What's the purpose of student talk? - This isn't a new thought, and one that I'm sure has reverberated around the #mtbos and one I've read about in Smith and Stein, among others: why do we ask children to talk in math classrooms? It's easy to identify culture/management reasons-- it keeps kids "engaged" (I could write a whole other post on that word, and @delta_dc has a lot to say about it too), not asleep, less bored, whatever-- to claim efficiency (students can ask their peers questions instead of waiting for the teacher), or to resort to tautological reasons (because discourse is important), and much harder to dig into why it matters for students to talk. But why it matters has implications for how we set them up to do it, so let's talk about why it matters.
Reading the article, however, is helping me articulate that I believe talk matters because learning is social: we construct stronger (better and also more deeply understood) ideas with others than we could arrive at independently. This happens through several mechanisms (which have undoubtedly been researched and laid out by smarter people than me), including:
- By having to express their own ideas to others, students clarify and refine their own thinking
- By listening to others' ideas, students evaluate (and add to, revise, or confirm) their own because they may be confronted with contradictory perspectives, different rationale for the same conclusion, other ways of explaining the same idea, etc.
- By connecting their ideas with others' ideas, students build something more inclusive (or generalizable or deeper or broader, depending on the goal of the conversation) than what they developed independently
- Supporting students in making contributions: this goes beyond simply eliciting students’ ideas—the ideas need to be valuable contributions to a conversation, and the teacher can help find the worth in each idea. By finding the logic in a thought that initially sounds incorrect, or asking specific follow-up questions (rather than just “say more”) that require students to elaborate on the key concepts they’re describing, the teacher both elicits fodder for discussion and reinforces the message that it’s not just enough for students to explain such that the teacher understands, but rather, they need to explain so their classmates can understand. Everyone needs to have access to the content if they’re going to be a full, equal participant in the building of it, and what allows everyone to gain access are the contributions each student makes.
- Establishing and maintaining common ground: you know those conversations where it feels like everyone’s just talking past each other? Political disagreements with extended family over Thanksgiving dinner, perhaps, or Q&As where the questioner is more interested in communicating his/her own point than actually asking the speaker a question? Establishing and maintaining a common ground is what the teacher does to ensure that students are actually having the same conversation rather than just pushing their ideas into the same space (think of a series circuit rather than a parallel circuit). Directing students’ attention to something worthwhile, stating what has been figured out so far, and maintaining a record so that all students can follow the conversation allows the class to build collectively from one student’s idea rather than simply taking a survey of what everyone thought and then picking the thought that’s correct.
- Guiding the mathematics: these collaborative discussions build students’ participatory, social, and dialogic skills, certainly (and very importantly), but we’re still in a math classroom, and students are developing particular mathematical ideas. Although they’re co-constructing their understanding of a topic, they’re not inventing that topic from scratch; they’re figuring out something that has, by and large, been figured out by others before them. So, the teacher has to know the ideas that are most important to a topic (and common patterns and progressions for their development) and then choose appropriate tasks and constantly assess and respond to where students are in their thinking.
Within these three functions, a few underlying principles or stances stood out to me as being most distinct from what I typically see in classrooms:
- The teacher doesn’t attempt to protect students from hearing “wrong” ideas. This strikes me as beautifully respectful; when we shield students from hearing “wrong” ideas because we think they’ll be confused or because we fear they’ll believe something untrue (good intentions, certainly), we’re essentially saying we don’t trust them to think for themselves, or that their grasp on reality is so tenuous that they won’t be able to realize that something is incorrect, or that if they do latch on to something false, they won’t have the wherewithal to recover. Relatedly, the teacher doesn’t send a simple “mistakes are okay because everyone makes them” message of tolerance, but rather, she embraces mistakes—not just because they allow us to correct ourselves and so we inevitably learn from them, but also because entertaining/weighing/invalidating discrepant information deepens our understanding and strengthens our conviction.
- There’s an example where one child calls another stupid, and the teacher’s response isn’t to quickly cut him off with “that’s not nice” or “we don’t disrespect each other in this classroom.” Instead, she demonstrates the value of the first student’s thinking by asking him to turn his confusion into a question, and then later validating that the class wouldn’t have reached its conclusion without his question. In this approach, the name-caller isn’t reprimanded or silenced (or made to feel like an outsider who just broke a norm), but rather is shown why calling his classmate stupid was wrong. The student who volunteered the idea is shown not only that he’s not stupid, but also that his thinking is essential to the shared work of learning.
- Staples writes about the use of representations as a scaffold, rather than the use of representations for representations’ sake. Duh. But I so often hear (and have said), in response to the (stated or implicit) question of why we are using graphs and tables and diagrams and equations and words, that “it’s important to know all the representations and translate between them because then you know all the ways something can be represented” or even “because some representations highlight mathematics that others don’t,” which are—though not untrue—different from “because doing so gives us access to more of the mathematics.”
- When the teacher attends to pacing, it’s not because of “urgency” or in order to “get through” the whole lesson, but rather to control the flow of information so that every student can process enough of what’s going on to maintain a foothold in the conversation. This doesn’t need to mean that every student understands everything that has been said at all times—just that every student is comfortable enough with what’s happening to remain a part of it.
The paper provides additional concrete examples through transcript excerpts and quotes, and also explains the process by which the practice of collaborative inquiry evolves across a year. Really, it’s brilliant, and you should read it for yourself; my only intention in writing about it is to gather my thoughts 1) on the distinction between true collaboration and simply working in parallel alongside others, 2) on how teachers support the co-construction of understanding (what Staples terms “collaborative inquiry,” hence the title of the paper), and 3) on how important it is to establish common ground when doing so (something that had never really occurred to me before reading this and that I now can’t stop thinking about). I’ll stop now. Go read it.