"Look! No hands!"
This situation is a math teacher's worst nightmare. Teachers spend hours planning standards-based lessons and problems designed to engage students (i.e., those raised hands). However, historically, math teaching and learning has focused narrowly on avoiding wrong answers and celebrating right answers. This type of math culture makes students reluctant to participate unless they can guarantee their correctness, and it discourages growth for all students in mathematics. As teachers, we have the power to include all students in a collaborative environment that fosters mathematics growth. We can do this by shifting thinking and questioning to focus more on the process of solving math problems, opening up a world of formative data that lets teachers see what students are thinking.
This list identifies some ways to shift teacher questioning in math from limited answers to open-ended questions that reveal formative data on math thinking skills and processes. These "formative open questions" encourage all students to participate, even if they are not confident in their final answer.
Instead of asking for the answer, ask students "formative open questions" like
- What does this problem make you think of?
- What skills have we learned in class that you can apply to this problem?
- What would be the first step in solving this problem? Or, tell your shoulder partner where you started.
- How did you solve this problem? Or, let's look at your work.
- Is there another way to solve this problem?
Whether or not they have the correct answer, this type of questioning invites every student to participate in classroom discussion because everyone knows something about the problem. What's more, the answers to formative open questions provide teachers with immediate feedback on what students are thinking. It is much easier to clear up misconceptions and get a broader picture of what student know using these questions. When the focus is not on the final answer, students are less likely to feel defeated by errors in the learning process. Errors become learning points that assist students in adjusting their thinking and reforming their solution pathway.
Formative open questions also lend themselves to collaborative work. The teachers I work with use a strategy that promotes both individual thinking as well as collaboration. Working in groups of four, students share a large piece paper with room for each student's work as well as a collaborative space for a final answer. The teacher poses a question to each group and allows time for students to problem solve in their individual sections of the shared work space. Students have the benefit of seeing how their team members are approaching the problem, which provides a starting place for any students who are truly stuck.
Then, during time allotted for collaboration, students share their individual thinking and process for solving the problem. Based on this discussion, each group comes up with a collaborative answer to share with the class. During this activity, the teacher circulates the room, monitoring individual work and collaborative conversations. This unobtrusive and low stakes approach to assessment provides rich data on student thinking that can be used for small group differentiation.
We will learn more about our students, and they about mathematics, when we design questions that invite everyone to participate in the process of learning.
