Graphing the Two Dropped Stones Problem

I asked the two dropped stones questions to a small class I have of intermediate and upper-division physics majors. This class is called “Reasoning in Physics I” and has evolved quite a bit over my time here. Anyway, after some intro to class and some diagnostic pretests, I wanted us to do some physics, so the question was asked:

“A dense stone is dropped from tall building. One second later an identical stone is dropped. As the two stones are in free fall (ignore any drag), does the distance between the stones increase, decrease, or stay the same. ”

Majority of students’ first thought was that it should stay the same at first (since acceleration is the same), but one student quickly convinced the others that they should increase because the first one got a head start on getting up to speed.

When the conversation naturally came to a lull, I re-voiced the conversation a bit, emphasizing how everyone seems to have good reason to believe that something is the same about the two stones (e.g., they have the same acceleration), but that some things might be different (because of the one second head start).

I prompted students to get up and go to a whiteboard and draw position vs time and velocity vs time graphs for the two stones. I then told students that they should be ready to explain (1) how those graphs illustrate what is the same and what is different about the two stones, and (2) how and whether the graphs illustrate the answer to the question.”

Students struggled with the graphs for a bit, not at first being able to distinguish the position vs time from the velocity vs time. Eventually, one of the groups drew a diagram like this:

The idea at the time seemed to be that the two lines had same slope, and the widening space between the the two lines showed the two stones’ increasing distance. Quickly, another student suggested that if the two had the same slope, the two lines had to keep the same distance apart on the graph.

Students corrected their velocity graph, so it showed lines with the same slope. The next graph they worked on was the position vs time and it sort of looked like this–with each yellow line to them being an indication of the increasing distance between the two balls.

I asked them a few questions about their graphs and got them to articulate how their two graphs showed the 1 second time delay. I said, “I’m going to label on the graph, in a particular way, something to help ussee that 1 second delay.” This made their graph look like this.

I then asked them to see if they could go about marking their position vs time graph, similar to how I had, where specific information is labeled as to clearly communicate how and where to “see” that information.

I left for a bit and came back to see thy had updated their drawing like this.

They were able to more clearly articulate what each of those lines meant. As discussions continued , I shared them with another representation using motion diagrams.

We ended the day talking about the different representations, even raising the question about how one might show the idea using the velocity vs time or even equations to illustrate increasing separation. We didn’t have much time to explore that, however.

Anyway, this class is going to be interesting to navigate. I’m definitely figuring out what the goals are supposed to be a bit on the fly. So far, we had a good first day, of reasoning through talk and diagrams.

The last semester of big changes… (phew!)

This semester, I’m working with a smaller instructional team–in what will be the last year of our structured roll out of new curriculum in our introductory algebra-based physics sequence.

Although, there were certainly advantages to having had started off with a big 10-person team last year, I’m quite happy to be working with a much smaller team (only 3 including me) this time around. It’s giving us the time and head space to talk about the content, the pedagogy, and also trouble-shooting. The two instructors I’m working with are both really great instructors, who have decades of teaching experience. We are working on the 2nd semester course, which has been in their responsibility and care for a long time. I really want to respect that and also leverage their expertise in making this curriculum something they can be proud of.

In terms of our department, these two definitely lean a little more conservative in their teaching orientations and are at times skeptical / hesitant of certain types of reforms. That said, right now, I have their good graces and their eagerness and interest, and I don’t want to spoil that. Also, both of them already have had a decent range of experience working in classrooms that involve interactive engagement. Our intro physics has long included collaborative problem-solving (i.e., white-boarding). Both instructors are familiar with and think highly of educational technologies like PhET simulations, which they have used in the past for both lecture demonstrations and laboratory activities. One of the instructors has experimented using peer instruction (clicker questions) with mixed feelings of success and self-efficacy–struggling to get it working in a large-astronomy lecture, but enjoying it in a intermediate-level physics course for applied physics majors. The other has no experience with these types of peer instruction activities. I imagine a decent focus for us as a group will be managing class discussions, not just to make them effective for learning, but really to help them to be enjoyable. People more readily continue do what they like and feel is going well, so that will be likely be a priority for me in working with them.

My work-life balance should be better this semester, and I’m hoping to have no major department-wide instructional responsibilities next semester.

For the Loathe of Teaching Statements

Colleagues and students of mine pushed really hard this past year to put my name in for several teaching awards at my university, of which I was fortunate enough to actually win two. As part of the nomination processes for the general education teaching award, I was asked to write a statement of teaching. I sort of loathe writing these things, because whatever I end up writing just seems to sounds like such bullshit (even if personally meaningful to me). Anyway, this was my best stab at it at the time, and I figured I would share it with all of you, since basically all I did was point to my blog.


“When I started this job, I imagine I wrote a statement of teaching with some measure of confidence that I knew what I was doing. These days about the only thing I am certain is that teaching is mostly uncertain. I write regularly about these uncertainties (at a blog titled teach.brian.teach), and have done so for the better part of a decade. This writing has not often been directed toward the production of polished educational writing or a generalized philosophy of teaching. Rather, its focus is mostly on the nitty gritty details of praxis–whatever aspect of teaching and learning I need to reflect on, document, or improve at the time. Through writing, I continue to learn that

  • Student dialogue matters a lot. I’ve written quite a bit on issues such as making use of talk moves, intervening with unproductive talk, and helping new teachers learn about and practice these moves. For general education, I believe that helping students connect science concepts to their own experiences and ways of talking is important, especially if they are going to take what they’ve learned beyond my classroom.
  • Not only does curriculum matter, but that articulations of curriculum matter. I have had to get better at articulating the underlying logic of a lesson, why some strategy might work and under what conditions, and even how you will know if it’s working or not. I have been striving to build curriculum that builds meaningfully from concrete experiences and ideas to abstract scientific concepts and skills. In general education, I believe the goal is to equip students not only with an understanding of those concepts and skills but also with answers to the question, “How do I know?”, “Why do I believe?”, “Why do I care?”
  • Getting feedback and responding to it is important; so every semester, I solicit student feedback, critically think about it, and engage my students in dialogue about it. This feedback is for me, but it also for students to pause and think about their own learning. In general education, getting students to reflect on what they are learning and how they are learning (I hope) better prepares them to transfer those skills to other contexts.

I suppose, one piece of writing from my blog that comes close to articulating my philosophy of teaching might be the following:

Brian’s Theory of Teaching (October 2017)

1st:  What you say and do doesn’t really matter and has no effect on student learning. 

2nd:  What you say and do strongly affects how students feel… how they feel about you, where they are, who else they are with, themselves, etc.

3rd:  How students feel about all that stuff affects what they do, but also how they go about doing those things.

4th: What there is to do depends on what an environment makes possible for doing. And since not every environment is equally good for all kinds of doing, a thoughtfully and carefully arranged environment is needed if you care about what it is students might do and how they might go about doing those things.

5th: Every once a while students will be doing certain kinds of somethings and feeling certain kinds of ways, and what you say will matter. It will be consequential to what they do next.

Conclusion: Spend most of your time on preparing that environment and on nurturing those feelings, so as to create a few moments here and there where what you say matters. Try not to fuck it up. But you probably will, at least some the time, and that’s ok too. Just get back to working on the things that matter. 

Final WordsI feel like one of the challenges for me as a teacher is simply that there is an overwhelming number of things that matter. Two in particular stand out, because I have the most control over them– the pursuit of meaningful, coherent curriculum and the rehearsal and enactment of effective pedagogy. I try to put hard work into both of those areas behind the scenes. After that, students and I have to figure out how to pull it off together. This is where I think cultivating relationships with students matters.

I certainly don’t expect every day to be magical. You could easily walk into my class one day and find all of us tired, frustrated, unmotivated, bewildered, or worse. If things are going well, however, there will be also many days filled with wonder, laughter, redemption, and a sense of belonging that will carry us through. It’s always a risk, but I’m happy to report that I am slowly getting better at pulling this off more consistently. I hope in another ten years, I’ll be a lot better than am I now.”


Postscript: One of my colleagues was a fair bit concerned about the word “fuck” appearing in my teaching statement in that it may offend certain kinds of committee members. At the time, my contention was that I wasn’t actually or personally saying “fuck” in my statement.  Rather, I was quoting / citing someone who had happened to have written “fuck” in a different publication venue, and it just so happened that this someone was me. I was busy enough at the time, that I didn’t have many fucks left to give, but I am glad for my colleagues sake that it didn’t end up being detrimental to their efforts.

Magnetic Vector Manipulatives

Here are the files I’ve currently been using to make the magnetic vector manipulatives. You basically just print, laminate, cut, and add magnetic tape. 

PDF

PPT

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Oh, and here’s a video of me making a velocity s. time graph from a motion diagram for simple harmonic motion.

Which AAPT worlds do you navigate?

I’m not sure exactly how many worlds there are at AAPT conferences (or even if the world metaphor is right), but at the impromptu twitter meet-up, a few individuals were discussing that there might be four basic worlds:

  1. Physics Education Research World
  2. University Physics Educator World
  3. High School Physics Teacher World
  4. PIRA / Demo / Apparatus World

I’m not committed to this being the right carving, but there definitely seem to be different worlds one can navigate. The assumption in my mind (which can’t be exactly correct) is that the worlds do not overlap much, but that there a small number of border crossers / world straddlers. Or it could be that some worlds overlap more than others, because they actually have borders. And some worlds overlap very little, because they do not share borders. And there are probably some people who are not native to any one world, and wander all the worlds.

Anyway, I’m curious where people see themselves. Like I feel like I was born in PER world, but since beginning border-crossing to high school physics teacher world, PER world doesn’t feel so much like home anymore.

  • Do some feel like they have a home, but have friends in another world they can visit?
  • Do others feel more like dual citizens?
  • Does anyone feel homeless (in a good or bad way?) Does anyone feel stuck in one world?
  • Do some people feel squarely in one world?
  • Is someone deeply offended or shocked by the idea that there are different worlds?
  • Do certain worlds feel more isolated than others?
  • Do you have a different way you would want to carve up the worlds?

I’m not even sure if this way of thinking about people and community is helpful or harmful, but it’s been on my mind, so I’m writing about it.

Final thoughts:  Making up such carvings can be damaging. And so I think it deserves critical introspection to open this conversation. For example, many times, I have heard it suggested that there are producers and consumers of PER. When a few people offered this to me as a way of understanding my transition, it felt alienating. It felt like a very  “PER”-centric world view, where the only thing of true value was PER, and there are those who create and those who use. I don’t think of myself as either of those things, and so that way of carving the world felt wrong. I’m not deeply offended, I’m just saying that in that moment, I felt so misunderstood. Other people talked about being “nourished” in different ways by different parts of community at different times, and that better resonated by me. Like, for a while, PER was the intellectually, rich place about teaching and learning that nourished me; and now I found other intellectually, rich places to be nourishing me.

Final Final Thoughts: I’ve been thinking about the structure of High School Physics Teacher Camp (very unconference style) vs the AAPT meeting structure. A lot of AAPT meeting structure feels like it is designed for benefit of some worlds more so than others. This isn’t a criticism (I think), so much as a description. When teachers run workshops by themselves for themselves (supported by AAPT but organized outside the official AAPT structure), they organize in very different ways.

My experience at HS teacher camp felt like both “the rate of knowledge exchange” was crazy high, and support for fermentation / synthesis of ideas was high as well. It was also just better designed for joy. This seemed embodied in many ways — how sessions are formed, the different types of sessions that exist (breakouts, invited talk, share-a-thon, working time), and even in how collaborative notes are constructed in real time during the conference. I’m not saying that this format is generically “better”, but that it has advantages that seems to be really good for that world (high school teachers). My experience at AAPT standard sessions, this year was not as enjoyable. Once again, I’m not saying that the structure is generically awful, but it didn’t feel like it worked very well for me. 8+2 min contributed talk sessions seemed like the worst. Even when interesting people were doing and sharing interesting work, it mostly felt miserable to be there.

OK, this has turned into a diary entry / rant. Sorry.

 

Moderating the PERC Session on “Conceptual Resources”: Reflection on Structure and Facilitation.

I was asked to co-moderate (with Lisa Goodhew) a discussion at the end of a Thematic PERC Poster session on “Identifying Conceptual Resources for Understanding Physics Ideas”

The way we structured the session was as follows:

5 Minute Introduction to the Session (providing an overall framing)

40 Minutes to Explore Poster Presentations (30 minutes  structured timed rotations + 10 min to mingle more freely)

40 Minutes for Structured Moderated Discussion (details below)


 

I. Individual Time to Articulate Questions

Each person was asked to take some time to think about a question and to write it down on a note card.

II. Small Groups Tasked with Choosing or Crafting One Questions to Elevate

What they did: We had about 40-50 at the session people, with 40 people being present for the discussion period. A little clumsily, I broke people into five groups. Each group was anchored by a presenter.

What I did: Groups shared their questions while my goal was to keep them on task by reminding them that the goal was not to start discussing questions, but to stick to the task of coming up with a question to elevate for whole discussion. I make decisions about how much time they really needed while also pressing them to get the task done, which worked fairly well. While getting questions from each group, I made sure to ask questions to make sure I understood the essence of their question / concern, rather than worry about the exact wording.

III. Moderated Panel Discussion with Everyone:

After small groups, the presenters were seated at the front in panel, while audience was seated in more rowed seating. Instead of just reading questions as presented and having the panel addressed them, I tried to look for questions that were driving at the same issue, and offer the questions together or a framing of their questions that got at what relation I saw them having. In addition, after reading a question, time was given before the panel would address it. Here’s how I did this.

A.  Time for Audience and the Panel to Discuss:  For each question, time was given for the audience and panel to talk with each other. This was like “think-pair-share”. I felt this was good for audience to think about what they think before hearing from the panel, but to also make sure they understood the question in their own way. For the panelists, this gave them time for each of them to try out saying things, and decide individually and collectively what parts of their thoughts might be best to share.

B. I opened up the first question to the Panel. Over the course if our time on this question, a few panelists ended up speaking a few audience members. I was pretty heavy-handed in my moderation, re-voicing ideas, making connections (or contrasts) between contributions, and even shutting down a contribution when it was clear that it was going to lead to a “new question” from an individual (one we hadn’t collectively elevated). For the second question, the panelists told me after discussing that they think the question should be initially answered by the audience. The question involved comparing and contrasting the researcher’s, and the panelists felt like the audience was better position to say some meaningful things since they had actually visited multiple posters. So, it began with more audience contributions and shifted to the panelists responding.


We ended up only having time for two questions, but the discussion (I think) felt engaging and meaningful. It felt like the question was a launching point to discuss an issue, not “answer a question”.  That’s not to say that things were perfect or that my moderator moves were always best, but any faults and mistakes didn’t drastically undermine the wholeness of what we were doing. I’m not everyone felt that way, but my sense was that the structure and enactment worked out well for many. One feedback I got (which is not surprising for me) was that I was talked “way too fast” for international participants.

I don’t want people to think that this structure is the best structure, and so I want to share my thinking about why I chose this structure. I think the “thinking” here is valuable:

  1. Who are sessions for? I wanted to strike a balance between the session being useful and fun for the presenters and also for the audience. This is why, even in the panel format, every question was first discussed in pairs, and then we would hear from the panel. This engaged the audience I think while also highlighting the expertise of the panelists we had invited.
  2. Are there multiple outlets for thinking (and fermentation of thinking)? I wanted to give people outlets for thing “they need to say” to someone that don’t need to be said to the whole group. This was designed into first asking groups to write a question and share, in the think-pair-share for the audience, and the think-pair-share for the panelists. Everyone got to have and share ideas, before having to decide if that idea would be elevated to the entire group. Ideas and thoughts need space for fermentation, and all the products and processes of that fermentation don’t make it to the end product.
  3. Who has power in the session? I wanted to disrupt the standard questioning format of, “asking questions” to the panel based on who gets called, and to distribute more of the power around. That’s not to say the the power dynamics would flatten out completely, but that more of the decision-making process about what questions would be asked and what ideas might be discussed was distributed. I held a lot of power — my plan use it judiciously but unapologetically. I was invited to be the moderator for a reason — someone felt I had the skills and know-how to carry out that responsibility well, and I counted on the audience trusting me in that role. I think moderators often cede too much power in facilitation. I think of it more was “sharing power through structure” (notecards, groups, pairs), but then exerting power during facilitation. I want to use my power to empower the group to do something more meaningful than if just left to our own. I’m not saying that my structure of my facilitation accomplished that completely, but that was the goal.

 

Anyway, I just wanted to reflect on this and write about it. If you were there at that session, I’d love to get your feedback about your experience of how the session was structured – what worked and what didn’t, and how my facilitation did or didn’t advance and elevate our collective work in the session (both in terms of enjoying it and in terms of the substance of what was enacted in the collective).

 

 

 

 

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