My Preschool-age son likes to read with us, and one of the books in his “favorites” rotation teaches shapes and colors. On the page with the rhombus, I always use the term “rhombus” rather than “diamond,” which is what is printed in the book. While reading with his mother last week, she read the term on the page rather than substituting “rhombus.” My son quickly corrected her; he shared what his preschool teacher taught him: “Diamonds are shiny things in jewelry. That is a rhombus.”

This got me thinking about how important vocabulary is for both teachers and students in the math classroom. It also brought back some research that I’d read while in graduate school, from a math educator and researcher named David Pimm. He wrote an article regarding the development of language in math, and included this diagram to provide some structure to his thoughts:

His belief was that students’ progress to formal written mathematics step by step. Experience has proven that this is true. We all begin by informally speaking about the math we are learning. Through a process of instruction, modeling, and feedback, we formalize our spoken language while also beginning to write informally about math. Finally, we put these two together and have the formal written language that rigorous standards and assessments demand.

This process requires frequent input from the teacher. It includes some key points:

  • Vocabulary: We need to take the time to develop students’ mathematics vocabulary in the same way we develop their primary language vocabulary. Using models, pictures, and mnemonic devices to help students understand math terms helps them use the language of math.
  • Modeling: When I was doing professional development with teachers, I told them that they had to model the use of math language. The majority of our students are not going to learn the language of math at home, so the teacher bears the responsibility of demonstrating how to speak (and later write) about math.
  • Feedback: As students’ progress from informal spoken math to formal written math, they will need feedback on their use of the language. Teachers again have a responsibility to provide this feedback to students, and it should be done both formally and informally, and continuously throughout the year.

There are, of course, other elements to learning and using the language of math. I like to summarize this process this way: If we want students to write about math in a way that is coherent and accurate, then they must have the opportunity to talk about math. I think my son is off to a good start, and his teacher deserves credit for her role in helping him use the language of math.


View our Math Language resources here.