Teaching Mathematics to English Language Learners

In the United States today, as families from different countries continue to immigrate, many teachers have the privilege of introducing children to the study of mathematics in English within the American school culture. They are faced with interesting challenges since it is doubtful that they speak the children’s first languages and they probably have not been formally educated in the practice and theory of teaching children who are learning to speak English while they are learning everything else.

Why is it a privilege?

There are two fundamental reasons that having English Language Learners (ELL) in a classroom is a boon. First, all the principles of best practice for teaching the ELL student match best practices in the field of mathematics education. While honing lessons to make them accessible to EL Learners, teachers will be improving overall teaching.

Second, most mathematics programs foster respect for the different ways of doing things. One of the central tenets of mathematics reform is that diverse strategies are encouraged, that different ways of understanding a situation are respected, and that divergent thinking is hailed as creative. Having students from another culture in a class enriches and increases diversity, maybe even giving majority culture students a moment to see themselves through the eyes of others.

But teachers are trained to teach math, not to deal with language...

Most math teachers’ formal training revolves around the elementary classroom, or is centered in the specialty of mathematics. Vital background information on teaching English Language Learners is available on the Web, especially through the National Clearinghouse on Bilingual Education (e.g. “Myths and Misconceptions about Second Language Learning: What Every Teacher Needs to Unlearn,” by Barry McLaughlin, 1992, Educational Practice Report: 5, the National Center for Research on Cultural Diversity and Second Language Learning, http://www.ncbe.gwu.edu/miscpubs/ncrcdsll/epr5.htm. Another great resource is “Working with English Language Learners: Strategies for Elementary and Middle School Teachers” by A. Zehler, NCBE Program Information Guide Series, Number 19, Summer 1994, http://www.ncbe.gwu.edu/ncbepubs/pigs/pig19.htm)

Where does NCTM stand?

In July, 1998, NCTM published its position statement on mathematics for second language learners (http://www.nctm.org/about/position_statements/position_statement_06.htm). NCTM states that “Language and cultural background must not be a barrier to full participation (in mathematics education).” Specifically, they recommend that students receive mathematics instruction in both first and second languages, that each student be carefully assessed before curricular decisions are made, and that the teaching and assessment take students’ previous knowledge and cultural experiences into account.

Guidelines for teaching math to ELLs include:

•  Increase your focus on the math language you use

•  Establish a safe classroom culture

•  Know your students

•  Collaborate with your colleagues

•  Expect high-quality thinking from everyone

•  Create a relevant curriculum that requires active participation

•  Take special care to build on informal mathematics insights

•  Assess your students authentically

Increase your focus on the math language you use

When planning lessons, make it a habit to pull out the handful of mathematical terms you will need for the lesson’s activity introduction, demonstration, or invitation to discussion. Check the format of your current lesson planning instrument. Redesign it to give yourself a daily reminder to concentrate on these terms. When conducting the lesson, find a way to define these words in ways that rely more on demonstration than on more language. Incorporate a routine to write these words publicly so that all your students will become more aware of them in another modality. The public list will be invaluable for all the students in the class when they are writing up their discoveries for their math journals.

Increasing your focus on math language can also include thinking carefully about providing opportunities for students to communicate their mathematics understanding. Remember that talking promotes thinking, and active use of new vocabulary is the key to making it real. This principle holds true regardless of the language your students are speaking. As two students are investigating a math problem in their first language, the snippets of English you are most likely to hear are the math vocabulary words you presented for that lesson. As the math content is new, so is the vocabulary. (For more concrete examples, read “Classroom Strategies for Encouraging Collaborative Discussion” by Carmen Simich-Dudgen, Directions in Language and Education, National Clearinghouse for Bilingual Education, No. 12, Summer 1998, http://www.ncbe.gwu.edu/ncbepubs/directions/12.htm.)

When promoting mathematical communication, try to remember that ELL students will not do their best work quickly. Thoughtful, accurate expression is intensely difficult when collecting one’s ideas to present out loud to a large group. Consider creating small groups as well as large ones, and remember to provide some alone time. Writing is an excellent way for ELL students to take more time to search for the proper (perhaps not easily pronounceable) language to crystallize some new thinking. Every student will benefit from this approach.

Remind yourself that effective thinking takes time. Often, the pressure of wanting to cover or “get through” material promotes a “sped-up” classroom discourse, in which “sound bites” are acceptable and students rarely have the opportunity to speak in full sentences, much less in full thoughts. Providing realistic waiting time (some say at least three seconds) improves the quality of students’ responses. Some teachers wait on both ends, giving students time to compose their thoughts and to finish them. “Do you have more to add?” after a brief silence is an invitation to be thoughtful.

Establish a safe classroom culture

It is widely acknowledged that the study of mathematics requires the freedom and safety to take risks. A class in which risks are supported is a safe place. Many teachers have noticed that when they encourage students to take risks, they end up with more creative solutions and, over time, increased tolerance for frustration.

The practice of creating a safe classroom culture for learning mathematics will support English Language Learners, too. When a divergent response is met with a response such as, “Wow, what an interesting way to do that!” students will contribute more readily.

A safe classroom is one in which students are free from ridicule, one in which time and respect are given to people doing serious thinking, and one in which students begin to listen to each other’s way of seeing things with patience and respect.

Know your students

Knowing your students is a goal for all teachers at all times. We are more effective teachers if we know who is having her first successful year in math, who is outstanding at problem solving, and who has a weak rote memory. With students new to our school system, the mandate to know who they are and what their experiences have been is incumbent on us. Some of the English Language Learners who enter our classes have been in formal educational settings their whole lives and bring a wealth of content knowledge and school culture expectations. Others have had little or no formal education and are learning English as they learn the formal counting system and the basic operations. Without a little research, you will not know who is who.

In addition to learning about the depth of your students’ previous schooling, you may also seek to learn about the norms of that culture's schools. What patterns of behavior does this student expect? For example, how is respect communicated from student to teacher in that student’s former classrooms? From teacher to student? Specifically, what is the role of eye contact? In what ways do students ask questions? What is the role of competition? Are students accustomed to working alone? In groups? How are mistakes and imperfections interpreted? As inaccuracies to be tolerated? As clear signs of inadequacy? As strategies that offer insight? How are parents likely to react to the proposition of a parent-teacher conference? What range of behaviors are the parents of this student expecting from teachers?

Don’t forget that the parents and the extended community of your English Language Learners are a rich source of information, support, and networking. They will be the ones to help you understand how the American school culture differs from the one in their previous homeland. This community is the source of math tutors for your students who need continued math support in their first language (as proposed by the NCTM Standards).

Collaborate with your colleagues

There is always much to learn from talking to the other professionals who come into contact with your students. Sometimes it’s the gym teacher, art teacher, band conductor, or coach who has a way of understanding one of your students that puts her in a different light, adding new possibilities to what you may expect. Whether in pull-out or join-in programs, the learning disability specialist often models or describes teaching techniques designed to include as many students as possible. Here, too, the “regular” teacher learns alternative ways to structure detailed lessons and modifications to the curriculum that provide entry levels for students of differing experience and ability.

Teaching English Language Learners brings the English as a Second Language (ESL) specialist into the math teacher’s direct orbit. The ESL professional brings a wealth of techniques and practical advice to the math teacher, from helping design language-focused lessons to conferencing about a particular child. ESL teachers can remind math teachers that oral discrimination of numbers like 14 from 40 is extremely difficult, for example.

While many teachers are already collaborating closely with their building administrators, teaching English Language Learners is supported significantly by this connection. The principals and content specialists of your particular school or district can make changes in programs that best serve newcomers to our schools. For example, an administrator may be able to find and “liberate” the funds necessary to provide regular math instruction in the student’s first language, so that he doesn’t fall behind in content learning while his English facility is “under construction.”

Expect high-quality thinking from everyone

One of the linchpins of the NCTM Principles and Standards is that all students are capable of high-order mathematical thinking and that adequate foundations must be laid in every curriculum, without prejudging who will “need” it. It is essential to remember that thinking is not specific to thinking in English. In fact, it is highly likely that students who have had formal education in another culture will continue to think “internally” in their first language for many years (if not forever), whether or not they can converse easily with their classmates. If we agree that talking promotes thinking, it is incumbent on us to pair students who speak the same language, if possible, so that they may converse, challenge, extend, and develop their mathematical ideas. NCTM believes that “second-language learners should be given appropriate first- and second-language support while learning mathematics.”

All math teachers, with some thought about the points outlined above and below, will be able to provide “appropriate second-language support” for the English Language Learner. But it is be essential to find adults who speak the child’s first language and who understand the mathematics you’re teaching. Sometimes this is relatively easy, as when the ESL teacher speaks the child’s first language and you’re teaching long division, simple graphs, and symmetry. But what about the sixth grader who has just arrived from the former Soviet Union when you are teaching proportions, measures of central tendency, and angle measures in various polygons? You, the ESL teacher, and the principal, with help from the child’s parents, will need to find someone in the community to meet regularly with this student.

Create a relevant curriculum that requires active participation

Constructive learning, in which students get actively involved in making meaning, is at the core of science and mathematics instruction. The teaching of science, with hands-on experiments and a routine of teaching students to observe, think, and write, is an excellent model for mathematics instruction. (See “Teaching Science to English Learners, Grades 4-8” by A. Fatheman, M.E. Quinn, and C. Kessler, NCBE Program Information Guide Series, Number 11, Summer 1992, http://www.ncbe.gwu.edu/ncbepubs/pigs/pig11.htm.) Yes, there are standard practices that are conveyed to students (order of operations, conventions for expressing numerals in base ten, units with which this culture measures, standard symbols and their meaning), but much of what is told to students is meaning that they could put together, or construct, for themselves, given the appropriate lab requirements. (See “Reforming Mathematics Instruction for ESL Literacy Students” by K. Buchanan & M. Helman, NCME Program Information Guide, Number 15, Fall 1993, http://www.ncbe.gwu.edu/ncbepubs/pigs/pig15.htm)

Take special care to build on informal mathematics insights

Children do have informal mathematics insights, regardless of the amount of schooling they have encountered. Make it your business to learn what they have made sense of. Try to incorporate mathematics lessons and daily routines that include “everyday glue.” Listen carefully to see if you can design a mathematics investigation that builds on students’ concerns or interests. These investigations might involve the fairness of games as a way to understand fairness in other contexts, or they may involve plotting pay scales for after-school jobs. A study of symmetry, rotations, and transformations may revolve around the art of the cultures represented in your class.

Assess your students authentically

The term “authentic assessment” is one that implies that you, as the teacher, parent, student, or advocate for one of these, want to know what the student really knows. A paper-and-pencil test, the traditional method of finding out how much someone knows, is but one component of a useful, authentic assessment. All students should be assessed in multiple ways in order to get the clearest, most accurate and helpful picture of the student’s abilities. This might include, but is not limited to, one-to-one interviews; depth, creativity, and thoroughness scores on long-term projects; oral responses in class; portfolios; and daily contributions.

It should be clear that an important element of authentic assessment for English Language Learners is an interview in the student’s first language.