Teaching Math to English Language Learners, by Kanushri Wadhwa

Today, I have the privilege of being in a PhD program and have access to research on how to support English Language Learners (ELL students) in learning mathematics, including how to encourage their participation in the classroom community and development of math identity. However, when I initially began teaching in 2015, I didn’t have any of these resources or knowledge, and struggled to adapt my skills to the benefit of my ELL students. My first year of teaching mathematics at a Massachusetts high school included careful coaching from my alternative teaching program. I incorporated Teach-Like-A-Champion strategies in my lesson plans and scripted them into my directions and feedback every day. In 2016, I approached my second year under the misconception that I would not be met by any striking new challenges. But my beloved school was short-staffed and very under-resourced. I was assigned to teach five Algebra 1 classes, each with thirty students who were all Level 1 ELL. From my first encounter with my students, none of whom could understand what I was saying when speaking English, I realized my folly and how much learning was indubitably before me. 

In 2015, the pass rate of the ELL population at our high school had been a measly 6%. My students faced problems beyond their English and academic language literacy. The majority of them came from Guatemala, a country stripped of its higher schooling because of a civil war that caused schools to close without any alternatives for education. Many of my students, some of them so naturally sharp and intuitive that you would have never known, had only completed between third and sixth grade. On arrival, they were quickly enrolled in high school simply because they were teenagers.  Additionally, there were problems of documentation along with the fact that many of them had migrated without their parents. This meant that they had to care almost entirely for themselves. Julio, who always completed his homework, had an appalling after-school work schedule (for anyone, much less a child) in that he worked from 3pm-3am seven days a week packaging fish.  Schedules like his were all too common amongst my students.

 As I ungracefully learned to communicate with my students and create materials accessible to them, I was blessed that I had the support of fellow teachers, including the other math teacher for ELL students at our school. I also had the encouragement of my students, who helped me edit and preview lesson materials. My teacher colleagues and my students were my partners in building a classroom community and showed me kindness in times of demoralization. With their help, two years later, the 6% pass rate for ELL students had become 38%. Every day, I think to myself what those numbers mean to me and how I intend for them to continue to change. 

Now, my PhD program allows me to research how to effectively teach mathematics to ELL students, and to pass that knowledge on to other teachers. Specifically, how to make sure ELL students participate in mathematical discussion and high-level thought. 

Positioning ELL Students as Mathematically Competent

            Positioning is one of the ways that teachers can make sure that students understand themselves to be both bringers and developers of knowledge in mathematical communities. Studies have found that while European- and Asian-background students often get positioned as mathematically competent, ELL students of other backgrounds often get cast in marginal roles within the classroom. In my first year of teaching in a general classroom, I had a student, Ashley, who was in the process of developing her English proficiency. While her classmates got called on to problem solve, I called on Ashley to support her English learning by having her practice reading aloud or answer definitional questions. Although my pattern of calling on Ashley was an attempt to be kind, this meant I gave her no positive messages about her ability to be part of our mathematical conversations. I know now that she could have been a part of these conversations if she had been given opportunities to express herself with gestures, drawings, or by telling a classmate to translate Ashley’s thoughts. On top of this, my other students bore witness to how I positioned Ashley and probably mirrored me in casting her in a marginal participant role. 

After working for two years with an entire class of ELL students, I did become fluent in Spanish, the home language of many of my students. I could translate for certain students to make sure that their mathematical ideas are brought to the class’s attention in whole-group discussion. But even if a teacher isn’t fluent in each of their students’ native languages, it’s imperative that any available communicative resources, such as students who can translate, are used to make sure ELL students aren’t cast aside. It’s also not necessary for students come to entirely correct responses before engaging them with mathematical discussions. For example, I could have used any of Ashley’s mathematical understanding of the problem to make sure that Ashley herself, her classmates, and I were understanding and recognizing her mathematically valid thoughts.

Within the population of ELL students, there is a great variety in needs. And students, regardless of what these needs may be, should be given full opportunity to participate. One my students, Clayda, was from Cape Verde. She was very bright and also completely blind. There had been no school for her in Cape Verde, but this did not seem to affect her abilities much. When the class was observing the work of other students, Clayda’s work (completed with an aide) was often brought forward for others to view. But if I were to do it again, I would have made sure Clayda gained comfort with verbally explaining her own ideas to the class, thereby positioning her as having mathematical authority. 

Awareness of Students’ Strategies

            Cognitively Guided Instruction (CGI) research and other math education research shows that students of all levels and abilities use different strategies to negotiate their understanding of mathematical concepts and to problem solve. Research has also shown that even if these students are using imprecise language, teachers should not stop student thinking to correct this imprecise language or require that students use precise language when speaking to the whole group. Students need to be supported to learn the precise mathematical language but lack of such knowledge does not indicate a lack of understanding.

            In the case of any student, but especially ELL students, mathematical thought may not be fully expressed using linguistic resources like speaking or writing. These students often use other resources like gesture, pictorial representation or graphical display to show their thinking, and this should not be discouraged. Teachers can model these other resources to show the entire classroom that these are legitimate ways of expressing mathematical ideas. For example, a teacher can validate students’ use of gesture by building on their gestures with her own gestures as they engage in dialogue. In my classroom, one of my students was trying to explain how he knew that the slope of a graph was positive. He held his arm slanted like the graph and used his fingers on his other arm to walk up the slanted arm, indicating a positive slope. After seeing him do this, I began to use the same gestures to show both positive or negative slope, thereby being able to participate in mathematical discussion and build upon their verbal explanations. This validation of communication strategies further empowers students in developing a positive active math identity. 

Revoicing, Questioning, and Teacher Talk

            Teachers can use different methods of revoicing, questioning, and purposeful talk to positively position ELL students and increase awareness of students’ strategies. Revoicing what students say can draw attention to the important parts of their mathematical explanation through repetition or elaboration. Furthermore, it can also allow teachers to model how to convert what students are thinking into formal language. Much of what I have written about thus far has had to do with not being so beholden to traditional modes of explanation, but we do know that formal language is necessary for students to build their skills and understanding in a second language. In revoicing mathematical thought using formal language, teachers need to make sure that they are not making students feel that their original thoughts are invalid because their teachers are changing the way they are expressed. 

            The kinds of questions teachers pose to students can also convey to those students how teachers gauge their abilities and thereby position them in the class. Some teachers have spoken about the necessity of rephrasing questions in multiple ways to simplify them so students can understand. But it is equally, if not more important, that teachers consider the quality of the questions they are posing. Closed-ended display questions where students perform less involved tasks do not position students as capable mathematicians in the same way as open-ended questions that engage their mathematical thinking

            There is growing research as to what educators can do to incentivize ELL students to participate in as much mathematical thinking and exploration as their English-speaking peers. I am greatly excited to see what my teacher colleagues do in the future to ensure ELL students see themselves as capable problem-solvers in any high-level thinking environment. Having resources for competency in two or more languages will allow ELL students to see themselves as confident mathematical thinkers.

This blog post was supported in part by the U.S. Department of Education, through grant award number U423A180115 to Florida State University. The opinions expressed are those of the authors and do not represent views of the U.S. Department of Education.

Edited by Hallei Halter