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English Language Learners in the Mathematics Classroom

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Strengthen mathematical understandings and academic vocabulary with standards-based strategies!

With straightforward language and examples, the authors help teachers develop specialized understanding and knowledge of strategies for supporting a high level of mathematics learning along with language acquisition for ELLs. Providing specific suggestions for teaching standards-based mathematics, this resource:

  • Demonstrates how to incorporate ELL supports and strategies through sample lessons
  • Uses concrete materials and visuals to connect mathematical concepts with language development
  • Focuses on essential mathematical vocabulary
  • Includes brief research summaries with rationales for recommended practices

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Editorial Reviews

Alma Ramirez
"A must-have both for teachers of English learners and those of us who support teachers. Moves far beyond the notions of vocabulary lists or word walls to really tackle the complexities of scaffolding and academic discourse in ways that are comprehensible to all of us!"
Ryann Fletcher
"Provides elementary school teachers with multiple ways of presenting research-based strategies. This book can also help build a foundation for teachers in training."
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Product Details

  • ISBN-13: 9781412937603
  • Publisher: SAGE Publications
  • Publication date: 1/30/2007
  • Edition description: Older Edition
  • Pages: 144
  • Product dimensions: 8.40 (w) x 10.90 (h) x 0.50 (d)

Meet the Author

Debra Coggins is a mathematics education consultant with experience advising districts, coaching teachers, and developing and delivering professional development. As a writer, she has helped develop a number of professional development programs for teachers of mathematics. These include creating CORE Math: Building Strong Foundations, assisting with the development of the Math Case Methods Project and Math Pathways and Pitfalls at WestEd, and coordinating the writing of America’s Choice Core Assignments. She was the lead writer of A Mathematics Source Book for Elementary and Middle School Teachers: Key Concepts, Teaching Tips, and Learning Pitfalls, a resource book for teachers and professional developers. Debra has presented at local, state, and national conferences, with a particular interest in strategies for supporting English learners, and the use of diagrams when teaching concepts related to operations and proportional reasoning. Debra currently assists the West Contra Costa Unified School District with mathematics intervention programs and Oakland Unified School District small schools with teaching strategies for reaching English learners in mathematics classes. Debra has 17 years teaching experience in grades K-12.

Drew Kravin is a mathematics coordinator for the Alameda County Office of Education (ACOE), where he co-directs and teaches in several specialized professional development programs for teachers, K-12. Among his responsibilities, he serves as co-director of ACCLAIM, the Alameda County Collaborative for Learning and Instruction in Mathematics, a professional development program in partnership with California State University East Bay that has provided training for over 2500 teachers since 2000. He also serves as co-director of two California Mathematics and Science Partnership grants, whose purpose is to institutionalize mathematics coaching support in several districts. Additionally, he is coordinator of the Student Work Profile, Internet-based software that facilitates teacher analysis of student work and that also includes a student online reasoning component. Drew served as mathematics and assessment specialist at ACOE prior to his position as mathematics coordinator, was a visiting educator at the California Department of Education, and was a writer for state and national standards. Drew has had a long-standing involvement in bilingual development both personally and professionally, including its connections to mathematics. Drew has been a classroom teacher primarily at the elementary level and a mathematics educator K-12 for over 22 years.

Grace Dávila Coates is the Director of FAMILY MATH, an international program dedicated to bringing families together for the purpose of investigating mathematical ideas, raising awareness of the role of mathematics in education, and opening doors to mathematics understanding and appreciation. FAMILY MATH is based at the Lawrence Hall of Science at the University of California at Berkeley. Grace is the primary author of Family Math for Young Children and Family Math II: Achieving Success in Mathematics. She has designed many professional development models used statewide, nationally, and internationally, focusing on the needs of English learners in mathematics. Grace has presented at local, state, and national conferences and has published numerous articles on mathematics education, English learners, family involvement, and language development. Grace has been a bilingual classroom teacher in grades pre-K through 8 and a mathematics educator for 24 years.

Maria Dreux Carroll is an adjunct professor at San Francisco State University and Holy Names University in Oakland, California where she teaches pre-service teachers mathematics methods. She recently retired from her position as mathematics specialist with the Alameda County Office of Education, but has continued to co-direct the Regional Mathematics Peer Coaching Support Network. Maria also worked as a mathematics specialist, coach and classroom teacher with the Oakland Unified School District, where she created a mathematics coaching support program for 25 Title I schools. Maria became interested in the intersection of bilingual education, English language development (ELD) and mathematics. As a result, Maria began to develop special staff development presentations to address the needs of bilingual and English language learners. Maria has presented at local, state and national conferences addressing the needs of teachers in mathematics content and pedagogy. Maria has been a classroom teacher in grades K-9 and a mathematics educator for more years than she wishes to count, including service in Washington D.C., Baltimore, Maryland, and Oakland, California.

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Table of Contents

Preface     ix
Foreword   Miriam A. Leiva     xiii
About the Authors     xv
Developing Conversational Language: Help English Learners Talk-to-Learn During Mathematics Lessons     1
Rationale From Research     1
Mathematics Teaching Example     2
Geometric Attributes     2
Discussion of the Mathematics Teaching Example     6
Mathematics Goals     6
Language Goals     6
Students of Varying Language Proficiency Levels Working Together     7
Talking and Doing Help With Thinking     7
Developing Awareness of Attributes of Geometric Shapes     8
Teaching Tips     8
Discussion of Conversational Language     9
Why is conversational language important in learning mathematics?     10
Why is a problem-solving approach to mathematics helpful to English learners' language development?     10
What are characteristics of effective prompts for stimulating conversational language?     11
How can you ensure that all children will have a chance to speak and to ask questions?     11
Conversational Language Research     12
Practice and Discussion Questions     14
Developing Academic Language: Develop MathematicsConcepts and Vocabulary for English Learners     15
Rationale From Research     15
Mathematics Teaching Example     16
Word Problems     16
Discussion of the Mathematics Teaching Example     20
Mathematics Goals     20
Language Goals     21
Support Through Primary Language and Cognates     21
Developing Specific Math Vocabulary     21
Opportunities to Use Academic Language     22
Teaching Decisions     22
Teaching Tips     23
Discussion of Academic Language Development     25
Why is it usually not productive to go over new key vocabulary at the beginning of a math lesson?     25
Why is it suggested that we not emphasize key words in math problems?     26
Why do we need to differentiate discussion goals for levels of English language development?     26
Academic Language Research     27
Practice and Discussion Questions     28
Scaffolding: Give Support for Both Mathematics and Language Learning     29
Rationale From Research     29
Mathematics Teaching Example     30
Algebraic Reasoning     30
Discussion of the Mathematics Teaching Example     34
Mathematics Goals     34
Language Goals     34
Advance Organizers     34
Creating Access to the Lesson     35
Creating Support During the Lesson     35
Teaching Tips     35
Discussion of Scaffolding in Mathematics     36
How does cooperative group work provide scaffolding?     37
What are benefits of emphasizing problem solving in mathematics lessons for English learners?     38
How is scaffolding of new mathematics concepts different from carefully planned direct instruction?     38
How is scaffolding used to support English language development during mathematics lessons?     39
Scaffolding Research     39
Practice and Discussion Questions     40
The Role of Concrete Materials: Utilize Objects to Develop Mathematical Understanding for English Learners     41
Rationale From Research     41
Mathematics Teaching Example     42
District Fifth-Grade Benchmark     42
Discussion of the Mathematics Teaching Example     46
Mathematics Goals     46
Language Goals     47
Building Understanding by Using Concrete Materials     47
Expanding Understanding Through Multiple Representations     47
Preplanning Key Lessons     48
Teaching Tips     48
Discussion of Concrete Materials in Mathematics     49
When is it appropriate to use concrete materials in the mathematics classroom?     50
What should teachers be aware of when using concrete materials?     51
Is the concrete-pictorial-abstract sequence still promoted?     51
Concrete Materials Research     52
Practice and Discussion Questions     53
Visual Learning: Provide Mathematical and Organizational Representations as a Regular Component of Instruction     55
Rationale From Research     55
Mathematics Teaching Example     56
Two-Digit Multiplication     56
Discussion of the Mathematics Teaching Example     65
Mathematics Goals     65
Language Goals     65
Use of an Advance Organizer     66
Visual Learning Strategies, Cognitive Tasks, and Language Development     66
Teaching Tips     67
Discussion of Visual Learning in Mathematics     68
What are graphic organizers, advance organizers, and diagrams, and why are they important?     68
Are all learners visual learners?     70
Visual Learning Research     71
Practice and Discussion Questions      72
Questioning Strategies: Ask Questions to Foster Students' Learning of Mathematics and English     73
Rationale From Research     73
Mathematics Teaching Example     74
Probability Introduction     74
Discussion of the Mathematics Teaching Example     79
Mathematics Goals     79
Language Goals     79
Multiple Goals When Asking Questions     80
Questions and Discussions Between Students     80
Teaching Tips     80
Discussion of Questioning Strategies in Mathematics     81
How does placing a focus on questioning affect English learners and their teachers?     82
Should the levels of questions we ask students change as their levels of fluency increase?     83
How can we ensure that we are challenging our students through our questioning?     83
What are levels of questioning that can elicit verbal responses from students with various levels of English acquisition?     84
Questioning in Mathematics Research     86
Practice and Discussion Questions     87
Comprehensible Input: Combine Many Strategies to Develop Mathematics Concepts Through Clear and Effective Instruction     89
Rationale From Research     89
Mathematics Teaching Example      90
Perimeter and Multiplicative Scaling     90
Discussion of the Mathematics Teaching Example     95
Mathematics Goals     95
Language Goals     96
Teaching Decisions     96
Continuously Creating Access     96
Successfully Getting Started     97
Using Strategies to Provide Comprehensible Input     97
Teaching Tips     98
Discussion of Comprehensible Input in Mathematics     99
How can we maximize students' comprehension of a mathematics lesson?     100
How is comprehensible input incorporated in the teaching of mathematics concepts?     100
What is the role of constant monitoring in English learners' mathematics classes?     101
What is the role of thinking and learning strategies in English learners' mathematics classes?     101
Comprehensible Input Research     102
Practice and Discussion Questions     102
Appendix     105
Geometric Shapes     106
Blank Planning Map for Effective EL Mathematics Lessons     107
Lesson-Planning Map: Example From Chapter 3-Planning Map for Effective EL Mathematics Lessons     109
Snail Races: Instructions and Game Board     111
Sample Questions to Support All Learners and Develop Mathematical Thinking     113
References     115
Index     121
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