09.08.11
Teaching Mathematics to English Language Learners
SUMMARY
In the article, “Bridging the Language Barrier in Mathematics,” Matthew S. Winsor (2008) describes how he approached teaching math to a large population of Hispanic ELL students at a Southern California High School from 1995 to 1999. Winsor hypothesized “that the main barrier for [his] students was learning mathematics in their new language” (p. 372). He reviewed research on how people learn a new language and how people learn math and used similarities between the two to develop techniques for teaching his students. In his research, Winsor found that students learn both a new language and math better if they write about their learning, if they collaborate with other students, and if their learning has context and relevance. Winsor then implemented a program called “Mathematics as a Second Language,” or MSL, based on this research (p. 373). He used pretests and posttests to measure student learning and to assess the success of his program.
The writing aspect of his program involved students in vocabulary exercises and journal writing. One successful vocabulary exercise required students to create a Word Square, developed by Quinn and Molloy (as cited in Winsor, 2008), for each new vocabulary word. On index cards, students recorded the new term in their own language and in English, the term’s definition in whatever language they felt most comfortable, and an example of the term either with words or images. In the journal, students wrote about math concepts in their own language except that they had to write the math terms in English.
The collaboration aspect of his program involved students working in groups. Students in each group had varying levels of English proficiency, which required them to interact more and improve their math communication skills. Winsor also moved students around so they could gain new perspectives from students they had not worked with before.
The context and relevance aspect of his program involved projects centered on real-life scenarios such as the stock market or current social concerns. Students also presented their projects to the class.
Winsor evaluated the success of his program using Mary Brenner’s framework (as cited in Winsor, 2008). Did his students’ communication about, in, and with mathematics improve as a result of his program? Winsor concluded that “MSL did seem to promote communication about mathematics …[and] communication in mathematics” (p. 376), however, he thought that MSL was not as successful in improving students’ ability to communicate with math. Using mathematical language as a “tool for everyday life takes time” (p. 377), and there was not enough time to develop this skill in his students.
CRITIQUE
Many people think math is a nonverbal subject and should be easy to teach to ELL students. However, understanding and communicating in math requires words as much as numbers and symbols. The numbers and symbols are merely shorthand for expressing rather sophisticated concepts. Furthermore, the concepts are what make math interesting. The relevance of math to real life requires students to understand the “how” and the “why” behind the computations. This requires words. For example, in a middle school math lesson I developed, I ask students to read graphs of various objects in motion and use words to describe what is happening to the objects. The point of this lesson is to prepare students for one of the biggest ideas in calculus, i.e. things change and we can determine the rate of change at any point. The activity sheet that I developed for this lesson is attached to illustrate how important language is to math.
The National Council of Teachers of Mathematics (NCTM, 2011) also emphasizes communication in math and has outlined communication standards for all instruction from prekindergarten through twelfth grade. These standards state that students should be able to “organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others; analyze and evaluate the mathematical thinking and strategies of others; [and] use the language of mathematics to express mathematical ideas precisely” (NCTM, 2011). The program Winsor developed not only addressed the specific needs of English language learners but also incorporated the NCTM communication standards for all students. The vocabulary exercise, journaling, and real-life projects enabled students to organize and consolidate their thinking. Students had to analyze the math and the vocabulary before, during, and after they wrote about their mathematical thought processes. Winsor also had his students critique and discuss each other’s journal entries, which reinforced vocabulary and led to better understanding and exposure to new perspectives. Finally, the students’ project presentations helped them practice using mathematical language to express their ideas within the context of real-life scenarios.
The implication of Winsor’s research is that his approach would benefit all students, not just ELL students. Richardson, et al (2009) addresses the misconception that “good teaching for native speakers is good teaching for ELLs” (p. 412). While this statement is inaccurate, I believe the converse is true: Good teaching for ELL students is good teaching for native speakers. When it comes to math, native speakers can be as unfamiliar with using mathematical language as ELL students are with using their new language. Therefore, native speakers can only benefit from a curriculum that makes adaptations for ELL students.
Winsor’s article (2008) would benefit all classroom teachers, whether or not they have ELL students. Winsor describes activities that he tried and explains how those activities improved his students’ understanding. Teachers who read this article will learn that “the Word Squares acted as a condensed set of mathematical notes” (p. 374) and that students used the Word Squares in subsequent math classes with different teachers. They will also learn that group work may help more fluent students gain a deeper understanding of math because teaching requires a deeper understanding. Similarly, less fluent students may benefit from reviewing concepts with students who speak their language and who have a fairly good grasp of both English and math. Finally, teachers will learn that bilingual journaling “helped students to associate the English term with the mathematical concept already in their minds in Spanish” and “forced students to decide what they did and did not understand and to put those thoughts on paper” (p. 375). Winsor’s research provides teachers with a few successful activities to try. When trying new things, it is helpful to start with ideas that others have used and found successful.
The article does not provide an exhaustive list of activities, however. The strength of the article is in Winsor’s explanation of how he chose the activities for his program. Winsor’s research on how students learn math and how students learn a new language led him to incorporate writing, collaboration, and real-life problems into his teaching. This research provides a foundation on which classroom teachers can build a program that works for them and their students.
REFERENCES
National Center for Educational Statistics. (2010, November). Kids’ Zone: Create a Graph. Retrieved from http://nces.ed.gov/nceskids/createagraph/default.aspx
National Council of Teachers of Mathematics (NCTM) (2011, June). Communication Standards for Grades 9–12. Retrieved from http://www.nctm.org/standards/content.aspx?id=4004
Richardson, Judy S., Morgan, Raymond F., Fleener, Charlene E. (2009, 2006). Reading to Learn in the Content Areas Seventh Edition, Wadsworth, Cengage Learning. Chapter 11, p. 412.
Winsor, Matthew S. (2007, December / 2008, January). Bridging the Language Barrier in Mathematics. Mathematics Teacher v. 101 no. 5 p. 372-378.
