Student Engagement

Elementary students benefit from questions that create conversations about math concepts and give all children a chance to answer.

May 17, 2024
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I recently observed a fifth-grade class that would have felt completely familiar to most teachers. A problem was put on the board, and students worked for a few minutes to solve it. Then the teacher asked for a volunteer to explain the solution. Lots of hands went up.

The question, at first, looked easy: It was 5 + 5 x 5 - 5. When Abby, one of the students who had been identified as struggling in math, raised her hand, I had a sinking feeling in my stomach. When the teacher called on her, she confidently answered 45. The teacher wrote down Abby’s thinking: 5 + 5 = 10, 10 x 5 = 50, 50 - 5 = 45.

But what looks just like an easy string of computation is really a test about whether students remember order of operations. The teacher turned to the class and asked if everyone agreed. There was an immediate chorus of “nos.” He then called on one of the other students, who gave a long explanation about PEMDAS, and concluded (correctly) that the right answer would be 25. Abby visibly shrank in her seat. Even if the teacher responds kindly, as happened in the class I observed, this moment would be deflating.

### How questions are typically asked in elementary math

The problem in Abby’s classroom is not that she got the wrong answer. Instead, the problem is that almost all of the questions a teacher asks in a math class are answered correctly, because we purposefully select for right answers by how we call on students. We only call on those students who raise their hands.

This is a problem because we do not hear all of the voices in the room. In most classrooms, less than a third of students answer almost all of the questions. Students who do not participate are not engaged, and students who are not engaged do not learn.

This way of choosing students also leaves everyone with the impression that most students “get it.” It gives the teacher a false sense of confidence about what the students know and makes it less likely that misunderstandings will be addressed. A struggling student often assumes they are the only one who doesn’t know the correct answer, and this belief reinforces their feelings of inadequacy.

Finally, it creates a classroom culture that does not encourage risk-taking or productive struggle. Even if we talk about growth mindsets and celebrate student thinking, the rarity of wrong answers makes mistakes stand out as abnormal rather than part of the process of learning.

Having students formulate a question based on a situation or a picture changes the role of the student from a passive answer machine to a mathematical thinker. The goal of our questions should be to create a conversation around the mathematical content.

Steven goldman

### Moving toward more mistake-friendly participation

The picture of students eagerly raising their hands to answer a question is so ingrained in our mental images of what a good classroom looks like. But eliminating this practice is one of the most important changes we could make. What would replace it?

Asking different, and better, questions: Before we can replace hand raising, we first need to improve the questions themselves. Too many of our questions are procedural and require a simple answer, delivered almost immediately. This kind of question in itself encourages students to think that their role is to answer quickly and accurately, rather than to engage in a thoughtful process that builds understanding.

For example, if we really wanted to explore the idea of order of operations, we could have started with what students can tell you about the problem. They might notice that it has all fives and that it involves three different operations. The most interesting thing about the expression is whether there is only one order you can solve it in. Students who are overly procedural will insist that you have to multiply first and then work left to right, but there are multiple ways to begin.

A good question should focus on ideas and on what a student is thinking rather than on something that is categorically right or wrong. Questions about what patterns you notice, or how two approaches are similar or different, open up the discussion in a way that everyone can participate in. You can also focus on the process, eliciting where you might start on a problem or how to identify important skills that a problem presents.

Or you might analyze a possible solution together and talk about what you see. Analyzing a solution that doesn’t work is even more engaging. Having students formulate a question based on a situation or a picture changes the role of the student from a passive answer machine to a mathematical thinker. The goal of our questions should be to create a conversation around the mathematical content.

New ways of getting students to answer: With better questions we can be more comfortable taking the next step, which is finding a neutral mechanism to call on students. Some teachers use equity sticks or even phone apps that help randomize who is called on. There are teachers who bypass the calling on students and use whiteboards or Post-it Notes for responses. I prefer old playing cards onto which I have written the student’s name with a big black marker. Cards are easy to hold and to shuffle. To use this form of cold calling requires some up-front work with the students to establish a nonthreatening environment where they can feel comfortable admitting they don’t know.

Often the best alternative to hand raising is simply to curate the discussion. If students are working by themselves or in small groups, it gives the teacher a chance to observe and select which student responses to talk about. In a curated conversation, the teacher chooses who will share based on which responses will create the most engaging debrief. Curated conversations often begin with sentences like “I notice that Abby and her partner were…” Curating allows a wider range of choices about who participates and allows the teacher to build toward a more productive conversation by managing the student work that serves as the focus.

To help a student like Abby, it is not enough just to make her feel OK about her mistake. We have to have more opportunities where she sees that other kids make mistakes too and that she has something real to contribute. We have to make sure that she feels like she belongs in this classroom and that her participation is valued. We can’t do that if we have created an environment where it feels like we only care about the students who have raised their hands and provided us with a right answer.