In Part 1, I dove into the first of the five practices: anticipating. When teachers effectively envision student responses, they give themselves a chance to plan. In this post, I'll explain the significance of monitoring.
The second practice
The second of the five practices is monitoring. This is when a teacher circulates the classroom while students work, and pays close attention to their mathematical thinking. To what extent are they approaching the problem in the way the teacher anticipated? In addition to listening and watching, teachers practice monitoring by asking students questions to help make their thinking visible. Many of these questions can be planned in advance of the lesson, on the basis of the anticipated solutions.
“It is important to note, however, that monitoring involves more than just watching and listening to students. During this time, the teacher should also ask questions that will make students’ thinking visible, help students clarify their thinking, ensure that members of the group are all engaged in the activity, and press students to consider aspects of the task to which they need to attend.” (Smith & Stein, 2011, 10)
Why is the second practice important?
If anticipating represents the teacher’s hypothesis for student thinking, then monitoring represents the data collection. What do students actually do with the problem? This is a critical question because it helps teachers determine what comes next. It sets up the third practice—selecting. Given what a teacher sees and hears during the second practice, what student examples do they want to select?
How is the second practice supported in curricula?
Teachers are equipped to incorporate the second practice when a curriculum comes with a set of anticipated student responses for which to monitor and questions that help reveal student thinking.
The Illustrative Mathematics 6-8 Math curriculum was designed with the five practices in mind, and LearnZillion’s curriculum support helps teachers to apply them. For each lesson, key visuals are placed alongside teaching notes, and the teaching notes provide teachers with anticipated student responses and suggested questions to ask.
An example of monitoring support can be found in this lesson.
With this integrated set of tools, teachers are prepared to ask students questions in order to reveal their thinking. How are they approaching the task? To what extent are their approaches aligned with the anticipated responses?
In the next post, I'll go over the third practice: selecting.
Eric Westendorf is the Co-Founder and CEO at LearnZillion.