I’ve been doing some reorganizing of my blog to make resources I’ve developed and shared over the years more readily available.
There are now permanent pages where I will the following:
I am continuing to reflect and write about my ideas leading into PERC 2018: So far I’ve written two posts about teaching and learning in ways that involve positioning students’ as authors of scientific ideas that can serve as resources for learning.
I’ll start with here with this notion: Having routines (and a culture) in your class where students regularly make their thinking visible is great, in part, because it provides opportunities for you as the teacher to encounter students’ spontaneous thinking about the content you aim to teach. This is probably the main way that teachers learn to hear and see their students’ ideas as wonderful and to see them as resources for learning.
When I was first teaching, it was easiest to see students’ thinking as being useful for learning when it neatly fit some correct aspect of my own understanding. For example, in my first year teaching here at MTSU, “Ashley’s conjecture” was an idea from one of classes about how, in free-fall, the speed on the way up and down might be same at as the object passes through the same location. With Ashley’s conjecture, we set about working problems to see if it was always true (gaining trust) and even later revisited the idea in when learning about energy. Toward the end of the semester, Stan, a student from Ashley’s group even made it the focus of an independent project later in the semester. In the introductory motivation for the project, Stan writes in a way about his project that touches upon his own epistemic agency and its embedded-ness within our class.
From my first year, I also remember “Cherish’s Rule”, which was the idea that the equation for velocity and the slope of a position vs time graph should give you the same answer. “Cherish’s rule” became a standard in my class, so much that the chair of department was thoroughly perplexed when passing by my class trying to figure out what I was teaching the students because he had never heard of anything called “Cherish’s Rule”, and I even had included it in the powerpoint slides:
In both cases, instead of telling students they were right, I made time in class to investigate these claims (I knew to be correct) and in doing so this lent students’ some agency and authorship over ideas from class by “naming” their ideas and making space for us to either investigate or make continual use of these ideas.
The above ways of listening and responding to students’ thinking was (and is) a good start, but there is also a sense in which it is quite limited. Ashley and Cherish in my classes were proposing ideas that sounded very much like ideas that I had knew to be consistent with the body of knowledge we aimed to learn. For these reasons, it was easy for me to understand their ideas, and to recognize their utility and respond positively, and also to imagine ways of taking up their ideas that would advance the entire’s class understanding. I’m not saying this is totally easy – for sure, you have to already have routines and culture in place where students’ share their thinking, plus successful talk moves that help elevate students’ thinking as ideas for consideration. This is no easy task, in part, because many of us had little training, mentoring, and apprenticeship into how to do this. I’ve written about why it’s so hard to do this before in a post on talk moves.
In a follow up post, what I aim to do is further explore the complexity of taking up of students’ ideas from class, especially in regards to situations where students offer ideas (that can be useful resources for furthering understanding), but their ideas are not just simply made as statements that you as the physics teacher would recognize as correct.
I have posted these on twitter in the past, but I don’t think it’s ever made it to my blog. I have come to see asking students these types of questions as really important (for students and me). For students, pausing to think about what has been interesting helps make things more interesting. For me, I get insight into what stands out to students in a unit. In addition to reading quizzes that include these types of questions, I used to ask these on every exam. I’d like to get to asking about them on exams. I actually feel like asking it on exam is more important.
In this blogpost, I continue to write about my thinking going into the 2018 Physics Education Research Conference.
I’ll start by saying this. It can be hard to have it both ways: I want my students to have a degree of epistemic agency in the construction of their own personally-meaningful, scientific knowledge. And I want my students to develop robust understandings of established scientific concepts as a body of knowledge. Trying to do so is fraught with uncertainty.
One of the things that has helped to navigate these uncertainties over the years is the following way of thinking about the content I aim to teach: I try to decide in advance what understandings (of a scientific concept) function as necessary “anchors”, for which I must carefully plan for, and which understandings (of a scientific concept) I can leave as open territory for sense-making [Foot note]
In my previous post, I wrote about an example in which students were learning about Newton’s 2nd Law. In the sequence of learning, students were carefully guided through an understanding of contact forces as arising from tangible mechanisms. To me, this was a necessary anchor, because I felt it would be crucial for students’ understanding that they have a sense for what is (and what is not) meant by force, and also how one goes about identifying its occurrences in actual situations. The next anchor point I wanted us to get to was an understanding that constant force causes constant acceleration; and, furthermore, I wanted this understanding to be anchored to actual observations that would help students answer questions like, “How do I know? Why do I believe?”
I could go into more detail concerning other necessary anchor points, but the point is that I try to carve out the aspects of an understanding which are “must haves” for my students as we learn about a topic or concept. I carefully prepare, plan, and scaffold for these as anchors for students in the body of scientific knowledge.
The second part is to then build pedagogical space for others aspects of the content that will remain more open–that is, I expect there to be territory in landscape of understanding (that needs exploring) but does not need to be explored in a particular way that I prescribe in advance. Rather, it is more important that students meaningfully explore the territory around and in between the anchors I help us to forge.
In my previous post about N2nd Law, the open territory my students explored around these anchors concerned questions like, “Why does constant force produce constant acceleration?” This particular year, students explored this space in a particular way that involved thinking about the details of what happens to the degree of compression between two objects as they press into each other and they get away. It is often tempting the following year to try to make this conversation happen again, but I am learning that this is not the goal. Sure, knowing that this conversation can happen, should leave me better prepared to notice it as a possibility, but it need not become a new “anchor point” that I prescribe. Instead, to keep the space alive as a open territory for sense-making is to help students explore that space (meaningfully in a broad sense), and that will vary from year to year.
Other semesters this conversation has gone in different directions–for example one year my students explored the space by more carefully thinking about friction vs. non-friction. Students introduced the idea of a “lurch” –what happens when you push an object against some rough surface and it doesn’t go until it suddenly does; and how with the hover pucks and low-friction carts there is no “lurch”. The hover pucks and carts just start going. The lack of a lurch was how students made sense of why a constant force produces constant acceleration.
While different educators are likely to disagree about what exactly should be the anchors and what exactly should be the open territory, the practice of carving out the two is I think critical for navigating the tensions described above.
It helps to perhaps give a second example:
For uniform circular motion, a standard way that physicists understand the sensation of an outward force is to say “there is no outward force. The so-called centrifugal is a fictional force resulting from a non-inertial reference frame.” Over the years, I have decided that this is not an anchor for me. The main anchor for me is, “only an inward force is needed to maintain circular motion,” but I try to leave open questions like “why is only an inward force needed? and “What is the outward force we seem to feel?” open While I carefully scaffold students’ understanding of the anchor, the lesson is structured in a way that encourages students to meaningful explore the territory around that anchor. Various ways that my students have made sense of the outward force include “The outward force is the Newton’s 3rd law pair to the necessary inward force (in other words a force by the object moving in the circle),” and and that maybe “the outward sensation is the result of torque on an extended body, like the ones that results in tipping over.”
So what’s the point? I think one of the main points here is that careful instructional planning is required for both the meaningful establishing of anchors and the exploration of open territory. I know that this should not not surprising to anyone who aims to teach this way–thinking about improvisational acting / music or even wandering in the woods / city benefit immensely from careful planning and knowledge of anchor points that provide structure, but also allowing space and time for exploring the territory around these anchor points. Said another way, filling your travel schedule completely full both day and night does not readily allow for opportunistic explorations–all you can to is keep onto the prescribe path. As a teacher, what I have found is that this way of thinking about concepts (i.e., anchors and territories) provides me with tools for planning and carrying out instruction in ways that lessens some of the tension between discovery and coverage.
Foot Note: I sort of steal this language from this paper, and while I think my sentiment here shares some overlap with the meanings developed in this paper, I know that it is not a one-to-one correspondence.
At upcoming Physics Education Research Conference in D.C., I am giving a talk and also moderating a poster symposium. In preparing for these, I wanted to spend some time writing about related things. The talk I am giving and the session I am moderating are the following:
Is there room for wonderful student ideas within the canon of introductory physics?
Introductory physics courses often come with constraints that make them less than the ideal setting for responsive teaching efforts that aim to support students in having wonderful ideas of their own. In this talk, I present cases of students having wonderful ideas in introductory physics courses for the purpose of providing rich illustrations of how wonderful ideas may emerge when parts of the canon are opened up for student sense-making. I follow up with a discussion of how such moments benefit from careful instructional planning and curriculum design that are aimed at supporting both traditional and non-traditional outcomes.
Identifying Conceptual Resources for Understanding Physics:
Historically, research identifying student ideas in physics has focused on what student misunderstandings, misconceptions, or difficulties. This work has supported the development of curriculum that elicits and addresses these misunderstandings and has informed instructors’ knowledge of student ideas. More recently, research has begun to systematically identify student conceptual resources for understanding physics — that is, the productive “beginnings” of physics that students bring to bear as they learn. This session showcases some of this research, highlighting a range of samples (K-12 students, university students, and teacher-learners) and physics topics (thermal physics, energy, electricity and magnetism, and pressure).
So, here is a question that has been a favorite of mine the past few years:
The question by itself isn’t all that amazing, but the timing of the question in our curriclulum seems to make for a good conversation, so it’s relevant to know the background.
First: by the time I am asking this question to students, they will have spent a lot of time with velocity-vs-time graphs– they are embedded into many exercises, clicker questions, card sorting tasks, example problems, quantitative problems, and lab activities. All students would have some familiarity, most students would be al least proficient, and some quite adept.
Second: This question comes at the end of day focused on helping to define and investigate what forces are–with careful attention to the mechanisms by which various contact forces arise.
Within this context, the students in my class one semester discussed the above question and over a period of time ended up convincing each other that the only reasonable outcome was for the hover puck to continually speed up.
The persuasive argument–initially provided by a single student– eventually was taken up broadly. The argument was essentially this:
1st: When you press your finger against the hover puck, it’s going to have to speed up a bit as it to starts to move.
2nd: In doing so, however, the hover puck gets away from you;
3rd: As the puck gets away from you (even just a little bit), the amount of pressure against the puck goes down. Your finger isn’t as squished into it as much.
4th: Thus, in order to maintain the same amount of pressure, you have to speed up with the puck. You have to keep up in order keep the same level of squish.
5th: Once you are moving along with the puck again and you are again pressing into; the puck again tries to get away, speeding away from you.
6th: So, as long as you keep pressing against the puck (and don’t let it get away from you), the puck is going to just keep speeding up (because you keep pressing into it).
7th: Of course, this will be hard to do, because you are going to have keep speeding up with the puck to maintain the pressure, but if you can keep the pressure up, the puck will keep on speeding.
In class, the argument was never so cleanly articulated, but I do remember the first words that uttered by this student a few minutes into the discussion. The argument developed and became elaborated progressively over a period of at least 20 minutes, with lots of people adding on, giving examples, and counter examples, and clarifying what was meant. ” By the end, the feeling in the room was almost: “It’s so obvious that this is what will happen, we don’t even need to the do the experiment.”
Of course, we still did the experiment, but the reason for doing the experiment was NOT so much to see if it “does continually speed up”, but rather to investigate the more pointed questions and claims that had arisen about why, such as
We ended up doing these experiments out in the hallway with hover pucks, and then again more carefully in the classroom with fan carts and motion detectors. The fan cart was introduced basically as a technique for maintaining a more steady pressure –> the argument being that the cart can’t get away from the fan (or the air). That is the fan could do a better job of keeping the pressure constant. This is what allowed us to decide that the answer was A (constant force –> constant acceleration).
It’s true that I’ve written about this specific class discussion before, but I’ve been wanting to return to it again, because it’s a story with lots of interesting aspects that has stuck with me.
First, it’s important to note what the question did NOT ask. The question did not say, “A constant force acts on an object…” Instead, by keeping the focus on constant pressure (here meant in our class informally as a degree of squish), it helped students to attend to that aspect of the mechanism. This was additionally supported due to fact that we had spent entire day looking at the details of these types of interactions. Generally, however, students’ concept of “force” could more easily anchor to other aspects of the motion–> for example it would be common for students to attach constancy to some other aspect like the “speed of the pushing” is constant or the “effort of the pushing” is constant. rather than the constancy pertaining to a degree of squish between the finger and puck.
Second, my previous experience, with physics education and my own teaching, had always been more focused on using these conversations as more of a lead into to getting students to meaningfully consider the observations. That is, the conversation guides students to think about what they think, make a prediction, and then see how the observations compare to what they thought. Lots of good research to support the notion that this type of prior engagement with the ideas (predicting and discussing) is critical to creating the conditions in which students will actually be able to understand and learn from such observations. Here, however, students did not arrive at the conclusion that “constant push causes endless speeding up” through direct observation, but rather through thought-experiment. This is more akin to the kinds of reasoning we liken to scientist such as Galileo and Einstein.
Taken together, this kind of learning is a glimpse of the kind of teaching that I was apprenticed into while at the University of Maryland–one that aims to value helping students to build on and refine their own “sense of mechanism“, to “shop for ideas” in their experience, and to engage in a process of seeking out “coherent explanations” for phenomena. To a significant degree, for me and others, this kind of teaching has been easier to take up in courses that live outside the standard introductory physics course sequence and are perhaps less tethered to the canon of introductory (see here, for example). It is certainly more challenging in many contexts where pace and content can pull you more strongly away from commitments to teaching in this manner (and supporting learning in this manner).
My talk at PERC will be on the topic of to what extent this kind of teaching / learning can find space in the standard introductory curriculum–where students are supported in having and developing scientific ideas that are not precisely predetermined. While in this lesson, I planned for and knew that we would be making progress toward learning Newton’s 2nd law, I did not know in advance that the specific understanding that would emerged would be built around ideas like “pressing against something leads to it trying to get away” and “getting away involves both speeding up and a lessening of pressure”.
These specific student ideas are (I think) the types of ideas that are the focus on the Symposium I am moderating– researchers whose goal is to identify ideas that students have that can serve as “resources” for making progress in learning specific scientific ideas (rather than, for example, researchers whose goal might be to identify misconceptions or student difficulties). One of the challenges I see for these researchers doing the work is to meaningfully situate the resources they identify in ways that give them “life” such that teachers can see their continuity with the actual practice of teaching. In the story above about my students, I would hope that readers get a feel for what these students ideas actually were and how these ideas actually served as resources for making progress in learning Newton’s 2nd law. Pivoting from the Symposium to my own talk, my talk will focus on how such moments of teaching and learning benefit from instructional planning and preparation (even if you necessarily cannot prepare and plan for some of the details of what exactly is the form of students’ understanding will that emerge).
One thing I’m certain all physics teachers develop over time is new and varied ways of talking about physics concepts–especially ways that are more informal than textbook definitions. These informal ways are less focused on giving a precise definition and are more focused on trying to offering insight into a concept through metaphor, image, story that provide a grasp of concept.
Here is an example of an informal way of talking about net force
When multiple forces act on an object simultaneously, it’s useful to think of their combined efforts as being equivalent to a single hypothetical force–one with just the right direction and just the right magnitude to cause an identical acceleration. We call this Net Force.
Net force is NOT an additional force that acts on the object, but a measure of what a “team” of forces accomplishes together when acting on the object. Experiments suggest that when individual forces act together on a single object, the net force is equal to the vector sum of the individual forces.
This property of forces appears to be universally true, and scientists refer to this as the principle of superposition.
What are concepts for which you think you have developed powerful ways of talking about them? What are the concepts? What are they ways of talking about them?
Note: I am not under any illusion that me saying these things is of utter importance for learning, for I know it is students that must do this type of construction for themselves. That said, having such varied ways is critical to being able to help students do that construction.