All mathematics classrooms are linguistically diverse with learners from a range of cultural, linguistic, and social backgrounds. Communication-responsive mathematics teaching aims to support all learners with the language demands that are involved in learning mathematics. These language demands not only include the vocabulary involved, but also the styles of communicating, reasoning, and explaining that are specific to mathematics and mathematics classrooms. Language-responsive mathematics teaching focuses on supporting learners to develop a conceptual understanding of the mathematics they are learning concurrently with developing their abilities to communicate and reason mathematically. These language aspects of mathematics are used by learners for learning and thinking and are integral to developing a conceptual understanding.

Principles of Communication-Responsive Mathematics Teaching

There are five key principles that underpin language-responsive mathematics teaching that have arisen from a range of research over many years. These principles need to influence the planning of lessons, tasks and activities as well as the practices and activities within a lesson. Many of these are principles of good mathematics teaching more generally but with a particular focus on the language aspects of these practices.

Engage learners in rich discourse practices

There are a range of rich discourse practices involved in learning and doing mathematics. The most common ones are explaining meanings, formulating mathematical problems or models, analysing relationships between concepts or representations, arguing or following a mathematical argument, and explaining issues or conclusions. Focusing on these demanding rich discourse practices rather than keywords or vocabulary supports developing a conceptual understanding.

Learners need opportunities to engage with these practices through speaking, listening, reading and writing. These opportunities can arise through working on specific mathematically rich tasks, discussing or analysing examples or models offered by their teacher, or solving cognitively demanding problems.

Establish mathematical ways of working that support language

Lessons often run more smoothly when there are routines or patterns in ways of working where learners know what is expected of them. There are several common routines that can be language-responsive. Teachers often model new procedures, offering learners the opportunity to listen to and see how connections are made between the steps of a procedure, or the similarities and differences to procedures already known, or ways in which meanings are explained. Using mini-whiteboards can offer students the opportunity to write using symbolic, graphical or diagrammatic representations. Think-pair-share or talk-tasks can offer learners the opportunity to discuss mathematical meanings, ideas or connections.

There are several ways that these routines can be established, including modelling the expectations, explicitly stating these expectations, or using particular patterns of activity across lessons (e.g. think-pair-share). For example, a routine could be established where students can expect to offer explanations for their answers or responses and these explanations need to focus on the ideas, connections or decisions involved rather than a more simple reporting of what they did.

Connect languages and representations

Mathematics is often communicated using symbols, diagrams and words. Learners also bring their own linguistic resources, such as ways of arguing or fluency in another language. Connections need to be made between these different languages and representations. For example, connections are needed between the everyday language that learners are often familiar with, the more mathematical or meaning-related language that teachers are interested in, and the underlying mathematical concepts. Moving from everyday language to a more mathematical language involves more than a change in vocabulary, it also demands precision, conciseness, and logical inferences. Learners can also draw upon other languages they use to support mathematical reasoning with connections being made between the ideas expressed in the different languages.

Connections also need to be made between different representations, such as algebraic and diagrammatic representations. While it is common for different languages and representations to appear alongside each other, or to switch between these different representations, the connections between them are not often made explicit.

Amplify not simplify language demands

As using language is a fundamental part of learning, thinking about and doing mathematics, simplifying language demands often also involves simplifying the mathematical content or the cognitive demand of what is being learnt. This can limit the opportunities learners have to learn mathematics. Scaffolding tasks and activities in language-responsive ways needs to ensure that that the central mathematical focus remains.

An alternative is to draw attention to these language demands to raise learners’ awareness of them, for example by comparing mathematical and language-related structures, explanations, representations and examples. For example, looking at families of words such as equal, equation, equate and discussing what kinds of words these are, or comparing and contrasting the use of everyday words that take on specific mathematical meaning such as ‘evaluate’, ‘of’, ‘or’.

Value the resources learners bring with them

Learners bring with them a range of resources and skills that have not necessarily been valued in mathematics classrooms. Many learners speak more than one language, are able to construct arguments in different contexts such as at home or in their history classroom, and can represent things in different ways. Learners with different social, cultural or linguistic backgrounds have often had fewer opportunities to participate meaningfully in lessons or experience high-quality mathematics teaching, sometimes as a result of societal and teacher expectations about what they can or cannot achieve. Focusing on what learners can do and what they bring with them can help to address this.

Valuing learners’ resources can include using their other languages when working on tasks, but also by focusing on what learners can do in the lesson. This might include how they tried an example to make sense of a question or problem, identified a limitation or restriction, followed a logical structure or reasoning process, made a connection between representations or used one representation to make sense of another, and expressed their solution concisely using symbolic notation. This contrasts with more deficit views of learners such as ones that focus learners’ misconceptions, rather than challenges and difficulties in the often abstract mathematical ideas, process or procedures they are learning.

References

These principles are derived from:

Erath, K., Ingram, J., Moschkovich, J. & Prediger S. (2021). Designing and enacting instruction that enhances language for mathematics learning: a review of the state of development and research. ZDM - Mathematics Education. 53(2), 245-262. https://doi.org/10.1007/s11858-020-01213-2

We have also referenced:

Adiredja, A. P. (2019). Anti-deficit narratives: Engaging the politics of research on mathematical sense making. Journal for Research in Mathematics Education. 50(4) 401-435. https://doi.org/10.5951/jresematheduc.50.4.0401

Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading and Writing Quarterly. 23(2) 139-159. https://doi.org/10.1080/10573560601158461

Walqui A, Bunch GC, (Eds.). (2019). Amplifying the Curriculum: Designing Quality Learning Opportunities for English Learners. Teachers College Press.

Zahner, W., Velazquez, G., Moschkovich, J., Vahey, P. & Lara-Meloy, T. (2012). Mathematics teaching practices with technology that support conceptual understanding for Latino/a students. The Journal of Mathematical Behavior. 31(4), 431-446. https://doi.org/10.1016/j.jmathb.2012.06.002

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