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Making Math Accessible to English Language Learners: Practical Tips and Suggestions (Grades K-2)

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Making Math Accessible for English Language Learners provides practical classroom tips and suggestions to strengthen the quality of classroom instruction for teachers of mathematics. The tips and suggestions are based on research in practices and strategies that address the affective, linguistic, and cognitive needs of English language learners.

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Chapter 1: The Challenges Facing English Language Learners and Their Teachers

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The Challenges Facing English Language Learners and Their Teachers

Every student should have equitable and optimal opportunities to learn mathematics free from bias—intentional or unintentional—based on race, gender, socioeconomic status, or language. In order to close the achievement gap, all students need the opportunity to learn challenging mathematics from a well-qualified teacher who will make connections to the background, needs, and cultures of all learners.

—National Council of Teachers of Mathematics

Reflection 1.1

Choose one or more of the following questions, and respond in the margin. Write from your heart, your beliefs, and your past experience. Compare your answers to those on page 131.

•   Why do some students transition to English very quickly while others attend English-speaking schools for many years without acquiring academic English?

•   How can we make grade-level mathematics accessible to all students regardless of language proficiency?

 

Chapter 2: Providing Affective Supports for English Language Learners

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Providing Affective Supports for English Language Learners

There are hundreds of languages in the world, but a smile speaks them all.

—Anonymous

Reflection 2.1

Imagine you are going to be an exchange student in a country where you do not know the language. What positive classroom aspects could motivate you to learn the language relatively quickly? Compare your answers to those on page 133.

The National Council of Teachers of Mathematics (2000) has articulated the importance of a positive classroom climate in learning mathematics. The classroom environment communicates subtle messages about what is valued in learning and doing mathematics and encourages students to participate in the learning and doing of mathematics. The English language learner’s first impression of the classroom and the teacher sets the tone for learning and success. Putting yourself in the place of the student and envisioning what would make you feel welcome will put you on the right path toward creating a positive classroom climate that meets the needs of English language learners in learning mathematics.

 

Chapter 3: Providing Linguistic Supports for English Language Learners

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Providing Linguistic Supports for English Language Learners

Mathematics knows no race or geographic boundaries; for mathematics, the cultural world is one country.

—David Hilbert

The following example in figure 3.1 is what a student at the beginning level of language proficiency might read and comprehend. The blanks indicate words that the student likely would not be able to read or understand. Take a moment to try to solve the problem, thinking about what you can determine from the information given. Then do the same with the problem for each level that follows.

Figure 3.1: Comprehension at beginning proficiency.

A bit frustrating, isn’t it? The student can understand nothing except that there are multiple sketches of a butterfly, a grasshopper, and an ant. Even if the student has the mathematics background in his or her primary language, he or she cannot determine enough information to solve the problem.

 

Chapter 4: Providing Cognitive Supports for English Language Learners

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Providing Cognitive Supports for English Language Learners

The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.

—Bertrand Russell

In chapter 2, we looked at factors that affect language acquisition. Since the factor over which educators have the most control is the quality of instruction, we will continue to emphasize the importance of the role of the mathematics teacher as we look at increasing student understanding, participating, and communicating. In much the same way that we examined how to provide linguistic supports for language acquisition in chapter 3, here we will examine how to provide cognitive supports for the development of the skills, conceptual understanding, and thought processes that lead to mathematical proficiency.

When students encounter a word problem, they must not only read the text but also decode the mathematics involved. They must determine relevant concepts, including whether there is extraneous information, and decide which operations to use on any numbers.

 

Chapter 5: Applying Strategies for ELLs: A 5E Lesson

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Applying Strategies for ELLs: A 5E Lesson

Learning without thought is labor lost; thought without learning is perilous.

—Confucius

In the first four chapters, we examined the needs of English language learners and how to support them in the affective, linguistic, and cognitive domains. The question now arises of how to incorporate the tools, practices, and strategies into practical classroom use. Perhaps you are asking yourself:

•   What does a lesson look like that meets the needs of my English language learners?

•   How can I meet the needs of my English language learners and still meet the needs of other students in my classroom?

Echevarria, Vogt, and Short (2004) identify the critical instructional features necessary for the academic and language development of English language learners.

Lesson preparation: Planning should result in lessons that enable students to make connections between their knowledge and experiences and the new information being taught.

 

Chapter 6: Adapting a Traditional Textbook Lesson

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Adapting a Traditional Textbook Lesson

A small part of even the most reluctant student wants to learn.

—Anonymous

Traditional textbook lessons present several concerns. The lesson format generally lends itself to teacher-centered instruction instead of student-centered instruction. The content of standard textbook lessons rarely includes examples and problems with the cognitive rigor necessary to prepare students for success—whether success is measured by standardized tests or readiness for post–high school education. Such lessons seldom include strategies for building common background, developing vocabulary, providing comprehensibility, and solving authentic problems in an atmosphere ripe for interaction. Therefore, teachers are often faced with the challenge of adapting traditional lessons to meet the needs of English language learners.

 

Tell me and I’ll forget, show me and I may remember, involve me and I’ll understand.

 

Appendix A: Selected Glossary

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Appendix A

Selected Glossary

Basic Interpersonal Communication Skills (BICS): This is the language ability required for social communication. It takes between one and three years to attain this basic level of oral proficiency.

bilingual education: Students are allowed to develop language proficiency in two languages by receiving instruction in some combination of English and the student’s primary language.

cognates: These are words in English closely related to the student’s primary language.

Cognitive Academic Language Proficiency (CALP): This refers to the mastery of academic language necessary for students to succeed in context-reduced and cognitively demanding content areas. It takes between five and ten years for a second-language student to perform at grade level without ELL support.

comprehensible input: This is content in which the level of language difficulty has been adapted to the student’s proficiency level to enable him or her to understand.

 

Appendix B: English/Spanish Cognates in Math

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Appendix B

English/Spanish Cognates in Math

English

Spanish

activity

actividad

algebraic

algebraico

analyze

analizar

apply

aplicar

appropriate unit

unidad apropiada

approximate

aproximado

area

área

bar graph

gráfica de barras

calendar

calendario

capacity

capacidad

circle

círculo

common

común

compare

comparar

conclusion

conclusión

concrete model

modelo concreto

cone

cono

construct (v.)

construir

cube

cubo

cylinder

cilindro

data

datos

day

día

 

Appendix C: Sample Responses to Tasks and Reflections

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Appendix C

Sample Responses to Tasks and Reflections

Reflection 1.1

Some students transition to English very quickly because they are eager to learn, have supportive families, and are encouraged by teachers who care and provide appropriate instruction and a welcoming environment.

Task: Identifying Language Proficiency Levels

Case Study: Li

Early intermediate

Possible indicators:

•   Attempts to speak English but relies heavily on gestures and facial expressions

•   Becomes frustrated when solving word problems

•   Shows some understanding of the lesson vocabulary and concepts

Case Study: Heinz

Proficient

Possible indicators:

•   Understands and uses academic language

•   Demonstrates understanding of abstract mathematical concepts

•   Functions on grade level

•   Uses advanced sentence structure, including academic language, in justifying answers

 

Appendix D: Reproducibles for Lesson on Three-Dimensional Figures

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Appendix D

Reproducibles for Lesson on Three-Dimensional Figures

Who Am I?

Making Math Accessible to ELLs (K–2) © 2010 r4 Educated Solutions • solution-tree.com Visit go.solution-tree.com/ELL to download this page.

Cooperative Grouping Guide Cards

Making Math Accessible to ELLs (K–2) © 2010 r4 Educated Solutions • solution-tree.com Visit go.solution-tree.com/ELL to download this page.

Vocabulary Organizer

Making Math Accessible to ELLs (K–2) © 2010 r4 Educated Solutions • solution-tree.com Visit go.solution-tree.com/ELL to download this page.

Three-Dimensional Geometric Figures Cards

Making Math Accessible to ELLs (K–2) © 2010 r4 Educated Solutions • solution-tree.com Visit go.solution-tree.com/ELL to download this page.

Three-Dimensional Geometric Figures

Making Math Accessible to ELLs (K–2) © 2010 r4 Educated Solutions • solution-tree.com Visit go.solution-tree.com/ELL to download this page.

 

Appendix E: Cooperative Grouping for the ELL Classroom

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Appendix E

Cooperative Grouping for the ELL Classroom

Advanced Preparation

•   Copy, cut, and glue the grouping shapes on page 153 to index cards.

•   Cut teacher cue cards (page 154).

•   Laminate index cards and teacher cue cards to make them last longer.

How to Use

Assign Cooperative Grouping Cards based on the student’s ability level, using the following guide, for example:

•   Beginning and early intermediate English language learners—bear

•   Intermediate English language learners—zebra

•   Advanced English language learners—lion

•   Proficient English language learners—giraffe

Cards will need to be reassigned every two to three weeks based on the amount of cooperative grouping used during the time frame and the changing dynamics of the classroom. For example, the beginning English language learners could be changed to the zebra.

Teacher cue cards will help facilitate smooth group transitions and aid the beginning learners in the classroom.

 

Appendix F: A 5E Lesson Plan Template

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Appendix F

A 5E Lesson Plan Template

A 5E Lesson Plan Template

Making Math Accessible to ELLs (K–2) © 2010 r4 Educated Solutions • solution-tree.com Visit go.solution-tree.com/ELL to download this page.

 

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