One of my favourite professors in university taught a second-year course on solving differential equations. He would bounce into class, silver hair flying, making us feel like it was our lucky day to be studying math on a beautiful day in that stuffy old classroom. I still remember how he would preface the problems we would solve with: “Alright, so that’s the game! Let’s play the game.” And off we would go. After all these years, this phrase stuck with me – admittedly, more than the mathematics I learned during the course. Maybe he was referring to the fact that we were working with “toy problems,” as other professors would say, suggesting that they had little resemblance to the problems mathematicians actually work on day to day; I like to think, though, that he was talking about how mathematics itself can be a form of play. Continue reading “Radical Cheat and Playful Mathematics”
It’s February break, which means that I can finally start making a dent in the reading piling up on my bedside table. I kicked things off with Embarrassment by Thomas Newkirk (2017, Heinemann), a book exploring how embarrassment and its associated emotions can get in the way of or even sabotage our students’ and our own learning. (Naturally, there is an entire chapter devoted to “math shame,” with the subheading “Why are we all on the outside looking in?”) It’s an engaging, provocative, and powerful read, with take-aways for teachers and learners of all levels and at all stages in their career. So far (I am halfway through), the most illuminating section for me has been the one entitled “Asking and Receiving.”
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. Continue reading “End-of-semester reflections”
There are a lot of quotes (maybe as many as there are teachers) that begin something like this: “The goal of education is…” For example,
“The one real goal of education is to leave a person asking questions.” –Max Beerhohm
Undoubtedly, many of these are spoken in a hyperbolic manner, and should be interpreted as such. (Myself, I would be wary of anyone who believed that there are precisely N goals of education, true for all places and at all times.) Nevertheless, this sentiment came to my mind last week, the first week of school. Continue reading “Love the questions”
Every being cries out in silence to be read differently. Do not be indifferent to these cries. – Simone Weil
I was substitute teaching today for a group of students I had taught last semester. I noticed that one of the girls had new glasses, and I told her that they looked nice. She replied, surprised, “You’re the only teacher that’s noticed, and you don’t even teach me.”
Not pretending to be a hero. There have undoubtedly been countless occasions that I’ve been blind when I should have seen. Just tying a knot in my mind to notice, amidst the chaos, the students I’m not seeing in my own classroom.
tl;dr: Sometimes, a “problem” in the classroom is really a symptom of a bigger issue.
Here’s the backstory. Lately, I’ve been struggling with a lack of engagement in whole-group discussions after small-group work. I was growing increasingly frustrated that the majority of the students – especially the students who had a good grasp on the concepts – didn’t volunteer to share their thinking, and that they had no qualms about chatting with their friends when a student (or me) did choose to put forth a question or share an idea. Increasingly, I was feeling like I was losing them, and searched for explanations ranging from summer being around the corner, to deficiencies on the part of my students (kids these days!), to the possibility that I am a terrible teacher for whom there is, frankly, no hope. (During a recent conversation, Jimmy Pai described teaching as a balancing game between overconfidence and despair, and these days I’ve been leaning heavily to the right.) Continue reading “Reframing a classroom culture problem”
At some point last semester, I remember feeling apprehensive about using balance scales as a model to introduce linear equations. I think I was worried about students’ ability to move beyond the model and consider things like negative and decimal coefficients. Would they be lost when they no longer had their crutch?
I should have trusted them.
Nat Banting has written about balance scales here. Although the metaphor of balance scales is referred to often in math classrooms – during the linear equations unit, students must hear the mantra “whatever you do to one side, you do to the other” at least 1000 times a class – the model really becomes powerful when students actually work with balance scale problems, and that they do so right from the start. Nat writes:
My Grade 9 students don’t see an equation for the first two weeks of their unit of solving linear equations. That is because I think students get all bogged down in the notation, and lose their problem solving intuition.
I decided to follow Nat’s advice. For a few days, my students worked through sequences of problems such as these, increasing in difficulty, where the goal is to find the “weight” of the square: Continue reading “On balance scales and trusting your students”
I paused the Act 2 video after the first weighing:
How much might each bottle and glue stick weigh? Continue reading “Linear systems: Substitution woes”
Quelle est une chose qui devrait être interdite à l’école ?
I often start French class with a question. The students reflect and discuss in their table groups, then share their responses with the rest of the class during the whole-group discussion. Yesterday, I opened with the above. In English: “What is one thing that should be banned at school?”
“Littering!” “Homework!” “Vaping in the bathrooms!”, a few students volunteered (in French). Then, a student offered, “Cell phones!” I’m sure you can imagine the disbelief and anger that this response evoked from a class of Grade 9 students, the majority of whom have an iPhone permanently glued into their hand and probably could not imagine a time without them. Once the others died down, I gave the student the floor, who argued with sincerity: “Cell phones are a huge distraction. We’re paid to be here by tax payers, which means we have a responsibility to learn and not waste time on our phones.” Once again, the other students erupted. It took a minute to calm them down.
Finally, a student responded bitterly: “If we’re paid to be here, where’s my money?”
I knew at that moment that French class, strictly speaking, was over. This was going to be something different, and I liked where we were going. Continue reading “The kids are alright”
One of my favorite conversations to have with my students (Grades 9-11) has quickly become centered around the concept of zero.
It first arose naturally last semester, when a Grade 9 student blurted out: “But 0’s not a number, it’s the absence of number!” (I’ve forgotten the context of this remark.) I remember a few other students laughing at this, and I know that this was unfortunately a negative formative experience for her, because she wrote about it in her end-of-year reflection. And yet, when I prodded further at a later point in time, I found that many other students, if not most, held the same belief. We had a whole-group conversation about it, talked about how 0 behaves in a similar way as other numbers in many ways (you can add it, subtract it, multiply it…), but still, I think a lot of students held on to this conception. This was especially clear when the students were solving equations and came to a problem such as this: Continue reading “The absence of number”