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.