I don’t take any opportunities for granted, because not everyone gets them, and I’m feeling a little ‘Dayenu’ at the moment – or maybe a lot –
- Getting to go to the Exeter Math Conference two summers in a row should have been enough –
- Meeting a whole lot of awesome tweeps at TMC13 in Philadelphia should have been enough (well, not really…there’s the two I have missed since then) –
- Going to PCMI last summer – truly, truly enough –
but then I had the opportunity to spend a lovely weekend getting another taste of the summer math teacher camp extravaganza at a boarding school which looked like a cross between Hogwarts and a whiteboard showroom. The weekend was professionally and engagingly run by Tina Cardone, Brian Hopkins, Cal Armstrong and Jennifer Outz, and it was wonderful to reunite with not only PCMI folk I met last summer, but also some tweeps who I had met in Philadelphia in 2013, or never met in person at all. I’m truly grateful for all of this.
We spent approximately half of our time working a set of problems put together by Brian Hopkins, involving pennies, modular arithmetic, and combinatorics (or not), and a kinesthetic exploration called “Duck Duck Die” (I was the last one alive once!). These problems pushed me out of my comfort zone, but I worked in two very collaborative groups, which helped me make some connections I don’t think I would have made on my own. For a full description of the mathematical work of the weekend, I suggest you read Tracy Zager’s post here.
Reflecting on Practice comprised the other half of our work time; the topic was Worthwhile Tasks: what makes a task worthwhile and how to execute them in the classroom for deeper conceptual learning. Some of the work felt similar [but not identical] to what we did over the summer, but I found anything I had previously encountered appeared to have taken on a deeper dimension – a vote for spiraled curriculum. The tasks we reviewed covered both middle high school topics, with a smattering of elementary school, and there was always much to glean, regardless of whether or not the topic was directly pertinent to my current teaching assignments. For example, we looked at an activity including twelve cut-up systems of equations, and sorted them according to any criteria we wanted before attempting to solve any of them. When that task was compared with a worksheet which had the twelve systems and directions to solve them, a groan arose from some of us (myself included). For me, I recognized work that I have given that missed the opportunity to engage students collaboratively and conceptually, and to provide an entry point for different readiness levels. There is definitely a place, time and need for procedural practice, but that becomes meaningless without the deeper understanding that may come from a sorting activity. And what a great way to uncover student thinking!
Cal and Jennifer also modeled the 5 Practices for Orchestrating Productive Mathematics Discussions for us by giving a simple open ended task, and allowing us to take it in a direction of our choosing. After we had generated ideas, formalized the one we selected, made our posters and took a gallery walk, we discussed the sequence in which would have the ‘students’ present their work. The beauty of this activity is that it felt like the natural flow of a classroom. So often when I read about a new technique/strategy/practice, I have trouble imagining how to use it in my classroom without logistical obstacles. Our facilitators demonstrated that transformative practices are possible in your classroom by tweaking existing materials, or modifying how you use them (just like Kate Nowak apparently said in her NCTM Nashville talk).
The weekend was professionally restorative for me in some very important ways. I have been feeling philosophically isolated in my math department, and frustrated by the resistance to changing our practices. I’ve had classroom management issues that I haven’t seen in five years, and unpleasant verbal exchanges with students that definitely have no place in my classroom. I had begun making lists of options of my ‘next steps’. But the weekend reminded me that I can change what goes on inside my own room, and that I have a professional learning community, and thanks to the Interwebs, most of them are always there, ready to communicate and share.
Energized and emboldened by my experience, I adopted a ‘no more excused’ attitude and decided to modify my next Algebra 2 lesson on Function Inverses. I turned my Do Now into an exploration of finding the inverse of a line. (I’m glad I used this activity for more than its original objective; I now know that half of my students forgot how to write equations of lines from a graph.) After the students shared their observations (and without giving complete resolution to the Do Now), I distributed iPads for the lesson. I used, for the first time, Classkick – no small feat since I made the decision at 4:00 on Monday for Tuesday’s lesson. Classkick is an app which allows students to move through lesson screens at their own pace (unlike Nearpod), allows the teacher to see what her students are doing all at once, permits on the spot feedback (and stickers!), and if desired, students helping other students. I took my lesson on Function Inverses, made a pdf of my
NoteBook, and dumped it into an activity. Classkick refers to each screen as a ‘question’, but there were several screens that contained notes for students to copy. I was even able to leave recorded notes and hints on the screens, and got to hear a mash-up of me saying “It’s not an exponent!” (regarding inverse function notation). 100% engagement, lots of collaboration and discussion. I actually had NOTHING TO DO but walk around and eavesdrop. The question remains whether this was an effective way to deliver the content; formative assessment and review will take place tomorrow. On Thursday, we will begin exploring exponential functions hopefully with an activity I am going to borrow from Laurie B-Worthington over at The Angles Have the Phone Box.
Until this past weekend, the events I attended were held during the summer, as I was reflecting on the school year behind me and beginning to think about the one ahead. “Scaling the Teaching Curve,” as our weekend program was entitled, came at a point in the school year when the September honeymoon is definitely over and the winter holiday break is still a chunk of time away, and for this teacher it was perfect timing. It recharged my batteries, reconnected me with my professional community, and reminded me of the teacher I want to be.