I have my students in all of my classes complete reflections about their experience in my class at the end of the semester, which help me reflect on how I can improve my practice as I transition into the next semester. Here are the prompts:

**In this class, I felt like I, my ideas, and my questions mattered.**(scale of 1-5, from Never to Always)**In this class, I felt challenged.**(scale of 1-5, from Never to Always)**In this class, I often felt stressed out.**(scale of 1-5, from Never to Always)**The best aspect of this course was…****The worst aspect of this course was…****One surprising or interesting thing that I learned was…****One thing I’d like to tell Mlle V, in all honesty, is…**

And here are some highlights from my Grade 9 class.

**The good**

- Many students commented on the organization of the class and the “teaching style,” with most comments being positive. Students enjoyed that we often worked on problems in groups and on whiteboards, practiced through games or other interactive activities, and didn’t see much of the textbook in class. This was heartening to hear, because many of these same students were very concerned at the beginning of the semester that we weren’t relying on the textbook and were openly distrustful of the learning activities (“Oh god, we’re going to fail the final,” one student exclaimed during the second class). The shift in routine was unexpected and maybe even scary for some students, who seemed to need something tangible to hold on to to prove that they were learning something. I’m glad that most of them came to find value in our learning activities.
- At the beginning of our unit on polynomials, we spent a few days exploring binary and other base arithmetic. Several students pointed to this as the most interesting thing they learned during the semester. I had enjoyed these lessons too, but I am reconsidering their value as an introduction to polynomials. As engaging as these classes were, the connection was tenuous to say the least; next year, I will spend much more time building on students’ understanding of the base 10 system and its representations (e.g., base 10 blocks). Seeing how much students enjoyed exploring arithmetic in different bases, though, I’ll have to find another place for them in the semester, maybe as an extension of our unit on rational numbers.
- “Thank you for helping me with my homework, I couldn’t have done it without you!” Appreciation doesn’t fuel our work as teachers, but it’s still nice to hear once in a while that your efforts are valued by your students.
- “You are amazing and I am very happy that you were my teacher.” Alright, now I’m just showing off.
- “I talked too much and disrupted the class.” “Thank you for helping me and I’m sorry for being distracting.” The kind of notes that remind me I that love these kids… yes,
*all*of them, even the one who took to crawling under the desks last week while others were trying to focus on reviewing for the final exam.

**The bad**

- A few students commented on my relative lenience with regard to classroom behaviour, finding it difficult at times to concentrate because of students who–let’s say things as they are–wouldn’t shut up. I guess many teachers simply show students the door when they’re being disruptive, which my students sometimes went so far as to suggest that I do; not wanting my students to miss out on learning, though, I tried my best to redirect them towards their work. This isn’t to say that I always succeeded, and did ask students to leave for a period of time several times during the semester. Of course, I’m aware that students often disengage from a task not because they don’t want to learn or because they want to distract others, but because they don’t know how to get a foothold into the problem or how to use the resources within their group (i.e., themselves and the other students). I am still working on the larger goal of helping students become persistent problem solvers, and I can’t say that I have consistently done this well. Next semester, I am going to try to be more explicit in teaching good problem solving practices, including what to do when you get stuck.
- A few students suggested that more time should be spent in the classroom working on problems from the textbook. I take this as a call for more individual work and practice in the classroom, which is definitely something to take into account. This is something I will try to consistently try to make time for next semester as I work on developing instructional routines in my classroom.

**The ugly**

At the beginning of this class period, the last one before the final exam, I had students complete an entrance slip on solving inequalities. The first question asked:

I was discouraged to find many, if not most of my students unable to solve this problem, even if they could now virtually solve inequalities in their sleep. I tried to guide them by asking, “What does it mean to solve an inequality?” and “When you solve an inequality, what are you looking for?” To which many responded, “isolate the variable” and “*w,*” and not something along the lines of “find all of the values of the variable that make the inequality true.” Although I felt that we had laid the groundwork for making sense of solving linear equations by working on a variety of balance scale problems early on during the unit, representing them with inequality statements, and connecting the process of determining the unknown value to that of solving inequalities, clearly the connection was lost on or discarded by many of my students once they latched on to key aspects of the procedure (“isolate the variable,” “what you do to one side, you do to the other,” etc.). Task propensity seems to be a relevant idea here. Evidently, they had mastered the procedure, but lost the *meaning* of the process along the way. Interpreting solutions and connecting these to big mathematical ideas is something we clearly need to focus more on going forward.

A humbling experience, and a lot to reflect on as I prepare for the next semester.