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195 Pages·2015·1.71 MB·English

by  Paul Rose

THE ROLE OF TRANSLANGUAGING IN LATINO
MATHEMATICS CLASSROOMS
By
Carlos Alberto Mejía Colindres, B.S., MBA
A dissertation submitted to the Graduate Council of
Texas State University in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
with a Major in Mathematics Education
August 2015

Committee Members:
Samuel Obara, Chair
Gilbert Cuevas
Mary Esther Huerta
Alexander White
COPYRIGHT
by

Carlos Alberto Mejía Colindres

2015
FAIR USE AND AUTHOR’S PERMISSION STATEMENT
Fair Use

This work is protected by the Copyright Laws of the United States (Public Law 94-553,
section 107). Consistent with fair use as defined in the Copyright Laws, brief quotations
from this material are allowed with proper acknowledgement. Use of this material for
financial gain without the author’s express written permission is not allowed.

Duplication Permission

As the copyright holder of this work I, Carlos Alberto Mejía Colindres, refuse permission
to copy in excess of the “Fair Use” exemption without my written permission.
DEDICATION

A mi familia: Todd, Daisy y Eva.
ACKNOWLEDGEMENTS
I would like to thank all the teacher participants of the project CAREER:
Mathematics Instruction for English Language Learners (MIELL) for entrusting and
allowing me to collect an enormous amount of data through a survey and interviews. This
dissertation is the result of focusing on a very small and rich part of the data I collected,
along with digital data collected for the MIELL project. I am especially grateful to the
three teachers that are the subject of this collective case study. Their candor and
willingness to share their language practices during mathematics instruction were
essential in answering my research questions.
Additionally, I would like to thank my dissertation committee for their
encouragement and feedback. In particular, the support of my committee chair, Dr.
Samuel Obara, was fundamental to me in achieving my academic goal. I thank him for
believing in me and accepting the invitation to be my advisor and join my committee. I
am also very thankful to Dr. Mary Esther Huerta for introducing me to the theoretical
frameworks of bilingualism that are the foundation of this study, and by proving detailed
and valuable feedback all along. Likewise, I was fortunate to have Dr. Gilbert Cuevas
and Dr. Alexander White in my committee. Dr. Cuevas’ unconditional support to all
graduate students was very important for me in difficult times, and Dr. White’s insight is
always an asset on any dissertation committee.
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Finally, I would like to acknowledge Texas State University and its Department
of Mathematics for welcoming me to the Mathematics Education doctoral program when
I was an international student from Honduras; my former advisor, M. Alejandra Sorto, for
giving me the opportunity to collaborate with MIELL, a project funded by the National
Science Foundation (grant No. DRL 1055067); Larry Franzen, MIELL’s videographer,
for making the excellent classroom videos that I analyzed for this study; and my favorite
classmate, Rachel Bower, for being my friend and helping me collect teacher data in
South Texas.

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TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ................................................................................................ v

LIST OF TABLES ............................................................................................................ xii

LIST OF FIGURES ........................................................................................................ xiii

ABSTRACT ..................................................................................................................... xiv

CHAPTER

I. INTRODUCTION ............................................................................................... 1

Autobiographical Statement.............................................................................. 1
Background of the Problem .............................................................................. 2
Latino language-minority students ............................................................... 2
English as a second language (ESL) and bilingual education ...................... 5
Research on language and mathematics ....................................................... 9
Statement of the Problem ................................................................................ 10
Purpose of the Study ....................................................................................... 12
Significance of the Study ................................................................................ 13
Research Questions ......................................................................................... 14
Definitions of Terms ....................................................................................... 14
Delimitations ................................................................................................... 16
Summary ......................................................................................................... 16

II. LITERATURE REVIEW ................................................................................. 18

Theoretical Framework ................................................................................... 18
vii
The zone of proximal development ............................................................ 18
Language as a tool for reflection and thinking ........................................... 19
Teacher Characteristics ................................................................................... 19
Support of Students’ First Language .............................................................. 22
Bilingual acquisition ................................................................................... 22
Social language, academic language, and bilingual learners ..................... 24
The interdependence hypothesis and the Common Underlying
Proficiency .................................................................................................. 25
The threshold hypothesis ............................................................................ 26
Bilingual education ..................................................................................... 27
Successful Schools for Multilingual Children ............................................ 28
Code-switching ........................................................................................... 30
Bilingual learners’ code-switching in mathematics classrooms ................. 32
Bilingual teachers’ code-switching in mathematics classrooms ................ 33
Flexible convergent arrangements ......................................................... 36
Flexible multiplicity arrangements ........................................................ 37
Bilingualism and Mathematics ....................................................................... 37
Costs of bilingualism in mathematics ........................................................ 38
Benefits of bilingualism in mathematics .................................................... 39
Divergent and critical thinking .............................................................. 39
Metalinguistic awareness and executive control.................................... 40
Limitations of research results on bilingual advantages ............................ 42
Translanguaging .............................................................................................. 43
Origin and definition .................................................................................. 43
Connection to Cummins’ bilingual theoretical frameworks ...................... 44
Translanguaging in bilingual mathematics classrooms .............................. 45
Summary ......................................................................................................... 47

III. QUALITATIVE METHOD............................................................................ 50

Research Questions ......................................................................................... 51
viii
Study Setting ................................................................................................... 51
Research Participants ...................................................................................... 52
Qualitative Approach ...................................................................................... 52
Interviews ........................................................................................................ 53
Classroom Observations ................................................................................. 53

IV. ANALYSIS OF INTERVIEWS ..................................................................... 55

Introduction ..................................................................................................... 55
Teacher Characteristics ................................................................................... 56
Mrs. Aguirre. .............................................................................................. 56
Mr. Long. .................................................................................................... 60
Mrs. Quiróz. ............................................................................................... 64
Synthesis. .................................................................................................... 68
Support of Students’ First Language .............................................................. 70
Mrs. Aguirre. .............................................................................................. 70
Mr. Long. .................................................................................................... 75
Mrs. Quiróz. ............................................................................................... 77
Synthesis. .................................................................................................... 79
Bilingualism and Mathematics. ...................................................................... 81
Mrs. Aguirre. .............................................................................................. 81
Mr. Long. .................................................................................................... 82
Mrs. Quiróz. ............................................................................................... 83
Synthesis. .................................................................................................... 84
Translanguaging .............................................................................................. 85
Mrs. Aguirre. .............................................................................................. 85
Mr. Long. .................................................................................................... 91
Mrs. Quiróz. ............................................................................................... 92
Synthesis. .................................................................................................... 99

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V. ANALYSIS OF CLASSROOM OBSERVATIONS ..................................... 101

Introduction ................................................................................................... 101
First Classroom Observation......................................................................... 102
Mrs. Aguirre. ............................................................................................ 102
Mr. Long. .................................................................................................. 108
Mrs. Quiróz. ............................................................................................. 113
Second Classroom Observation .................................................................... 121
Mrs. Aguirre. ............................................................................................ 121
Mr. Long. .................................................................................................. 124
Mrs. Quiróz. ............................................................................................. 128
Third Classroom Observation ....................................................................... 135
Mrs. Aguirre. ............................................................................................ 135
Mr. Long. .................................................................................................. 137
Mrs. Quiróz. ............................................................................................. 140
Synthesis of the Classroom Observations ..................................................... 144
Support of students’ first language. .......................................................... 144
Translanguaging. ...................................................................................... 145

VI. DISCUSSION ............................................................................................... 148

Introduction ................................................................................................... 148
Teacher Characteristics ................................................................................. 149
Support of Students’ First Language ............................................................ 151
Bilingualism and Mathematics ..................................................................... 153
Translanguaging ............................................................................................ 154
Implications for Practice ............................................................................... 158
Limitations of the Study................................................................................ 159
Directions for Future Research ..................................................................... 160

APPENDIX SECTION ....................................................................................... 162
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