In the teaching of physics, we have been learning about student difficulties in kinematics. So far, we have mostly

• Examined, interpreted, and discussed artifacts of students’ written work in kinematics
• Read and discussed research articles describing student difficulties in learning kinematics
• Read and discussed teacher accounts about the teaching and learning of kinematics
• Worked through problems and curriculum designed with knowledge of student difficulties
• Applied knowledge of student difficulties to generate example student solutions

There have been four broad categories of things we’ve examined in context of student learning about kinematics.

• Student being capable and being in habit of mind to discriminate concepts that similar but different.
• Student being able to relate representations of motion to actual motions, and relate kinematic definitions to actual ways of observing, determining, and measuring
• Students being able to verbally interpret the meaning of kinematics concepts and use those interpretations to reason about an object’s motion.
• Students having a “flexible” tool kit of strategies, representations, and mindsets for engaging in problem-solving that goes beyond substituting into equations.

Yesterday, we began work in consolidating parts what we have learned. Our first consolidation activity was to create icons, diagrams, drawings, situations, phrases that represent each of the different kinematic distinctions that need to be supported as part of learning. Here are examples of what we came up with.

Interval of Time vs. Instant of Time

“An 8 O’Clock Class” vs “An 8-hour long Class”

(Both are miserable, but for different reasons)

Position vs. Change in Position vs. Distance

Position vs. Velocity

Average vs Instantaneous Velocity

Acceleration vs. Velocity

Going 60 mph for 4 seconds

Going “0-60” in 4 seconds

One group tried to put everything into one diagram with a GPS, either as something embedded in one snap shot, or something concerning what’s change from one snap shot to next.

Following this activity we discussed a few of the instructional ideas we had encountered for helping students to distinguish these concepts as part of their understanding of kinematics

• Being explicit about these distinctions (rather than shoving them under the rug or hoping they will come along for the ride)

The shortcuts, omissions, and ‘simplifications’, which are meant to reduce complexity are not conducive to understanding; they are specious, and they make genuine understanding extremely difficult. (Arons, “Teaching Introductory Physics”, pg. 24)

• Being aware of subtleties in language (e.g., “at” often indicates instants/locations and “for” often indicates durations/distance ), and pressing for specificity in language (i.e., asking “What it is ?” when students use “it” instead of naming quantity specifically)
• Using problems that require students to make such distinctions (e.g., problems where objects don’t start at origin; problems with information given as both distances and positions or clock-readings and elapsed times).

• Requiring students to explicitly articulate the difference themselves verbally and in writing (coming up with examples, analogies), like this one from Physics by Inquiry

• Requiring students to consider and respond to faulty reasoning in which such distinctions are not made (similar to one’s we’ve seen in Physics by Inquiry)

• Requiring students to respond to and argue in context of potentially ambiguous situations (e.g., kinematics traffic court)

Anyway,that’s a quick brain dump. There’s a whole lot more for us to consolidate and reflect on, and so much more for us to learn…. how will we ever get there?

[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?

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.

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)

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.

“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”

One thing I have returned to this semester  is daily sheets in inquiry. Every day, the last 5 minutes of class is dedicated to students writing answers to the following questions:

• What did you do, think, or hear today that made sense to you? What specifically about it makes sense to you
• What did you do, think, or hear today that didn’t make sense to? What specifically about it didn’t make sense to you?

Because I have two learning assistants in class, a really useful debriefing has been the following: We divide the stack of papers in three, and we read through them. As we read, we share interesting things we find and discuss common patterns that arise. Then and only then do we talk about how things went today, where we think students are at, and what we should think about doing next. I feel like this is a really good practice for me and my learning assistants–attending to student thinking, using data to focus conversations about teaching and learning, and using data to talk about instructional planning.

After we are done, I go back to my office and read through all the daily sheets, making at least some comments on every individual person’s writing. This is important. Students need to know that I am reading and thinking about what they are writing. It’s not busy work. I make sure to return them first thing the next time I see them.

I’m really glad to be back to doing this. I needed more structured formative assessments, where I get feedback from individual students.

Here is a reflection from one of the undergraduate TAs enrolled in my teaching and learning seminar.

This week I discovered upon reflection that most of the questions I asked were very convergent. So, what I thought had been a fairly good dialogic conversation, was just a disguised univocal one. Last Friday I also noticed that I tended to have a lot of teacher-student-teacher interactions. So as Wednesday approached I tried to remain conscious of this and aim for more divergent questions and group discussions.

One of the biggest things I did differently was that when I noticed a student seemed unsure of themselves about an answer I’d just tell them to try explaining their reasoning to a random member of the group. This usually easily got discussion going and allowed me to avoid the usual teacher-student-teacher interaction. Other than that I got less timid about posing questions to groups and I found questions I initially found barely worth asking provided more discourse than I thought. This helped to remind me that I have to keep in mind that all of this material is entirely new to these students and trivial questions may very well still be worth asking.

A specific interaction I had in which I tried to engage in dialogic discourse using the questioning technique actually resulted because I was not prepared for the question. It was one of the QODEC multiple choice questions that I had looked over, but not really thought about. So, I initially just asked them to explain why they thought the answer they had picked was correct. After that, we were all still a bit unclear as to which answer would be correct, so I suggested we go through each answer and try to see what it would mean if it were correct. Doing this resulted in most of the members of the group talking to one another about why they thought certain answers were good candidates for the correct answer or not. Eventually, in this way we narrowed the answer down to two questions and I got a bit excited and accidentally gave the answer way. I did not realize that I had done so until I asked them why they chose the answer they did and they responded that thats what I picked. Luckily, this did not get them out of having to justify this answer to themselves before they could bring themselves to actually submit it.

Overall, I found that it was actually a bit of a challenge to listen carefully enough to figure out where students are having problems so I could ask appropriate kinds of questions to help lead them to a discovery. I hope to think more about the questions before this next lecture so that I can perhaps have some anticipated question sets prepared.

I love how this student is able to “sop” up ideas from our readings and discussions and use them as lenses on his own experiences in the classroom. I love how honest and reflective he is about what’s happening around him–what he thinks is going well, and what he’d like to improve, what’s it like for him, and what it’s like for students. I love the fact that he writes about being with student in terms of an inclusive “we”–as in “We were all still unclear as to which answer would be correct”. I love that he is managing to keep his mind on sooo much–discussion, questioning, listening to students, soliciting reasoning, etc. I love how at the end he invents the idea of proximal formative assessment, as a challenge he has faced and wants to pursue as a goal.

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.