culturally and linguistically diverse...

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Chapter1. . . . . . . . . . . . . . . . . .

Culturally and

Linguistically Diverse Learners

A few years ago I was working with teachers in an elementary school.

The first time I observed a particular class of fourth-grade students I noticed

Maria and Sara, neatly dressed and sitting next to each other. They were very

diligent about doing their work and trying to work with others in spite of their

inability to speak or understand much English. Still, it wasn’t the fact that

they spoke no English that caught my attention. After all, there were nearly

twenty languages represented by the students who attended this school. No,

it was that each girl seemed to be at least thirteen or fourteen years old. Their

teacher told me that these girls were from Bosnia and had not attended any

formal school for more than four years. Eventually, they joined classes with

other students who were the same age. This age gap was becoming common-

place for the school district and continues to as families move to America from

Eastern Europe, Somalia, the Sudan, and other places where civil unrest has

interrupted the social fabric. World events seem to dictate that there will be

even more students like Maria and Sara in our classes in the years to come.

Johnson Rev Ch1-2.indd 1 10/27/08 2:44:03 PM

� Teaching Mathematics to Culturally and Linguistically Diverse Learners

Growing Diversity in the Student Population

Our schools are becoming increasingly more diverse. Figure 1.1 shows the explosive growth in public schools of students who speak English as a second language (ESL) compared to the general school population in the United States.

Immigration in the United States from 2000–2006 was the highest for any seven-year period in American history, with more than 10.3 million new arriv-als (Preston, 2007). The most recent estimates (2004) by the U.S. Department of Education suggest there are 5.5 million students in American schools who have limited English language proficiency. More such students will be enter-ing school soon. According to the U.S. Census, 45 percent of all children under five are minorities (U.S. Census Bureau, 2006). Census data show that diversity across the country is increasing. In 318 counties (more than 10 per-cent of the nation), the population of non-white residents is more than 50 per-cent, with another 205 counties showing more than 40 percent of non-white residents (El Nasser & Heath, 2007). In California, Arizona, Mississippi, Louisiana, and New Mexico, a majority of students speak a language other than English as a first language (Education Statistics Quarterly, 2005).

Our traditional view of the United States as a melting pot is partly based on schooling immigrant children, preparing them to achieve success and to assimi-late into our society. Latino children have been in the classrooms of border

states with Mexico for many years. The north-ern New England states experienced an influx of French Canadian families in the first decades of the twentieth century. In 1942, the Bracero Program that brought four million immigrant workers from Mexico also brought some of their children. Decades earlier, Mexican migrant work-ers and their families worked and lived in several states, including California, Colorado, and Texas. Today, the impact of CLD students in the class-room is being felt across the entire country.

The U.S. Census Bureau found that as recently as twenty years ago, 75 to 80 percent of immi-grants settled in one of half a dozen gateway states, such as California and New York, and tended to stay there (Lyman, 2006). That is no longer true. The Pew Hispanic Center found that since 2000, only 58 percent of immigrants have settled in the traditional gateway states (Lyman, 2006).

Figure 1.1

Growth in ESL School Population vs. Growth in General School Population, �990–�00�


Culturally and Linguistically Diverse Learners �

Consider what is already happening around the United States. Lewiston, Maine, has seen an influx of CLD students and their families in the last few years. Des Moines, Iowa, now has a sizeable Latino population. In the past ten years, the Latino population of New Hampshire has increased by more than 125 per-cent (Wang, 2004). The number of CLD students in Idaho schools has grown 27 percent from 2000 to 2004 (Idaho State Department of Education, 2005). In the southeastern United States, the number of English language learners in the public schools grew more than 400 percent from 1993–1994 to 2003–2004 (Goldenberg, 2005). According to Audrey Singer of the Bookings Institute, “What’s happening now is that immigrants are showing up in many more communities all across the country than they have ever been in” (Lyman, 2006). As the trend for the families of CLD learners to move away from gateway states and urban areas continues, the result will be an increasingly diverse student population across the entire country.

Some educators hold out hope that as families settle in the United States, the children born here will learn to speak English as preschoolers and will not present the same challenges in school as English language learners do. However, as Figure 1.2 shows, the majority of English language learners in public schools in the United States are born in the United States (Zehr, 2007a). So, it would appear that children born to immigrants in the United States might need the same attention as children born in a different country.

Figure 1.2

Background of English Language Learners in U.S. Public Schools



The richness of language diversity in the United States can be seen by one estimation that there are more than 460 language groups represented by students in the public schools (Kindler, 2002). Some individual schools house student populations that speak fifty to sixty different native languages at home. Most of these students will be schooled in English-speaking classrooms.

In 1997, Proposition 227 was approved by voters in California, essen-tially eliminating California’s bilingual programs. Similar legislation a few years later in Massachusetts had the same result. There are ongoing efforts to implement the same changes in bilingual programs in other states. One conse-quence of these changes is that students who used to stay in native-language classrooms until they had developed proficient English skills are now placed in English-only classrooms almost immediately upon registering in a school district. Thus, not only is the number of students who do not speak English at home increasing, but the number of these students who will be placed in English-only classrooms is also increasing. This means that it will be a rare teacher who does not have CLD learners in the classroom.

The Need for Equity in the Classroom

In Principles and Standards for School Mathematics (2000), the National Council of Teachers of Mathematics (NCTM) lists equity as the first of six overarching principles for school mathematics. “Excellence in mathemat-ics education requires equity. . . . Equity is a core element of [our] vision” (NCTM, 2000). A key aspect of the Equity Principle is that “All students should have access to an excellent and equitable mathematics program that provides solid support for their learning and is responsive to their prior knowledge, intellectual strengths, and personal interests” (NCTM, 2000).

In a recent Position Paper, NCTM expanded the Equity Principle as follows:

Excellence in mathematics education rests on equity—high expectations, respect, understanding, and strong support for all students. Policies, practices, attitudes, and beliefs related to mathematics teaching and learning must be assessed continually to ensure that all students have equal access to resources with the greatest potential to promote learning. A culture of equality maxi-mizes the learning potential of all students.

Community members respect one another and value others’ contributions.

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Schools accept all experiences, beliefs, and ways of knowing mathematics.

Students and teachers have access to all necessary resources for opti-mal learning and personal growth.

High expectations, culturally relevant practices, attitudes that are free of bias, and unprejudiced beliefs expand and maximize the potential for learning.

All students have access to and engage in challenging, rigorous, and meaningful mathematics experiences. (NCTM, 2008)

NCTM has taken a leadership role in the mathematics education of CLD stu-dents and will continue to do so as more and more students require teachers’ attention and efforts to reach their full mathematics potential.

The Culturally and Linguistically Diverse Student in the Classroom

Culturally and linguistically diverse (CLD) students can display a wide range of English proficiency. Perhaps one student speaks no English, has a poor mastery of his native tongue, and can barely read. Another student reads and writes his native language very well but speaks little or no English. Still another CLD student is fluent in her native language and can carry on a sophisticated conversation in English with her English-speaking peers. Thus, the designation CLD student can refer to a broad range of students who can fall at any place along the continuum of English proficiency shown in Figure 1.3. Regardless of where students fall along this continuum, they require attention if they are to reach their full mathematics potential.

One point to clearly understand about CLD learners is that no matter how long they reside in the United States, and no matter how accomplished their English speaking becomes, they still have their native language as a resource.

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Figure 1.3

Continuum of CLD Learners’ Proficiency in English



Individuals who live in a foreign country for many years and who can speak the language of that country fluently will sometimes think and reason to themselves in their native language, and other times reason in the language of the foreign country. In the case of mathematics, a typical CLD student may be doing mathematics in two different languages, possibly at the same time. This can be illustrated in the case of a Turkish mathematics student who processed mathematics in three languages. He attended a local elementary school in Turkey. He studied mathematics at a German technical high school, and then came to the United States for his college education. As a result, he did elementary mathematics, such as counting, in Turkish, solved his algebra equations in German, and worked on his calculus problems in English!

This may also apply to CLD learners who have studied mathematics in their native land. They may frame the mathematics they learned before com-ing to the United States in their native language, while they are learning and conceptualizing the mathematics they study in the United States in English. Furthermore, many CLD students will use their native language to transfer knowledge to English, and the more academic schooling students have in their native language, the better able they are to make this transfer. However, if CLD students have never learned academic content in their native language, then they will likely frame all their mathematics in the academic voice of English. Nevertheless, few CLD learners will completely abandon their native language. A key consideration for teaching CLD students is the time they need to acquire proficiency in English.

Time Needed for English Language AcquisitionIt is self-evident that the more time CLD learners spend in an English-speaking class, the better they will be able to speak, read, and write English. Their progress is not linear, however, and CLD learners who have spent two years in English-speaking classrooms are not necessarily twice as adept at communicat-ing in English as students who have spent only one year in English-speaking mathematics classes. Table 1.1 can serve as a framework for this discussion. (See www.doe.state.in.us/lmmp for a similar table from the Indiana Department of Education.)

You can observe that the longer CLD students spend in English-speaking classrooms and communities, the greater their English language acquisition. As the table clearly shows, however, CLD learners require a minimum of five to seven years in English-speaking classrooms before they are able to read and communicate effectively at grade level. For most of the first year, CLD learners will be capable of only extremely limited communication skills, both in understanding and in expressing themselves. It is only after about



two to three years in the classroom that CLD learners can begin to ask perti-nent questions, explain mathematics relationships, and follow the oral (and written) arguments of their teachers and their peers in class discussions and during class dialogues. At this stage CLD learners can begin to hold their own in mathematics discussions and “arguments.” (For more detail, see Teaching Strategies that Match English Acquisition Levels in Chapter 3.)

It may be possible to accelerate CLD learners’ ability to engage in mean-ingful mathematics discourse in a classroom. Fuson and Murata (2007) report their findings using the Clear Learning Path Model approach in middle school mathematics classes. They explain that in the program “all students are expected to learn how to explain their thinking in English, and with

Stages of Language Acquisition Classroom Behavior of CLD Learners

Silent Stageup to 500 words6 months to 1 year

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point to objects or pictures; act, nod, or use gesturesrespond yes or norepeat what is spoken, speak hesitantly

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Pre-Emerging Fluency Stageup to 1,000 receptive/active words6 months to 1 year

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speak one- or two-word phrasesuse short language chunksfocus on key words in context

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Emerging Fluency Stageup to 3,000 active words1–2 years

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engage in simple dialoguerespond with simple phrasesinitiate short conversations

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Intermediate Fluency Stageup to 6,000 active words2–3 years

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employ more complex statementsexpress opinions/share original thoughtsask pertinent questionsengage in more lengthy conversations

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Advanced Fluency Stagemastery of specific content-area vocabulary5–7 years

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converse fluentlyunderstand grade-level classroom activitiesargue and defend academic pointscomprehend grade-level textbooksdiscuss academic topics on grade level

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Source: Haynes (2000), Collier (1995), Cummins (1992)

Table 1.1

Time Required for Language Acquisition



considerable modeling, they learned to do so.” As a result, students in the Clear Learning Path Program were able to explain math concepts at a much higher level of English than they could address any other academic subject. Thus, with a focused effort, it may be possible for CLD learners to become fully engaged in mathematics discussions in advance of the years indicated in Table 1.1 (Fuson & Murata, 2007).

The information in Table 1.1 assumes that the time required to achieve the various levels of language acquisition represents consecutive years spent in an English-speaking environment. In many instances CLD students return to their native lands for a vacation or family trip that sometimes lasts several months. During such trips CLD students speak English infrequently, if at all. Thus, the years shown in the chart may need to be extended if students spend a lot of time in their native land.

There are additional factors that affect the time CLD learners require to master English. For example, individual student propensity for language learning, native-language proficiency, motivation, formal schooling, and fam-ily support can all influence the time needed for a CLD student to become English proficient.

One factor to note is that conversational English is not the English of the classroom, and certainly not the English of a mathematics classroom. One study determined that classroom, or academic English, trailed conversational English by three to five years (Cummins, 1992). That means that the student who can talk socially in the school corridors might not be as able to follow what is hap-pening in the classroom for several years. Another consideration is that the English demanded in mathematics class is at a high level. One linguist estimated that the English level of a successful elementary school student in mathematics must be two years in advance of the mathematics grade (Cantieni & Tremblay, 1979). In other words, a student in third grade must read at a fifth-grade level to fully comprehend the mathematics materials presented in grade-level textbooks.

The issue of what English a student has mastered is a critical one. Social language, sometimes referred to as Basic Interpersonal Communication Skills, refers to everyday social conversations, the face-to-face conversations that everyone has. Such a language is context imbedded. The beginning of the conversation establishes the context, and further conversation is grounded in that context. Students discussing a football game may use vocabulary words such as bomb, blitz, and fly pattern, which would be confusing or unintel-ligible to a CLD learner. In addition, there are visual cues that convey the message to all students in such conversational settings. In contrast is aca-demic language, sometimes referred to as Cognitive Academic Language


Culturally and Linguistically Diverse Learners 9

Proficiency (Cummins, 1992). This is the language of the academic classroom that focuses on concepts and relationships. It is abstract, specialized, and content reduced. CLD students need more time to master cognitive academic language than to master the English of the corridors and the cafeteria.

Another aspect of English acquisition to consider is that CLD learners are really playing catch-up, but they are trying to hit a moving target. It is important to note that many English-speaking students enter kindergarten with a working knowledge of about 20,000 words in English. Some entering CLD students may have a vocabulary list that is around only 3,000 English words (Cavanaugh, 2004), meaning that they are behind from the start of their schooling. Moreover, as CLD learners improve their English proficiency, English-speaking classmates are also improving their mastery of English. So, to truly catch up, CLD learners must improve their English skills at a faster rate than their English-speaking peers. In order to catch up with grade norms in six years, CLD learners have to make fifteen months’ gain every ten months of school, compared with an English-speaking student’s ten months’ gain in a ten-month school year (Collier & Thomas, 1989). This is a difficult challenge, but one that CLD students can meet.

The Role of CLD Students’ Age in English Language AcquisitionBesides the length of time CLD students spend in English-speaking class-rooms, their age is important. Generally, older CLD learners (grades 6–12) have certain advantages over their younger counterparts. They can rely on gen-eral cognitive learning strategies they have developed, especially if they have a solid foundation in their native language. Students who have a reasonable command of their native language are more efficient at acquiring proficiency in a new language (Collier & Thomas, 1989). Once students can read in their native language, they can apply the similar constructs to reading in English (August & Shanahan, 2006). Likewise, CLD learners may not have to learn basic concepts of mathematics operations or geometric relationships because they learned them in their native schools. In addition, older students are not as likely to have as much difficulty organizing their thoughts about mathematics in their native language, and so they are better able to recast these thoughts into English. Finally, older students do not face the prospect of learning their own language at the same time they are learning the languages of English and mathematics, a three-fold challenge that younger students may face (Cummins, 1998; Collier, 1987; Fillmore, 1985; Krashen, 1982; Scarcella & Higa, 1982).


�0 Teaching Mathematics to Culturally and Linguistically Diverse Learners

In some cases, younger students (grades 1–5) could have an advantage. One research finding compared students of different ages with the same level of language proficiency. In this instance the lower-grade students advanced their language proficiency at a faster rate than their older counterparts (Cook et al., 2008). There are many possible reasons for this. Some younger students may not be as self-conscious about learning a new language and making all the grammatical and vocabulary errors that anyone new to a language makes. Younger children can imitate and adapt to native pronunciation more easily than can older students who have been accustomed to making only the sounds of their native language (Lightbown & Spada, 1998). Further, some younger students may be less inhibited than older students (grades 6–12) in front of a group. (Adolescents are notorious for discomfort in front of a group.) Finally, younger students may not have native customs, traditions, and routines as embedded as older students, and so will be able to focus more intently on the academic challenges in school rather than on social challenges.

The dichotomy of considering all CLD learners as younger or older ignores the special attention that students in middle grades require. Middle school is where students are trying to forge their identity; it is the age when students begin to formulate the likes and dislikes that will last into young adulthood and beyond. In addition, they are maturing physically—some too slowly, some too quickly. For CLD learners, all this happens while they are learning a new language and culture. Clearly CLD students in middle grades face a great challenge. However, they also have one distinct advantage: children ages 8–12 learn English faster than any other age group (Kottler & Kottler, 2002).

Eventually, age ceases to be a factor in language acquisition. Collier (1987/1988) found that “The effect of age diminishes over time as the acquirer becomes more proficient in the second language” (generally after about the first five years of English learning). Young or old, CLD learners require under-standing and consideration as they work to develop proficiency in English and mathematics. Regardless of their age and regardless of how far along they are in learning English, it is helpful to remember that all CLD learners have a ten-dency to regress to a lower language development stage when confronted with new content or content for which they lack an adequate background.

The Challenge of Literacy StudentsThe preceding discussion assumes that CLD learners have an age-appropriate mastery of their native language. This is not necessarily true. One study sug-gests that 23 percent of CLD learners do not have appropriate oral proficiency


Culturally and Linguistically Diverse Learners ��

for their age/grade in their native language and that 38 percent do not dem-onstrate appropriate written proficiency in their native language (Rubenstein, 2005).

The reason for such differences may be due to a number of factors, includ-ing limited or interrupted schooling in their first language, level of school-ing, parents’ native-language proficiencies, the number of languages spoken at home, and previous exposure to English (as in a Mexican-border town). These students are sometimes termed “literacy students” because they are trying simultaneously to attain literacy in their native language and in English (Buchanan, 1997). Literacy students must learn in a culturally and linguisti-cally unfamiliar environment, build their understandings without the academic background experiences their CLD classmates employ, and process new infor-mation. More so than other CLD students, literacy students can face demanding challenges because they lack an academic foundation in their native language.

A special obstacle some literacy students encounter is that they may be at a maturation level far above their academic level. This gap can impact what materials are appropriate for literacy students. A student who is seventeen may not find fourth-grade materials engaging, even if they match the student’s academic level in mathematics and/or English acquisition. Teachers must adapt the setting of real-world problems to meet the interests of literacy stu-dents. For example, if the topic is percents, younger students might compute the sales tax on a skateboard. A seventeen-year-old might be more interested in computing the various amounts that are withheld from a paycheck. Such accommodations are essential for literacy students who are working to catch up to their peers in both mathematics and level of English acquisition.

Cultural Conundrum. . . . . . . . . . . . . . . . . . . . . . You are a seventh-grade teacher with new students from Mexico. You sus-pect that they are not literate in their native language because they don’t attempt to read any Spanish math materials. You also wonder why they don’t seem to respond to the Spanish teacher when she speaks to them.

Further discussion of this Cultural Conundrum appears at the end of the chapter. As you consider the points in this chapter, reflect on what factors in the students’ cultural background might explain the situation.


�� Teaching Mathematics to Culturally and Linguistically Diverse Learners

External Factors Impacting English Language AcquisitionThere are external factors that also affect CLD learners’ ability to learn English. If no English is spoken at home or at few social/community events, then the students’English learning will be slowed. Some CLD students may approve of their parents’ present standard of living, an improvement over what they had experienced in their native country, and one achieved in spite of their speaking little or no English. Consequently, the CLD students may see no need for becoming proficient in English, reasoning that they can reach the same comfortable living standard as their parents. In some cases, the parents might perceive learning English as an abandonment of their cultural heritage. At the other extreme, the families may plan to return to their native land in a few years, so the students’ motivation to learn English is greatly diminished. Any students in these situations will show slow progress in learning English, if they learn it at all.

If there are siblings at home who are also in school, this can help CLD learners with their English acquisition. Their siblings are also working to learn English. The siblings can talk to each other in English, practice what English they are learning, and compare experiences in English settings (although perhaps out of earshot of their parents, in a show of respect for their native language and culture).

Eventually, many CLD learners will adopt English as their primary lan-guage. A study of 5,700 young adults in Southern California found that although 87 percent grew up speaking another language at home, only 34 percent spoke it well by adulthood, and nearly 70 percent said they preferred to speak English (Sacchetti, 2007). A subsequent study found that 88 percent of second-genera-tion Latino families described themselves as English speakers, a figure that rose to 94 percent for the grandchildren’s generation (Preston, 2007). Neither study examined the question of how much of their cultural identify the subjects main-tained, but CLD learners in previous generations maintained a strong cultural identity even after speaking English as a primary language.

Levels of English Language Acquisition

Ludwig Wittgenstein, an educational philosopher, wrote, “The limits of my language are the limits of my world.” Certainly this is true of CLD students in mathematics. The mathematics progress that CLD learners can achieve in an English-speaking mathematics class will be directly proportional to their



mastery of the English they use in class. TESOL* has developed Proficiency Standards that delineate five categories of English language proficiency levels for CLD students.

TESOL Categories for English Language Proficiency

1. Starting Up

2. Beginning

3. Developing

4. Expanding

5. Bridging To

In the 2006 Language Proficiency Standards, TESOL describes the appropriate expectations for each of these five categories at five different grade clusters: Pre-K–K, 1–3, 4–5, 6–8, and 9–12. It can benefit both teacher and students when CLD students can be identified with one of these cat-egories, because then the mathematics expectations for listening, speaking, reading, and writing mathematics can be aligned with their English language proficiency.

A sample of the Mathematics Proficiency Standards appears in Table 1.2 on the next page. This sample shows the Writing Standard for grade cluster 6–8.

The full set of Proficiency Standards for all five grade clusters is avail-able from TESOL. (See www.tesol.org for more information.) The remaining Mathematics Proficiency Standards provide similar detailed descriptions for each grade cluster across the Proficiency Categories. These Standards provide reasonable expectations for mathematics achievement from CLD learners given their grade level and English Proficiency Category.

Determining and Tracking CLD Students’ English Acquisition LevelCLD students will display varying levels of English proficiency, as well as different rates of progress toward achieving full proficiency. It can be helpful for a classroom teacher to determine and monitor their CLD students’ prog-ress as they increase their level of English acquisition.

*TESOL is the acronym for Teachers of English to Speakers of Other Languages, Inc. It is a professional association with a mission to ensure excellence in English language instruction. The organization offers a variety of resources and networking opportunities. See www.tesol.org for more information.



Assessing English Language Acquisition by Anecdotal Recording

It is important to assess each CLD student’s level of English acquisition. Teachers might track a specific student’s progress in English language development by employing an informal anecdotal checklist for the student. The checklist in Figure 1.4 is adapted from the National Clearinghouse for Bilingual Education (Buchanan, 1993). It provides a way to informally assess a student’s progress across the four linguistic domains.

You can use the anecdotal guidelines in Figure 1.4 to first establish a baseline for a CLD learner’s level of English proficiency and then track devel-opment through the school year (see the Appendix for a blackline master). As the CLD learner’s English proficiency improves, you can change the nature and complexity of oral and written expectations.

Another instrument for determining a CLD learner’s proficiency in oral English is the Student Oral Language Observation Matrix (SOLOM) as adapted from Echevaria and Graves (2007). This matrix appears in Table 1.3. The teacher locates the student’s abilities along the matrix, which shows five levels in each of the five oral proficiency categories. By carefully observing a student in several different settings during class, teachers can develop a rea-

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Table 1.2

Mathematics Proficiency Standard for Grade Cluster �–�

Starting Up Beginning Developing Expanding Bridging To

Show pictorial representa-tion and label math terms (e.g., parts of whole num-bers, algebraic equations, or geometric relations)Record and label outcomes of events involving chance (e.g., coin flips or rolling cubes)

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Express the meaning and give examples of math terms (e.g., games or recipes from cookbooks or the Internet)Compare concrete representations using estima-tion language (greater than, fewer than)

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List the step-by-step pro-cess of math operations, procedures, patterns, or functionsEstimate prob-ability with sentences and illustrations from a sample of observed outcomes and describe results

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Create every-day math word problems and explain prob-lem-solving strategiesDescribe combinations possible based on probability

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Summarize, reason, predict, and compare/contrast math information or problem-solv-ing strategiesExplain and justify which combinations are most likely based on probability

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sonable description of their oral ability in English. After locating a student in this grid, teachers can then frame reasonable oral expectations for the student.

These instruments make it possible to identify a student’s oral English ability. Teachers can then track the learner’s progress as the year progresses. It is helpful to bear in mind that for many CLD learners, oral communication is sometimes better than written communication.

Determining General English Acquisition Levels with Formal Assessment

Teachers may want to have a more formal assessment of the student’s English acquisition level. There are a number of assessment tools that are available. Table 1.4 on page 17 lists some of the commonly used assessments by category

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Figure 1.4

Anecdotal Guidelines



Table 1.3

Student Oral Language Observation Matrix

Level 1 2 3 4 5

AComprehension

Cannot under-stand even sim-ple conversation.

Has great dif-ficulty following what is said. Can compre-hend only social conversation spoken slowly and with frequent repetitions.

Understands most of what is said at slower than normal speed with repetitions.

Understands nearly every-thing at normal speed, although occasionally repetition may be necessary.

Understands everyday con-versation and normal class-room discussions without difficulty.

BFluency

Speech is so halting and fragmentary as to make conver-sation virtually impossible.

Usually hesitant, often forced into silence by lan-guage limitations.

Speech in everyday conversations and classroom discussion is fre-quently disrupted by the student’s search for the correct manner of expression.

Speech in every-day conversation and classroom discussions is generally fluent, with occasional lapses while searching for the correct manner of expression.

Speech in every-day conversation and classroom discussions is fluent and effort-less, approxi-mating that of a native speaker.

CVocabulary

Vocabulary limitations so extreme as to make conver-sation virtually impossible.

Misuse of words and very limited vocabulary make comprehension quite difficult.

Frequently uses the wrong words; conversa-tion somewhat limited because of inadequate vocabulary.

Occasionally uses inappropri-ate terms and/or must rephrase ideas because of lexical inadequacies.

Use of vocabu-lary and idioms approximates that of a native speaker.

DPronunciation

Pronunciation problems so severe as to make speech virtually unintelligible.

Hard to under-stand because of pronunciation problems. Must frequently repeat in order to be understood.

Pronunciation problems neces-sitate concentra-tion on the part of the listener and occasionally lead to misunder-standings.

Always intelligible though listener is conscious of a definite accent and occasional inappropri-ate intonation patterns.

Pronunciation and intonation approximate that of a native speaker.

EGrammar

Errors in gram-mar and word order so severe as to make speech virtually unintelligible.

Grammar and word order errors make compre-hension difficult. Must often rephrase and/or restrict him/herself to basic patterns.

Makes frequent errors of gram-mar, which occa-sionally obscure meaning.

Occasionally makes grammati-cal errors and/or word order errors, which do not obscure meaning.

Grammatical use and word order approximate that of a native speaker.

Source: Echevaria & Graves (2007)



Table 1.4

Assessment Instruments for Determining English Acquisition Levels

Category Name of AssessmentNumber of States

Using

IDEA Proficiency Test (IPT) www.ballard-tighe.com/assessment.html

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Language Assessment System (LAS) www.ctb.com/products/category_home.jsp?FOLDER%3C%3Efolder_id= 2534374302057165&bmUID =1156189729545

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Off-the-shelf

Maculaitis Assessment of Competencies (MAC II) http://store.cambiumlearning.com/ProgramPage.aspx?parentId= 019005529&functionID=009000008&pID=&site=sw

2

Stanford English Language Proficiency (SELP) Test http://harcourtassessment.com/HAIWEB/Cultures/en-us/dotCom/SELP/ Stanford+English+Language+Proficiency+Test.htm

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Woodcock-Muñoz Language Survey www.assess.nelson.com/test-ind/wmls-r.html

2

English Language Development Assessment (ELDA from SCASS) www.ccsso.org/projects/ELDA/

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Assessing Comprehension and Communication in English State-to-State for English Language Learners (ACCESS for ELLs from WIDA) www.wida.us

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Consortia Mountain West Consortium—items from the assessment www.measuredprogress.org/Assessment/GeneralEducation/MountainWest/MountainWest.html Some individual states have information on their sites (e.g., www.schools.utah.gov/eval/Documents/Ell_Intro.pdf and www.nmabe.net/noticiero.html)

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Pennsylvania Enhanced Assessment Grant Consortium (PA EAG) 1

Source: From National Clearinghouse for English Language Acquisition and Language Instruction Educational Programs (see www.ncela.gwu.edu/expert/faq/25tests.htm)



and number of states using them. For more information about a particular assessment, see the respective website.

Most states use a formal assessment to determine English acquisition lev-els of CLD students. Teachers might explore how students are selected for the assessment, who administers the assessment, and how to access a student’s score. For a list of specific acquisition assessment instruments used by each state, go to www.ncela.gwu.edu/expert/faq/25tests.htm.

Although there is no typical description that fits every CLD student, there are some factors that transcend all cultural/ethnic/national backgrounds. Ability to read and write in their native language, motivation, and out-of-school support can affect the time CLD students require to become English proficient. The longer

Points to PonderYounger CLD learners must learn basic mathematics concepts at the same time they are learning the grammar, vocabulary, and syntax of a new language.

Class discussions for older students are more demanding and involve more chal-lenging subject matter.

Older CLD learners who have had formal schooling in their native land do not have to learn foundational mathematics concepts at the same time they are learning founda-tional English.

Some CLD learners will solve elementary mathematics in their native language and more recent mathematics in English.

When CLD learners confront confusing or cognitively demanding mathematics, they may process the problem in their native language.

CLD learners who are twelve to fifteen years old may require up to eight years of formal English before they can com-municate fluently in English (Collier &

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Thomas, 1989). (Perhaps it may take even longer, given the contemporary distractions of video games, iPods, and other personal electronic devices.)

A typical CLD student will require 15,000 hours of exposure to English in the class-room and social situations before becoming proficient (Collier & Thomas, 1989).

Fluency in an English-speaking classroom trails conversational fluency in the hallway by about five years.

CLD learners’ progress in acquiring English is delayed if English is not spoken at home. (However, if the parents speak English very poorly, they might slow their children’s English acquisition.)

Even when CLD learners are approaching English fluency, they may process informa-tion in their native language.

Some Asian cultures compute a person’s age at birth as one year old. This could result in a student being placed in a class where all the students are one year older.

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Culturally and Linguistically Diverse Learners �9

CLD learners spend in English-speaking classrooms, the more they will exhibit English fluency. It is important for teachers to match mathematical experiences to CDL learners’ English fluency level. CLD learners make the most progress when mathematics activities dovetail with their English acquisition level.

Soon, nearly every school district in the United States will have CLD learners in the classroom. Certainly every subject is important for these stu-dents, but, as cited in the preface, some research suggests that mathematics plays a large role in determining whether these CLD learners will complete their public schooling. It is the responsibility of all mathematics educators to help CLD learners succeed in mathematics so that they will be fully invested citizens in their new country. Only with genuine learning experiences can CLD students learn meaningful mathematics.

Subsequent chapters will consider effective teaching practices for teachers with CLD learners, what classroom arrangements benefit CLD learners, the differences in mathematics background in CLD learners, and how multicul-turalism can benefit all in a class, but especially CLD learners.

Solution to Cultural Conundrum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . These students from Mexico do not speak Spanish but are from a rural town where a Mayan dialect is spoken. One way to help these students is to seek out English speakers in the school district who also speak Mayan. There will also likely be some English speakers in the local Mayan commu-nity who can serve as translators and as resources for cultural materials.

Such a program exists in Lake Worth, Florida, where the Mayan-speak-ing students weren’t Mexican but Guatemalan. They had been mistakenly placed in special education programs, because school officials reasoned that since these children could not even communicate in what was thought to be their native language (Spanish), they must require assistance for their special needs. The Mayan-speaking children are now thriving under a program that provides support for Mayan speakers (Wildes-Muñoz, 2007). See General Multicultural Sites in the Appendix for several websites that will translate between English and other languages.
