5 Ways to Encourage Students to Use the Language of Math
By Twana Young, VP of Academic Design in Mathematics, McGraw Hill School Group
What is mathematical discourse?
Mathematical discourse is the vibrant exchange of ideas using the language of math. It engages students in collaboratively sharing mathematical insights, problem-solving strategies, thoughtful questions, and expressing mathematical solutions.
Put simply: it’s bringing math to life through meaningful conversations that help develop, reinforce, and extend student mathematical understanding.
Why is mathematical discourse important in PreK-12 education?
Discourse is a formative assessment both for the student and for the teacher. It makes student thinking visible and enhances students’ understanding and retention of mathematical concepts by encouraging them to articulate their thinking and reasoning. Math education is not just about teaching students to do math — it is equally important to give them the tools to talk about math.
Talking about math is connected to thinking about math. Talking about math promotes a deeper understanding of complex concepts and helps bridge connections to big mathematical ideas. It helps students explore multiple perspectives, grapple with complex concepts, identify and correct misconceptions, and build a deeper, more connected understanding of mathematics. Mathematical discourse allows students to participate in a larger mathematical community, articulate their thinking in dynamic contexts, and apply their mathematical ideas in the real world.
Finally, promoting mathematical discourse also promotes equity. Research has shown that discourse improves academic performance and participation in classrooms with diverse student populations. An emphasis on mathematical discourse is also crucial for multilingual learners. As students engage in conversation their language development improves as does their ability to communicate and apply their social skills.
Math discourse isn’t just about the language of math itself. It’s a window into students’ thinking and their development of math skills and concepts. By listening to students talk to each other about what they know about math, what they wonder about math, and their approach to solving problems, teachers can uncover a treasure trove of insights into student understanding.
How can teachers encourage students to use the language of math?
1) Build a community of mathematicians. Collaboration is key! Students can’t use mathematical language without plenty of opportunities to talk with their peers. The use of discourse strategies in the classroom is an avenue to support learning and reveal student thinking. Open lessons with a sensemaking activity that allows students to turn and talk with peers, prompt conversations throughout lessons, or invite students to collaborate to solve problems whenever possible. It’s important to foster a classroom culture that makes students feel confident and comfortable enough to engage in these conversations. Students should always feel respected by their teacher and their peers and should be able to see themselves as mathematicians.
2) Encourage curiosity, experimentation, and productive struggle. Students should always feel empowered to ask questions and explore new mathematical concepts. As students try out new mathematical language with their peers, they should have plenty of opportunities to revise and improve their solutions. Give students the space and freedom to ask questions, try strategies, fail, and try again. This allows them to see the continuous process of learning and understand that their thinking drives their learning. It also empowers them to talk about math and discuss their thinking without fear of verbalizing the “wrong” answer.
3) Embed discussion in hands-on learning and relevant contexts. 1) Mathematical language shouldn’t be in isolation, but rather in a context that allows access for all students to relate to the content, participate, and communicate their mathematical thinking. Part of language development is learning to effectively communicate math understanding. Students experience non-traditional math every day of their lives. Give students plenty of time to develop the language to communicate the mathematics they experience in their lives in relevant, engaging, hands-on activities that reflect their day-to-day encounters with math. You’ll empower all your learners to access the language of mathematics and communicate effectively, in the classroom and beyond.
4) Use instructional routines. Routines are a useful tool for integrating math language throughout instruction. For example, begin every lesson with a warm-up activity that builds students’ proficiency with number sense and sets students up to talk about their reasoning for solving unknown problems. (Did you know? Instructional routines are a proven effective tool across disciplines!)
5) Provide scaffolds for multilingual learners. All of the above strategies are also effective for multilingual learners. They will especially benefit from routines, an inclusive culture, plenty of time to practice discourse, and support in language development. It’s important to provide appropriate scaffolds to ensure equitable instruction. Provide additional vocabulary words to multilingual learners to make discussions with peers fully accessible.
What does mathematical discourse look like in California Reveal Math?
Here are just a few examples of how California Reveal Math fosters mathematical discourse and gives students plenty of meaningful opportunities to use math language to explore the big ideas in math:
Introduce, Talk, Connect discourse framework: The Introduce, Talk, and Connect discourse framework is woven throughout each lesson, giving teachers a solid foundation for facilitating discourse while giving students a familiar access point to collaborative instruction across grades. Introduce includes a prompt to draw on prior knowledge and engage students in thinking, questioning, analyzing, and making connections. Talk invites students to explore, discover, discuss, and collaborate, all while engaging in opportunities for hands-on and active learning. Students Connect by summarizing, reflecting, and synthesizing the learning.
Essential questions connect to Big Mathematical Ideas: Essential questions frame the unit and invite students to explore, discover, and reason with and about mathematics. They encourage students to make connections to the Big Mathematical Ideas and support communication through the language of math.
In-lesson supports for teachers: California Reveal Math intentionally embeds supports at the point of use so that teachers can confidently provide context for mathematical language as it’s being taught, allowing all students to access and relate to the content and communicate their mathematical thinking. Teachers are provided with discourse questions to promote student thinking and “Listen to” prompts to focus on how students are thinking. These different types of formative assessment practices allow for diverse perspectives, provide a foundation for further exploration, and offer opportunities for students to connect ideas and expand their thinking. “Language of Math” prompts highlight language related to the lesson content, so that teachers can help their students build and reinforce language development appropriately.
Embedded discussion prompts and routines: Embedded discussion prompts encourage productive conversations around approaches to problem solving directly connected to the lesson’s learning outcome. These prompts help students develop mathematical thinking habits, connect big ideas, cultivate curiosity, and support language development. California Reveal Math also makes use of routines to promote discourse: Each lesson has a math language routine to support language development and each lesson opener has a number routine that supports fluency.
Hands-on activities: Investigations, collaborative activities, authentic examples, probing questions, and a flexible lesson model are designed to cultivate curiosity and empower every student to ask questions, solve problems, and forge meaningful connections to mathematics. Investigative questions are situated throughout the unit to support student understanding and application of math concepts. Mathematical modeling activities provide authentic investigations as a culmination of math concepts learned through the unit and connect them to big mathematical ideas.
To learn more about California Reveal Math, visit mhecalifornia.com/reveal
Twana Young, M.Ed. is a visionary leader deeply committed to empowering educators, families, and students through mathematics. With over 25 years of experience in education, she has been a leader at both the district level and in the education industry. Her extensive expertise encompasses curriculum, professional learning, and assessment development, instructional design, educational leadership, and strategic planning. She is currently the Vice President of Academic Design — Mathematics at McGraw Hill, where she oversees the development of high-quality, engaging, and effective math curriculum and resources for students and teachers across K-12 math education.
Prior to joining McGraw Hill in 2023, Twana served as the Vice President of Curriculum and Instruction at MIND Research Institute. During her career, she has collaborated with organizations like EF+Math, Digital Promise, and Beyond 100Kin10 where she has contributed to and led research initiatives aimed at elevating math education and product development on a national scale. Her contributions have been prominently featured in influential reports like “Strengthening Executive Function Skills to Improve Mathematics Learning” from EF+Math and “Doing the Math: Building a foundation of joyful and authentic math learning for all students” from Beyond 100Kin10. As an engaging thought leader, Twana shares her expertise through blogs, articles, and public speaking engagements, advocating for transformative change in math education on
prestigious platforms like SXSW EDU, the Gates Foundation, and the National Council of Teachers of Mathematics Conferences.
