Yesterday, we had a break from the pace in Physics II, Instead of introducing new material, we had a day to review what we had learned about blackbody radiation and the photoelectric effect. So far this semester, most have my warm-ups have been forward looking–the aim being to prepare students to maneuver more efficiently and confidently through the rest of the day. But today, the warm-up was backward-looking.
The warm-up consisted of a table I had constructed at the front board. The two columns were, “Blackbody Radiation” and “Photoelectric Effect”. The rows of the table were the following questions
– What is being emitted? Where is it being emitted from?
– What causes this emission to occur?
– What physics quantity (or quantities) characterize how strong the emissions are? (words, symbols, units, any relevant equations)
– What, if anything, does “color” have to do with it? (words, any relevant equations)
– In the situations/problems we’ve discussed, what’s typically happened to the emissions after being emissed?
Students were in groups of three and were asked to discuss each question as a group, and then to write their response on a sticky note. Groups populated the board with their responses, and were asked to look over other groups responses.
Students took to the task pretty well–seriously engaging in the questions and in the efforts to compare and contrast what’s happening in each case. What was nice is the range of “correct” answers. For example, with the photoelectric effect someone might say,”Light is emitted” or “Electromagnetic radiation is emitted” or “Photons are emitted”. For what causes this, someone might write, “Light that is incident on metal,” or “Photons colliding with electrons”. For what happens to blackbody radiation, students might say, “It spreads out and gets less intense”, or “It goes off and heats up a planet =)” While some of what students was more vague or more precise than others, very few things were way off the mark.
After they were done, I mostly just reviewed the things that students had written and helped connect their ideas to the more precise ideas and quantitative relationships they had learned. The one place we needed to talk about the most was the role that “color” played in the photoelectric effect. I asked students to talk about that one in particular back in their small groups. Back in whole class discussion, the main idea that came up was, “Bluer light tends to be more effective at ejecting electrons from the metal”. When I asked how we knew that was true, there were two different ways that students offered for making sense of this. First, was reference to observations with the PhET simulation, that we found that UV light almost always emitted electrons but red light almost never emitted electrons. I added how, when the light got even bluer, the electrons came off faster as well. Another student worked through the reasoning that bluer meant lower wavelength, and that lower wavelength meant higher frequency, and that higher frequency meant more photon energy, which meant larger lumps of energy to give to electrons” That chain of reasoning, of course, involves drawing on several different relationships and chaining them together, so I did some work to clarify that. Looking back, I could have slowed down even more on that reasoning, asking students to go through that reasoning careful amongst themselves in groups.
In general, the warm-up went well, with student engagement being high; contact with important disciplinary ideas being high; and students expressing that they felt like it was a valuable activity from which they learned a lot (and being able to articulate what they had learned). It’s a good day when you get all three of those things. I think it’s fairly easy to get either of the first two–engaged students but not with important disciplinary ideas or a lesson that should put students in contact with disciplinary ideas but they aren’t engaged. And then, even when you get both of those things occurring, it’s not necessarily true that students leave class feeling like they have learned a lot and can express what learning took place.
Two other things on my mind are these:
– The activity went well, in large part, because of the students. I more and more see how–despite the fact that I do have a strong influence on student engagement–a good classroom is really a mutual activity in which the teacher and students coordinate their activity to achieve engagement and learning (or don’t). In particular, this activity of writing on sticky-notes and putting them on the board is not something we typically do in this class, and it might have been easy for students to think it was juvenile or just weird, and disengage as a kind of passive resistance. For whatever reason, that didn’t happen. It makes me think about Dewey’s notion of submitting to an experience–letting the experience happen to you.
– Compare and contrast is not a strong part of our curriculum. Students are rarely asked to think about how ideas or phenomena are related. We just march through… one thing to the next. I’m hoping that by asking students to do more compare and contrast that students can, to a limited extent, experience a more coherent curriculum. Not sure, exactly how it will unfold, but returning the comparison contrast makes sense as next week we encounter atomic spectra and nuclear radiation. Many of the same questions above are relevant…
I’m following up my previous post about warm-ups in Physics 2, where I’ve been trying to use warm-ups as a venue for extracting more value out of class without giving up much time. So far, the experiment seems to be paying off.
But, what do I do on a day when I really don’t have much time to give up to warm-ups and I really don’t have much time to plan a whole activity? For this, my go to move over the past few weeks is to just look at some of the tricky mathematical or procedural aspects of the problems we will be solving and make them warm-ups.
For example, we were doing problems with diffraction earlier this week. I know that students struggle with unit conversions in these problems because the exponents are large. For example, in diffraction problems you are dealing with nanmeter wavelengths, micron apertures, grating densities described in cm or mm, lengths describes in m or cm, and diffraction patterns described in mm. I also know that students do not know or remember anything about the small angle approximation, which comes up in a our lab. So there you go, two warm-ups for the day– a little bit of practice doing unit conversions with a focus on talking about different strategies, and little mini-exploration of how tan, sin, and theta compare for different triangles. I actually pick values for them to practice that show up in my example problem, their problem, or the lab.
During class, I realized another warm-up that we needed was thinking about how to relate “slit density” to “slit spacing”. Not sure exactly what that warm up would be, but that reasoning is always a struggle for students. It’s the same reasoning that shows up elsewhere in physics, so I’ve seen students struggle this and resort to memorization of formulas like T = 1/f.
All and all, the key I think to these “obstacle” warmups is to emphasize the reasoning and strategies, and this alone helps makes them pretty good warm-ups even if how I structure the warmup isn’t all that great. By front-loading some of the obstacles well before they encounter them in the midst of problem-solving, it makes the classroom more manageable. Without warms ups, I’ll often get six of out of eight groups stuck at the same spot at the same time. With warmups, maybe only one or two groups will need some help from me on those areas, and usually it’s just a reminder of the strategies we talked about in the beginning. Students feel a little more equipped to tackle the problem.
I imagine you could certainly go overboard, trying to frontload all the obstacles and that would be a mistake. I think my goal is to front-load the obstacles that obscure thinking about the underlying physics. I could also think about front-loading such obstacles for pre-class assignments, but then I think it would be harder to focus students on the reasoning and strategies.
Note: I think one reason I’ve been thinking about this part of my planning so much is this: I want to be able to circulate around the room and have interesting conversations with my students about their understanding of the physics, but that just doesn’t happen if my students are frustrated, or bogged down in things like unit conversions, or all simultaneously stuck on the same part of the problem. My best attempts at proximal formative assessment (e.g., listening to students, asking good probing questions) get destroyed if I am circulating around the room putting out fires.
I’ve known for a long time that planning has always been the weakest part of my skillset, having written almost 4 years ago:
“I will say that my weakest area is as architect (choosing tasks to use with student as well as deciding how those tasks should be carried out), especially thinking about the design of a whole course. I haven’t had a lot of experience designing courses, but I think I am also weakest here because I am a decent enough in the other areas that I get away with not being a good architect. In this sense, the willingness and ability to improvise is both an asset and a liability.”
I think now that I wasn’t getting away with anything. And I even think my thinking about planning (or warmups more specifically) now is nothing unique or special, and not even particularly great. What I think is amazing is how much even small improvement to my planning (and my thinking about planning) can make a difference.
Our second-semester introductory algebra-based physics course is jam-packed with labs. In 13-14 weeks, we do 22 labs! Combined with the in-class problem-solving students are expected to work through, I found it very difficult to find time for meaningful discussion questions or mini-activities that help build conceptual understanding or connections with the everyday world.
So, this fall is my second semester teaching the course, and I have been taking the route of using warm-ups as an opportunity to build in a few discussion and mini-activity opportunities. The constraints in doing so are the following:
- The discussion questions or mini-activity must flow into problem-solving or lab fluidly so as to be coherent to the students’ overall experience in class. It should emphasize key ideas they need that day, not just be enrichment ideas that I think are valuable in the big picture.
- The discussion or mini-activity cannot take up much time, because we are pretty squeezed for time. Furthermore, the activity should be designed to actually save me time later. In reality that means, I get some of the invested time back, but not all of it. So, a 10 minute mini-activity might mean students take 5 less minutes struggling with the problem or mean I can take 2-3 less minutes with a particular part of my sample problem.
An example of the kind of things I’ve been aimed for is this:
On Thursday, I was supposed to model how to solve a thin-lens problems, and then have students work together on a thin-lens problem, and then have students take data for a thin-lens lab. I had the following warm-ups:
– The opening question revolved around getting students to think about what they know about a camera, a projector, and a magnifying glass. On the front whiteboard I had made a table, which prompted students to consider whether or not the each of these technologies involved (i) capturing an image on a screen or viewing an image through a lens, (ii) whether it typically involved creating an image that was bigger or smaller than the actual object, and (iii) whether the image was viewed relatively close or relatively far from the apparatus. I had students discuss briefly in groups and then quickly collected student responses on the board in a whole class format. To make links to the their reading and later problem, I introduced the relevant vocabulary (e.g., virtual and real image, magnification, and image distance).
– The 1st mini activity involved giving students a converging lens and giving them the challenge of using the lens, a whiteboard, and some power point images to emulate a camera, a projector, and a magnifying glass. We turned off all the lights, so the only light was coming from the powerpoint slides. The slides were just a small, medium, and large yellow arrows. I circulated around, being more helpful than I should, due to need to keep the activity compressed in time. We then added one more column to our table, which was whether the image was right-side up or inverted. I then linked this again to concept of magnification and its sign.
– The 2nd mini-activity involved a powerpoint slide at the front of the room with nine different paths that a red laser light took through a lens. The optical axis and focal lengths were shown (but not in words). Basically, there were three examples of each of the principal rays. I briefly explained what the images were showing (a red laser light shining through a lens), and students were prompted to “Discuss what they notice” and then “See if they can come up with any generalizations or rules ” I circulated around. To keep time down, I didn’t collect responses. Rather, I talked about the patterns like, “One pattern I heard come up while I was circulating was concerned Image B, E, and F… In each of these cases, we see.” I then had a quick power point slide that summarized the three principal rays.
– Afterwards, the day proceeded as normal. I modeled how to predict where an image will form using ray diagrams and the Thin Lens equation. My example was a camera situation. Students’ first problem was a projector situation, and then their extension problem was a magnifying glass situation.
So, how did the warm-ups go in terms of my goals and constraints?
– The opening discussion took a little too much time, but I could easily tighten up my facilitation. It didn’t drag on per se, but it needed a quicker pace. It definitely helped students have a concrete understanding of the concepts of real/virtual and magnification, and help them see how what they were doing was related to their everyday world. It was easy to follow up with students, asking, “So is this situation like a camera, a projector, a magnifying glass, or none?” This prompted students to interpret the meaning of their work, which is good. This activity may not have paid back time, but it did pay back in terms of engagement (because students felt what they were doing was relatable) and in terms of sense-making (students had a feel for the important features of an image and what concepts describe them).
– The “Notice and Generalize” activity went quickly. My sense is that this paid off in terms of time in two ways. First, when presenting my example problem, I wasn’t introducing the principal rays in the middle of the problem. This saved me a few minutes. Second, I think students procedural fluency was bolstered just enough that it took them significantly less time to draw correct ray diagrams. During the problem-solving, there were no groups whose hands were up signaling they had no idea how to proceed and no groups that had diagrams that were way off the mark.
Both of the activities clearly supported students needs for learning that day, so I think we met the first constraint pretty well.
My memory is that each of the warm-ups took about 10 minutes, which means I invested up 30 minutes up front (within a 2.5 hour class). I think, we made up about 15 of those minutes. I think my goal should be invest 20-25 minutes, and hope to get 10-15 minutes back.
Final Note: What I find pretty interesting about my own learning to teach recently is this. More and more, I find myself being able to throw together warm-ups like this with very little time investment in planning. Before I might spend hours planning a warm-up that didn’t go very well or went well but didn’t pay off. Now, I can drum up a warmup that is fairly effective in less than 30 minutes. And while I know I must *know* things that allow me to do this, almost none of seems very conscious. I actually that I think plan most of these activities in my sleep, because I’ll some half-baked ideas when I go to bed, and then I wake up, sit down in front of the computer, and its done in about 10-15 minutes. I’m not saying my activities are gems, but teaching becomes a lot easier when what you throw together in 15 minutes is better on average than what used to take your hours.
Final Final Note:
OK, I partially change my mind. I think that my activities have gotten a lot better because I care more about the coherence of students’ learning experience. By that I mean, my activities are almost always designed to slip into the flow of the curriculum I have to follow. Previously, I would want to take too many side trips–to destinations that I felt were important to understand the material. And while I do take some detours, I use them sparingly. I’ve let go of some ego which says, “I know best what’s needed for students to understand this material”, and instead accept that, “The curriculum we are working with needs them to understand these things in this manner”. I’m much more willing (and able) to enhance students’ experience of a learning trajectory that I don’t necessarily think is so great. And the truth is, working to make the overall experience more coherent is way better than trying to sprinkle on top what I think is best. Within that analogy, I think it’s been better to try to improve the existing cake batter than to smatter it with fancy ingredients from a different recipe.
I’ve been trying to think about what the purpose of lecture should be in our introductory algebra-based physics sequence.
Students spend 5 hours per week in an integrated setting: A mix of teacher led worked examples, collaborative problem-solving, mini lectures and skill practice, discussion of conceptual question, and problem-solving.
The course is taught by many instructors who follow a common curriculum pacing not only a topic level but each problem and activity. There is room for teacher choice about how to fill gaps and free time, alter questions, and to a lesser extent make some adjustments to sequence of instruction.
The glue that binds the common pacing is lecture. In lecture is where a lead instructor administers exams to all students every 3-4 weeks. For lecture, students meet with 1.5 hours each week. During non testing weeks , instructors have 1.5 hours with the whole group to do whatever with–in the range of 75-200 students.
Typically instructors work to review or preview what students should have or are going to learn in the integrated setting. Most instructors balance didactic instruction with worked examples, with half the instructors using a clickers throughout the lecture.
Certainly one point of lecture is just to have a place for testing. Many instructors also speak of the importance of the lecturer showing worked examples so they know what kinds if question the lead instructor will give on tests. One instructor used lecture to really debrief on labs, but it seems most instructors now use the time to re-present material with their own emphasis and elaborations. While our egos make us believe that our special take on things is important, I’m disinclined to take this approach .
Of course, none of this tells me what the purpose of lecture is or should be for student learning. Some ideas I’ve been considering are:
– A focus on evidence and reasoning about evidence – how do we know and why do we believe?
– A focus on connecting physics to everyday experience and enjoyment of physics and physics learning?
– A focus on learning how to learn physics–epistemology and more practical issues.
All of the above is largely absent from the course, for the most part. And while I think filling these gaps is important, it’s also important to connect to other aspects of the course.
What other purposes for lecture should I be considering?
How can I both attend to above goals while also feeling integrated with the rest if the course?
I was motivated during my flight today to come up with physics problems that have multiple right answers, have a low barrier to entry and a high ceiling. Here’s my go at it, along with thoughts.
The idea behind these is students are supposed to come up with as many ways as possible.
1. Draw as many velocity vs time graphs that show an object moving +45m from where it started.
Extend 1: Describe each in words.
Extend 2: Pick one and draw its corresponding position vs time graph.
2. Draw pictures depicting situations where a normal force exerted on an object is different than the objects weight.
Extend 1: Pick one to draw a free-body diagram that will help you to explain your reasoning.
Extend 2: Categorize them by Fn > mg and Fn > mg.
3. Draw a picture of a situation where the initial and final states consist entirely of potential energy.
Extend 1: Draw energy pie charts for the initial and final state and at least two in between.
4. Identify the mass and initial velocities for two objects objects that when they collide, they stick together and remain motionless.
5. Draw free body diagrams for an object that will accelerate at 1 m/s/s.
6. Draw a velocity vs time graphs and categorize them into those that involve an object turning around and those that do not .
Extend 1: Come up with a rule.
Extend 2: Do the same for position vs time.
7. Draw a force that acts on an extended object such that the Torque due to that force is CCW.
Extensions: multiple forces where net torque is…
Brian’s Development Rules of Thumb:
– Situations should involve relationships with wiggle room. For example, consider a = Fnet / m. Not only can Fnet and m vary but the same Fnet can be accomplished in different ways. Torque similarly has wiggle room in location, angle, choice of pivot qualitatively and force, distance, angle quantitatively.
– Design around tasks that get close to known difficulties, but don’t over constrain things to make it narrowly about the difficulty. For example, don’t do, “Negative acceleration and speeding up”. Just do speeding up velocity graphs and see what happens. Or if you are going to go right at difficulties, don’t make it a trick or you being clever. My normal force situation I think tackles a difficulty in a straight forward manner and it may work, because there are do many ways to do this.
– I like processes where initial and end states are constrained but not the process in between. (Energy example above). This provides a large variety.
– I think you want choose representations very deliberately. Perhaps, ask students to start with or move to representations that support semi-quantification, or ask them to extend to multiple representations. I think it’s OK to start with picture, but it’s important to bridge to a representation (Normal and Energy are examples)
– When using in class, I would want to think carefully about the sequence of individual work leading to group work leading to whole class sharing and discussion.
– If I designed the task with a particular issue to come up and it didn’t spontaneously, I would just introduce it and ask students to consider it.
– I think these tasks are very amenable to the Five Practices for Orchestrating Productive Discussions framework. (Link to come on an edit)
Anyway, what do you think? I’m interested in what others would come up with.
I stumbled across a decent simulation, while I was reading up about ISLE. The simulation can be found here:
I think these simple kinematics simulations are pretty cool, especially the four problems at end, where you have to adjust the initial position, initial velocity, and initial acceleration to match the motion map. Nothing fancy, but pretty engaging.
Content Learning: It’s a nice bridge between qualitative and quantitative representation of kinematics, supporting mathematical sense-making rather than plug-and-chug approaches. It would likely support students distinguishing between position, velocity, and acceleration. It would also provide students with opportunities to wrestle with the meaning of algebraic sign for each of those quantities.
Pedagogical Affordances: The sequence begins with observations and moves toward application. It’s game-like in a productive way–fun, challenging, easy to jump into and try, and provides immediate feedback. You’d probably just have to help students from mindlessly manipulating values to match the motion.
The full range of simulations, which I haven’t looked at closely is linked here: http://wps.aw.com/aw_young_physics_11/
This is not a comprehensive treatment of some complex ideas, but here are some thoughts from today.
I bought myself a copy of Greg Jacob‘s 5 steps to a five to add to our library for pre-service physics teacher. In reading it, I’ve come across a statement that is representative of ontological differences in how physicists think about a few concepts in introductory physics, which I think stems from differences in how one can interpret the equal sign. I don’t have the exact quite, but Greg I think in the text implies that Impulse is both the change in momentum and the product of Net Force and its corresponding time interval.
Impulse = Fnet.Δt = Δp
From this perspective, the equal sign allows one to say that all three things are equally, both quantitatively and ontologically. Impulse is a word for both things.
My thinking about this mathematically is more like
Impulse ≡ F.Δt We’ll define impulse for a single force to be the product or integral.
Then we we can add up individual impulses, to get the Net impulse ≡ Σ Impulses = Σ F.Δt = Fnet.Δt
By applying Newton’s 2nd law, you get that Fnet.Δt = Δp.
Thus Net Impulse = Δp
To me, impulses are causal influences that together cause a change in a momentum, which is the effect. So to me, impulse is not change in momentum, not ontologically, because one is the cause and the other is the effect. So, I guess I see two differences, and they may or may not be related. First, I think we can define impulses for individual forces (and I’m not sure what Greg would think), and I also think that impulses are events whereas change in momentum is a change in state. Since I think they are ontologically different, I would never want to say that impulse is a change in momentum.
Of course, you can take such a momentum perspectives even further, such that even static situations involve momentum flow. In this case, individual impulses each actually flow momentum, such that the net momentum flow is zero. That is, in this perspective, it’s taken even further that each impulse (cause) has an effect (momentum) flow and the momentum flows combined to create a net momentum flow. In other words, the mathematical steps above are different, because Newton’s 2nd law is applied first and then the sum is taken.
And of course, similar differences in conceptualizations exist when we think about work, net work, change in kinetic energy, and the product of Force and displacement.
I’m not necessarily convinced that any way of thinking about this is “correct”, but I do think it’s useful to be able to acknowledge and attempt to reconcile the different ways of thinking about it.
People who I suspect will have an opinion on this: Leslie Atkins, Andy Rundquist, Benedikt Harrer, and many others.