Wednesday, July 6, 2016

Math Practices to Provide Clearer Focus for Tasks


Last year, I totally revamped my first unit on linear relationships. My goal was to have the students develop procedural fluency from conceptual understanding and also to work from concrete to abstract problem situations. I designed the unit so that it was extremely heavy on tasks, and had students notice patterns/generalize rather than a lot of direct instruction. I anticipated that students would build their conceptual understanding at different paces and tried to choose low-floor, high-ceiling tasks where all students could make progress wherever they were in their understanding. I also anticipated that it might be hard to measure and track the development of understanding. I had seen students experience learning trajectories  where it seemed like nothing was building in exposure after exposure and then all of the sudden something clicked about the concept.

In many ways, my revamp of this unit totally failed. While there were probably many factors in this failure, I think that one of the biggest ones was lack of student buy-in. I did not do a good job of communicating my vision to students. I didn’t tell them where we were headed in the long run because I felt like that would give away the end and defeat the purpose of their own building and discovery of knowledge. Because my main goal was for them to slowly make connections and I expected them to do it at different paces, I didn’t have a neat, tidy goal for every task. This required my students to put their trust in a vision they couldn’t understand or see, which was an unfair expectation for them. Although students did engage in many of the problems and start to get at the big ideas, the overall result was that students who came in confident in math felt as though the class lacked rigor and students who came in less confident in math felt like they still weren’t making any progress.

So I am going to revise again. I still believe in the premise of using a series of tasks for repeated exposure to build conceptual understanding over time.  I think most of the tasks that I used do a good job with that. What I am going to change is my messaging around the tasks. I need to do a much better job in getting my students to believe that they are learning math through this process, even if it doesn’t seem like it. I also need to do a better job in building a common understanding of how students (and I) can tell if they have used their time in a worthwhile manner.

I want to join this idea with my desire to figure out a way to have students explicitly reference and use the math practices. When I explained my math team’s focus on tasks, one of my other colleagues asked, “If the goal isn’t to get the answer, what is the goal?” For me, the process is the goal and I think the math practices could help both my students and me assess their process of trying to solve a problem.

I am imagining having students take some time to reflect at the end of their work time (or even in the middle if work time extends more than one day) on each task. They would identify one of the math practices they had used and give an explanation or illustration of how they had used that practice in their work. I would introduce the practices one at a time and spend several weeks choosing tasks that particularly lent themselves to that practice, so that we could develop a common understanding of what that practice was and what it might look like as you are working on a problem. As the year went on, kids would be able to choose from an increasing number of math practices as the focus for their evidence. I would probably start with math practice 1 and then 3, as I see those as the most over-arching, and then sequence the rest based on which practices are the best fit for the tasks we are working on at the time.

It would be my hope that this focus and reflection time would give my students a much better illustration of what to value during the time we spend working on tasks. Whether or not this is something that I will grade (or have the students self-evaluate), I have not decided yet. I also hope that the explicit teaching and re-visiting of the math practices in this manner will help students develop those skills so they can really leverage them to access new content. It doesn’t address how I will share the end-goal and overall trajectory, but I will keep thinking on this.

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