Silvia Aparicio, Ed.D.

Common Core Mathematics Standards and Standards for Mathematical Practice

The Common Core State Standards (CCSS) and Standards for Mathematical Practice require students to create meaning and discuss mathematics at a new level. While the CCSS focus on conceptual understanding, procedural skills, fluency, and application to the same degree of importance, the Mathematical Practices “describe the thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics” (CCSSO & NGA Center, 2019; Rutherford, 2015, p.13). Students are required to increase their use of academic language in the math classroom to explain, make conjectures, argue, reason, critique, analyze, justify, describe, compare and overall have a deeper conversation about the mathematics content at hand (CCSSO & NGA Center, 2019a).

Problem-Based Enhanced Language Learning in Math

Problem-Based Enhanced Language Learning (PBELL) is one instructional method that provides the integration of language across all content areas while allowing students to work collaboratively to solve a meaningful problem. In a math classroom, we expect our students to sound like mathematicians. To promote this language we must prepare students to use mathematical discourse in the classroom. “Mathematical discourse includes not only ways of talking, acting, interacting, thinking, believing, reading, writing but also mathematical values, beliefs, and points of view” (Moschkovich, 2003, p. 2) Within a PBELL, students are explicitly taught a language function highlighted within the content-language objective, practice the language needed to discuss the math content throughout the experience, and also have the opportunity to continue to develop their reading, writing, speaking and listening simultaneously. All of this learning is rooted in a meaningful problem. By focusing on the language students need to discuss the content, students are better able to access the content.   

In mathematics, discourse can come in many forms. The most predominant language functions in math are the language of justification and the language of problem-solving. To justify, students need procedural language to describe the steps they took and the language of justification to be able to explain their reasoning behind each step. With the language of problem-solving, students explain the process they went through to solve the problem (Bickmore-Brand, 1990).  This includes the steps they took to understand the problem and their solution path. When students are able to justify or explain their processes with the language of problem-solving, teachers are quickly able to assess student’s content knowledge and provide support in areas students are still struggling. 

Final Thoughts

Not only will PBELL engage all students in solving real-world problems and enhance how they use language to discuss the topics at hand. Mathematical concepts and ideas are made relevant and meaningful to students by linking them to real world problems and providing students time to grapple with these problems and develop and share solutions with an authentic audience. By infusing explicit language instruction into math experiences we can help all students develop the skills they need to demonstrate math proficiency and use mathematical discourse.

Connect with Silvia Aparicio, iTeachELLs Instructional Coach at

For more information on planning a PBELL, check out our Lesson Plan Guide, or visit the iTeachELLs Resources page.