Reflective Reading Summary Template (Supporting Language Learners)

Supporting language learners

Author(s): Jo Ann Cady, Thomas E. Hodges and Clara Lee Brown

Source: Teaching Children Mathematics , April 2010, Vol. 16, No. 8 (April 2010), pp. 476- 483

Published by: National Council of Teachers of Mathematics

Stable URL: https://www.jstor.org/stable/41199521

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Incorporating these instructional practices for two mathematical tasks

into lessons to support English learners gives them access

to an excellent, equitable program. À

Language Learners (ELLs) have an

English increasing presence in our nations' class- rooms. From 1991 to 2004 the number of

ELLs nearly doubled in grades K-12. Further- more, new forms of accountability have school personnel concerned with the progress - or lack of progress - of our ELLs. Principles and Standards also reflects this concern: The Equity Principle states that "all students should have access to an excellent and equitable mathemat- ics program that provides solid support for their learning and is responsive to their prior knowl- edge, intellectual strengths, and personal inter- ests" (NCTM 2000, p. 13). However, to achieve this goal "requires raising expectations for stu- dents' learning, developing effective methods of supporting the learning of mathematics by all students, and providing students and teachers with the resources they need" (p. 12). To meet these high expectations, some students - ELLs for example - will need assistance.

Specific instructional practices that target the needs that language learners have in learning math concepts also provide support for all stu- dents, regardless of their cultural backgrounds. These strategies can be grouped into two main categories:

1. Strategies to support English language acquisition

2. Strategies to promote low-anxiety classrooms

To illustrate how these tactics might be incor- porated into a mathematics lesson, the authors describe them in relation to two mathemati-

cal tasks from Navigating through Algebra in Grades 3-5 (Cuevas and Yeatts 2001).

Link new concepts Every lesson in every subject will benefit from linking students' past experiences to new con- cepts. Advanced organizers help language learn-

ers link prior knowledge to the new information ^^^ they will be presented in the lesson and prepare ^fl^s them for what is to follow. Шг ^

Use advanced organizers ^^^Hfl Organizers take on different forms depending^^^^B on students' familiarity with the concepts of ^^И the lesson and developmental level. Exposi- ^ tory organizers explain the main ideas and the meanings of unfamiliar words and are used to link new information with prior information when the material is relatively unfamiliar to the student. Comparative organizers, on the other hand, show how new material compares with or contrasts to familiar ideas and concepts. Such organizers help integrate new material with material that is already understood. As stu- dents' language acquisition develops, advanced organizers can become more abstract and can incorporate the use of Venn diagrams, oral read- ings, and debates. However, ELLs will still need concrete props to demonstrate new vocabulary words (Herrell and Jordan 2008).

Develop students' vocabulary Teachers must identify which words might cause confusion for their students and address

these words during the lesson (Khisty 1997; Torres-Velasquez and Lobo 2005; Weist 2008). Keep in mind that conversational language differs from academic language. Students may be conversant but still find academic language or mathematical terms a challenge. However, mathematical language can be used as a vehicle to extend and strengthen students' language proficiencies (Khisty 2002). For example, explaining homonyms - some and sum, hole and whole - affords opportunities to distinguish between the conversational meaning and the mathematical meaning as well as the spelling variations that determine meaning. The teacher could also translate terms into students' native

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шт tongue or ask a student to translate. Bilingual dictionaries at the appropriate reading level or picture dictionaries with labels in students' native tongues and in English are also helpful in developing vocabulary.

Use visual cues

Diagrams, props (realia), and photographs help students develop vocabulary. Photographs and drawings (even stick figures) can illustrate mean- ings of unfamiliar vocabulary. Start a collection of realia (real-world objects) to help make con- crete connections between the vocabulary word and students' lives. Realia can include puppets,

stuffed animals, toddler toys (people, houses, etc.), toy cars, trucks, dolls, and geometric fig- ures. Label the items in English and in the ELLs' native language. Empty cans and boxes of food and household items can also be helpful.

Using realia, drawings, or models as well as providing the written word on an overhead pro- jector or blackboard will minimize the amount of time language learners spend just listening (Khisty 2002; Torres -Velasquez and Lobo 2005; Weist 2008). Writing key words on the board or overhead as you say them aids students who may not recognize the spoken words as the same words they are familiar with in written form (Khisty 2002; Weist 2008). Visual cues can be extended to include graphic organizers or pictograms to help students see relationships between words and concepts.

Adjust teacher talk Participating in classroom mathematical discus- sions involves more than learning vocabulary. Students are expected to be precise or use repre- sentations to support their claims (Moschkovich 2002). The spoken language so common in aca- demic instruction is difficult for ELLs to master.

The gestures and cues of conversational vocabu- lary building are more difficult in academic language (Khisty 2002). Consequently, it takes more time for students to process the words they hear. Therefore, as they are thinking about what was said, they miss the next few words or sentences. In addition to the increased process- ing time, new English Language Learners often have difficulty distinguishing when one word has ended and the next begins when they hear a fluent English speaker. To further compound an ELL's difficulty with understanding verbal direc- tions is the fact that opportunities rarely occur to review what was said. Language learners benefit when teachers use strategies to enhance clarity and reduce the complexity of the language.

• Repeat important explanations and directions to improve ELLs' comprehension.

• Slow down; it is the simplest and most help- ful strategy you can use. But do not speak so slowly that it seems unnatural. Pausing an extra beat or two at natural breaks (between

phrases or sentences) gives language learners extra time to process information. Highlight important words by raising or lowering your

I 1

Teachers can use such activities as "Catch of the day" (Cuevas and Yeatts 2001) to support ELLs with various strategies: advanced organizers, realia, photographs, and manipulatives.

Catch of the Day Name

You are going fishing and must catch a specified number of fish each day. All "catches" must

include the following fish: snapper, grouper, and tuna. The captain of the fishing boat has deter-

mined how many of each of the three kinds of fish are needed and has provided clues for the crew

to use to figure out how many of each type of fish must be caught. You may use colored chips or

cubes to represent the fish caught.

Monday's Catch of the Day Tuesday's Catch of the Day 3 snapper 6 snapper

2 more tuna than snapper 1/2 as many tuna as grouper 15 fish in all 12 fish in all

S =

Wednesday's Catch of the Day Thursday's Catch of the Day 3 snapper 1/4 of the catch is snapper.

4 times as many tuna as snapper 1/3 of the catch is grouper. 23 fish in all 12 fish in all

S =

Friday's Catch of the Day ^L® &¿?s

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1 m m

voice level and your pitch (Reiss 2008). Enun- ciate clearly.

• Simplify your sentence structure. When read- ing directions or passages from the text, para- phrase long and complex sentences or split the sentence in two, pausing between sen- tences. Pronouns also involve extra processing time and can slow comprehension. Substitute nouns for pronouns as often as possible, and limit the use of contractions. Contractions

such as they're and it's are often confused with their other forms, their and there and its.

• Be consistent. When teachers use consistent

words and phrases to give directions, language learners better understand and follow direc- tions. These words should also be consistent

with the words and terms that the textbook

uses. Language learners can advance to more formal terminology by using an informal term followed by the formal term. As students

develop their vocabulary, they can drop the informal word.

•Avoid idioms and jargon (Reiss 2008).

The first task Consider the "Catch of the day" activity (see fig. 1). To support language learners with advanced organizers to develop their vocabu- lary, first discuss fishing and boats. Use realia such as a stuffed fish and toy boats to tell the story about the fishing boat and the fisherman. Photographs of fisherman, fish, and boats would also be helpful. Provide students with colored fish crackers as manipulatives when they begin to solve the problem. Draw or place a cutout of a red fish on the board with the word tuna next

to it. Use a green fish for grouper and an orange fish for snapper.

A quick check for understanding of the terms fewer, more than, four times, and in all would benefit non-English speakers. To check whether students understand these concepts, create cards on which the terms more than, less than,

fewer, and same as are printed. Also create about six cards with pictures of sets of four to twelve objects. For example, give a student a card that pictures six objects. Then show him a card with four objects and ask him to choose one of the word cards to tell you whether the set of four objects is more, less, or the same [number] as the set of six objects. Repeat this exercise with various cards until you have assessed all the

Pictorial representations can help teachers check students' ' understanding of fractions represented as numbers. '

(a) The set of blue cubes has four times as many cubes as the set of red cubes. 1

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(b) The set of green cubes has half as many cubes as the set of yellow cubes. I

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students' understanding of these words. This У check helps teachers determine whether these ^^ terms are familiar to language learners, are likely f to require some discussion, or are likely to need / replacement with more familiar terms, such as ^^^ИЦ^^^^^ total rather than in all. For advanced language (m ^^Ш^^^^Ш learners, create sentence strips to show how to S^^^^_____H use the math terms fewer and less than in com- wT j^^^^^^B plete sentences. 3^tJ______l Similarly, just because an activity shows Br^^^^^^^^B '

fractions symbolically (e.g., 1/2, 1/3, 1/4) does ЖГ ' "^BI^^^B not mean that students understand a frac- Щ .J^^H^^H tion's meaning. Using multiple representations КГ ' ' ll^^^^^^H encourages students to make connections Ш- l^^^^^^B among language, symbols, pictures, and con- Щ __J^^^^^^B crete materials as well as offers an avenue щ^ш^^^^^^^Ш for teachers to check for understanding. For ^^^^^^^^^^^^Ш^^^ instance, to see whether students understand ^^^^Ш^^^^^^Ш^^^к the part-whole meaning of fractions written ^^^^Ш^^^^^^^^^^^Ш symbolically, you might include a series of ^^^^^^И^^^ШЕЕШЕ^^г pictorial representations equivalent to the frac- ^^^k tions, then have students match symbols to the ^^^m pictures. Helping students make these connec- ^Ш tions offers you several opportunities to connect ^™

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You can rewrite directions for such activities as "Building houses" (Cuevas and Yeatts 2001) by using words that are more familiar to ELLs.

Building Houses Name

An architect has left plans to build houses on each island. Bridges connect the islands. The number on each bridge tells the total number of houses on the two islands it connects. Use cubes to find out

how many houses are to be built on each island. Represent each situation as an equation. Show that your solution is correct.

TOTAL NUMBER OF HOUSES: 24

2 „

TOTAL NUMBER OF HOUSES: 30 TOTAL NUMBER OF HOUSES: 27

Copyright С 2001 by the National Council of Teachers of Mathematics.

the terms total, sum, and whole (e.g., the total number of regions or objects is the sum of the individual parts and represents the whole). Mov- ing between representations allows students to develop vocabulary by linking written or spoken language to symbols, pictures, and concrete objects.

However, most important, these multiple opportunities increase the likelihood that stu- dents will understand concepts correctly while mastering vocabulary. Terms such as half as many ox four times as many are as problematic for English-speaking children as they are for ELLs. Thus, check such terms for understanding, too. You can use the fraction pictorial represen-

tations or such pictures as those in figure 2 to check for understanding.

You may want to guide language learners through a simpler problem first. You might edit the problem from figure 1 to look like this:

2 snapper 1 more tuna than snapper 7 fish in all

S =

The second task In the "Building houses" activity (see fig. 3), realia props could include miniature houses, such as those found in a monopoly game. Pho- tographs of islands and bridges and a discussion of using bridges to get to islands could serve as the advanced organizer. Place key words on the board: bridges, islands, and houses.

You could rewrite the activity directions using words that are more familiar to language learn- ers. For example, if you think that the words situation and represent are not yet in your stu- dents' vocabulary, you might replace the phrase "Represent each situation as an equation" in the directions with "Write a number sentence that

shows the number of houses on each island and

the bridge between those islands." When the authors presented "Building

houses" to a class, they discovered how simplify- ing the directions made them more accessible to language learners. Consider this rewrite:

Each problem has three islands. Bridges con- nect the islands. The number on a bridge tells how many houses are on the two islands that the bridge connects. How many houses are on each island?

Simplifying the directions - removing the word architect, shortening the length of the sentences, and removing the strategies - helped students focus on the problem's primary context but left the teacher to decide which pedagogical strate- gies were best for language learners to use when solving the problems.

The most difficult idea to explain to students is that the number on the bridge is the sum of the number of houses on the two islands con-

nected by the bridge. To help all students - not just language learners- understand, the authors provided an even simpler problem with two

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islands connected by a bridge. The bridge had the number 5 on it. Students then found all pos- sible combinations of houses that could be on

the islands if there were 5 houses total.

Promote low-anxiety environments

For language acquisition and learning to take place, students must feel safe and comfortable in their environment. Students who are in the

process of acquiring English language profi- ciency may not be able to express what they know. Their inability to verbalize their thoughts in the manner in which they desire frustrates them. They will make many mistakes when learning a new language and be relegated to using simple language with incorrect grammar. In turn, making mistakes will inhibit their par- ticipation in discussions about mathematics. However, teachers can promote a low-anxiety environment by emphasizing that mistakes (both in math and in English) are common and that mistakes present opportunities to learn the language and the subject matter.

Not all ELLs are adjusting to a new homeland, but peer approval is especially important for those who are trying to understand the nuances of an unfamiliar culture. A supportive environ- ment - where students know that their attempts to participate and explain their mathematical thinking will be accepted and applauded rather than ridiculed - encourages further participa- tion in discussions and contributes to success in

language acquisition and mathematics (Rothen- berg and Fisher 2007).

Use predictable routines Students who know the sequence of events, where to find manipulatives and calculators, and generally what to expect are able to focus more energy on instruction (Herrell and Jordan 2008). Predictable routines and signals are among the easiest strategies for teachers to implement, and they are extremely important in reducing stress for language learners.

On the classroom wall, post a schedule that uses pictures (see fig. 4). Select specific places for students to post homework, submit assign- ments, and store belongings. By designating classroom areas for group work, partner work, and individual work, you help language learners understand the behavior you expect when they

are in those areas. Have students model and

practice these classroom routines. For instance, if you expect students to use manipulatives and work in groups when solving the problems in the "Catch of the day" or the "Building houses" activities, language learners must understand how to obtain and apply manipulatives and where to move for a group setting. Having

Posting a schedule that uses pictures will help ELLs know what to expect and will support their language skills, too.

Daily Schedule

^fe Pledge 9:00

щ Reading 9:05

^£ Gym 9:50

JJjif I Music 10:20

шШ Lunch 10:50

Щ& Math 1 1 :20

Jjipfr Science 12:15

AjlA Recess 1:15

Дг Social Studies 1 :45

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classroom routines for gathering materials and moving to group settings reduces the stress for language learners and allows them to focus on the math of the tasks.

Use signals By displaying hand signals, ringing a bell, flashing the classroom lights, or using a verbal prompt in the students' native tongue, you can indicate the close of one activity and the beginning of another to aid students in understanding expectations.

Contextualize

When you give directions, contextualize. For example, hold up the textbook when you instruct students to "take out your math book." The concurrent physical demonstration and verbal explanation is another simple but power- ful strategy to help language learners (Herrell and Jordan 2008).

Assign student buddies Partner work is a particularly effective strategy because it provides opportunities for verbal interaction and support (Amaral, Garrison, and Klentschy 2002; Herrell and Jordan 2008). Pair language learners with student buddies who can help them learn the routine and offer assistance with routines and vocabulary. Working together in small groups encourages discussion and greater levels of language use (Amaral, Garrison, and Klentschy 2002). Language learners appre- ciate peer help and support, and the volunteers feel a sense of satisfaction in helping.

• Give guidance. It is helpful to offer volunteers some guidelines and support in how to pose questions that support thinking, when to translate into the first language, and how to encourage vocabulary development.

• Distribute responsibility. Although language learners benefit from pairing with someone who speaks their native language, teachers must be aware that placing translating respon- sibilities on only one child may overburden the translator (Reiss 2008). Moreover, other bi-

lingual students may also want to help the newer students. Thus, rotating translator responsibilities among several children not only reduces the burden on one child but also offers opportunities for other bilingual students

to strengthen their English-speaking skills.

Hold high expectations All these suggested strategies support language learners while enhancing instruction for all stu- dents. In addition to using such tactics to help language learners in the mathematics classroom, teachers should also continue to hold high expectations for all students. High expectations play a profound role in the success of students who are learning English (Gutierrez 2002; Khisty 2002; Slavin 2001). Because language acquisi- tion is important to such students in learning mathematics, teachers may be tempted to lower standards and expectations, accept inferior work, or make excuses for students' poor achieve- ment. Doing so does not help students develop mathematical understanding, prepare for more advanced coursework, or become increasingly competent members of the mathematics class- room. The strategies included in this article pro- vide a starting point for maintaining high expec- tations of language learners while also offering support as they learn English.

REFERENCES

Amaral, Olga Maia, Leslie Garrison, and Michael

Klentschy. "Helping English Learners Increase

Achievement through Inquiry-Based Science

Instruction." Bilingual Research Journal 26, no. 2

(2002): 213-39.

Cuevas, Gilbert J., and Karol Yeatts. Navigating

through Algebra in Grades 3-5. Resto n, VA: National Council of Teachers of Mathematics, 2001.

Gutierrez, Rochelle. "Enabling the Practice of Math-

ematics Teachers in Context: Toward a New Equity

Research Agenda." Mathematical Thinking and

Learning 4, nos. 2 and 3 (2002): 145-87. Herrell, Adrienne, and Michael Jordan. Fifty Strategies

for Teaching English Language Learners. 3rd ed.

Upper Saddle River, NJ: Allyn and Bacon, 2008.

Khisty, Lena Licón. "Making Mathematics Acces-

sible to Latino Students: Rethinking Instructional

Practices." In Multicultural and Gender Equity in

the Mathematics Classroom: The Giñ of Diversity, 1 997 Yearbook of the National Council of Teachers

of Mathematics (NCTM), edited by Janet Trenta-

costa and Margaret J. Kenney, pp. 92-101. Reston, VA: NCTM, 1997.

Student: Suggestions from Research for Class-

room Practice. Teaching Children Mathematics 9

(August 2002): 32-35. Moschkovich, Judith. "A Situated and Sociocultural

«

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Perspective on Bilingual Mathematics Learners."

Mathematical Thinking and Learning 4 (2002): 189-212.

National Council of Teachers of Mathematics

(NCTM). Principles and Standards for School Mathematics. Reston, VA: NCTM, 2000.

Reiss, Jodi. 102 Content Strategies for English Lan-

guage Learners: Teaching for Academic Success in Grades 3-12. Upper Saddle River, NJ: Pearson Prentice Hall, 2008.

Rothenberg, Carol, and Douglas Fisher. Teaching

English Language Learners: A Differentiated Approach. Upper Saddle River, NJ: Pearson Pren- tice Hall, 2007.

Slavin, Robert E. "Expecting Excellence." American

School Board Journal 188, no. 2 (February 2001): 22-25.

Torres-Velasquez, Diane, and Gilberto Lobo. "Cul-

turally Responsive Mathematics Teaching and

English Language Learners." Teaching Children

Mathematics 1 1 (December 2004/January 2005): 249-55.

Weist, Linda R. "Problem-Solving Support for

English Language Learners." Teaching Children Mathematics 14 (April 2008): 479-84.

^^^^^^H ; • ^^^ Jo Ann Cady, jcady@ ^^^^^^^B ~,:/^^^^b utk.edu, is an assis- ^^^^^^^1 "'' :^^^^H tant professor at the ^^^^^^^| ^i^^^E' University of Tennes- ЛП1 IflHHife see. She is interested

ННВЦ in helping teachers implement reform ^^Щ^Н practices and developing mathematics ^^^Mj^H knowledge for teaching. Thomas E. ^^^^^^B Hodges, [email protected], ■ИИ^^И teaches mathematics methods courses

at Western Carolina University in Cullowhee, North

Carolina. He is interested in professional development for mathematics teachers and innovative uses of tech-

nology in mathematics classrooms. Clara Lee Brown,

[email protected], an associate professor in ESL

education at the University of Tennessee, teaches ESL methods, assessment and evaluation, and multilin-

gualism and multiculturalism.

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