Problem-Solving Discussions in Elementary Math

The National Council of Teachers of Mathematics encourages student-centered classrooms where children engage in discourse with supportive language structures, move toward making connections between each other’s math ideas, and cultivate positive math identities.

From 2020 through 2025, we worked as professional development facilitators with teachers and language coaches to help them implement a reform-based approach to math instruction in grades 3 through 5. Collaboratively, we shift math classroom norms by inviting students to solve story problems (for example, equal sharing or fraction problems) on their own, using their prior knowledge to come up with any strategy that makes sense to them, sharing their ideas with a partner, and then presenting those strategies to the whole class.

The teachers implement this during integrated English language development time so that multilingual (ML) students have opportunities to talk to each other about math. Although the example we present focuses on ML students, these strategies are beneficial for all learners’ mathematical development. When children authentically share their solution strategies, by making claims and justifying their reasoning, they develop their academic language and mathematical conceptions at the same time.

Teachers support these conversations using various moves and language structures during each stage of the problem-solving lesson. By implementing these strategies, teachers will see meaningful gains in students’ math identity, academic achievement, and sense of agency.

Stages of the problem-solving lesson

Launch of the open-ended story problem. Guide your students to discuss the situation aloud, collectively making sense of what is going on in the problem, relating it to familiar experiences, making note of important mathematical features, and determining what the problem is asking them to solve.

First, students hear and read the problem aloud several times with you. Invite them to share personal associations. For example, if the problem asks how much cake each person can have at a birthday party if the cake is shared equally among all the sharers, ask your students about parties they’ve attended where food was shared. Children can also state and restate the number of sharers and number of cakes several times. Encourage your students to ask clarifying questions and add onto their peers’ ideas.

You can check to see that all children are clear about what they‘re trying to figure out before they start solving it individually. This process allows students to see, say, and hear the important features of the story before delving in on their own and can be used for any type of math problem.

Problem-solving stage. Guide your students to individually solve the story problem using any method that makes sense to them, then share their strategies with each other in pairs or small groups. Encourage your students to individually write their explanations, verbally share their explanations, and listen to and make sense of their peers’ explanations by asking questions or paraphrasing their work. Consider giving your students sentence frames and scripted questions to guide the conversations.

This is a great opportunity for students to practice using mathematical language in an uninhibited space by clarifying and justifying their ideas, as well as asking their peers questions. Students benefit from the script that is provided during the problem-solving stage of the lesson. The script allows students to take turns sharing their thinking and hearing their peers’ strategies. When the script includes the question “Can you paraphrase my work?,” student engagement increases because it requires students to pay attention to peers’ strategies.

Whole class discussion. At the end of the lesson, several students should be strategically chosen to present their ideas to the whole class. During this time, children make connections between the ideas they discovered by asking clarifying questions, paraphrasing their peers’ work, and collectively making sense of the new ideas using verbal and nonverbal types of talk (oral language, written words/symbols/diagrams, and hand gestures). Students, especially ML learners, should have many opportunities to read, write, talk, and listen to their peers during each stage of the problem-solving lesson.

Structuring peer conversations

Before the lesson. Teachers can anticipate the strategies students might use by solving the problem in different ways, by looking at previous student work, and by considering students’ mathematical and linguistic assets. Teachers can use these anticipated strategies to plan for instruction and to offer differentiated support (questioning, pairing, sequencing).

During the lesson. Teachers circulate the room to observe students’ individual solution strategies and pair students who solved using different or slightly different ways. Learners have something to ask each other when they have different perspectives. It is important for teachers to consider English language proficiency levels when pairing ML students, depending on your language objective. Create purposeful pairs so that students can make connections between their solution strategies, identify differences, and question each other about their work. Monitor the partner conversations to plan for the whole group discussion.

End of the lesson. Sequence presentations in ways that build upon the students’ strategies so that they can connect each other’s ideas at the end of the whole class discussion. For example, you can choose to order the presentations from easiest to understand (usually a guess and check method) to the most abstract (usually using algebraic notation). Other times, focus on comparing what appears to be two different answers so that, as a class, students can talk about multiple representations (for example: fraction equivalence, such as 2/3 = 6/9). Learning goals for the lesson and what students are developmentally ready to take on will determine how to sequence student presentations.

Opportunities to talk about math with peers help all learners’ mathematical understanding and simultaneously strengthen language development for ML students. It is a shift from silent classrooms where students individually practice rote procedures to a lively classroom where students work with a partner or in groups, persevere to solve math problems, and explain and justify their thinking. Instructional and linguistic support can be helpful for ML students when developing their language skills and facilitating participation in classroom discussions, specifically in math.