On October 26th, 2021, I observed Jim Evans teaching a lesson for his ISCI 312 – Symmetry classroom. Note, he is not one of my CATL mentors, but I am doing my Term 2 practicum in his classroom. Of the 57 students enrolled in the class, 37 attended in person. Jim does his best to run the class in a hybrid manner, by teaching in person and recording all his lessons (since coming back to in person due to the COVID-19 pandemic) live over Zoom, however, I did not take note of how many students attended the lesson virtually. From my observation of this lesson, I think that Jim values lecturing paired with pedagogical content knowledge, experiential learning, and low-stakes formative assessment. Jim’s lesson was lecture-dominant, where he had ~10–15 minutes carved out near the end of class for a low-stakes formative assessment.
When introducing the idea of frieze patterns, Jim showed how concepts that the students had previously learnt about (in this case, the lattice, translations, and 2-D point groups) linked to frieze patterns. He did this by showing how when you combine a 1-D lattice with a 2-D pattern, this creates a frieze pattern. He then showed the 7 possible frieze groups, what symmetrical operations are used to create each group’s pattern, and where the unit cell lies within these patterns. To assess if the students were able to follow along with what he had been lecturing about, he had the students complete some practice questions identifying the respective frieze group of a couple sample frieze patterns.
Prior to Jim’s assessment, he walked through a sample frieze pattern problem so the students could listen to and observe his thought process and approach to solving such problems. Modelling this gave the students a foundation of what type of questions they may be asked during future assessments and how to possibly approach solving these types of problems. The formative assessment that followed this example was in the form of presenting a couple sample problems of different frieze group patterns on the lesson slides and getting the students to attempt to identify the unit cell (e.g., location and shape) and decipher the appropriate group (e.g., P2mg) for the frieze pattern either alone or with nearby peers. Jim gave the students ~5 minutes to solve each pattern. During the time the students worked on the questions, Jim remained at the front of the classroom instead of circulating around the room. Once the 5-minutes was up, Jim would ask for volunteers to share with the class what they got for their answers and how they approached solving the problems. He offered volunteers to come up to the whiteboard to draw out how they solved the problem, but no one was comfortable enough to do so (perhaps because of a fear of being wrong in front of their peers).
Regardless of giving the students a demonstration and having them work together on these patterns, a lot of the students struggled with coming up with the correct answers. I think this struggle signified that there was (1) a lack of ability due to a lack of exposure since this was a new concept to the students, and/or (2) an inability to identify the simple symmetrical operations that make up each part of a pattern (so a lack in understanding of the fundamentals preceding this new concept) leading to the lack of ability to combine the operations together to determine the frieze group pattern as a whole. Because of this struggle, Jim had to spend a bit of extra time going over each of the sample patterns with the students. Since there was a prevalent struggle in understanding how to successfully identify frieze groups in different patterns, I think that Jim could have (1) gone back to the fundamentals of identifying 2-D point groups and the isometries that construct frieze groups and assess which one of these concepts the students may still be struggling with, and then (2) provide more sample patterns for the students to work through during the class so that they could become more aware of why they struggle with the process of working through these problems, confront that/those issue(s), and then become confident in their ability to identify frieze patterns. I also think that during the time the students were working on the frieze patterns, Jim could have circulated around the room in an attempt to listen in on how the students were going about solving these problems to get some immediate feedback if the students are going in the right direction or if they are completely stumped.
Something I liked from Jim’s lesson is that he had a list of “Key Takeaway” points at the end of the lesson, which acted as his summary—this served as a nice list of items the students are expected to understand to succeed in the course. Something I thought was missing from this lesson was the far transfer of how frieze patterns represent themselves in different disciplines. I think this would have been useful for the students to either see some examples provided by Jim or two have been given some time to find how frieze patterns prevail in the students’ respective disciplines and then share them with the class. An example of where frieze patterns manifest themselves in my discipline is in the atomic structures of minerals, which translates well to how frieze patterns exist in crystalline materials that may be more prevalent when in other disciplines (e.g., DNA in Biology).
Overall, Jim’s lesson slides were very “clean” (minimal text, large figures), and there were clear communication guidelines between Jim and the students who were attending in person (raising of hands to ask questions). However, I thought there was a bit of a disadvantage being a student attending via Zoom with respect to communication in a hybrid class setting. For instance, when student’s in-person ask questions, the students attending via Zoom were not able to hear those questions. To combat this, I think Jim could have repeated student questions before providing his answers to them to help provide context to those attending virtually. Another disadvantage is that those who attend via Zoom are not able to see Jim’s physical cues in class, e.g., where he points to on the screen when singling out a step in a problem. To combat this, I think Jim could have heavily annotated his slides prior to the lesson, or he could have attempted to annotate them live (although, he only has a mouse for such annotations, so it may be tricky to draw). Finally, students attending virtually don’t often (if ever) have their questions answered. This is because (1) Jim doesn’t stand next to the computer the entire time that he teaches, so when he walks around and lectures he is not aware of the questions being asked in the Zoom chat, and (2) it is incredibly challenging to teach in-person and virtually as one person, as you are not always able to manage all the questions that may arise virtually. Perhaps a way to combat this would be having a TA sit in the classroom and monitor the Zoom on their personal laptop, where they could put up their hand (physically) for those attending virtually and state their questions (if needed) or respond via the chat function.