Somewhere along the way in my early days of teaching ESL, I heard the phrase “math is a universal language”. At the time, that statement seemed perfectly reasonable to me. After all, math is comprised of numbers and computations, and surely that would be much easier to navigate than a verbose English or Science lesson. Math is math.
Over the course of my career, researchers, colleagues, and students have taught me otherwise.
The following is a short list of some reasons why math may not be as ‘universal’ as we think it is. None of these are my original findings. Rather, I am indebted to numerous educators over the years for making the language of math visible to me.
1. Vocabulary. In my last blog I recounted learning that a significant number of words in math are exclusive to math. “Divisor” and “tetrahedron” really aren’t going to come up in many other contexts. So intentional vocabulary instruction is crucial for multilingual learners (and all learners for that matter).
2. Multiple Meaning Words. Math is packed with them. Let me introduce you to some of the duplicitous characters lurking in our math lessons: Expression, Operation, Odd, Even, Order, Plot, Mean, Prime, Rational, Block, Meter, and Right. Just when a multilingual learner thinks they’ve learned the meaning of a word, they are walloped with a new definition. And I will say that the math word “Table” is more than duplicitous: times table, data table, water table, end table, off the table, under the table, table the bill … this word alone stresses to me how much language work is necessary for math.
3. Word problems. They can be long, overwhelming, and difficult to extract salient information from, even for native speakers of English. And multilingual learners have the added burden of translating the language first before they even attempt the math.
4. Different algorithms and notations. The procedures and steps for math computations can vary widely internationally. If you have a copy of Van de Walle et al’s Teaching Student Centered Mathematics, the authors display some interesting differences in subtraction and addition algorithms. Simple web searches for “long division algorithms by country” yield fascinating variations.
5. Different expectations of student role. Some students may not be familiar with group work, explaining their thinking, or working with manipulatives. They may be more familiar with memorization, mental math without showing their work, and deference to the teacher.
6. Culturally-embedded word problems. It is not uncommon to see a student, skilled in math, freeze up and be unable to complete familiar computations — simply because the context of the problem was unfamiliar to them. Calculating the area of an ice rink when you have never been skating may be a more daunting task than one might think.
7. Exhaustion. This one may be original data from my own experience. I have lived and worked in a country where I did not speak the language. And one of the things that shocked me the most was the amount of time and effort everything took. Even the simplest tasks, that would take me seconds to complete in Canada, would take ages to complete overseas. I shudder to think how long it took me to make a simple withdrawal from an ATM the first few times, simply because I was trying to read and understand the characters on the screen. At times, I was worn out by mid-morning, as a full-grown adult. I cannot imagine the fatigue some of our students must feel.
So what do we do with all this? Again, skilled educators have shared plenty of strategies with me over the years, and the following are a few of my favourites: Slowing the rate of speech, gesturing to visuals throughout lessons, explicitly modelling the use of manipulatives, initiating student-created dual language dictionaries of math terms which multilingual learners can refer to throughout math units, using sentence stems for participation in math discussions, and learning about the diverse algorithms and math experiences students may have, to capitalize on their strengths and celebrate multiple ways of doing math.
The above list only scratches the surface of possible support strategies. To this day, I find myself still on the journey of becoming “fluent” in math approaches for multilingual learners. May we continue to learn from each others’ travels.
Van de Walle, John, et al. Teaching Student Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5. Pearson, 2014, New Jersey.