By Marjan Hong, posted January 04, 2017 —

Consider for a moment the following scenario: A new student joins your class toward the end of February. To complicate matters, this fifteen-year-old girl speaks no English beyond yes, no, and house; and you have no idea what her mathematical background might be. What do you do? 

In Principles to Action: Ensuring Mathematical Success for All (NCTM 2000), teachers are challenged to take action in the area of access and equity by developing “socially, emotionally, and academically safe environments for mathematics teaching and learning—environments in which students feel safe to engage with one another and with teachers”(p. 115). This applies to all students, including students who don’t speak English, students with learning differences, students from diverse socio-economic backgrounds, and students whose life experiences we can’t begin to understand. 

An English language learner (ELL) meets new language and new learningat the same time. When it comes to English language acquisition, James Cummins differentiates between basic interpersonal communication skills (BICS) and cognitive academic language proficiency (CALP). BICS—the language between peers, the day-to-day language of engaging socially—are developed rather quickly at an average rate of six months to a year. Unfortunately, BICS are not the skills that enable students to be successful in school. Here, success depends on the development of CALP. CALP is more complex, and its development is much slower, with average acquisition rates between five and ten years. In addition to learning new vocabulary, academic language skills include many of the educational goals listed in Blooms’ taxonomy, such as comparing and making connections, analyzing, inferring, evaluating, and synthesizing.

Structured inquiry tasks, such as Jamie’s task proposed in my previous blog, provide opportunity for English language learners to purposefully engage with academic language. For a given task, students might use both academic and nonacademic language as they dig in and try to interpret the task at hand. This could include a restatement of the problem, clarification of the vocabulary involved, or peer discussion of previously learned concepts that are central to the task at hand. 

One central component of inquiry-based instruction is questioning strategies. In his book Teaching for Excellence, Spence Rogers devotes an entire chapter to effective questioning techniques. One such question is, “What did you hear somebody say?” This is an empowering question for English language learners. An ELL at the beginning of language acquisition mimics and processes the result. This student may have background knowledge of the mathematics that is being explored but not the academic language necessary to communicate the understanding. This type of question promotes active listening, but it also provides the critical academic language the student can mimic and process. 

Another key take-away from this chapter is what I refer to as the power of might. Consider the differences in the possible structures of the question for Jamie’s task:

•           What does Jaime’s “less complicated” expression look like?

•           What might Jaime’s “less complicated” expression look like?

In the first version of the question, there is an implied correct answer, which is intimidating to some students. Moreover, it kills discussion much like yes/no questions. You either come up with the expression, or you don’t. The second version of the question allows for a variety of answers, providing opportunities for clarifying questions, justification, revision, and more. The simple substitution of the word might opens up the task and invites all students in. 

This brings me back to the question posed at the beginning of the blog: A new student joins your class toward the end of February. To complicate matters, this 15-year-old girl speaks no English and you have no idea what her mathematical background might be. What do you do? How might you respond?

When faced with this situation, my math teacher stood in front of our class, wrote a question on the board, and prompted students to work in small groups. He then came to my desk, crouched down, and started to draw. My first CALP words in math class that day were rectangle, area, and perimeter. The next day, I worked with two other students on problems involving area and perimeter of rectangles.

Marjan Hong, [email protected], has worked in mathematics education for nearly thirty years as a teacher, mentor, curriculum specialist, and consultant. She is currently curriculum content developer for Discovery Education. Her passions include access and equity in mathematics education, empowering teachers, and inquiry-based learning.