Helping K–8 students think, talk, and reason like mathematicians
The Overlooked Link Between Language and Math, and How to Strengthen It"
When you ask a student to explain how they solved a math problem, what do you usually hear? If you're a K-8 educator, these responses probably sound familiar:
"I just did it in my head."
"I know it, but I can't explain it."
"If I got the right answer, why do I need to explain?"
When students struggle with math, it's often not just the numbers that trip them up, it's the words. Word problems, explanations, and multi-step reasoning tasks all demand more than computation. They require the ability to process, discuss, and express mathematical thinking clearly. As Education Consultant Karie Gladis explains, "There is a reciprocal relationship [between math and language]. You can't really have one without the other. You can't have mathematical understanding and proficiency with a standard or objective without knowing the language of it."
The Missing Piece in Math Struggles: Language
Language and math are deeply intertwined, and many students can "do" the math in their heads, but struggle to explain how they got there, either rambling through unclear responses or shutting down completely. Gladis puts it plainly, noting that, "When we're building mathematical language, we're building mathematical understanding, skills, proficiency, thinking, reasoning."
Without this foundation, students often face trouble later on, because as math grows more abstract, those who relied solely on mental shortcuts or procedural tricks may hit a wall. Gladis recounts working with a student who experienced this precisely, “Their mathematical proficiency was built on a house of sand. They weren't aware of their own thinking."
Developing the language to articulate mathematical thinking is foundational to learning, and when students can clearly express how they approach a problem, they're not just doing math, they're understanding and retaining it.
Intentional Language Development in the Math Classroom
When educators are intentional about how math vocabulary is introduced, both language and math skills grow together.
Content Specialist and Contributing Author of Primary Mathematics, Jessica Kaminski. explains, “There’s a lot of research that talks about the way students develop vocabulary through experience, and then the vocabulary is labeled… when we get into school, we can go backwards by introducing vocabulary without experience.”
She urges educators to mirror how toddlers learn by letting students experience math first, allowing them to manipulate it, explore it, and discuss it before introducing the formal language. This is where the Concrete-Pictorial-Abstract (CPA) approach shines, helping students gradually build understanding from hands-on exploration to mathematical terminology.
Why Precise Vocabulary Matters
Introducing precise mathematical language, without watering it down, is key. Gladis emphasizes how directly this ties to instructional quality, "When students learn and inquire about precise mathematical language, we're getting to the rigor of the standard.”
Gladis goes on to note, "When we give students alternative words, simpler terms, we're actually diluting the standard." The goal isn't to overwhelm students with jargon, but to equip them with tools to express what's already in their heads.
Gladis adds that the benefits extend even further, "By building that precise language, we're giving them the words to express their thinking.” Gladis explains, “This also builds their metacognitive power so they can replicate that thinking if it's effective, or change it if it's not."
Maintaining high expectations around mathematical vocabulary helps improve communication and ensures students are actually learning the rigor embedded in each standard.
Creating Space for Discourse
Programs like Primary Mathematics, by Marshall Cavendish Education, integrate these tools throughout the lesson. Gladis explains, "students have opportunities to express their thinking in writing as well, and to share and show that thinking through written discourse." She goes on to say, "The teacher is provided questions and sample student responses… which is something I haven't seen in really any core programs."
Sentence frames, conceptual questions, and structured problem-solving routines support all learners, especially those who are multilingual or hesitant to speak up. Author Susan Resnick describes how this looks in practice,"We help them get a sentence starter or a sentence frame so they can formulate the language." She adds, "Then we have them do a lot of drawing and explain their thinking from the drawing."
Helping students find the words to explain their thinking turns confusion into understanding and it can make all the difference for those who would otherwise shut down.
Helping Reluctant Students Find Their Voice
Not every student is ready to jump into math talk, and some avoid explaining altogether. Often, as Gladis shares, this avoidant behavior masks a deeper struggle, because students simply don't know how to communicate about math.
By shifting questioning strategies, offering choices, modeling vocabulary, and building from visual models, educators can open the door for these learners. "That avoidant behavior now becomes a roadblock we can jump over," says Gladis. With the right support, even the quietest students can begin to engage, transforming hesitation into meaningful participation.
Why It All Starts Early
The foundation built in the early grades shapes how students approach math for years to come. Kaminski underscores why this matters from day one, sharing that, "If students begin their mathematical journey using incorrect language, that's going to impact everything they do." She emphasizes the need for consistency across classrooms, explaining, "It's really vital that educators have correct language and that we use the same language because we want our students to be able to carry that language into the upper grades."
From teaching kindergartners the basics to guiding fourth graders through fraction equivalencies, every conversation builds more than just math skills, it nurtures clear communication, sharp reasoning, and the confidence to speak up and think critically, both in math class and beyond.
The Bigger Picture: Language, Math, and Confidence
In the end, language is about both identity and access. When students can talk about math, they begin to see themselves as capable thinkers, and when they can explain their reasoning, they're developing skills that support success not just in math, but across academics and beyond.
We often overlook how much attitudes toward math shape outcomes, but the truth is that they matter a great deal. With the right resources and instructional support, students can build lasting confidence that serves them in school, in relationships, and in their future careers.
Want to learn more about how Primary Mathematics by Marshall Cavendish Education supports language development and deeper mathematical understanding? Explore the program or connect with a specialist today.