As I'm reflecting on my school year and how I can improve my practice, I've been thinking a lot about how to improve Problem-Based Learning (PBL) in my classroom. Let me use a musical analogy to describe the problem I'm uncovering. Yesterday I was reading a great blog post called Getting Kids to Practice Music - Without Tears or Tantrums.. In the comments, one reader suggested "For longer pieces, don't always start at the beginning. If you do, the result will be a wonderful beginning, a so-so middle and often a non-existent ending. Once something has been mastered, leave its comfortable safety and concentrate on the next challenge. Every part should receive the same level of attention." This resonates with me because, as a violinist, I have been there and done that. Sometimes, when I'm performing a violin concerto, I feel great at the beginning and then as the end creeps nearer and nearer, I can feel my anxiety levels begin to rise. The lack of attention that I have given to the ending is amplified by the fact that often the most technically difficult passages fall at the very end of the piece.
When I read blog posts and attend trainings about the 5 Practices for Orchestrating Productive Mathematics Discussions, I encounter a similar tendency. We teachers could spend all day talking about how to select a rich task, how to monitor student work time. I've been in groups that have gotten side-tracked for nearly half an hour debating the most effective way to sequence a particular set of student work. That's all fine and dandy, but aren't we neglecting to practice the end? The Connecting?
As a I lead students through a task, I get excited about the beginning and the middle. I love the flashy "Act 1" prompt that gets students Noticing and Wondering exciting things. I love watching and hearing them branch off and try different strategies to solve the problem. I even like watching them wallow a bit with some of the mathematical concepts that are still a little and confusing nebulous. But as the task starts nearing its end, I start to feel anxiety because I realize that the load is now squarely on my shoulders to guide my students out of their different levels of 'unengaged-ness', 'productive struggle' and 'active confusion' into something that is hopefully an Ah-Ha! Moment resulting in a deep conceptional understanding of the mathematics content at hand. Yep, that's right, the hardest part of this concerto has landed at the end once again and, as usual, I've gotten so caught up in the beauty of all the other sections that I've neglected to prepare for the end. It seems to me that the Connection stage of the 5 Practices is where all the 'Magic Teacher Moves' happen. But since I'm no magician, too often my grand finales turn out to be what Smith and Stein describe as a session of "Show-and-Tell" with me trying fill the missing content pieces at the end. This inevitably falls flat.
It's time for me to start practicing my endings. As I've been looking for help in this process, I've been surprised by how very little discussion there is about the Connection process. Some of the teacher-bloggers to whom I've looked to as PBL Beacons are silent on this topic. Maybe it's out there and I'm just not finding it? If that's true, would you leave a comment pointing me in the right direction?
I was very intrigued by the conversation between Christopher Danielson and Dan Meyer in the comments of this post. I think a large portion of the online math-education world is leaning toward Dan Meyer's teacher-centered Act 3 'reveal' to summarize the lesson rather than the student-centered discussion method of synthesizing the lesson that Christopher Danielson describes. That makes sense because there seems to be a very clear formula for the 3-Act task reveal, which makes it easy to implement. Both strategies have their place in a math classroom, but I've seen fewer clear examples of the discussion-based, student-centered lesson closing/synthesis. I want to know the formula.
Here's where I'm headed now: I'm looking into good questioning strategies right now, since that seems to be the direction that Christopher Danielson and because it is discussed in the Connections section of the 5 Practices.
In the 5 Practices, Smith and Stein outline nine types of questions, focusing on numbers 3-5
1. Gathering information, leading students through a procedure
2. Inserting technology
3. Exploring mathematical meanings and/or relationships
4. Probing, getting students to explain their thinking
5. Generating discussion
6. Linking and applying
7. Extending thinking
8. Orienting and focusing
9. Establishing context
As a first step, I'm planning to read through David Cox's "First Idea; Best Idea..." and categorize each of the questions he asks his students. I will do the same with Max Ray-Riek's "26 Questions You Can Ask Instead" and see if I can find a pattern in these questions and when would be the most appropriate time to ask them in a lesson. I'm very curious to hear what other people have to say about this topic, so please leave a comment.