Social Justice Through Visual Math

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)

The Sweetest Sound

It was the end of September, and my grade sixes were standing in a circle on the grass. It was a touch cooler now, the day bright and sunny, a bit of a breeze.  The students knew the activity we were about to do.  We had been using it over the past few weeks as one of our warm-up games before drama class. 

One at a time, each student would say their own name out loud, and simultaneously create an action to go with it. And then, in an enthusiastic chorus, the rest of the circle would mirror their action back to them and repeat their name. This would continue around the circle  until everyone’s name had been said.   

Personalities always revealed themselves in chosen actions. Abdul said his name with impossibly cool gestures. Jin liked twirling as she said hers. Mike tended to do a short dance move or two. And without fail, the whole class would echo each classmate’s creation, a happy call-and-response comprised only of names and movement, filling the playground with unified sound. 

The simplicity of this game belies its complex benefits to learning and community. 

We have heard much over the years about the positive connection between movement and the brain, with benefits to mood, learning, and focus. The physical representations in this game certainly encourage movement, exploration of physical space, and rhythm.  As teachers, we also know the importance of collaboration within the classroom, of creating situations such as this, where students are engaged with one another in learning tasks. And of course, in order for students to learn optimally, there must be a strong sense of community, connection, and trust in the classroom. Team-building and collaborative games like this may represent one step towards this goal. Indeed, there is something deeply satisfying in seeing all students quietly looking, not at a worksheet or iPad, but at one another. Present in the moment. Waiting for their classmate’s contribution. In our busy and increasingly digitalized world, I wonder how often we stop like this, just for a few minutes, to truly look at each other, acknowledge one another’s presence. And this leads me to perhaps the most important benefit of all for students:

Someone says their name. 

There is power in hearing our names spoken aloud, that one word that represents and encapsulates all that we are. We all know that uplifting feeling when someone remembers our name and addresses us, and the slight umbrage we feel when someone forgets or mispronounces it. It is one of the first things small children learn to recognize and write because of its power to engage; children are naturally interested in their own names. It is one of the first gifts we are given by our parents, one of the first ways we are called into the world. As Dale Carnegie once said, “names are the sweetest and most important sound in any language.” 

I fear some students may not have this experience as often as they should, may not often hear their names uttered by classmates … The student just learning English, who does not yet have the linguistic capital to easily forge friendships. The quiet student, struggling with anxiety or social cues. The new student, who braves a sea of unfamiliar faces every day and tries to find their place among them. 

In my experience, this unassuming game — with virtually no preparation required other than finding an open space — can sometimes accomplish what no amount of labelled photos, friend books, or other “name-learning” activities can. It engages. It connects. It creates a space of knowing. 

Everyone says each other’s names. 

I do not suggest the above game is the only way to engage students and begin to foster connection. There are numerous, effective activities, used across multiple contexts and subject areas. I offer this activity as a springboard, to consider and share the many ways we can help students connect.

I have used this drama game with countless students over the years, from primary to junior to intermediate. And every time it is a joy to see my students call their names into the learning space, and see those names returned back as a resounding gift. In whatever way you choose to bring forth your students’ names, may your classrooms always be filled with those sweetest sounds. 

*student names have been changed

September Leaves

September Leaves 

I met Farah* early in my teaching career, just after she arrived from Iran. Farah was a top student at her former school, already spoke two languages, and was learning English for the first time. As she settled into her new class and environment, Farah’s abilities quickly became apparent. She easily mastered math concepts. She also seemed to have an intuitive understanding of science topics, and nodded in recognition when she saw visuals and demonstrations. She began to pick up on English vocabulary quickly. 

But every now and then there was a moment, just after she had understood a lesson or connected with a topic, where she grew quiet. She would lean forward, about to speak, and then stop. Sometimes she would frown slightly, searching for the words. Sometimes she just ended up shaking her head, as if the English she knew was insufficient to express her thoughts. In moments such as these, it seemed that no amount of sentence starters or alternative ways to demonstrate her knowledge would adequately replace her need to explain in Farsi.

As countless students, teachers, and scholars have noted, first language is an intrinsic aspect of our identities.   It allows us to connect with culture, history, and the people we love. It is through our first language we express everything that matters to us, in ways unique and irreplaceable. Through our language, we make ourselves and our ideas heard in the world. And as many have also noted, in a way our first language isn’t just a part of us — it is us.

That sentiment was confirmed during one of Farah’s library visits.

A new shipment had arrived at the school that week, and when Farah walked into the library a few days later, I picked a book off the shelf and handed it to her. It was one of the stories we had been studying in class, but this version was in dual language, written in both Farsi and English. She held it in her hands a moment and then looked up at me, eyes wide, and gasped.

“I know this!” 

Her face and her voice in that moment are as clear to me today as they were all those years ago. Recognition, surprise, joy, relief … it was a jumbled mix that I still struggle to describe. I will never forget her smile. 

Moving from an English-only school environment to a framework of multilingualism is vitally important, and not just for students like Farah. When it is natural and common for all students to hear, see, use, and recognize the value of many different languages, all students benefit. As teachers, we strive to ensure that students see themselves reflected in curriculum and learning spaces, to ensure that everyone’s identity is affirmed and included — not as an afterthought, but embedded from the very beginning. Language is a fundamental part of that inclusion.

Over the years, I have encountered many different ways to embed multilingualism in learning, such as researching and writing class projects in first language, multilingual counting games in math and physical education, dual language books and multilingual collections, and subject-specific dual language dictionary sheets, with key curriculum vocabulary listed in home languages as well as English. The preceding is by no means an exhaustive list; recommendations from colleagues and researchers continue to expand options and opportunities for students.  The multilingual framework continues to grow. 

A few months ago I attended a conference given by U.S. educator and ESL specialist Cristina Sanchez-Lopez. During her presentation she described visiting a Canadian school; she recounted walking through the front doors to see, as she had many times before, all of the languages spoken by the students adorning the entrance way. But this mural, she noted, was different. She then produced a photo, and in it we could see a tree, its painted branches stretching across the walls. Set onto the leaves was the word “welcome”, each leaf bearing the greeting in a different language. 

But then she pointed to a far branch, where we noticed a few leaves with nothing on them, their blank surfaces waiting. Waiting for the new students not yet present, waiting for the new languages yet to arrive, but that would one day become a part of their multilingual school. A space was ready for them.

As I begin teaching this September, I wonder what languages will colour our learning spaces throughout the year … what stories they will tell, the experiences and hopes they will express, the knowledge they will share.

This year, may the trees in your school grow bright.

*names have been changed