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. 



This slideshow requires JavaScript.

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

Blog at

Up ↑