Volume 20, Number 6

November/December 2004

# “The Language Game of Math”

Approach draws on language arts methods to help English-language learners solve math problems

In September 2003, nine-year-old Marisol Rivera hesitantly entered Mary Wright's third-grade classroom at Sullivan Elementary School in Holyoke, Massachusetts. Mary's first impression was of a quiet, thoughtful girl who seemed tentative and unsure of herself, particularly when it came to math. Early on, Marisol told Mary that she "hated math," and Mary noticed that during math Marisol often hid behind other students and avoided eye contact, which made it hard to determine how much she understood.

Since moving to Holyoke from Puerto Rico three years earlier, Marisol had attended classes where she received some support in her native Spanish, while also getting assistance in learning English as a second language. Marisol had repeated second grade and had received assistance from the special education team for "processing problems in language arts and math."

With this background information, Mary reflected on Marisol's participation in her class, but she wasn't sure what the problem was: Was it English? Was it math? Was it something else? What Mary was certain about was the need to rethink the way she was teaching the English-language learners (ELLs) in her class, especially the way she was teaching math.

This need was even more pressing given two major shifts in education policy at the federal and state levels that began in 2002. In January, President Bush signed the federal No Child Left Behind Act, and the following November, voters passed anti-bilingual education legislation in Massachusetts. With these changes, Mary and her students were being held accountable—sometimes publicly in local and major newspapers—for meeting new state and federal standards in a language of instruction that many students were still in the process of acquiring.

Mary's third-grade class had 25 students, two-thirds of whom were Latino and almost half of whom were learning English as a second language. Teaching this class was one of the greatest challenges of her career because of the range of experiences and abilities of her students. She had ELLs whose prior schooling experiences in Puerto Rico had equipped them to speed through skill-based worksheets quickly and accurately, but who had trouble approaching the district's required math curriculum. This curriculum centered on teaching mathematical problem-solving rather than computational speed and accuracy. She had other students who were fluent English speakers. These students had experience with more process-oriented approaches to learning math, but really didn't have either the skill or conceptual base they needed to approach some of the tasks Mary was required to assign.

Mary describes the math hour as the time of the day when "it all came out." She says, "If someone is having a bad day, it'll show up in math. I know I'm going to get more bathroom requests, more fights, and more tears than any other time of the day." This level of anxiety was not limited to students but extended to teachers and administrators because of an ongoing investigation by the state. (The state Department of Education was considering taking over the district in the wake of scores on the Massachusetts Comprehensive Assessment System, or MCAS, the state's standardized testing program.)

Collectively, these classroom, district, and state-level pressures led Mary to focus on how to teach the language and content of this new math curriculum. In a journal entry, Mary wrote:

In conducting an analysis of the language of math, Mary identified a task called "show your thinking." This was a multistep task that required students to (a) read a mathematical word problem; (b) draw a picture representing the elements of the problem; (c) describe in narrative form how they would solve the problem; (d) write a corresponding mathematical formula; and (e) solve the equation correctly. Testing proved that the skills associated with this task were especially important for Mary's students: almost all of the ELLs in her school had either skipped this open-ended section of the fourth-grade math MCAS or thought it was a multiple-choice question and responded accordingly.

Since moving to Holyoke from Puerto Rico three years earlier, Marisol had attended classes where she received some support in her native Spanish, while also getting assistance in learning English as a second language. Marisol had repeated second grade and had received assistance from the special education team for "processing problems in language arts and math."

With this background information, Mary reflected on Marisol's participation in her class, but she wasn't sure what the problem was: Was it English? Was it math? Was it something else? What Mary was certain about was the need to rethink the way she was teaching the English-language learners (ELLs) in her class, especially the way she was teaching math.

This need was even more pressing given two major shifts in education policy at the federal and state levels that began in 2002. In January, President Bush signed the federal No Child Left Behind Act, and the following November, voters passed anti-bilingual education legislation in Massachusetts. With these changes, Mary and her students were being held accountable—sometimes publicly in local and major newspapers—for meeting new state and federal standards in a language of instruction that many students were still in the process of acquiring.

"It All Came Out" During Math"It All Came Out" During Math

Mary's third-grade class had 25 students, two-thirds of whom were Latino and almost half of whom were learning English as a second language. Teaching this class was one of the greatest challenges of her career because of the range of experiences and abilities of her students. She had ELLs whose prior schooling experiences in Puerto Rico had equipped them to speed through skill-based worksheets quickly and accurately, but who had trouble approaching the district's required math curriculum. This curriculum centered on teaching mathematical problem-solving rather than computational speed and accuracy. She had other students who were fluent English speakers. These students had experience with more process-oriented approaches to learning math, but really didn't have either the skill or conceptual base they needed to approach some of the tasks Mary was required to assign.

Mary describes the math hour as the time of the day when "it all came out." She says, "If someone is having a bad day, it'll show up in math. I know I'm going to get more bathroom requests, more fights, and more tears than any other time of the day." This level of anxiety was not limited to students but extended to teachers and administrators because of an ongoing investigation by the state. (The state Department of Education was considering taking over the district in the wake of scores on the Massachusetts Comprehensive Assessment System, or MCAS, the state's standardized testing program.)

Collectively, these classroom, district, and state-level pressures led Mary to focus on how to teach the language and content of this new math curriculum. In a journal entry, Mary wrote:

I have begun to take advantage of students' normal curiosity about the MCAS test. . . . They know they have to take this test every year until 10th grade, and that their ability to graduate from high school depends on this test. . . . I keep telling them they are all very capable and they will pass the test . . . [but] I have to start teaching them about the types of open-ended word problems they are going to get—how to spot them and how to respond to them. We have started calling this a game, the language game of math. Third graders love games and can relate to the idea that if you know the rules, you can win.I have begun to take advantage of students' normal curiosity about the MCAS test. . . . They know they have to take this test every year until 10th grade, and that their ability to graduate from high school depends on this test. . . . I keep telling them they are all very capable and they will pass the test . . . [but] I have to start teaching them about the types of open-ended word problems they are going to get—how to spot them and how to respond to them. We have started calling this a game, the language game of math. Third graders love games and can relate to the idea that if you know the rules, you can win.

In conducting an analysis of the language of math, Mary identified a task called "show your thinking." This was a multistep task that required students to (a) read a mathematical word problem; (b) draw a picture representing the elements of the problem; (c) describe in narrative form how they would solve the problem; (d) write a corresponding mathematical formula; and (e) solve the equation correctly. Testing proved that the skills associated with this task were especially important for Mary's students: almost all of the ELLs in her school had either skipped this open-ended section of the fourth-grade math MCAS or thought it was a multiple-choice question and responded accordingly.

**Using Language Arts Methods to Teach Math**

Mary soon realized that her students' math performance depended not just on arithmetic skills, but also on their language development. She thus began to apply language arts methods to teaching a content area that she had previously associated only with numbers and symbols. Beginning in the fall of 2003, Mary instituted the following changes in her math program.

**Grouping students heterogeneously by language and math ability**. This allowed Mary to focus on each student's strengths (in language, mathematics, or both) and to encourage the children to share expertise and support each other in learning both mathematical concepts and the language of math.

**Using oral language to support reading and writing**. Mary encouraged students to "talk and draw" their way through complex math problems, using their home language, before they started to write their answers on paper.

**Modeling and providing explicit instruction in language**. Mary helped students to recognize specific action words and phrases that are important to tackling open-ended math problems successfully (e.g., "label," "number," "describe," "explain," "list," "draw," and "give evidence") and to use these terms to approach and solve their "show your thinking" problems.

**Creating a math "word wall."**Students kept an inventory of important math words (e.g., "numerator," "denominator," "digit") and words and phrases that signaled different kinds of mathematical operations (e.g., "sum," "divided by," and "divided into") and posted these words on a math "word wall" to use as a resource when they were working independently.

**Using the writing process**. Mary asked students to draft and revise their math work following the same processes they used in their language arts activities: sharing drafts; responding to each others' ideas using guides, graphic organizers, and various worksheets; making revisions; and proofreading their work.

**Marisol: A Case Study**

Marisol's efforts illustrate the changes that occurred in Mary's class after she started implementing language-arts-based approaches to the teaching of math.

Marisol wrote the first sample in September. For this assignment, she was asked to illustrate her understanding of the commutative property of addition (i.e., to explain why it didn't matter in what order she added the numbers in a list). In analyzing Marisol's work, Mary observed:

*Marisol showed no strategies for how she combined the numbers. . . . She did not show or label which numbers she combined to tell how she found the totals. She did not use any of the math vocabulary we talked about. She did, however, make a good attempt to describe what she noticed. She used the words "all around" to explain that the numbers were in mixed-up order. She also tried to let me know that no matter what order the numbers were in, the sum would be the same ("they anyway the disam number 40").*

In an assessment in the middle of the year, Marisol was asked to read a math problem in which she had to divide 36 butterflies evenly into two separate rooms in a "butterfly house." She was to show how she had solved the problem in graphic form, then explain her approach to the problem in a narrative. In response to Marisol's midyear work, Mary noted:

*Marisol has begun to organize her thoughts in expected ways. Through her use of "first," "then," and "finally," she seems able to put her actions in order. . . . She can explain that she counted by 4s. I wish that she had explained to me how she knew to put 18 butterflies in each box. . . . Her progress is slow, but she is showing some of the features I had hoped for.*

Finally, in a sample collected at the end of the year, Mary asked students to make up their own word problems and to solve them using the procedures and language practices they had been working on all year. In response to this sample, Mary wrote:

*What kind of an impact has all of this teaching had on Marisol, my self-proclaimed hater of math? Last week I gave out math papers for homework. I asked the students to make up their own division story problems, illustrate them, and write a math equation representing their word problem. . . . Marisol came up to my table at dismissal and asked for a bunch of extra papers so she could make up extra math division stories for homework.*

This analysis of Marisol's math work and Mary's journal entries over the 2003-2004 academic year show how changes in instructional practices supported this student in "owning the language of math" and in shifting from a self-proclaimed "hater" of math to being the kind of student who asks for extra math homework. It also attests to how breaking disciplinary barriers can enhance learning not just for ELLs, but for all students.

The ACCELA Alliance (Access to Critical Content and English-Language Acquisition) is a school-based teacher-education program in western Massachusetts. A federally funded partnership between the University of Massachusetts Amherst, three area school districts, and the diverse communities of western Massachusetts, the alliance's purpose is to help teachers develop the knowledge base and strategies necessary to meet the needs of linguistically and culturally diverse students in urban schools.

Meg Gebhard is codirector of the ACCELA Alliance. During the 2003-2004 school year, she taught a course in second-language acquisition and academic literacy development in which Mary Wright was a student. The research on which this article is based was jointly conducted under Gebhard's direction by Wright and Andrew Habana Hafner, a former classroom teacher and doctoral student at the University of Massachusetts Amherst.

*A longer version of this article appears in the new book*Teaching Immigrant and Second-Language Students: Strategies for Success*, edited by*HEL*editor Michael Sadowski and published by the*Harvard Education Press*.***The ACCELA Alliance**The ACCELA Alliance (Access to Critical Content and English-Language Acquisition) is a school-based teacher-education program in western Massachusetts. A federally funded partnership between the University of Massachusetts Amherst, three area school districts, and the diverse communities of western Massachusetts, the alliance's purpose is to help teachers develop the knowledge base and strategies necessary to meet the needs of linguistically and culturally diverse students in urban schools.

Meg Gebhard is codirector of the ACCELA Alliance. During the 2003-2004 school year, she taught a course in second-language acquisition and academic literacy development in which Mary Wright was a student. The research on which this article is based was jointly conducted under Gebhard's direction by Wright and Andrew Habana Hafner, a former classroom teacher and doctoral student at the University of Massachusetts Amherst.