Make visible what, without you, might never have been seen.

– Robert Bresson

I noticed Samira as soon as I walked into her classroom. Students were sitting in noisy clumps, some chatting over iPads, some jostling and joking. But Samira was silent. Although seated at a table with five others, she was visibly separate from the laughter and exchanges surrounding her.

Samira was a multilingual learner and new to English. Peer relationships are vital for all students, but Samira did not yet have the linguistic capital to easily join conversations. And on top of that, she now had to learn curriculum in a brand new language. This bright student faced many challenges — and isolation — in her new setting.

“All right everyone, let’s get started,” the teacher announced. Conversations trailed off and bodies settled.  After a brief review of the previous day’s math work, the teacher handed out paper, pencil crayons, and manipulatives to each group. There was one instruction: “Show 0.75.”

The teacher and I had co-planned the day before, and decided to use visual math for the lesson. The question, “show 0.75”, prompts students to represent this number in as many different ways as they can. Some may write the fraction 75/100; others may plot it on a number line; some may colour in 3/4 of a pizza; still others may place three 25-cent coins down for the group to see.

Multiple studies have documented the importance of visual math, revealing a positive correlation between representing concepts pictorially and improved math performance.  On the YouCubed website, Stanford math education professor Dr. Jo Boaler describes some of these studies, as well as related neuroimaging findings. Remarkably, when people do math calculations using only symbolic digits (such as 6×3, etc), some of the neural pathways that light up in the brain are visual. As Boaler succinctly puts it, “our brain wants to think visually about maths.”1   So while visuals may help solidify conceptual understanding for all students, for multilingual learners like Samira there is an additional advantage.

As Samira’s group attempted the question, there were several false starts. A couple of students weren’t sure what to draw. Some started sketching but then quickly erased their work. Samira however steadily jotted down fraction equivalents and drew connected visual representations for each. Before long the others noticed, and stared at her intricate work. “Is that right?” one of the boys finally asked. The classroom teacher leaned over, and smiled.  For the first time that day, someone looked at Samira and addressed her directly: “How did you know that?”

In this simple, visual task Samira was able to demonstrate her math knowledge — free from the usual language-based constraints of our predominantly verbal linguistic classrooms. In the space of one group session, Samira had moved from near-invisibility to knowledge-holder. She had gained social currency and standing in the group.

As the teacher bent over the group’s work, gesturing to pictures and numbers as she spoke, I could see Samira listening intently, mentally attaching English terms to math concepts she already knew. And while Samira needed this intentional highlighting of math language to learn English, all students in her group benefitted. I once heard during a seminar that 90% of the vocabulary used in math is exclusive to math. Although I have been unable to locate the original source of this data, when I think of terms such as isosceles, scalene, and divisor, anecdotally I am inclined to agree. In what other context do we ever encounter words such as these?  As for our lesson, both the visuals and vocabulary inherent in the math task were necessary for some, and undeniably good for all.

At times, multilingual learners may be unintentionally viewed through a deficit lens.  “She can’t speak English” and “We have to help him” are common refrains. But when the bell rang that day and everyone grabbed their books for the next class, Samira rose and stood a little taller, a new confidence in expression. The task, which had been rich and beneficial for everyone, provided the first key towards unlocking her voice, and re-imagining her not as someone who needed help, but as a valued and contributing member of the class.

1. https://www.youcubed.org/resource/visual-mathematics/

(student names have been changed)

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