*Jeff Shriner is a graduate student at the University of Colorado at Boulder.*

As a reminder, I taught 2 sections of pre-calculus in the Fall semester — one evening class meeting twice weekly for 2 hours, and one online class. I aimed to keep the courses as consistent as possible, but there were some key differences due to the different formats. Please refer to Jeff: The First Inning for some more details about the main methods I implemented in an effort to engage students in each of these classes.

In the weeks since the end of the semester, I’ve spent time reflecting on what went well, and where I would like to grow. I will say that my overall ‘feeling’ about the semester as a whole is very different than previous semesters that I’ve taught. Previously, my sense about a course throughout the semester was more-or-less constant; generally, the semester felt smooth and agreeable. This semester, my sense was much more erratic, filled with peaks and valleys. I think some of this is due to the fact that I was trying many new things. But I think this also illustrates the nature of how we learn, which lecture hides, and IBL techniques emphasize.

In the following, I’ve summarized my reflections on what went well (and what I believe contributed to this), and the areas I’d like to grow in for next semester (and the actions I plan to take to achieve this).

*What went well:*

*Increased student-to-student interaction.*Students were talking to each other about the material more, by far, than any other course that I’ve taught. The two strategies that contributed most were think-pair-share questions/exercises which I embedded into lectures, and weekly small group problem solving sessions for assigned homework problems. The latter was something that I actually was nervous did not go well most of the time, because it felt messy. To my surprise, this activity was mentioned in multiple end of semester feedback forms as a favorite. Students said that they appreciated the space to talk with classmates in a low pressure environment. I also learned about an unintended benefit from one of my international students, who said he appreciated this time because he was able to practice his conversational English skills.*Modified perceptions about what math is and what it looks like.*Because our course structure was based on interacting with each other and effectively communicating our ideas, students could see math as a creative process in which we experiment and ask questions. There were students who were noticeably more comfortable at the end of the semester asking questions and attacking a new problem that they didn’t know the answer to right away. One student told me confidently at the end of the semester that he was ready for calculus — he didn’t say this because he aced the final exam, but because he better understands the mathematical process, and is not intimidated to approach a new concept.

*Areas for growth:*

*Providing clear spaces for productive failure.*If we tell our students that they learn by making mistakes and that this is part of the mathematical process, we must give them space to do this and not be penalized. I did provide some spaces to make mistakes, but I think I need to provide more, and also make it explicit to my students what these spaces are. Specifically, I plan to*Implement a 2 week cycle for written homework.*I previously used a 1 week cycle: homework problems were assigned, due a week later, then returned with a grade/feedback. My intention was that students would take the week to ask questions, struggle with the problems they found difficult, and submit a final version; but this did not happen nearly to the extent I was hoping. I think part of this is because they don’t know what they don’t know. I plan to add an extra week to this cycle, in which they have time to ask questions and correct problems that they misunderstood the first time around.*Emphasize group work/presentations as spaces to make mistakes.*This is one of those things that sounds really simple, but I think can make a huge impact. I think I need to simply say ‘It’s OK to make mistakes here’ more often, giving them permission to explore their ideas without knowing whether they’re ‘right’ or ‘wrong’.

*Moderating full class discussions.*I found this extremely difficult to do effectively. It was hard to get more than a small core to participate, and it was also hard to keep them from looking at me whenever anyone asked a question. I plan to*Formalize class presentations.*Students did get to the board, but it was always informal. Because of this, there wasn’t enough investment in what they were doing, and there wasn’t enough diversity on who went to the board. I plan to make presentations a requirement (something like one presentation per exam) to get everyone involved, and also hopefully make everyone more prepared to have a productive discussion. I will identify specific written homework problems which are candidates for presentations.*Improve worksheets and discussion board prompts.*One of the contributors to my problems in this area was just bad content. There were certain worksheets and discussion board prompts (for my online course) that just didn’t work the way I envisioned. I plan to do a content review and try to update the activities that didn’t work.

As always, I appreciate feedback and suggestions for improvement!