Teaching Mathematics to English Language Learners (Teaching English Language Learners Across the Curriculum)

185 Pages·2008·1.98 MB·English

by  Gladi Kersaint

Teaching Mathematics to
English Language Learners
Today’s mathematics classrooms increasingly include students for whom English is a second
language. Teaching Mathematics to English Language Learners provides readers with a compre-
hensive understanding of both the challenges that face ELLs and ways in which educators might
address them in the secondary mathematics classroom. Framed by a research perspective, this
book presents practical instructional strategies for engaging learners that can be incorporated
as a regular part of instruction. The authors offer context-specific strategies for everything from
facilitating classroom discussions with all students, to reading and interpreting mathematics text-
books, to tackling word problems. A fully annotated list of mathematics web and print resources
completes the volume, making this a valuable reference to help mathematics teachers meet the
challenges of including all learners in effective instruction.
Special Features:
ƒ Practical examples of mathematics problems and exercises make turning theory into practice
easy when teaching ELLs
ƒ Engaging vignettes vividly illustrate real-life interactions of veteran teachers and ELLs in the
classroom
ƒ Graphs, tables, and charts provide additional access points to the text in clear, meaningful
ways
Gladis Kersaint is Associate Professor of Mathematics Education at the University of South
Florida.
Denisse R. Thompson is Professor of Mathematics Education at the University of South Florida.
Mariana Petkova is a doctoral student in Mathematics Education at the University of South
Florida, and a high school mathematics teacher in Hillsborough County.
Teaching English Language Learners Across the Curriculum
Series Editors: Tony Erben, Bárbara C. Cruz, Stephen J. Thornton
Teaching Mathematics to English Language Learners
Gladis Kersaint, Denisse R. Thompson, Mariana Petkova
Teaching English Language Learners in Career and Technical Education
Programs
Victor M. Hernández-Gantes and William Blank
Teaching English Language Learners through Technology
Tony Erben, Ruth Ban, Martha Castañeda
Teaching Social Studies to English Language Learners
Bárbara C. Cruz and Stephen J. Thornton
Teaching Mathematics to English
Language Learners
GLAdiS KErSAinT, dEniSSE r. THoMPSon,
MAriAnA PETKovA
First published 2009
by routledge
270 Madison Ave, new York, nY 10016
Simultaneously published in the UK
by routledge
2 Park Square, Milton Park, Abingdon, oxon oX14 4rn
Routledge is an imprint of the Taylor & Francis Group, an informa business
This edition published in the Taylor & Francis e-Library, 2008.
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All rights reserved. no part of this book may be reprinted or reproduced or utilised
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Trademark Notice: Product or corporate names may be trademarks or registered
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infringe.
Library of Congress Cataloging in Publication Data
Kersaint, Gladis.
Teaching mathematics to English language learners/Gladis Kersaint, denisse r.
Thompson, Mariana Petkova.
p. cm.—(Teaching English language learners across the curriculum)
includes bibliographical references and index.
1. Mathematics—Study and teaching—Curricula. 2. English language—Study and
teaching—Foreign speakers. i. Thompson, denisse rubilee, 1954– ii. Petkova,
Mariana. iii. Title.
QA11.2.K47 2008
510.71—dc22
2008001565
ISBN0-203-89452-9(cid:13)(cid:10) Master e-book ISBN
iSBn 10: 0-415-95788-5 (hbk)
iSBn 10: 0-415-95789-3 (pbk)
iSBn 10: 0-203-89452-9 (ebk)
iSBn 13: 978-0-415-95788-5 (hbk)
iSBn 13: 978-0-415-95789-2 (pbk)
iSBn 13: 978-0-203-89452-1 (ebk)
Contents
List of Figures � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �ix
List of Tables � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � x
Series Introduction � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �xi
Preface � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �xiii
ParT 1 — Your English Language Learner Tony Erben� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1
1�1 — Orientation � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 3
1�2 — The Process of English Language Learning and What to Expect � � � � � � � � � � � � � � � � � � � � � � � 5
Principle 1: Give ELLs Many opportunities to read, to Write, to Listen to, and to
discuss oral and Written English Texts Expressed in a variety of Ways . . . . . . . . . . . . . . . . . . . . . 6
Principle 2: draw Attention to Patterns of English Language Structure . . . . . . . . . . . . . . . . . . . . . 7
Principle 3: Give ELLs Classroom Time to Use their English Productively . . . . . . . . . . . . . . . . . . . 8
Principle 4: Give ELLs opportunities to notice their Errors and to Correct their English . . . . . . 8
Principle 5: Construct Activities that Maximize opportunities for ELLs to interact
with others in English . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1�3 — Deciding on the Best ESOL Program � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 13
1�4 — Teaching for English Language Development � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 18
vi Contents
1�5 — Not all ELLs are the Same � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 22
Stages of Cultural Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Cultural Practices at School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1�6 — Culturally responsive Pedagogy � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 27
1�7 — Not all Parents are the Same: Home–School Communication � � � � � � � � � � � � � � � � � � � � � � � � 30
ideas: on Fostering Access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
ideas: on Fostering Approachability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
ideas: on Achieving Good Follow-Through . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1�8 — English Language Learners with Special Needs � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 33
ParT 2 — Influences on the Mathematical attainment of English Language Learners � � � � � � � � � � 37
2�1 — Overview: Influences on the Mathematical attainment of English Language Learners � � � � � 39
2�2 — Providing an Equitable Mathematics Education to English Language Learners:
Mathematics Education Standards � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 42
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2�3 — The Nature of Mathematics Language � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 46
vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Linguistic difficulties Associated with Mathematical discourse (oral and Written) . . . . . . . . . 50
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2�4 — Mathematics Teaching and Learning � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 53
Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Classroom discourse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Learning Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Teacher Preparedness to Work with ELLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2�5 — Cultural Influences on Mathematics Learning and Engagement � � � � � � � � � � � � � � � � � � � � � � 60
Cultural Links to Mathematics Content and Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Cultural Links to Mathematics Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Culturally responsive Pedagogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2�6 — assessment results, Practices, and Procedures � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 66
Language Proficiency and Mathematics Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Cultural influences of Language Used in Test items . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Contents vii
Test Accommodations and the ELL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2�7 — recommendations for Improving the Mathematics Preparation of
English Language Learners � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 72
Curriculum and instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Assessment Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Teacher Education and Professional development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
ParT 3 — Best Practices to Support English Language Learners in the Mathematics Classroom � � 77
3�1 — Overview: Classroom Environments that Support English Language Learners � � � � � � � � � � � 79
3�2 — Orchestrating Classroom Discourse to Support Mathematics Concept and
Language Development � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 81
Speak and Enunciate Clearly to Make Language Comprehensible . . . . . . . . . . . . . . . . . . . . . . . . . 82
Simplify and Elaborate Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Express information in Multiple Ways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Use Controlled vocabulary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Limit the Use of Pronouns and Adjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Limit the Use of and Explain idiomatic Expressions or Culturally Based Terms . . . . . . . . . . . . . 84
Limit “Asides” or Conversations that Are not Linked to the Lesson at Hand . . . . . . . . . . . . . . . . 85
Pause Frequently and increase Wait Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Use drawings and illustrations to Support Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Use dramatic Gestures, Actions, and verbal intonations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Engage ELLs in Classroom discourse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3�3 — Strategies to Help English Language Learners Understand Mathematics Language � � � � � � � 91
Strategies for Students at the Preproduction Stage of Language development . . . . . . . . . . . . . . . 92
Make vocabulary Learning a natural Part of instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
reading Mathematics: Extending Strategies for Use with ELLs . . . . . . . . . . . . . . . . . . . . . . . . . . 105
incorporate Writing in Mathematics: Extending Strategies for Use with ELLs . . . . . . . . . . . . . . 107
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3�4 — Emphasizing and Supporting Problem Solving � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 112
Connect Mathematics to Life occurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Elaborate the Meaning of Words Provided in real-World Problem-Solving Contexts . . . . . . . 113
Use representations to Translate and visualize Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Explicitly Teach and Model Problem-Solving Processes and Strategies . . . . . . . . . . . . . . . . . . . . 114
Embed Clarity Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Provide opportunities to Work with Peers to Solve Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Limit the number of Problems Assigned . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Avoid a Focus on Key Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Address the Use of Extraneous information in Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Be Sensitive when Using Cultural references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
viii Contents
Encourage Students to Write original Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3�5 — assessing English Language Learners in Equitable Ways � � � � � � � � � � � � � � � � � � � � � � � � � � 121
Provide Access to Learning Tools during Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Avoid Linguistic Complexities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Provide Test Accommodations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
daily Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Projects as Assessments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3�6 — Teaching Mathematics in Ways that are Culturally responsive � � � � � � � � � � � � � � � � � � � � � � 130
Teacher Critical Self-Examination and Self-reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Provide a Welcoming Environment for ELLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Attend to individualized Cultural Characteristics and Experiences . . . . . . . . . . . . . . . . . . . . . . . 132
Create a Culturally respectful Learning Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Use Cooperative Learning to Facilitate Language Acquisition and
Mathematics Comprehension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Allow Students to Use First Language as a resource for Learning Mathematics . . . . . . . . . . . . 136
Enhance ELLs’ Self-Awareness as Members of Cultural Groups that Have
Contributed to Mathematical developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Work with others to Make Links to Students’ Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
3�7 — Strategies for Mathematics Teachers Who are Themselves English Language Learners � � 139
Create a Learning Environment that is Accepting of Linguistic differences . . . . . . . . . . . . . . . . 141
Alert Students to Areas of Potential difficulty related to Language . . . . . . . . . . . . . . . . . . . . . . . 141
review the Mathematics Text for Linguistic and Symbolic differences . . . . . . . . . . . . . . . . . . . . 141
Use various Strategies to Produce Comprehensible output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
Collaborate with English Speaking Colleagues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Keep a Journal of idioms/Expressions for Use in Teaching Mathematics . . . . . . . . . . . . . . . . . . 144
Engage in ongoing Professional development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Share and receive Cultural information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Connect with Parents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
resources � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 146
internet resources to Support Mathematics Teaching and Learning . . . . . . . . . . . . . . . . . . . . . . 146
Print resources for Further Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Glossary � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 154
Notes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 156
references� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 157
Index � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 167
Figures
2�1� Division algorithm as represented by different cultures � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 62
3�1� Parallel lines � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 84
3�2� Use arrows to connect ideas and language � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 86
3�3� Four sets of linear equations to look for patterns in slope and y-intercept � � � � � � � � � � � � � � � 96
3�4� Two lines with x- and y-intercepts labeled � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 96
3�5� an example of parallel lines � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 97
3�6� an example of median in the real world � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 98
3�7� Illustrating two different meanings of solution � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 99
3�8� Word wall and personal dictionary entries for function � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 101
3�9� Template for personal dictionary entry � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 102
3�10� Concept map for polyhedron � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 103
3�11� Link sheet for obtuse angle � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 108
3�12� Version 3: Simplified version of the lilies problem � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 125