Why notice-and-wonder? It lowers the barrier to entry-- everyone can notice or wonder something-- and gets students thinking and talking early in the lesson, which means they're more likely to participate later. It gives teachers a low-stakes opportunity to position students as competent and affirm their ideas (because really, no response is wrong here). It directs students' attention to the things that are mathematically important in the representation, particularly as they become more practiced with the notice-and-wonder. It gives them time to make sense of the problem without any pressure to solve it or even start trying. It allows teachers to build on what students have shared-- often borrowing their exact language-- to ease into the next part of the lesson, especially when students make an observation or pose a wondering that can be leveraged as a direct transition ("[student] asked what the next image in the pattern would look like; that's exactly what we're going to figure out next!" or "[student] noticed that the last part of the graph looks like a hill, and that's what we're going to focus on together today-- we're going to look at graphs that look like hills, and think about why they might look that way"). Basically, it's a lovely way to launch a mathematical task.
How did it go? Our novices loved it. So much so, in fact, that they used it almost every day, and sometimes multiple times a day (they taught 2-hour blocks). Too much? As a raw number, I don't think so-- for the most part, their students knew what was being asked of them, appreciated the consistency, and offered interesting noticings and wonderings. A few cautions though:
- Sometimes the notice-and-wonder dragged on for a bit, and there were two primary causes: a) because some teachers wanted more students to participate, they had a hard time moving on when there were still hands in the air, even when additional observations or questions became a bit redundant, or b) because they hadn't yet heard the exact noticing/wondering they were hoping for, they continued to ask "any more?" and wait even though no additional hands went up. Gradually, however, novices refined their sense of how long the notice-and-wonder should take, and it helped when they both knew exactly what information would be most important to elicit in order to prepare students for what was next, and also knew that it was okay to throw in their own noticing or wondering ("one thing I noticed was that time was on the x-axis...") as a nudge for students to shift their observations and questions in a particular direction as long as it didn't become all about them or have the tone of "by the way, here's the answer I was looking for."
- Not surprisingly, this didn't go as well in classrooms where students didn't yet have strong relationships with their teachers; they still participated, but languidly, just enough to move the lesson along. In classrooms like this I generally think about what role the pedagogy is actually playing in students' disinvestment because it often is, but I don't think the notice-and-wonder actually did any harm.
- After the first day, we rarely saw any irreverent responses, and the ones that did pop up popped up in good humor, were enjoyed by both students and teacher, and the class was able to move on quickly. I did see, however, a few instances where responses seemed to fall a bit flat.
- It's likely to surface some meaty conversation. In one lesson, a teacher used a notice-and-wonder after students read a scenario about charter school growth in their city (it was about to be a linear regression and extrapolation task). Students surfaced observations and questions like "I notice that charters are taking over the city" and "I wonder why people support charter schools when it sucks to go to one," which was followed by "I wonder why charter school teachers act like police." Given that all of our summer school students attend charters during the year, these statements would certainly be worth talking about further-- or at the very very very least, acknowledging that the humans in the classroom have some mixed feelings about charter schools. For the teacher to simply write the question on the board and move on felt awkward, at best, and minimizing, at worst, even though the teacher's reasoning was undoubtedly more along the lines of a) I'm trying to stick to my plan and b) I don't know how to have the conversation.
- It's insufficient preparation for the lesson. This was the most common challenge we saw, and I'll describe it in the context of the same lesson as above: in order to successfully tackle the regression task (they hadn't attempted regression before, although they had constructed scatterplots and studied linear functions more generally) and engage with the analysis questions in it, students would have benefited from spending some time thinking about the data presented in a table: what it said, what the units were, what the numbers indicated was happening over time, and hypotheses about how the data might be used to make a prediction. They would have benefited from thinking about the language in the scenario: what's meant by "enrollment," what's being asked by "predict," and what "trend" means. They would have benefited from thinking about the context: what the total enrollment in the district was, why more students might be attending charter schools, what factors might limit or bolster charter school growth, etc. I didn't make up this list: check out Jackson et al's article on Launching Complex Tasks to see which four things are most critical for preparing students for novel, problem-solving tasks. Simply noticing and wondering wasn't enough.
In sum? The notice-and-wonder is powerful, but, like everything else, not a magic wand. Use it liberally, but use it wisely, and prepare a few other tools for launching mathematical tasks. Have you found that it's more/less effective under conditions different from the ones I've described?