Under Construction: Conceptualizations of Mathematics Competence and Mathematics Self-Concept of a Group of African American Adolescent Students Open Access
Goings, Curtis Vandyke (2014)
Published
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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