Language-responsive classrooms

We have two underlying principles that underpin our work with learners

Amplify not simplify language
Reducing or simplifying the language also reduces the opportunities learners have for learning both language and mathematics
Enhance language and mathematics with understanding simultaneously
Learning and doing mathematics involves communicating in a variety of ways, including explaining meanings, describing processes and justifying decisions or results. Only by considering the interweaving of language and mathematical understanding can the learning of mathematics be enhanced.

We follow six design principles in the developing of the classroom materials and resources.

Teaching needs to

1) engage learners in rich discourse practices

Learners need opportunities to engage in rich mathematical discourse practices in a variety of contexts. These include actively listening to their peers, communicating explanations both verbally and in written form, both informally and formally, explaining meanings, constructing arguments, justifying procedures and processes, and making sense of written mathematics. These rich mathematical discourse practices also need to be modelled by teachers.

2) establish a variety of mathematics language practices and routines

There are lots of different ways in which learners can engage in rich mathematical discourse practices and learners need to experience this variety. These practices can be developed through peer- and self- assessment, through collaborative tasks, through tasks focusing on justification such as "convincing yourself, a friend, a skeptic" or "Always sometimes never". These routines need to be both meaningful and purposeful.

3) connect different representations and language varieties

Language varieties include the everyday languages that learners use both in and outside of the classroom, the academic language that is specific to classrooms and schools, and the technical language of mathematics. They also include different ways in which concepts and ideas can be represented including symbolically, graphically, diagrammatically as well as through gestures.

4) draw on students' own linguistic resources

These linguistic resources include named language that learners may speak at home or in their wider community, but they can also include ways of arguing, justifying and explaining that learners again use at home or in their home community.

5) combine language and mathematics learning opportunities through lesson design

Sequencing, connecting and coordinating opportunities to focus on language and mathematics together in combination is needed to support learners to gain conceptual understanding.

6) develop learners' awareness of the roles and form of language in mathematics

Language can play lots of different roles in learning mathematics. Comparing or contrasting these differences can help learners to understand these roles. This goes beyond defining mathematics specific terms to include discourse structures such as mathematical explanations or argumentations.

1) Plan and prepare collective discussions that focus on mathematical concepts

This planning includes choosing appropriate tasks and anticipating student responses to these tasks. It also includes planning whole-class discussions to pay attention to the mathematical concepts and enable learners to engage in rich discourse practices such as explaining and justifying during these discussions.

2) understand and connect learners' ideas and mathematics

This practice involves planning for and acting in ways that makes learners' ideas accessible to the whole class, and supporting them to make connections to mathematical concepts, representations or language practices. There are a variety of ways of doing this, for example by asking specific questions or inviting other learners to comment or build on an idea.

3) enhance language practices for learning mathematics

Enhancing language practices for learning mathematics include using a range of strategies or talk moves to encourage and support learners to explain meanings, justify their solutions or methods, and report their approaches.

4) encourage learner participation in demanding discourse on mathematics

This practice focuses on moving learners explaining how to why they did what they did. It highlights the importance of encouraging students to contribute to mathematically and linguistically demanding discussions that provide learning opportunities for deep and meaning related mathematics learning.

5) pay attention to feedback on learners' mathematics

This includes developing a shared criteria for what counts as a good mathematical explanation or justification., as well as a supportive culture that means that students are comfortable sharing their ideas even when they may include mistakes knowing that these will be learnt from.

6) purposefully use pauses and silence

Teachers need to leave space for students to contribute their ideas, and students often need time to think about their contributions. These practices involve giving learners opportunities to participate and allowing more time for learners and teachers to make sense of the ideas being expressed and building on them.