Learning mathematics is a critical skill in the 21st century. Mathematics builds critical skills, such as problem solving and applying logic. While some claim that mathematics might be an easier subject area for English learners due to the nature of the subject, this is clearly not the case as mathematics requires a significant amount of language.

In my 2016 MultiBriefs article, "Math is about numbers, so it’s easier for English learners, right?" this topic is discussed in more depth. The purpose of mathematical discourse is to deepen understanding of mathematical concepts. Teachers can facilitate mathematical discourse in their classrooms for English learners in a variety of ways.

## Discourse Within Instruction

While modeling is a key component of instruction for English learners, it is not sufficient. Traditionally, teachers in math classrooms show, model, and tell students how to utilize a specific strategy to solve a mathematical equation.

Generally, teachers work through a number of problems, demonstrating the specific strategies, at times including students through questioning and calling on specific students. In this model, teachers ask a question that relates to a next step, or to seek a specific answer, and students raise their hands. The teacher then calls on a student to answer the question.

If the student provides a correct response, the teacher validates the student and their response, and potentially expand upon the answer given. If the student provides an incorrect answer, the teacher may correct the student, and explain at length why the answer is wrong or the misconception that has arisen.

In this scenario, the teacher is using the majority of language in the classroom. Many of the students may be passively involved in the instruction.

One way to increase discourse is through the 10/2 rule. After every approximately 10 minutes of instruction, provide about 2 minutes for students to discuss the concept with a partner. The teacher can provide a specific prompt such as having the students review key steps or discussing the next steps to be taken, for example.

For English learners, their level of understanding of the instruction will be dependent on the level of comprehensible input. If the instruction was primarily language based, wherein the teacher primarily explained through words, the English learners may have understood at a surface level only, depending on their English proficiency level.

Teachers, of course, can include strategies to make their instruction more comprehensible, including using visuals and gestures, for example.

The purposes of building in mathematical discourse are to deepen student thinking, help students practice content and language, and for teachers to determine the students’ thought processes. When students engage in mathematical discourse, their engagement is increased as they verbalize their thinking and practice with others.

To increase mathematical discourse, we should start by creating an environment in which students are able to have discussions with peers and practice both using academic, mathematical terms as well as practice the content being studied in the classroom.

To facilitate conversation in the classroom, teachers should think through a number of factors before, during, and after the lesson, such as what is posted or not posted on the walls, the seating arrangement of the students, the questions and prompts they will be utilizing during instruction, and how to carefully listen to students in order to understand their thinking, validate the thinking process, and clarify misconceptions when necessary.

## An Environment Built for Discourse

There are several considerations for setting up a classroom that is conducive to discourse in the math classroom. The physical design of your classroom, including where and how students are seated, can impact student discussion opportunities.

To increase student discourse, seat students in pairs, triads, or groups of four. That way, when the teacher provides a prompt for students to discuss, there is someone nearby that students can talk with. If students are seated in rows, it is not as clear who the students should talk with.

In addition, rows provide more distance between the students, which makes discussion less natural as the physical proximity is greater. The physical arrangement in the classroom can include a space for individual instruction, small group work, and whole class instruction.

In addition to the seating arrangement, an illustrated math word wall is critical as a way to focus on the mathematical vocabulary that students should incorporate into their discussion. Word walls are an effective technique to highlight vocabulary, including content specific words, functional words and phrases, and general academic terms.

For the mathematics classroom, consider taking advantage of the wonderful illustrated math vocabulary cards create by the Granite School District in Utah.

Word walls can also help students, especially English learners, understand that many mathematical terms are homonyms, and may have differing meanings in a math. Take the following words, and consider how these words differ in math from other subject areas:

• Base
• Mean
• Even
• Table
• Round

Providing an illustrated math word wall will remind students of the mathematical meaning and help clarify misconceptions while broadening students’ vocabulary.

Word walls on their own, however, are insufficient. Students must utilize the vocabulary in their discourse in order to deepen academic language. Word walls can quickly become wallpaper if students are not referring to them throughout the day.

Teachers get creative about making word walls interactive: some teachers have students add pictures or sketches to serve as a reminder of the meaning. Other teachers challenge the students and tally the number of times words from the word wall are used accurately in speech.

Finally, a number line is critical in the mathematics classroom. While teaches of more advanced math classes may feel it is unnecessary, a number line can assist the English learners in more clearly understanding the abstract concepts that are sometimes presented in the math classroom.

The number line can help make instruction more concrete and comprehensible for English learners, and serve as a reminder to students of another tool that can be utilized to help them understand the content.

## Guiding Questions for Teachers to Increase Math Discourse

Teachers should use a variety of questions to guide student thinking and increase discourse. He idea is to move away from asking simple questions that have one right answer and move towards more open-ended questions that promote thinking and discussion.

The following questions illustrate the types of questions we can ask students as we engage them in discussion. Note that these questions and prompts should not be asked exclusively by the teacher. Rather, students should ask each other these questions as well.

• Make a model to show your answer. Describe it to me.
• What is another way to…
• Which representation/strategy is most helpful to you? Why so?
• Which tool is most efficient?
• What steps were involved?
• What have you already tried?
• What haven’t you tried yet?

## Listening to Students

Perhaps the most important aspect of mathematical discourse in the classroom is listening to your students. Consider, during student discussion opportunities, as well as when students are sharing their thinking, how the discussions relate to the objective.

Listen carefully to students to determine if they are making specific errors or if misconceptions are in place. When listening to English learners, it will be important to not focus on the grammatical aspects of the discussions as much as on the content.

This can be difficult for some teachers as they have to key in on the message, rather than on specific language errors the student is making. It is critical to listen carefully to both validate student thinking as they are working through the specific task, as well as identify any misconceptions that are arising.

Building discourse in any classroom can be a rewarding activity for both teachers and students. If the concept is new, consider how you can take some steps to increase discussion among students.

If you are already integrating a great deal of discourse opportunities in the classroom, consider how you can make participation more equitable by providing additional language frames and vocabulary to your students, helping them to build up ideas, build upon ideas, explain their reasoning, and finding new ways to explain their thinking.