By Beatriz Font Strawhun

Institute for Learning

It was Veronica’s third year in the country as a member of the dual-language program. She communicated in mixed English and Spanish, was liked by most of her peers, and had a great sense of humor. She struggled in math. She had been referred for special education testing by her 4th-grade teacher and had been largely dismissed during mathematics by her 5th-grade teacher. Now, as she sat in the 6th-grade classroom, the question was what might come of her mathematical learning, what had been missed? Why did she continue to be unsuccessful in our classrooms? Veronica moved to the U.S. from Honduras. She had limited opportunities to learn at a young age, due to the fact that her family missed much of her schooling as they tried to move to the United States. Her father, a chemical engineer by trade, worked as a bus driver for the local daycare and her mom, a university professor in her hometown, worked as an afterschool aid for the Just-for-Kids program at our school. They were both invested in Veronica’s education and were baffled by her lack of success when it came to mathematics. There was an extensive record compiled by her previous teachers of what Veronica did not know. What did Veronica know and how could her assets be leveraged?

There was also a greater question at play: How can teachers provide equitable opportunities for communication (and consequently increase their opportunities to learn) in a multilingual classroom?

How do we, as teachers, conduct discussions around mathematics when the students’ native language is not the dominant language in the classroom or the language of the teacher? How do we scaffold a rich discussion without losing the rigor of the task or reducing the discussion to a simple show and tell with no real connections to the context or the work of the other students in the classroom? Implementing the following four strategies in the mathematics classroom can promote equitable and rich math talk.

1. Let students speak! And that means in their native language or a mix of that and English

We cannot underestimate the power of acceptance of communication in whatever language a student feels comfortable using, even when it is a mix of language. Students’ ideas should be expressed in whatever language the child chooses and feels comfortable using. We must recognize the power of the student’s own voice and seek to understand the richness of knowledge that may be presented through the home language. The very nature of mathematics lends itself to a universal language from which a student may find a launching point to communicate in the classroom.

To that end, we must recognize the power of the visual mathematical representations that students create to represent their thinking. The scaffold for the teachers and classmates to understand a student’s explanation lies in the mathematical representation chosen by the student. This representation or solution path provides a roadmap of the student’s work—an anchor of communication.

During the first weeks of the school year, when Veronica was asked to share in class, she was largely reluctant. She would hand over her paper with her solution strategy and ask that the teacher explain her thinking, while her English-proficient peers groaned in the background. When working one-on-one with Veronica or observing her participation in a small group with whom she felt comfortable, the teacher could see that her mathematical reasoning was sound. Her computation was always a bit off, but her reasoning was sound. When positioned as an expert or equal among her peers, Veronica expressed her thoughts beautifully regarding her solutions to a math problem. When allowed to speak in her “Spanglish” she would explain how she thought about complex math problems with ease. Computation was still a barrier to Veronica’s success but communicating about rigorous math concepts in whatever language suited her allowed her to grow as a mathematician.

The identities people claim, refute, or are assigned by others are powerful factors in obtaining access to classroom discourse. For example, if students are positioned as incompetent, their contributions may be ignored or discredited. If students are positioned as experts or highly knowledgeable, their contributions will be given greater weight. Thus, through various classroom positioning patterns, students can gain or lose the right to act (Kayi-Aydar, 2015). How students are positioned in your classroom can affect their ability to develop content and language competencies in the classroom. Therefore, positioning is critical to each student’s success and learning in the mathematics classroom.”

Chval, K., Smith, E. M., Trigos-Carrillo, L., Pinnow, R. J. (2021). Teaching math to multilingual students, Grades K-8: Positioning English learners for success, (p. 11). Corwin Mathematics Series: SAGE Publications. Kindle Edition.

In essence, math is a common language with a universality in number and representations. Using these as an anchor can allow greater communication in the math classroom. With help and encouragement from the teacher, a student can use their math representation of choice and their language of choice to communicate their solution.

2. Make it a working word wall

When will multilingual students learn the academic vocabulary in English? It is true that a student needs to learn academic vocabulary in English, but as with all learning of new vocabulary, this must happen in context. Learning new vocabulary is futile without a context or experience upon which to hang the shingle. A student’s native language can be enriched with the appropriate academic language through the use of a math wall that includes visual representations where appropriate and cognates where possible.

Given the unique opportunity in the multilingual classroom of the need to find the correct words to accurately express yourself is a constant element of learning, what better opportunity than to teach that word in context. When learning about a Cartesian Plane and negative and positive integers, a word wall can be incorporated and these new words—these shingles of meaning—can be hung quite literally on the wall and referenced by the student seeking to express their thinking.

The elements of the word wall must be generated during the math lesson. These elements should include a student-generated definition with a picture or visual representation directly related to the lesson context in which it was learned. It seems so efficient to have these pre-made and laminated and used every year, but that strips the power of having a student-generated and student-designed word wall.

3. Let us help you get started . . . with sentence starters

Sentence starters or sentence frames are often used to help a student communicate their mathematical ideas. An effective sentence frame coupled with a student’s mathematical representation can allow a student to begin to express their mathematical ideas in the classroom. One key to using sentence stems, is to have them be focused on deep mathematics without taking over students’ thinking. Below are a few to consider:

    • I solved the problem by . . .
    • In my representation, the ___________ shows . . .
    • I agree with them because . . .
    • I started by . . . and then I . . . because . . .

4. Wait, wait! Use double wait time

Perhaps the most effective, yet simplest technique, that can be used in the classroom is wait time. Many of us know the standard 3 to 5 seconds of wait time following a question the teacher asks to the time they call on a student to answer (Rowe 1972, Lake 1973). Wait time serves as a moment for students to formulate their own answer before hearing that of others. This affords the multilingual learner a chance to interpret what has been said by the teacher and possibly to work on a translation of what is being said, formulate an answer in their native language, and translate that back into English. Perhaps most crucial is the time after someone has spoken, before the teacher begins to speak (a new question, a recasting of the student’s statement etc.) This time, wait time #2 (Rowe 1972, Lake 1973), is perhaps the most important as it allows a student to compare their own thinking with that of the student who responded. During these brief moments, the student has an opportunity to gather vocabulary that may describe what they were attempting to communicate, compare their thinking to that of another student, and formulate a response or question that might help further their own thinking.

Some Accountable Talk® community moves also act as wait time. By asking students to say back what they hear another student say, students get to hear another repetition of the idea, perhaps using additional vocabulary they understand, and it is one more time that they get to process the idea themselves.

So, what became of Veronica? She blossomed into a strong student and built a positive math identity where she saw herself as a mathematician. She entered junior high the following year to great success. She earned all A’s her first semester and even returned to her sixth-grade class as a presenter on her experience in junior high and how to navigate the first year with success.

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