What’s critical to look—and listen—for in observing student learning?
Teaching is an immensely complex act, requiring many decisions and adjustments in a short amount of time. By taking the role of observers during classroom activities, participants in a collaborative lesson inquiry cycle (CLIC) can focus on what students are actually saying, thinking, and doing.
For observations to be effective, there needs to be a clear lens, such as engaging quality interactions, which we define as sustained talk and quality interactions. Talk is sustained when students are able to expand, at length, upon their ideas and connections. Interactions between students are further reciprocal when they are responding to, challenging, adding on, and negotiating each others’ ideas.
Haiwen: Listening to and Looking at Students’ Interactions
We went in the classroom with a team of five teachers to observe students, deploying ourselves to “cover” the entire class while being able to focus on a single pair for the whole 54-minute class period.
In the initial “Five-Question Interview” task, we had students interview their partner by asking them interesting and controversial yes/no questions and recording their responses. We share some of this talk in the Mathematics Teacher: Learning and Teaching PreK–12 article. There was good evidence that their talk was both sustained (giving reasons, for example for wanting to listen to music while doing work, or using technology to assist) and reciprocal, responding to each others’ ideas.
Later, as they compiled the data into two-way tables and computed probabilities, their talk was a good deal more contextualized with gestures and references to where they were finding data. They were working together to make sense of the mathematical data.
Students were also engaged in reasoning about how real-world ideas may or not be independent of each other, such as the following partner discussion after the teacher posed a general question.
Teacher: | Do we think the music and tech might affect each other? Are they related? |
Student D: | Music and tech… |
Student C: | Like an acoustic guitar… |
Student D: | Hrm…trumpet, trombone. You can do like electric guitars. |
Student C: | [Laughing] I mean, I feel like they are independent but they are like…but related. It’s still going to be recorded in some way, but I don’t know if that counts. |
This sense-making, along with more formal calculations and definitions, extended into subsequent class periods.
Monique: Observing Quality Student Interactions
Similar to Haiwen’s observation, our team of four teachers spread out throughout the class, and each focused on a separate pair of students in a 54-minute period.
Pairs of students each received four graphs that teachers had constructed to match. In sharing their domain and ranges from their tables and graphs, student talk was sustained. Students shared values for their domains and ranges across, and found matches, without much discussion of the similarities or differences between their two relations.
Student B: | My graph has domain 0, 2, 4, 5 and range 0, 1, 4, 5. Do you have something that matches mine? |
Student A: | Yeah. Do I do next? |
Student B: | This is [names label]. Your turn. |
Student A: | My graph has domain 1, 2, 5, 6, and range 2, 3, 4. Does that match yours? |
Student B: | Uh-huh, mine is [names label]. |
Although the talk is sustained, where students are sharing their domains and ranges, the talk is not reciprocal. Students stated which graph or table it was, but did not build on one another’s ideas. This sustained talk without reciprocal discussion of ideas led to a shift in the lesson enactment for our second implementation.