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[Old Post] Jumping through Reasoning Hoops with The Spinning Hulahoop

[Note: I’m going to start pulling posts from my old blogger site to wordpress.]

This is a situation that I’ve been sharing and discussing with colleagues over the past few months:

Imagine you and friend are holding a hula hoop. Your friend grasps one part of the hula hoop in his hand (not so tight that it won’t move through his hand), and you start spinning the hula hoop around until it seems to reach a constant rate of rotation. At this point, I just want to consider what’s going on while the hula hoop is and continues to rotate at a seeming constant rate.

Now, based on my description, the hula hoop system can be described as having a constant influx of energy (from you pushing). That rate of energy in to the hula hoops is equal to the rate of energy being lost into your friend’s hands. The equality of inflow and outflow rates seems consistent with the idea that the hulahoop is moving with a constant speed, and thus has a constant kinetic energy.

Consideration #1
Energy would seem to flow into system at your hand, and flows out at your friends hand. But your hand and your friend’s hand are spatially separated. This leads us to question one: How would you explain how energy gets from one side of the hula hoop to the other?

Consideration #2
Once again, energy is being lost at your friend’s hand. But the speed of the hoop seems to be the same everywhere. More specifically, the speed of hula hoop pieces would seem to be the same on both sides of the hand. This leads us to question two: How would you explain how energy is lost at your friend’s hand, while, at the same time, the kinetic energy remains the same throughout the process of moving through the hand?

Insight #1
The hula hoop is not a rigid object. Every time you pass the hula past you, you compress a piece of the hula hoop. With your friends hand pushing back, one side of the hula hoop is actually in compression. (We’ll ignore for the moment whether or not the other side is in tension or not)

Insight #2
The compressed pieces of the hula hoop act as a energy storage mechanism. Your hand does work on pieces of hula hoop and that work goes into increasing the potential energy stored in the hula hoop. Alternatively, as pieces of hula hoop move across your friends hand, this potential energy is released as those pieces decompress. Thus, the energy lost at the hand is not the kinetic energy of hula hoop; rather it is the potential energy that was stored in the compressed parts of the hula hoop.

Consideration #3
The compressed pieces of the hula hoop are necessarily more dense than the pieces that are uncompressed (i.e., the compression forces the atoms closer together). Since the mass of the hula hoop must be conserved at each point in the circle, this requires that the less dense pieces move faster than the dense pieces (which move slower). This leads us to this questions: If your friend’s hand is pushing back on the hula hoop pieces that move through it, how would you explain how the hula hoop pieces end up moving faster on the other side?

Insight #3
The piece of hula hoop right in your friend’s hand is actually sandwiched between two different regions with distinct mass densities. Behind your friend’s hand, the hula hoop is squished up like a spring. This “spring” creates a force which accelerates the hula hoop piece through your friend’s hand, leaving it with a faster speed than before. This faster speed is consistent with the fact that the atoms are more spaced out. The faster speed allows it to get further away from the pieces behind it, which are still moving at the slower speed.

Oddity #1
Intuitively, your friend’s hand would seem to the agent slowing things down. On the other hand, as defined by the original problem, the hula hoop seemed to be moving at a constant speed through out the whole process. Through the reasoning we’ve walked through, we’re concluded that pieces of the hula hoop actually speed up through this region.

Loose ends and questions:

#1: It only really makes sense to describe the hula hoop as having a single rotation rate if it is a rigid body. Given that we’ve concluded it can’t be a rigid body, is there a single quantity which describes the flow rate. Is it momentum? Is it kinetic energy? Is it mass current? Does this necessitate a change to the chain of reasoning anywhere?

#2: Is the other side of the hula hoop in tension? Is there any reason to think the hula hoop arc length is longer than, shorter than, or the same as it’s resting arc length?

#3: How quickly does energy propagate from your hand to your friend’s hand? How does this compare to the rate at which hula hoop pieces make the same journey?

#4: What’s going on during the initiation stage before and as the hulahoop reaches steady state? Is this consistent with our stead state solution?

#5: What does this have to do with an electric circuit with a bulb, battery, and wire?

#6: Could you explore the validity of my story experimentally? How would you do it? Could you explore the validity of my story with a simulation? How would you do it? With either, what assumptions or approximations would you need to make?

#7: What parts of my story seem wrong? What assumptions have I made? Are they reasonable assumptions? What aspects of the situation am I ignoring? Is it reasonable? Overall, is this a viable model? How could you tweek it or refine it?

#8: Typically, we use energy to tell stories about initial and final states. Have we gained anything by trying to tell a spatially and temporally continuous energy story? Why is it so hard to tell such stories?

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Epistemology–Everything is Epistemology

Today, I tried to move our class  toward building “consensus statements” about how light gets from one place to another. I had referred our activity as trying to come up with “rules for light” That move didn’t go quite as well as it has in the past, and I was really struggling to understand why. From the daily sheets, I found this gem where a student describes what didn’t make sense to them:

Rules of light. Can there be any rules? What if light is an “outlaw” defying all rules placed on it? Does light really adhere to a strict set of rules? This is what is not making sense to me.

I love this. It’s like she was saying, “What right do we have to expect that nature could possibly be held accountable to a set of rules? Let alone rules that we come up with? Who would enforce these rules?”

* OK, so the truth is, this epistemological isn’t why the activity didn’t go well. It didn’t go well, because students were still really struggling in trying to understand a set of observations that had been made and some confusing, complex, difficult ideas that had been presented to explain those observations. I moved us on to rules too quickly, before it made sense to do so. Either way, this student quote speaks to an issue I think is interesting, complex, and worthy of my attention.

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Rights and Responsibilities (Spring 2013)

I forgot to post these before. I think it’s interesting to look at how at how rights and responsibilities get articulated differently each semester:

Fall 2011

Spring 2012

Fall 2012

Finally, this year

Student Rights    

To ask questions without fear of judgment

To develop our own opinions and ideas

To disagree–even assertively (at times), but never aggressively

To be wrong and to change one’s mind

To have a supportive environment in which to learn

Student Responsibilities    

To ask for clarification when expectations are not clear

To respect others’ opinions  and ideas

To  disagree constructively

  • Restating others ideas before disagreeing
  • Give reasons why you disagree

To stay on topic, but also be willing to go with flow at times
To  learn through participation, both as a class and in small group

  • To  be prepared
  • To  contribute
  • To  be engaged

To  actively listen to others, and not interrupt

To be honest (i.e., don’t pull a Lance Armstrong)
 

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Getting Better Diagrams from My Students

After the first assignment in inquiry where they had to both write and a draw in order to explain something, I gave them a list of criteria to help them to distinguish between what I think makes something more “diagram-like” and more “sketch-like”.

My criteria were the following:

Sketches:

  • Might be drawn small, crowded, or scribbly
  • Might only show the “gist” of what happened without much detail
  • Might not include any aides to help someone understanding
  • Might only depict a situation, without really helping to tell a story of how or why

Diagrams:

  • Are often drawn spaciously with every mark made with care and deliberation
  • Are often trying to show someone important details
  • Often include aides to help someone understand what’s being shown to them
  • Are aiming to tell a complete story of how or why something happens

In class, I had them look over and discuss the criteria in groups, and then I put diagrams from our homework under the document camera. Groups were asked to discuss what they notice about the diagram for a few minutes–what features of it are more “diagram-like” what features or more “sketch-like”? What’s something we could change about the drawing to make it more “diagram-like”? What’s something in this diagram that you might want to “steal” for your drawings?

For each drawing, after small groups talked, we shared things we noticed as a class. My goal was to press for specificity in what they were seeing in the diagram and to ask for explanations of why they thought what they did. I tried to keep in snappy, but it still took a while, because we repeated this for about 6 or 7 diagrams. At the end, I had students go back to discuss in their groups (and then write in their notebooks) any strategies and ideas they would like to incorporate in their next homework for crafting better diagrams. Things that came up as I walked around included things like

  • Meaningful color-use, not just color for color’s sake
  • Use of labels in diagrams or a key to the side of the diagram
  • Splitting up a big diagram into a series of diagrams
  • Using “inset” diagrams to show detail (e.g., a zoom-in of a city on a state map)
  • Using arrows to depict directionality or numbers to establish the sequence
  • Showing multiple perspectives of the same thing

We’ll see how the homework comes in next week, but I could already tell from students’ notebooks and their whiteboards that it had a big impact.

Leslie Atkins, by the way, has a great peer assessment activity for improving student diagrams that was published in The Physics Teacher recently.

 

 

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Daily Sheets Snippets

“I no longer believe that… but I also don’t think it’s…”

“I still can’t explain why…”

“I can’t wait to share my idea about light.”

“I am still wondering why…”

“It didn’t make sense that … when we…”

“I love that…”

“It blew my mind that…”

“I thought to myself why can’t we see… If it’s… and…, then we should be able to… but we can’t.”

“I’m still having a hard time understanding why…”

“Today, I’m starting to understand…”

“I still do not know and can’t make sense of how/why… I almost feel like it’s…”

“I get that…, but WHY?”

“I understand (or at least I think I do!) why the…”

“I loved their presentation. It made complete sense to my brain”

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Bouncy Ball Graphs

One of my favorite tasks for students to do is to create well-coordinated position, velocity, and acceleration vs time graphs for a bouncy ball, where careful attention is given to the moments of contact with the floor. I got this task from my high school physics teacher, but it’s in Arons’ book as well. The future physics teachers have this as a content standard in my class. There are many predictable obstacles, but the real meat I want them to get to is reasoning about the acceleration. This is so not easy for them-partially because they mostly know acceleration through special cases, and partially because they aren’t strong in thinking about vector kinematics. Mostly students say the acceleration is constant. It’s like the bounce isn’t even on their radar when considering acceleration. Part of what I like about it, is that students know enough to get started and the task itself is clear. My job when they ask to assess, is to keep them talking until they notice some inconsistency, and then to help them orient to that inconsistency and how they knew there was something wrong. Then I send them off.

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Revoicing and Retrospective Recontexualisation

Lemke writes in “Analyzing Verbal Data” about the concept of retrospective recontextualisation

“Discourse forms do not, in and of themselves, “have” meanings; rather they have a range of potential meanings. Words, phrases, sentences are tools that we deploy in complex contexts to make more specific meanings, to narrow the potential range of possible meanings down to those reasonably or typically consistent with the rest of the context. Even in context, at a moment, an utterance or phrase may not have a completely definite meaning. It may still express a range of possible meanings, differently interpretable by different participants or readers. This is very often the case at the point where it occurs. The context needed to specify its meaning very often at least partly follows its occurrence. So it may seem to have a more definite meaning retrospectively than it has instantaneously. In fact, depending on what follows, its meaning, as participants react to it, can be changed radically by what follows (retrospective recontextualisation).”

I thought about Lemke recently while reading Alex Barr’s post* about productive prior knowledge. In that post, he describes a discussion he had concerning the common misconception about the moon’s phases (i.e., the earth’s shadow is cast on the moon), and how you can think about that misconception in terms of kernels of productive knowledge (e.g., the moon itself blocks light from getting to the back half).

Lemke argues in the above passage that the meaning given to any student utterance happens in interaction, in part based on what proceeds the utterance itself. I’m imagining this in the context of teacher re-voicing. Specifically, I was imagining three different revoicings that might occur after a student makes a statement like, “The phases are casued by the earth’s shadow falling over the moon,” and how they might, retrospectively, change the meaning of the student utterance. Here’s the gist of several possible re-voicing.

“It sounds like you are trying to draw our attention to an important idea we should consider in explaining the moon’s phases–light from the sun can be blocked by objects that get in the way. “

“It sounds like you are saying that there must be something blocking sunlight from getting to certain parts of moon. And you’re proposing that one thing that could be doing that blocking is the earth.”

“So your idea is that if the earth were to block some of the light from getting to the moon, then we’d see changes to how much of the moon is lit.”

“It sounds like you are saying the

Its interesting to me how these different voicings may (or may not) change the meaning of the student idea. The first one (in my mind) attempts to re-voice the idea by focusing on what the teachers know to be a kernel of truth, downplaying subtly what is not true. The second one attempts to re-voice the idea as a particular case of a more general principle, perhaps opening up the idea, giving it room to breath and be connected to other ideas. The third one re-voices the idea as a conditional proposition–one that the teacher knows to be true about lunar eclipses. A more straight forward re-voicing such as, “It sounds like you are saying that the phases of the moon happen when the earth blocks light from getting to the moon,” seems to narrowly frame the idea, sort of pinning it down, giving it no where to go. The re-voicing doesn’t help to put the idea in a broader context or to highlight any parts of it as being more or less significant.

One reason I’ve been thinking about this so much is because next semester, one of the goals for teaching of physics is to develop skills at facilitating classroom discussion. One of the discourse “practices” we will focus on is “re-voice and toss“. There are of course, lots of reasons for re-voicing, but I feel like I’m circling around something here… hopefully more to write on this later.

* Alex is a burgeoning physics education researcher at the University of Texas at Austin, who you should say hello to, get to know, and keep your eye on. *

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Teaching Evaluations Data

I’ve been making my course evaluations public since I got here. Here they are again, whatever they mean.

Physics Fa 11 Sp 12 Fall 12 Dept Avg
Presentation 4.9 4.9 5.0 4.1
Organization 4.8 4.8 4.9 4.0
Assignments 4.8 4.9 4.9 4.3
Scholarly 4.7 4.8 4.9 4.0
Interactions 4.9 4.9 4.9 3.8
Motivating 4.7 4.7 4.8 4.0
Overall 4.5 4.6 4.5 3.7
Inquiry Fa 11 Sp 12 Fall 12 Dept Avg
Presentation 4.4 4.7 4.8 4.1
Organization 3.9 4.3 4.4 4
Assignments 3.9 4.3 4.4 4.3
Scholarly 4.0 4.2 4.7 4
Interactions 4.5 4.6 4.9 3.8
Motivating 4.2 4.6 4.6 4.0
Overall 3.0 3.5 4.0 3.7

 

 

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Notes to Self about Engagement with the Seasons

For the seasons unit, I’ve done a fair amount of giving students data sets to graph, looking for patterns, similarities, difference. We have been doing so in order to build evidence for or against various claims about what could cause the seasons. I think we’ve learned a lot along the way.

Anyway, there are two observations that have driven student a fair amount of engagement, and I don’t want to forget them:

#1 McCurdo Station in Antarctica has the sun shining on it for 4 straight months, but its average temperature is still below freezing during that time. [If duration was only factor, then we’d expect McCrudo Station to be very hot]

#2 In June, Murfreesboro, TN is 20 degrees hotter than Quito, Ecuador. [Shouldn’t the equator always be hotter?]

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Beginning a Short Unit on the Seasons

So, we are ending the year in inquiry by studying the seasons. We started by talking about the following situations:

(1) You are at a concert. What could you do to increase or reduce the impact of the sound on your ears?

(2) You are by a fire. What could you do to get hotter or colder?

After they muddled with those situations, I introduced a third test case.

(3) A person in the room has a smelly perfume? What could you that would make your experience of the smell more or less intense?

 The goal was to generalize a set of general patterns on what affects the intensity of “emanating stuff”. Our initial list was the following:

Volume (how strong the actual source of smell, sound, or heat is)

Proximity (how near are far you are from the source of smell, sound, or heat)

Duration (how much time you spend around the smell, sound, or heat)

Protection (how many barriers, blockers, or filters are between you and the source of heat, sound, smell)

We went into the detail explaining how these might work in each case, but that’s the gist.

An Experiment to Foster Thinking about A New Mechanism

Two identical heat lamps were set 10 inches away from a sheet of paper. Under the sheet of paper was a thermometer. The identical lamps fixed the volume. The 10 inches set the proximity. We set the duration time to 1 minute. The identical paper fixed the level of protection.  One lamp was set to shined directly down on the paper, and the other was set to shine at a very shallow angle (being careful to keep the 10 inch separation from the thermometer).

Students were asked to discuss what would happen to the temperature when I turned on the lamps.

Most groups believed correctly that the lamp shining straight down would make it hotter. Here is how we eventually built pieces of an explanation for why angle matters:

  • You are more likely to be burned by the sun from in the middle of the day, than the morning or evening, the sun’s rays must in some way be stronger when overhead than we angled low in the sky.
  • Direction also matters for our previous example. With fire, you can turn your cheeks toward fire to give it more direct access to fire’s heat. With a sound you can turn your ears away. With sound, you can turn your nose away.
  • With angled light, the rays of light hit the paper at a shallow angled creating a “glancing blow“, like skipping a stone on water, or a car hitting a wall at angle (vs. throwing a pebble straight into the water or driving you car head-on into a wall). The shallow angle creates only a glancing blow, which has less impact than a “head-on” collision.
  • With angled lamp, the light rays end up hitting a large area on the paper; where as the angled down rays hit the paper in a small area. This changes the concentration of the heat. It’s like heating up a large room or a small room with the same space heater. The large room will take longer to warm up, and may not even get up to same heat, because the heat gets spread out more.

We did the experiment, and in one minute the overhead lamp heated the thermometer to 130 degrees, while the angled lamp only heated up the thermometer to 78 degrees. Huge difference. I even rigged the deck in opposite way so that the angled lamp was actually closer than 10 inches and it got the thermometer that read a little higher. It was no contest. We added a new factor to our list, so that we now have:  Volume, proximity, duration, protection, and now direction.

Our goal over the next 3 days will be to figure out which of our 5 factors are most significant for explaining the seasonal changes to temperature–that is to collect evidence and arguments for the relative importance of each and to refine our sense of mechanism about how they work in the case of earth.

Why I’m liking this approach?

#1 We are drawing on knowledge from everyday experience : sitting by a fire to keep warm, smelling something rotten, being around loud music, etc. Had I asked what causes the seasons, it would have been about orbits and tilts. That would lead us down a frustrated track of sterile and unproductive school knowledge.

#2 We were generalizing quickly from a set of particulars, and naming them to help support generalization. We were not not just swimming in a vast sea of specific situations, and hoping that abstraction and connections were made. I specifically asked them to connect case specific mechanisms and to come up with general names.

#3 We are making sense of contrived situations in terms of everyday mechanism, such as getting burned, car crashes, skipping stones, and heating rooms. While I suggested the situations early on, students quickly extended to and built on other everyday sources of knowledge. This suggests that I helped “frame” the conversation as building on everyday knowledge. Going to the contrived could have tipped us out of, but it didn’t.

#4 Keeping the initial conversation away from the learning target (i.e., the seasons) and toward other phenomena (i.e., fire, sound, smell), keeps my “misconceptions” ears from perking up. Instead, I’m listening for useful ideas, analogies, observations, mechanism, insights, etc.  My listening patterns in turn influence my interactions with students, which in turn influences the nature of the discourse that emerges. My commitment and ability to focus on the good students say rather than the wrong stuff depends on the context I set up. I’m setting up a context, not only in which students will hopefully draw on everyday ideas productively, but I’m setting up a context in which I will be more likely to hear and draw on their ideas productively.

#5 I hope this will get us to “tilt” last, which is the empty vacuous understanding that many students have. Instead, I hope we will initially focus our explanations on locally observable changes, such as changing amounts of daylight and changing altitude of the sun in the sky. Tilt will be, hopefully, for the purpose of explaining the changing daylight and changing altitude. Thus, changing daylight and changing altitude will be the explanation for the seasonal variation in temperature.

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