Teaching mathematics to English language learners

List of Figures

List of Tables

Series Introduction

Preface

List of Contributors

Part 1. Your English Language Learner

1.1. Orientation

English Language Learners (ELLs): Who Are They? How Do They Come to Be in Our Classrooms?

Overview of Chapters in Part 1

1.2. The Process of English Language Learning and What to Expect

Principle 1. Give ELLs Many Opportunities to Read, to Write, to Listen to, and to Discuss Oral and Written English and Mathematics Texts Expressed in a Variety of Ways

Principle 2. Draw Attention to Patterns of English and Mathematics Language Structure

Principle 3. Give ELLs Classroom Time to Use their English Productively while Learning Mathematics

Principle 4. Give ELLs Opportunities to Notice their Errors and to Correct their English while Learning Mathematics

Principle 5. Construct Activities that Maximize Opportunities for ELLs to Interact with Others in English

Stages of ELL Language Development

1.3. Different Types of ESOL Programs

1.4. Teaching for English Language Development

Cummins' Quadrants

1.5. Not All ELLs Are the Same

Stages of Cultural Adjustment

Cultural Practices at School

1.6. Questions for Discussion and Reflection

Part 2. Influences on the Mathematics Attainment of English Language Learners

2.1. Overview: Influences on the Mathematical Attainment of English Language Learners

Overview of Chapters in Part 2

2.2. Providing an Equitable Mathematics Education to English Language Learners: Mathematics Education Standards

Summary

2.3. The Nature of Mathematics Language

Vocabulary

Symbols

Syntax

Semantics

Linguistic Difficulties Associated with Mathematical Discourse (Oral and Written)

Summary

2.4. Mathematics Teaching and Learning

Learning Environment

Tasks

Classroom Discourse

Teacher Preparedness to Work with ELLs

Summary

2.5. Cultural Influences on Mathematics Learning and Engagement

Cultural Links to Mathematics Content and Processes

Cultural Links to Mathematics Learning

Culturally Responsive Pedagogy

Summary

2.6. Assessment Results, Practices, and Procedures

Language Proficiency and Mathematics Achievement

Cultural Influences of Language Used in Test Items

Test Accommodations and the ELL

Summary

2.7. Questions for Discussion and Reflection

Part 3. Best Practices to Support English Language Learners in the Mathematics Classroom

3.1. Overview: Classroom Environments that Support English Language Learners

Overview of Chapters in Part 3

3.2. Orchestrating Classroom Discourse to Support Mathematics Concepts and Language Development

Speak and Enunciate Clearly to Make Language Comprehensible

Simplify and Elaborate Language

Express Information in Multiple Ways

Use Controlled Vocabulary

Limit the Use of Pronouns and Adjectives

Limit the Use of and Explain Idiomatic Expressions or Culturally Based Terms

Limit "Asides" or Conversations that Are Not Linked to the Lesson at Hand

Pause Frequently and Increase Wait Time

Use Drawings and Illustrations to Support Communication

Use Dramatic Gestures, Actions, and Verbal Intonations

Engage ELLs in Classroom Discourse

Summary

3.3. Strategies to Help English Language Learners Understand Mathematics Language

Strategies to engoge ELLs at the Preproduction Stage of English Language Development

Make Mathematics Language Development a Natural Part of Instruction

Use Representations to Support Sense-Making and Language Development

Extending Reading Strategies for Use with ELLs

Extending Writing Strategies for Use with ELLs

Summary

3.4. Emphasizing and Supporting Problem Solving

Connect Mathematics to Situational Contexts

Elaborate the Meaning of Words Provided in Real-World Problem-Solving Contexts

Use Representations to Interpret and Visualize Problems

Model Problem-Solving Processes and Strategies

Embed Clarity Checks

Provide Opportunities to Work with Peers to Solve Problems

Limit the Number of Problems Assigned

Avoid a Focus on Key Words

Address the Use of Extraneous Information in Word Problems

Be Sensitive when Using Cultural References

Encourage Students to Write Original Problems

Summary

3.5. Assessing English Language Learners in Equitable Ways

Provide Access to Learning Tools during Assessments

Avoid Linguistic Complexities

Provide Test Accommodations

Daily Assessments

Projects as Assessments

Summary

3.6. Teaching Mathematics in Ways that Are Culturally Responsive

Teacher Critical Self-Examination and Self-Reflection

Provide a Welcoming Environment for ELLs

Attend to Individualized Cultural Characteristics and Experiences

Create a Culturally Respectful Learning Environment

Use Cooperative Learning to Facilitate Language Acquisition and Mathematics Comprehension

Summary

3.7. Questions for Discussion and Reflection

Part 4. Collaborations to Support English Language Learners

4.1. Overview: Collaborations to Support ELLs

Overview of Chapters in Part 4

4.2. Strategies for Mathematics Teachers Who Are Themselves English Language Learners

Create a Learning Environment that Is Accepting of Linguistic Differences

Alert Students to Areas of Potential Difficulty Related to Language

Review the Mathematics Text for Linguistic and Symbolic Differences

Use Various Strategies to Produce Comprehensible Output

Collaborate with English-Speaking Colleagues

Engage in Ongoing Professional Development

Observe Others Teaching Mathematics

Share and Receive Cultural Information

Connect with Parents

Summary

4.3. Mathematics Teachers Collaborating with English as Second Language Teachers

Barriers to Collaborations that Need to be Acknowledged and Addressed

Different Approaches to ESL-Content Teacher Collaborations

Reflecting on Your Own Perspectives on Collaboration

Summary

4.4. ELL Home-School Communication

Ideas: On Fostering Access

Ideas: On Fostering Approachability

Ideas: On Achieving Good Follow-Through

Make Mathematics Links to Students' Families

Summary

4.5. Questions for Discussion and Reflection

Resources

Internet Resources to Support Mathematics Teaching and Learning

Print Resources for Further Study

Glossary

Notes

References

Index