see what the student was drawing, the student was able to offer her thinking via the small white board to the instructor who then was able to convey and discuss the student’s ideas with the whole group; several members of the whole group then contributed to the conversation, and made explicit the connection between the current discussion and the activity in which the students had participated earlier in the session.
 +

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