To begin the day's lesson, I double back to a problem very similar to the 1-question quiz, though this calorimetry warmup question asks students to consider the impact of the container. Struggling students are directed by the question to consult their notes, though I am also available for consultation.
My purpose is to assess whether students are fully prepared for the homework assignment distributed in the previous lesson. In addition, the pace has been brisk and taking some time to ensure understanding seems wise.
A suggested calorimetry warmup solution is provided, though the solution is shown up to the moment where students need only follow through on the algebra of the problem; all of the relevant physics is shown.
Before taking on anything new, I set aside some time for absorption. As students may be at different stages of understanding, this time needs to be differentiated.
For those who haven't yet completed the advanced calorimetry questions, they do so now. Those who have shown mastery of these problems (as assessed by the warm-up question) are allowed to advance on the next assignment (calorimetry summary questions).
Students may work alone or with a partner who is on the same path. This "paper-and-pencil" activity is characterized by quiet collaboration between students or between myself and the students. Students get the satisfaction of working on precisely the most beneficial problems while I am afforded the opportunity to provide timely feedback. During this time, I can see both individual and common misunderstandings and can intervene appropriately. For example, if I find there's a common misunderstanding, I stop the practice time to highlight the specific issue at the board. Otherwise a quick conversation with a single student (or student-pair) will be sufficient.
As a way of challenging my students without introducing the attendant anxiety about grades, I have created a system called "Pride Points." The first pride points problem of the year is introduced in this segment of class.
The idea is to place students in randomized work groups - their Pride Points Teams - that they will return to 10-12 times throughout the year. During Pride Points segments, the teams are given challenging questions or tasks to complete in a 25-30 minute window. Each team submits their best work (with work and logic clearly shown) at the end of that time and the assessment is out of 100 points. These points, however, are independent of the students' grades; they count only toward their pride points total. "League standings" are displayed at the beginning of each subsequent pride point event. No team wants to be at the bottom of the standings . . . hence each team is playing for pride.
The particular challenge can vary from event to event. Typically, however, each pride points problem forces students to confront a novel situation. Though novel, success can be achieved if students can transfer their thinking from one realm to another. In other words, students will need to synthesize seemingly disparate elements of their background to resolve the problems. For example, on this problem, students will have to use the scales provided, along with unfamiliar variables, to write a mathematical statement of the slope. That slope can then be used to resolve the problem.
I designed this activity after realizing that, while teachers are eager to provide non-obvious challenges to their students, we sometimes fail to take into account the fear students have about "being wrong." This can be a fun way for students to engage with such problems without worrying about grades.
From a teacher's perspective, the assessment must be fair but can be a bit loose as no official grade is being granted. I typically look for complete work, solid logic, and, naturally, a correct answer. I try to be generous with teams that have worked diligently but are off the mark. As an essentially formative assessment, I try to look for the value in the student responses without getting too trapped by the "grade."
A sample moment from the first pride points problem is shown below. Teams are generally struggling with the problem and I provide a clarification for all teams.
In the final segment of class, I ask my students to turn their thoughts back to the calorimetry problem.
In this section, I ask my students to engage in a thought experiment that will provide an answer to the question: How much energy is lost to the surroundings in a typical calorimetry experiment? We have a way of calculating the energy that ideally would go into the container and can experimentally verify that. But what about the surrounding air?
That's the question I want my students, in groups of 2-3, to wrestle with in this final segment of class. Students are expected to discuss possibilities, write out or sketch their best ideas, and be ready to implement their procedures in the next class. The grouping is casual - students can work with their nearest neighbors - as my goal is to have them generate a number of possibilities to consider for next class. Indeed, as this is a challenging task, I don't want my students emotionally attached to their quick answers today; it's better to have them brainstorm and share, then reconsider for next time.
My role during this time is to push back on student proposals by asking whether, given their scenarios, they'll be able to measure properties sufficiently, and determine how much energy left their experimental system.
One hint I share is this: if one can both predict the equilibrium temperature (from the characteristics of the materials) and measure the resulting equilibrium in the actual test, then the difference in the equilibrium temperature can be used to calculate how much energy is "missing" from the water.
Ideally, students leave with an idea that can be tested in the next lesson. If not, I will provide a suggestion at that time.