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whitepapers:narratives:ptchargeshort 2011/06/08 10:27 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=====
=====Physics Paradigms Physics 320, Thursday, September 27, 2007===== =====Physics Paradigms Physics 320, Thursday, September 27, 2007=====
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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]
-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:+====Example of Using a Small White Board to Clarify a Student’s Question [01:15:25.12]- [01:17:14.02]====
-Student: r minus r naught?+{{:whitepapers:narratives:sy07092704mpt1subclip2.mov|Video Clip}}
-Corinne: What about 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:
+
+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:
- + {{ whitepapers:narratives:070927ph320wb_9.jpg?300|}}
While viewing this segment of the video, Liz commented about this use of the small white boards, that Corinne was asking individual students to write mathematical expressions on the small white boards so that the students could communicate more clearly with Corinne and so that Corinne could use the white board to communicate their shared meaning to the rest of the class.  Not only can an instructor ask small white board questions to the entire class but one can also ask them of individuals to help clarify their meanings. While viewing this segment of the video, Liz commented about this use of the small white boards, that Corinne was asking individual students to write mathematical expressions on the small white boards so that the students could communicate more clearly with Corinne and so that Corinne could use the white board to communicate their shared meaning to the rest of the class.  Not only can an instructor ask small white board questions to the entire class but one can also ask them of individuals to help clarify their meanings.
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.
-So where is r and where is r naught?
-Student:  r naught is at the origin +Corinne: Ah. Ok!  He's trying to write a magnitude of $r$ minus $r$ naught.
+So where is $r$ and where is $r$ naught?
+
+Student:  $r$ naught is at the origin
Corinne: Where is the origin? Corinne: Where is the origin?
-[01:16:13.11]+
The student pointed at a representation of a coordinate system, the three dowel rods connected at right angles, that was sitting on a table in front of Corinne. The student pointed at a representation of a coordinate system, the three dowel rods connected at right angles, that was sitting on a table in front of Corinne.
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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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In viewing this segment of the video, Corinne commented that she was trying to get the students to see the difference between scalars and vectors and by manipulating the physical things, trying to get them to focus on the geometry. In viewing this segment of the video, Corinne commented that she was trying to get the students to see the difference between scalars and vectors and by manipulating the physical things, trying to get them to focus on the geometry.
-Example of a Student’s Spontaneous Correction of His Own Small White Board +====Example of a Student’s Spontaneous Correction of His Own Small White Board [webcam 1:26-1:27; 1:42-1:43]====
- [webcam 1:26-1:27; 1:42-1:43] +
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.
-Considering a Student’s Spontaneous Use of a Small White Board to Contribute an Idea to the Discussion [01:18:50.11] -  +====Considering a Student’s Spontaneous Use of a Small White Board to Contribute an Idea to the Discussion [01:18:50.11] - ====
- +
After establishing the meaning of r in the formula for the electrostatic potential due to a single point charge, Corinne had introduced a second charge.  How could one represent the electrostatic potential at a particular location due to two point charges?  In the midst of this discussion, Corinne paused.  In the video she can be seen bending forward to look at what one of the students was writing and drawing on her small white board at a table nearby.  Meanwhile another student responded verbally: After establishing the meaning of r in the formula for the electrostatic potential due to a single point charge, Corinne had introduced a second charge.  How could one represent the electrostatic potential at a particular location due to two point charges?  In the midst of this discussion, Corinne paused.  In the video she can be seen bending forward to look at what one of the students was writing and drawing on her small white board at a table nearby.  Meanwhile another student responded verbally:
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Corinne: All right.  So you want me, Corinne: All right.  So you want me,
You're going to make me work really hard for this answer You're going to make me work really hard for this answer
-[01:19:14.00]+{{whitepapers:narratives:070927ph320wb_10.jpg?300 |}}
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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)
-[01:19:22.09]+
Right? So then you can just use a scalar distance there Right? So then you can just use a scalar distance there
(points to board) (points to board)
-[01:19:28.28] +
-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
Corinne: What if I want to measure up here? (holds probe up high) Corinne: What if I want to measure up here? (holds probe up high)
-[01:19:38.29]
Another student explained the situation if there were only one charge: Another student explained the situation if there were only one charge:
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So if you go out from it at any radius in 3-D, So if you go out from it at any radius in 3-D,
you get the same potential. you get the same potential.
-[01:19:48.20]+
Corinne accepted her suggestion also, made it vivid by holding up the probe to represent measuring the potential anywhere in space around the charge, and then articulated the constraints in system with more than one charge. Corinne accepted her suggestion also, made it vivid by holding up the probe to represent measuring the potential anywhere in space around the charge, and then articulated the constraints in system with more than one charge.
Corinne: Right. If I go out anywhere around this one (holds up probe) Corinne: Right. If I go out anywhere around this one (holds up probe)
the same radius, I get the same potential.  Absolutely. the same radius, I get the same potential.  Absolutely.
-[01:19:55.23]+
But as I go probing around here (moves probe around) But as I go probing around here (moves probe around)
and I'm getting the same potential from this one (points to ball), and I'm getting the same potential from this one (points to ball),
I'm not staying the same radius from that one (points to basketball) I'm not staying the same radius from that one (points to basketball)
- [01:20:05.06]+
Corinne: So all I want is the mathematics of how I describe the distance Corinne: So all I want is the mathematics of how I describe the distance
between here (probe) and here (ball on table). between here (probe) and here (ball on table).
-[01:20:10.02]
Another student contributed a thought: Another student contributed a thought:

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