How often do you have discussions - real, deep, serious discussions - on how to best teach a topic? In my 22 years of experience, these discussions do not happen often enough and that's truly a sad thing for the future of math education, if not education in general.
In the month that I've been home from ICMI25, I have had so many ponderings and discussions on the future of teacher collaboration on a personal and district level and I keep having that weird squirmy feeling that I often get when I feel that I'm moving from my comfort zone to my learning zone. I know most of us would not describe a squirmy feeling as a positive thing, but for me, it's always that point at which I feel I'm at the cusp of a breakthrough in my personal / professional journey, that feeling of dissatisfaction with the status quo.
Which brings me back to my original statement. Last week, I was in a meeting with several other Geometry teachers and during a lull in the conversation, I asked them how they teach the Pythgorean Inequalities and how to help students remember which inequality is for the acute triangles and which or the obtuse triangles. I personally teach the inequalities using a hands-on method and some "Notice / Wonder" questions, but I also struggle with keeping the inequality sign straight in my head. A couple of teachers answered me, some reiterating the pattern of the c^2, which I already know, but only one of the responses really answered my deeper question on how to help students remember and I took it back to share with my students.
I've thought about this exchange several times over the past week - I'm a veteran teacher and for the first time in 20+ years of teaching, I have a solid way to help my students make connections to what they discovered via our in-class activity for this topic. But how students have I deprived of that because I had never asked? How many newer teachers use just the textbook (our "primary resource") and never dig deeper into "what is the best method to teach topic X?" How many teachers (myself included) teach the way we've been taught and not using what we know to be best practices? How do we change that paradigm? How do we get to a point of shared lesson planning and lesson creation and not just shared pacing?
The learning journey that I started at ICMI is picking up steam. I'm excited to explore these questions and more with my colleagues and my district. Where will this journey take us? What challenges will we face and overcome? How will this impact our students going forward? I really don't know, but it's a journey I know is necessary for growth.