12 Genuine Math Questions to Get Your Students Talking

To be successful mathematicians, students must do more than a share-and-tell; they must be able to talk about and justify their ideas, build mathematical arguments, and defend their thinking. With the 12 intentional and genuine math questions in this article, teachers can promote discourse opportunities to develop a deeper understanding of mathematics for all students. Plus, register for an on-demand webinar to further support
students in thinking mathematically.

Promoting Discourse with Math Questions

A teacher’s language choice plays an important role in developing student-to-student discourse. To begin, it is important to think about the math questions that we ask our students. Strategically open-ended questions focus on the process and not on the solution, and therefore invite students in mathematical discourse that boosts engagement and leads to better learning.

Teachers can engage students in discourse by posing genuine questions to encourage discussion and debate, and to require students to attend to the mathematics at hand while explaining and justifying their thinking. Discourse helps students notice, understand, and evaluate mathematical ideas—their own and others.

Genuine Questions

What makes a question genuine? A question is genuine when the teacher does not know the answer to it and is sincerely looking to deepen his or her understanding of students’ ideas. Genuine questions invite students to communicate their ideas during the process of thinking, and do not seek to elicit a correct answer from students. Genuine questions are used so that the math community (your students) can see ways of thinking other than their own.

Planning Math Questions

Developing questions on the fly can be very difficult as teachers juggle a variety of student needs—academic and social— that arise in classrooms. In these moments, it is easy to revert to asking closed questions that focus on solutions rather than on strategies. Therefore, noting what questions to use in lesson plans is essential. To do this, teachers must anticipate students’ knowledge of concepts being taught and must plan genuine questions to support different levels of student engagement.

Here are my top 12 genuine questions to get students talking about math:

What did you notice about _________?

Asking students to notice and wonder sparks curiosity about math, which we want all students to have. This math question helps students focus on the big picture of a math problem or concept, instead of the solution.

What do you think?

Mathematicians require critical thinking skills. This math question will help students communicate the knowledge that underlies their individual ideas and will give students an opportunity to make sense of and apply information within the context of their own understanding.

How did you figure that out?

This math question presses students to talk through their thinking, allowing them to describe the steps taken and explaining why they took these steps in their rationale.

Can you prove that?

Mathematicians prove their conclusions by utilizing multiple strategies. Give students the opportunity to share accurate and appropriate evidence to support their claims, whether data or experiences. Mathematicians also ask others to provide proof. Can students demonstrate an alternate way to solve a problem? Modeling this question for them is a way to encourage students to ask each other to prove their thinking.

What if….? (conjecture)

“What if…?” questions encourage and challenge students’ thinking, introducing new ideas for students to ponder and respond to. This question can elevate the discussion and demonstrates the importance of teacher planning in the facilitation of open, genuine questions in the math classroom.

Does anyone have a different way of thinking about this?

There are often many ways to solve a mathematical problem. Inviting multiple students to clearly communicate their unique thinking shows that all members of the mathematical community are valued and helps students approach problems through the perspectives and strategies of their peers and fellow mathematicians.

Can anyone add onto _____________’s idea?

Mathematicians look for new ideas and build on other people’s thinking. This is the highest level of student engagement. Contributing to others’ ideas builds community and shows that math is a team effort within this valued community of contributors.

Can you convince us?

Students need to be able to communicate clearly when it comes to mathematics, and this question gives them the opportunity to do just that. Invite students to convince their classmates with accurate and appropriate evidence, alternate strategies, and compelling arguments.

What do you predict will happen next?

This question supports students as they learn how to make predictions. Students must be inventive problem solvers. They need to be able to consider and converse about the connections among concepts and the patterns in mathematics. Predictions will help students organize concepts they are discussing.

How do you know what you know?

Students are always asked to show what they know. This question invites them to put into words their background knowledge, prior understandings, and observations from the problem itself using connections to their own experiences. Like other questions, it touches on proof and gives valuable insight for the teacher into the student’s thought processes.

Do you agree or respectfully have another idea?

This question invites students to work together to make sense of mathematics as they evaluate each other’s thinking and build on it. This question requires students to really listen to and make sense of the  mathematical ideas presented by others, to compare ideas, and then to potentially propose alternatives.

Do you see any patterns here? Are there any ideas that are similar to what we have explored before?

This math question is an invitation to be curious. Mathematicians look for patterns and relationships in mathematics and this question promotes continual connection-making for all the students in your community. With this approach, students uncover these patterns and relationships on their own for more effective learning.

A Scaffold for Deeper Thinking

As teachers begin to use these questions, it is important to acknowledge what they do not do. These questions do not replace the thinking of the students by praising or confirming student answers. These questions are designed to scaffold student thinking, to encourage students to reflect, and to challenge students to think harder and more deeply about the mathematical ideas at hand. Teachers can post these questions in their math classroom to promote discourse and understanding.

Regular student discourse in math, facilitated by well-planned, genuine questions, boosts engagement and helps students discuss and understand math. Discourse also helps nurture your community of math students and provides insights to teachers about students’ approaches and reasoning. Learn more in Mathematical Discourse: Let the Kids Talk! which offers specific strategies, methods, instructional approaches, resources, and activities to use with your students as they learn to make sense of mathematics daily.