More Than Just Answers: Mathematical Communication in Elementary Classrooms

By Dr. Sherri Lorton

Welcome to the first in our three-part series on the Standards for Mathematical Practice (MPs) in the elementary classroom! The MPs are the heartbeat of math instruction; they describe the ways of knowing and habits of mind that we want to cultivate in our students as they grow into mature mathematical thinkers. While the content standards tell us what students need to know, the practices tell us how they should engage with and do mathematics.

Over the next few posts, we will explore bundles of these practices to help focus our instruction. This series is for elementary educators, and a parallel series for the secondary level is being posted separately to provide a full K-12 perspective. We begin our journey with the powerful pair that forms the foundation of mathematical discourse: the Communicating Reasoning bundle, featuring MP3 and MP6.

Defining the Dynamic Duo: MP3 and MP6

At first glance, MP3 and MP6 might seem similar—they’re both about communication. However, they play distinct but deeply interconnected roles. Think of it this way: MP3 is about the substance of the argument, while MP6 is about the clarity and accuracy that make the argument convincing.

Math Practice 3: Construct viable arguments and critique the reasoning of others

This practice is the “why” and “how” of a student’s thinking. Mathematically proficient students don’t just state an answer; they build a logical case to justify their conclusions. In the elementary grades, these arguments are often built using concrete items, drawings, and diagrams. Just as important, students learn to listen to or read the arguments of others, decide if they make sense, and ask helpful questions to clarify or improve their arguments. This is where true classroom discourse comes alive—when students are not just sharing, but actively engaging with, challenging, and building upon each other’s ideas.

Math Practice 6: Attend to precision

This practice is about communicating with clarity and accuracy. Mathematically proficient students understand that the details matter. They strive to use clear definitions, state the meaning of the symbols they choose, specify units of measure, and label their work appropriately. Attending to precision also means calculating accurately and efficiently, checking work, and using mathematical vocabulary correctly as they move from informal, everyday language to more specific terminology.

An argument (MP3) cannot be truly viable if it isn’t communicated precisely (MP6). Likewise, precise language (MP6) serves its highest purpose when used to build a robust mathematical argument (MP3). Together, they empower students to express their conceptual understanding and build confidence in their mathematical authority.

Communicating Reasoning Across the Grades

The sophistication of students’ arguments and their degree of precision evolve significantly from kindergarten to fifth grade. Let’s look at how this development unfolds through a few grade-band examples.

In kindergarten and first grade, arguments are concrete and language is emerging.

• Task: A kindergarten student is asked to determine whether a group of 7 blocks is greater than, less than, or equal to a group of 5 blocks.
• MP3 in Action: The student builds an argument using concrete manipulatives. They might create two towers of blocks and directly compare them or use a matching strategy, pairing one block from each group until one group has leftovers. Their argument is the action itself, followed by a verbal explanation like, “This one is more because it has two extras.”
• MP6 in Action: The student communicates precisely by correctly counting each set of objects and using numbers to represent the quantities. A teacher might then help the student attach precise mathematical vocabulary to their discovery, such as “greater than” or “less than”.

In second and third grade, arguments become more abstract and procedural.

• Task: A third-grade student is asked to solve 8 × 7 and explain their strategy using the distributive property.
• MP3 in Action: The student constructs an argument to justify their strategy. They might say, “I didn’t know 8 times 7, but I knew 8 times 5 is 40 and 8 times 2 is 16. Since 5 plus 2 is 7, I can just add 40 and 16 to get 56”. To support this, they might draw an array and show how it can be broken into an 8×5 part and an 8×2 part, demonstrating a “chain of reasoning”.
• MP6 in Action: The student attends to precision by using correct symbols to record their thinking (e.g., 8 × 7 = (8 × 5) + (8 × 2)) and using vocabulary like “factor” and “product”. Their calculations must be accurate to support their argument.

In fourth and fifth grade, arguments rely on generalizations and established properties.

• Task: A fifth-grade student needs to explain why the product of 1/2 x 1/2 is 1/4, not 1.
• MP3 in Action: The student refutes the common misconception (a counterexample to the idea that multiplication always makes numbers bigger) by constructing an argument based on a visual model. They might draw a square to represent one whole, shade half of it vertically to show the first factor, and then shade half of that section horizontally. This action shows that the result is one of four equal parts of the original whole. They can justify their conclusion by explaining the meaning of multiplication with fractions.
• MP6 in Action: The student demonstrates precision by accurately drawing and labeling their area model, specifying what the “whole” is, and using the symbols correctly to write the equation 1/2 x 1/2 = 1/4. They use precise terms like “product,” “factor,” and “area” in their explanation.

Building Mathematical Communication Together

Bringing the power of MP3 and MP6 to life requires intentional planning and a supportive school culture. Here are a few reflective questions for your role:

Teachers

How can you plan questions that push students beyond “what” they did to “why” it works? In what ways can you explicitly model precise mathematical language and hold students accountable for using it with each other?

Coaches

During classroom observations, what evidence do you see of students building on, questioning, or refining each other’s ideas? What talk structures or tasks could you suggest to teachers to create more opportunities for this kind of discourse?

Administrators

How do you foster a school-wide culture where reasoning and precision are valued in every math classroom? How can you support teachers with high-quality instructional materials that are designed to promote the Standards for Mathematical Practice?

By intentionally pairing these two practices, we can transform our classrooms into vibrant communities of mathematical thinkers who not only find answers but can also confidently and clearly communicate their journey to get there. Additionally, secondary math teachers build on your work in elementary to prepare their students for college-level work, professional environments, and analytical thinking in all aspects of life. Our next math blog will explore Modeling and Data Analysis (MP2, MP4, and MP5), followed by a final look at Problem Solving (MP1, MP7, and MP8). 

How will you adjust your plans this week to prioritize students engaging in clear communication over just the final answer?

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