The previous day's investigation brought some new information to light: one of our assumptions was incorrect. We had assumed that, during a water-heating experiment, the beaker and water temperatures would "track" - that, moment by moment, they would have the same temperature. For reasons that are not entirely obvious, this turned out to be false when tested - the water and beakers heated at different rates.
The goal of this heater investigation warmup problem is to show how our thinking has changed from early lessons to this moment. The first part of the problem ignores the beaker. The second part includes the beaker and the assumption that it would change at the same rate as the water (our previous assumption). The final part forces students to consider what would happen when the beaker and water heat at different rates. Students can address these questions individually but are encouraged to talk to one another as they do. The conversations help them recognize where they had left off in their investigation which is precisely the desired outcome.
As a teacher, I want to start the day like this for two reasons. First, I want students to see the progression of thoughts. Second, not all student teams had a chance to see this discrepancy during the investigation. The warmup brings everyone to a common understanding of what happened. In the next section, I try to get a common understanding about what to do about this new information.
We transition from working in small groups to having a large group discussion. I provide the students with these heater investigation notes and facilitate a discussion about the impact of our new observation.
From a content perspective, the important idea is that some of the power is delivered to the water while some of the power is delivered to the container. Summing those powers will lead to the total power delivered which, naturally, is provided by the immersion heater. Students are familiar with measuring the slope of the water profile to get the power rating of the heater - today we add in the slope of the container profile to make a better measure of the immersion heater's power rating.
From an understanding perspective, I'm building on the students' well-developed sense of the water reaction. There are no new mathematics involved, just an extension of a previous idea. Specifically, I draw upon their understanding that energies are distributed between two or more objects and provide an algebraic argument to establish the idea that the power is also distributed in the same manner.
This is a teacher-led discussion though questions are encouraged. If students are not asking questions, I'll pose a "What if . . . " question to probe for understanding. As an example, I might quickly draw a graph similar to the handout, but with the slopes altered - perhaps just a simple swap between the original slopes. The point would be to push back on the silence to see if it represents true understanding. To get a better sense of the depth of understanding within the class, I'll preface the question by saying, "Raise your hand if you're ABSOLUTELY SURE you know how the problem will change under these new conditions. I'll wait until I see at least six hands." This technique will provide me what I need - a true sense of how widespread is the understanding of this new idea.
During this segment, I also hope to underscore the very big idea that scientists will reconsider new information and adjust their mental models accordingly. This is a key strength of the scientific process.
When finished with this segment of class, all students should have a clear understanding of how to incorporate their new findings into their results.
As is often the case with open-ended investigations, student teams will have a variety of needs near the end of the process.
Some teams will need to get more - or better - data and so will gather the lab equipment and run further trials to extend their data set. Some teams may need to create "Word-friendly" versions of their graphs and so will use my laptop to convert their Logger Pro files into Word document images. Whatever their needs, I am comfortable providing the time to address them.
During this segment, I circulate and ensure that students are benefiting from the time provided.
In the final few minutes, I provide my students with a preview of a calorimetry problem. The image is a cartoon of a hot material (rock, metal, etc.) being dropped into a cool bath.
My goal is to end the class with students thinking about the similarities and differences between the problem we've been considering (a source that provides a constant rate of energy) and the upcoming problem (a source whose rate of energy delivery changes over time). We need not have any deep insights during this time. The point is, rather, to simply have them recognize the differences and leave class thinking about adjusting their mental model again.
Students will do a one-minute free-write in their notebooks, then quickly pair-share in response to the question "How is this new scenario the same as our heater experiment . . . in what ways is it different?"
I end the class with jotting down their thoughts on the Smartboard and asking for elaboration on their ideas.