In teaching, it is essential that the planning of a lesson and the pedagogical methods used during that lesson address the diversity of learning needs represented by the students in the classroom. In the mathematics classroom, it is easy to assume that by teaching the processes involved in solving a particular problem, students will fully understand the concept being taught; however, students, who are considered English learners (EL), continue to struggle with the way the concepts are explained and applied in various settings. It is a misconception to think that mathematics is simply a list of calculations or a study of numbers. Mathematics is the study of the logical order that explains the relations that exist numerically, represented by a language that integrates both mathematical and colloquial vernacular interdependently. The IRIS Center for Training Enhancements expands on the use of mathematical and colloquial vernacular in understanding mathematics, “Math involves more than numbers and includes vocabulary terms such as numerator, quotient, and simplify. Furthermore, words like table and round have meanings in math different from their more common definitions.” In other words, the study of mathematics requires not only a fluency of numbers, but also a fluency of the language used to describe the relationships of those numbers.

To facilitate the learning of mathematics and address the learning needs of ELs, I would integrate a variety of Specifically Designed Academic Instruction in English (SDAIE) strategies throughout each lesson. For example, if I was talking about bisecting an angle, I would start by talking to students about the word “bisect.” I would write the word on the board and ask them if they know of any words that start with “bi-.” This also helps access the students’ background knowledge, allowing them to make connections with their current learning. If students mentioned a word with “bi-” meaning “two,” I would emphasize this on the board. It would even be beneficial to bring in pictures of a bicycle, and other objects representing the concept of “two” with the prefix “bi-.” If students mentioned words like “biology” that start with “bi-,” but not necessarily the “bi-” prefix, I would clarify this and create a graphic organizer to emphasize the difference. I would do the same for the part of the word “sect.” After the students understand that “bisect” means to cut in half, I would begin teaching them the concept of bisecting an angle. In my experience, it has been helpful to explain that bisecting in mathematics means to divide into two equal parts. By teaching students that bisect simply means “cutting into two parts,” they do not understand that the two parts must be identical.

Accessing the students’ background knowledge is another important strategy for addressing the learning needs of ELs, “Background knowledge helps students make connections with new information and helps them understand concepts” (IRIS Center for Training Enhancements). While strategies for accessing background knowledge may be simpler to convey visually through the use of graphic organizers, it is best to take a multimodal approach when possible. For example, when discussing the concept of combining like terms, I would start with a simple activity that every student could relate to. I would place a number of containers at each table, with various items placed in each container. Then, I would divide the class into small groups and instruct them to organize the items. After they completed that, I would begin a discussion where each group could share how they organized their items and their reason for organizing them that way. Using one of their solutions, I would write it on the board and review their steps for organizing the items while introducing some of the new mathematical vernacular. Instead of “organizing,” I would begin using “combining.” After a few demonstrations, I would then lead into the concept of combining like terms.

Another important strategy to include is providing students with a variety of

opportunities to engage other students in discussion of the concept being taught. This will increase the amount of exposure students have using the pertinent mathematical and colloquial vernacular while developing the students mathematical fluency. In particular, “Teachers can support student learning by allowing them multiple opportunities to participate in classroom discussion and by encouraging them to explore and share their own perspectives” (IRIS Center for Training Enhancements). One way to do this is by dividing the students into groups and engaging them in formative assessment tasks. Unlike summative assessments, formative assessments tasks would allow students to share their perspectives and collaborate with each other as they work toward solving a variety of tasks. Throughout the activity, I would circulate from group to group, facilitating the collaboration process.