‘Registering’ Math Academic Language: Providing Supports for English Learners – Center For Education Efficacy, Excellence, and Equity

By Anita Sundrani and Asia Ellis

In recent years, there has been a significant shift in the way students are taught mathematics. Math is no longer just about basic computation and procedures. Students are tasked with solving real-world problems that require a high level of proficiency in academic language. Strong academic language skills allow students to build a deep conceptual understanding of the mathematics content and practices necessary for success in today’s classrooms.

In light of these shifts, we share an overview of academic language, with a focus on three related facets that connect to E4’s research priorities: 1) mathematics academic language, 2) challenges faced by English Learners in developing their academic language toolkit, and 3) strategies mathematics teachers can use to support English Learners’ academic language development.

What is academic language?

At its core, academic language is the form of communication used in schools and in classrooms, which differs from the language that is used at home and in other contexts.

Researchers have proposed many different frameworks that explain how students develop academic language. Some focus more on the individual student’s experiences (i.e., cognitive), while others focus more on the surrounding environment (i.e., raciolinguistic, sociocultural, sociolinguistic).

Our exploration of academic language takes a sociolinguistic and sociocultural approach. This perspective highlights the unique nature of social interactions in the classroom and the ways they differ from everyday exchanges. In other words, they have their own register.

What is a Register?

In linguistics, a register is the way people use different types of language in different contexts – for example, a scientist needs to make specific language choices when engaging in a professional setting that may differ from their everyday language (See Moschkovich, 2015; Sarris & Chavez, 2020; Wilkinson, 2019). The term applies to both speaking and writing.

Components of a Language Register
Vocabulary	Syntax	Semantics	Discourse Features
Includes the unique terminology associated with a subject area	Focuses on appropriately structured phrases and sentences in the desired language and register, which can take the form of prepositional phrases, passive voice, clauses, and ellipses, among other	Refers to the meaning of a word or phrase, as well as sentences and larger texts within a certain context.	Involves the active oral and written communication of ideas associated with a subject area

How does academic language fit in math?

Standards in mathematics, such as the Common Core State Standards, require students to have a deep understanding of the language of mathematics to solve problems. Students should be able to demonstrate their understanding of a problem by listening to and reading descriptions of the problem and then discussing related concepts with peers and teachers. Underlying each of these expectations are the four equally important areas of language – vocabulary, syntax, semantics, and discourse.

Mathematics Academic Vocabulary

Mathematics academic vocabulary is the component of academic language that gets the most airtime, and experts agree: the unique vocabulary associated with mathematics (e.g., diameter, vertex, ratio) supports overall language development. When targeting mathematics academic vocabulary in the classroom, educators need to define terms explicitly, giving examples in the relevant context to illustrate meaning.

The National Council of Teachers of Mathematics (NCTM) cautions against teaching mathematics (and vocabulary) without a context, instead encouraging the introduction of real-world connections once students have mastered the mathematics content procedurally. A more decontextualized approach makes it more difficult for students to engage in mathematical discourse when the time arrives. Instead, vocabulary should be integrated into everyday instruction through high-cognitive demand activities that balance both conceptual and procedural understandings of mathematics. Teachers should also engage students in opportunities to discuss what they’re learning orally and in writing (one such example is provided below).

Source: Ellevation Math

Mathematics Syntax and Semantics

Semantics references the overall meaning of a statement in context. For example, “in a mathematical word problem, four plus seven times a certain number is 20; what is the number, students must infer that a certain number and the number are actually the same number.” This applied use of the mathematics register takes time for students to master, so it is important that students have multiple opportunities to make sense of word problems and symbols.

Syntax focuses on the structure of statements. For instance, students need to understand the relationship between words, such as “greater than” or “the same as”, in order to work with equations and inequalities. Taken together, students begin to learn how to speak and write as mathematicians and understand what is being asked of them in the mathematics classroom. Despite the language-rich underpinnings of the mathematics register, teachers may be hesitant to include literacy instructional practices in their teaching, believing that language learning is outside of their expertise and focus as math teachers.

Mathematics Discourse

Though most scholars agree that discourse is an integral component of language acquisition, they disagree on how it should be introduced. Some believe that students must first master vocabulary and mathematics procedures prior to engaging in discussion, while others believe that all aspects of mathematics academic language can be developed simultaneously through purposeful mathematics discourse. Expert Judit Moschkovich explains that mathematics discourse “involves not only written text, but also multiple modes, representations (gestures, objects, drawings, tables, graphs, symbols, etc.), and registers.” This means that math instruction should focus on conceptual understanding of math content and engage students in explaining, reasoning, and justifying their mathematical ideas with their peers, teachers, and in writing.

How does mathematics academic language affect English Learners’ success in math?

Due to the instructional shift toward conceptual understanding and real-world applications, English Learners (ELs) face unique challenges while learning mathematics. In particular, learning in a nonprimary language requires a heavier mental load to move from one register to another, a process more commonly known as “code-switching.” Code-switching (also known as translanguaging) can lead to more oral and written errors because the learner has to constantly switch between their primary language and nonprimary language, where the syntax may be different.

There is also the added challenge of “technical” and “subtechnical” vocabulary words. “Technical” vocabulary words that have a mathematical definition (e.g., circle) and “subtechnical” words that may have both a mathematical definition and colloquial one (e.g., “yard” is a unit of measurement and can also refer to an area outside a home).

This culmination of challenges, along with the misconception that mathematics should be separate from language instruction, may lead teachers to underestimate the true mathematical abilities of ELs compared with their English monolingual peers. Because of this, teachers may unnecessarily assign ELs more content below grade level than their English-only classmates, leading to widening gaps in mathematics performance (see here and here).

Mathematics Instructional Strategies for English Learners
It is more appropriate to provide ELs with high-quality tools that are responsive to their mathematical strengths and primary language to better enable them to access on-grade-level material. These strategies should emphasize:

a balance between conceptual and procedural understanding,
high cognitive demand,
positive beliefs about mathematics, and
the eight Common Core mathematical practices.

Potential strategies include:

Introducing Els to mathematics vocabulary in context with brief mathematics language lessons.

For example, Ellevation, an organization designed to both serve ELs and teachers of ELs, offers math primers to support Els in math. Math primers are quick five-minute lessons that introduce students to a mathematical term and present a real-world application of the term, aided by a mathematics representation as a visual anchor. Their goal is to use a contextualized approach to mathematics vocabulary to help ELs engage in rich discourse with their peers and, in turn, access grade-level material at any level of proficiency. A recent investigation found that implementing this strategy in isolation sporadically during the academic year does not have an impact on ELs’ mathematics knowledge. This finding supports Moschkovich’s assertion that mathematics academic language development should be a holistic endeavor that should combine language development and mathematics proficiency through mathematical discourse.

Focusing on students’ mathematical reasoning in their argument, as opposed to precise language usage.

This approach puts the emphasis on students’ understanding of concepts, instead of the register, which then allows students to gradually become accustomed to the register through repeated oral and written practice. Also, listening for students’ mathematical ideas frames them as knowledgeable about mathematics, and avoids a deficit mindset about ELs.

Acknowledging the complexity of language and the different ways it takes place in the classroom.

Students are expected to speak, read, and write in the mathematics register, recognize multiple representations (e.g., tables, graphs, pictures, symbols), understand different forms of text (e.g., textbook explanations of concepts, word problems), and communicate with different audiences. Therefore, teachers should provide ELs, as well as their peers, plenty of opportunities to engage in the complexity of language through different modalities and sequence them in ways that support comprehension (see related work on this topic by Moschkovich (2012), Peng and colleagues (2020), and Sarris and Chávez (2020)).

Conclusion

Academic language is complicated and nuanced, as each subject area requires instruction to be responsive to its specific register. Although there are commonalities across subjects–including a focus on vocabulary, syntax, semantics, and discourse–the strategies to develop these language components are distinct. Within mathematics education, language instruction is often overlooked as math is viewed as the subject of numbers. This forces English learners to simultaneously learn English and the mathematics register. However, there are numerous strategies that frame ELs as doers of mathematics while they learn both. When teachers recognize and build upon ELs’ mathematical strengths and knowledge, these students are better situated to grow and thrive as learners across the board.