Under Construction: Conceptualizations of Mathematics Competence and Mathematics Self-Concept of a Group of African American Adolescent Students Open Access

Goings, Curtis Vandyke (2014)

Permanent URL: https://etd.library.emory.edu/concern/etds/zg64tm68m?locale=en
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Abstract

This study explored the constructions of mathematical competence of six African American adolescent students who participated in a 2011 summer academic enrichment program in an urban setting in the Southeast. The study used a multiple case study design to address the following research questions:

1. What mathematical competence beliefs are held by a sample of adolescent African American students?

2. What mathematics self-concept beliefs are held by a sample of adolescent African American students?

3. In what ways do these students reveal that they construct these math competence and self-concept beliefs?

The multiple case study incorporated interviews with student participants and their parents. Although this research was designed as a qualitative exploration, it supplemented interviews with data collected from administrations of various instruments (e.g., SDQ-II, MIBI-t) and student-generated documents in order to further explore aspects of students' mathematics self-concept and racial identity, respectively, along with their mathematics identity and mathematics socialization.

Findings suggest that participants' beliefs about what comprises competence in mathematics can be compared to Skemp's (1976) notion of relational understanding and the five strands of Kilpatrick, Swafford, and Findell's (2001) concept of mathematical proficiency. Although every participant identified as a "student" or learner and several incorporated descriptions of intelligence in their self-descriptions, none identified in a way that was explicitly or exclusively mathematical--despite differing in levels of achievement, interest, and engagement. Students who exhibited the strongest mathematics self-concept beliefs tended to demonstrate the greatest stability in these beliefs during the period of the study. Participants noted that they were influenced by interactions with particular significant others, including teachers, parents, and peers. Students emphasized that their perceptions of teacher care often facilitated their openness to engage and persist in mathematics. Also, participants indicated that they engaged in constructing their mathematics competence and self-concept beliefs by evaluating the degrees of congruence in their classification of mathematics as a discipline, and their characterizations of themselves as individuals. Although participants who took the MIBI-t expressed high private regard for being African American, they uniformly acknowledged believing that other groups viewed the intelligence of African Americans with relatively low regard.

Table of Contents

Table of Contents

Chapter One: INTRODUCTION 1

Significance 7

Purpose 9

Research Questions 10

Conceptual Framework 10

Chapter Two: LITERATURE REVIEW 15

Prevalent Conceptualizations of Mathematics Competence 16

Student Beliefs about Mathematics 18

Student Perceptions of Mathematical Competence 24

Self-Concept and African American Students 28

Chapter Three: METHODOLOGY 44

Participants and Setting 47

Participant Biographies 52

Data Collection and Analysis 55

Student Interviews 57

Instrumentation 60

Participant-Generated Text Documents 65

Researcher Fieldwork Journal 66

Parent Interviews 67

Reliability 69

Internal Validity 70

External Validity 71

Researcher Subjectivity 71

Researcher Bias 73

WITHIN-CASE ANALYSES 76

Chapter Four: TAMAR: Open Skies 76

Mathematical Competence Beliefs 78

Mathematics Self-Concept Beliefs 82

Constructing Competence 85

The Sky's the Limit 100

Chapter Five: OMARI: Into the Zone 102

Mathematical Competence Beliefs 104

Mathematics Self-Concept Beliefs 112

Constructing Competence 120

Face-ing the Nation 140

Chapter Six: AMINAH: Marching to the Beat of a Different Drummer 143

Mathematical Competence Beliefs 145

Mathematics Self-Concept Beliefs 148

Constructing Competence 153

Marching On 167

Chapter Seven: TYSON: A Bird of a Feather 170

Mathematical Competence Beliefs 172

Mathematics Self-Concept Beliefs 177

Constructing Competence 183

Sticking Together 194

Chapter Eight: BRYAN: Tale of the Tape 197

Mathematical Competence Beliefs 198

Mathematics Self-Concept Beliefs 204

Constructing Competence 213

A Fighting Chance 227

Chapter Nine: GABOUREY: "It's Starting To Click In My Head!" 229

Mathematical Competence Beliefs 232

Mathematics Self-Concept Beliefs 236

Constructing Competence 244

Starting to Click 267

DISCUSSION OF FINDINGS 270

Chapter Ten: CROSS-CASE ANALYSIS 270

Research Question One 271

Research Question Two 287

Research Question Three 305

Mathematics Socialization 306

Mathematics Identity 323

Summary and Recommendations for Further Research 331

Conclusion 338

References 340

Appendix A: SDQII 355

Appendix B: Multidimensional Inventory of Black Identity--Teen 359

Appendix C: Fennema-Sherman Subscales 360

C1: Mother Scale 360

C2: Father Scale 360

C3: Teacher Scale 361

C4: Mathematics as a Male Domain 361

C5: Attitude Toward Success in Mathematics Scale 362

Appendix D: Mathematics Autobiography Protocol 363

Appendix E: Revised Social Knowledge Structure 364

Appendix F: Math Log 365

Appendix G: Student Participant Demographics 366

Appendix H: Student Interview Guides 367

H1: Student Interview Guide 1 367

H2: Student Interview Guide 2 369

H3: Student Interview Guide 3 370

Appendix I: Final Code Key 371

Appendix J: Participant Social Knowledge Structures 373

J1: Aminah's First SKS 374

J2: Aminah's Second SKS 374

J3: Bryan's First SKS 375

J4: Bryan's Second SKS 375

J5: Gabourey's First SKS 376

J6: Gabourey's Second SKS 376

J7: Omari's First SKS 377

J8: Omari's Second SKS 377

J9: Tamar's First SKS 378

J10: Tamar's Second SKS 378

J11: Tyson's First SKS 379

J12: Tyson's Second SKS 379

Appendix K: Multidisciplinary Inventory of Black Identity-Teen (MIBI-t) 380

Appendix L: Participant Math Logs 382

L1: Aminah's Math Log 382

L2: Bryan's Math Log 384

L3: Gabourey's Math Log 385

L4: Omari's Math Log 386

L5: Tamar's Math Log 387

L6: Tyson's Math Log 388

Appendix M: Parent/Guardian Interview Protocol 389

Appendix N: Tamar's Parent Scale Responses 391

N1: Tamar's Father Scale Responses 391

N2: Tamar's Mother Scale Responses 393

Appendix O: Participant SDQ-II Shifts 2011-2012 395

Appendix P: Participant Responses to Mathematics as a Male Domain Scale 399

Appendix Q: Participant Responses to Attitude Toward Success in Mathematics Scale 401

List of Figures

Figure 1. Martin's framework incorporating individual agency and socialization

List of Tables

Table 1. Number and Grade Level of Student Participants

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