In this second-grade classroom, students are learning subtraction. They will learn to solve subtraction problems on paper, but at this point they are learning to be flexible mathematical thinkers. Not only are they developing strategies to solve the problem mentally, but they are being asked to articulate why a strategy makes sense. By taking a moment for a turn and talk, the teacher gives every student the chance to put their reasoning into words.

The teacher’s next move with the whole class—asking a student to explain why taking away 6 is a good strategy—builds understanding. Notice that the teacher is not happy with a correct answer; she wants the student’s reasoning: that the 6 being subtracted represents the 6 ones in the number.

Her next move, asking a student to repeat what the first student said, promotes the practice of listening to other students’ reasoning. Listening carefully is a skill that requires development; for many of us, it does not come easily! When students know the teacher is interested in their interpretation of another student’s answer, they are more likely to tune in. In mathematics, new knowledge directly builds on more foundational knowledge. When students tune out—a normal response when something is not intrinsically interesting—they can miss critical, foundational ideas and practices, leaving students with a feeling of being lost. Asking a student to repeat an answer may seem unnecessary given limited instructional time, but if it means that students stay tuned in, then it will be well worth the seconds (32 in this case) that it takes.

In this segment, the teacher has the students discuss with a partner the step after taking away the 6 ones. The students seem to understand that they need to take away 2, but the teacher wants an explanation and providing one is a much more demanding task. One student says that she can’t explain why, and the teacher acknowledges that it’s hard. By asking another student to explain, the unsure student has an explanation modeled. When her partner explains well, the teacher chooses him to explain to the whole class.

When a student is once again called on to repeat the explanation, he can give the answer (take away 2), but when the teacher asks why, he is not sure. He answers “Because it will be easier?” This is important information! The student got the answer but he did not follow the reasoning. Note that the teacher does not correct him; she goes back to the student who first gave the answer. This gives students ownership of their learning, and signals that they have a lot to learn from each other as well as from the teacher. Importantly, she then returns to the student who was not able to repeat the explanation, and now he is able to do so.

In this final minute, the teacher asks, “where would we land.” When a student answers “18?” the teacher asks about the question in her answer. The student then makes her answer definitive. Because the students have reasoned through the problem, the teacher is looking for the confidence that comes from careful reasoning. In her explanation, the student says that 20 minus two is 18, and that 19 minus 1 is 18. It seems that this student thought about the second move (substracting 2) as having two more 1s to remove—one at a time. Without the opportunity to talk, the teacher would not have this information about the student’s thinking, and would not know to confirm that it is possible to get to the answer by subtracting one twice.

This has been productively challenging for students and the teacher’s final move, to have students talk with their partners about why they did minus to, gives students a chance to consolidate their understanding before moving on.