This is my midyear wake up call.
At the beginning of the school year I developed some goals. They were ambitious, to say the least. It was around the start of December that I realized how unreasonable my expectations were for 2016-17. I’ve been in the game for a while, I should’ve known better. Shame on me.
Despite my lack of judgement and setting myself up for failure, three of my goals came with a higher priority for me. This post serves as a self-critique on my progress towards one of those three: my use of instructional routines.
I worked on these routines a lot last summer through New Visions (here and here) and at TMC16. I had a crazy vision that they would transform my teaching this year. They were going to help my students leverage mathematical structure like never before. Being routines, I was going to get better at using them as the year progressed. I was going to learn to lean on them.
Well, next week the first semester is coming to a close and my use of them has been pitiful. Sure, my first unit in algebra 2 held much promise. I used the routines five times over the course of a few weeks, which was a huge win in my book. I started off strong. Slowly, though, I got bogged down with the curriculum. I got consumed with more immediate concerns and stressors, like being at a new school, running around to three different classrooms during the day. In the meantime, I forgot all about the instructional routines that I so zealously committed myself to back in September. I’ve used Connecting Representations one time since that first unit. I haven’t used Contemplate then Calculate at all.
Accepting this isn’t easy because of how much I really wanted to use these routines. That said, I know that it’s normal to unintentionally forget about goals. But I also know that if I recognize the struggle, write about it, and let it breath, I can begin realigning myself to the vision I had back in September.
What’s great is that I’ll soon begin digging into Routines for Reasoning and have scheduled a workshop with New Visions, both of which should help me find the routines that I so desperately want to implement.
I’m taking a Structured Inquiry course this summer offered by New Visions for Public Schools. As part of the course, we are required to design a Contemplate then Calculate instructional routine and rehearse it with the class. David Wees and Kaitlin Ruggiero have both done some inspiring work with #CthenC routines and much of my motivation comes from them.
If you’re unaware of Contemplate then Calculate, the goal is to get students thinking about mathematical structure. The routine leverages student observations, honors their approaches, and highlights reflections on their own thinking. There is a public collection already created by David, Kaitlin, and the New Visions team.
Here was my task.
- I initially planned for this to come at the end of an exponentials unit, but after some discussion, I think it would fit much better at the beginning of the unit – or at least before we discuss exponential equations. One thing I’m great at is having students get overly consumed with procedures, so my hope is to get them thinking instead about the structure of the equation and the relationships that exist within it before any mention of the term “exponential equation.” I want their mathematical insights to drive how we solve these equations…and the entire curriculum.
- To this end, I thought of four strategies that students may use, ranging from guess and check to equating exponents (excluding the one involving logarithms since the task would be presented before they appear). Interestingly, guess and check was not an approach that was adopted much during rehearsal (possibly because they were all math teachers).
- Since my phrasing of the number of solutions was ambiguous, Robin mentioned that students could use a graphical representation to address this. They could reason that only one solution exists because f(x) = 10^(x+5) -1 is one-to-one.
- I also considered how to represent the equation. Specifically, I thought about 100 = 10^(x-5), 10^(x-5) = 100, 100 – 10^(x-5) = 0, or using any other set of constants in place of 99 and 1. All of these alternatives have consequences for how students may approach the problem.
- During the rehearsal, I did a fairly poor job at annotating, which is a critical aspect of the activity because it models student thinking for the rest of the class. Although I anticipated all the strategies while planning, I rushed myself during the process and the result was unclear and unorganized.
- The reflection prompts should be tailored to the goals of the activity. The more specific they are, the more beneficial the reflection.
- I should omit the question (e.g. “find all values of x”) during the flash of the task. This move opens things up for more diverse observations and student thinking.
- An interesting extension was asking what if the 1 wasn’t there? How would this impact our strategy? This is a nice prelude to logarithms.
- Designing this activity made me think about mathematical structure like I never have before. Often times I take student thinking related to structure for granted. This activity helped me better value student understandings of mathematical structure – and how to leverage those understandings to enhance learning.
- One of the most beautiful aspects of this routine is that it goes beyond mere discovery learning. The goal isn’t for students to end up at the same strategy. The idea is to develop fluency and flexibility in their numeracy. It echoes the theme from my current book, Building Powerful Numeracy for Middle and High School Students by Pam Weber Harris.
- All of my planning materials can be found here, which include the anticipated strategies students will use, my planned annotations, the annotations I actually did during the rehearsal, and the slides.