The Power of Precision: Enhancing Learning in K-12 Mathematics Through Precise Language

The importance of using and inviting students to use precise academic vocabulary.

Written By vmillerbennett

On November 27, 2023

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Recently, I was working alongside one of my colleagues and we were presenting at a professional learning event designed for High School mathematics teachers.  Though our focus was not necessarily mathematics vocabulary, one of the teachers shared that she expected precise language from all of her students.  On that particular day, a student had remarked “Math is petty!” to his teacher.  According to Collins online Dictionary, “if you describe someone’s behavior as petty, you mean that they care too much about small, unimportant things and perhaps that they are unnecessarily unkind”.  So by definition, petty is usually used to describe someone’s behavior.  But I understood that student’s intent and feeling.  I have often heard similar remarks when asking students to use correct terminology when communicating mathematical ideas.  Convincing learners that the correct use of words such as “similar” and “congruent” matters is not always easily accomplished.  As pointed out in the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010), attending to precision is a habit of mind and practice in which all students should engage.  The importance of using mathematics vocabulary correctly and engaging students in dialogue is further emphasized in several NCTM publications including Principles and Standards (2000), Principles to Action (2014) and the Catalyzing Change series (2018-2020).

Though this blog post focuses on mathematics, many of the ideas relate to teaching students in any content area.  There are several reasons why educators should strive to use precise academic language while also expecting the same from all students.  First and foremost, clarity of communication is ensured. The precision in language reduces the likelihood of misunderstandings, allowing students to grasp mathematical concepts accurately. This precision is foundational in building a strong understanding of mathematical principles.  Understanding the equal sign is a first grade standard, according to the Common Core for State Standards.  (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010).   Though students often demonstrate a strong understanding of equality, the symbol used to represent equality is often incorrectly interpreted as “here comes the answer.”  Teachers can foster a correct understanding of the term and symbol by using “is the same as” instead of “makes” when reading equations aloud.  Compare “ Seven plus four makes 11” with “Seven add four is the same as 11.”  Using the correct terminology as well as a word that carries meaning presents terrific opportunities for very young students to develop robust understanding of addition and equivalence as well as the symbols used to represent them.  By consistently using correct terms, teachers contribute to the development of a solid foundation for conceptual understanding among all students. The use of accurate vocabulary aligns with curriculum standards, while promoting consistency and equity in educational practices.  The importance of correct vocabulary extends to the development of broader communication skills, preparing students for success in various academic and professional settings. Additionally, the use of precise language promotes a positive learning environment by building confidence among all students in their ability to articulate mathematical concepts and ideas. This confidence is vital for fostering a sense of inclusivity, supporting diverse learners, and creating a classroom where all students can access and understand at high levels. Finally, teachers serve as role models, and their use of correct mathematical vocabulary models professionalism as well as setting high expectations for students in their mathematical communication. 

Just as teachers should be held accountable for using correct mathematics vocabulary, all students should be encouraged to communicate ideas with clarity and accuracy.  Here are some effective teaching practices that foster the frequent and correct use of mathematics vocabulary.

  1. Word Walls are a terrific place to start.  Designate a place in your classroom that could be used to collect and display vocabulary from the current unit of study. This can be done on a classroom wall or a simple graphic organizer such as a paper copy of an Alphablock.  Be sure to provide multiple opportunities for students to interact with the terms.  Ask students to use the terms in their verbal and written responses.  
  2. Interactive classroom discussions can also foster student use of vocabulary.  Facilitate regular classroom discussions that encourage students to explain their reasoning, share solutions, and ask questions. Create a safe and collaborative environment where students feel comfortable using precise language.  Listen for and celebrate students who demonstrate their understanding (and misunderstanding) through classroom conversations.
  3. Think. Ink. Pair. Share. is another academic dialogue strategy that can get students talking.   In this structured discussion, it is imperative to provide individual students time to think about their response and also to capture their thinking on paper.  Next, guide students to discuss their mathematics ideas with a partner before sharing with the whole class. Remind students to use academic vocabulary as they craft their responses.    

The journey toward precision in mathematics vocabulary is significant, marked by its impact on clarity, conceptual understanding, and the development of broader communication skills. As educators, our commitment to fostering an environment where students not only learn mathematical concepts but also articulate them with accuracy is paramount. The “petty” details, as expressed by a student, are the building blocks of mathematical fluency and confidence.

By integrating effective teaching practices, such as Word Walls, interactive discussions, and structured dialogues like “Think. Ink. Pair. Share.,” we empower students to embrace and use precise language. Celebrating their efforts, acknowledging their understanding, and guiding them through misunderstandings contribute to a positive learning atmosphere. In doing so, we not only adhere to educational standards but also cultivate well-rounded and confident learners prepared for the challenges of academic and professional pursuits.

Returning to the “math is petty” quote from the beginning of the post, I agree with the student assertion.  The small details are not small and it definitely matters which words we use and ask students to use when communicating about our mathematics ideas. For further reading, here are some articles of interest.  

Bay-Williams, J. M., & Livers, S. (2009). Supporting math vocabulary acquisition. Teaching Children Mathematics, 16(4), 238-246.

Karp, K. S., Bush, S. B., & Dougherty, B. J. (2014). 13 rules that expire. Teaching Children Mathematics, 21(1), 18-25.Powell, S. R., Stevens, E. A., & Hughes, E. M. (2019). Math language in middle school: Be more specific. TEACHING Exceptional Children, 51(4), 286-295.