THE ROLE OF TRIBAL ELDER IN TEACHING CALCULUS THROUGH AN ETHNOMATHEMATICAL LENS A DISSERTATION IN Curriculum and Instruction and Mathematics and Physics Presented to the Faculty of the University of Missouri-Kansas City in partial fulfillment of the requirements for the degree DOCTOR OF PHILOSOPHY by ROBERT RIGGS M.A., University of Missouri-Kansas City, 2003 B.A., University of Missouri-Columbia, 1983 Kansas City, Missouri 2012 © 2012 ROBERT RIGGS ALL RIGHTS RESERVED ROLE OF TRIBAL ELDER IN TEACHING CALCULUS THROUGH AN ETHNOMATHEMATICAL LENS Robert Christensen Riggs, Candidate for the Doctor of Philosophy Degree University of Missouri-Kansas City, 2012 ABSTRACT In action research study I was the classroom teacher of high school-aged African American students participating in the six-week summer portion of the Reach Up program. The purpose of Reach Up is to help students improve study skills, build confidence, motivation, self-discipline, maturity and better grades so that they can go to the college of their choice. Students selected have demonstrated academic promise, are “first-generation” college students, and have been selected from the city’s urban core high schools. This study examined the relational and instructional dynamics that took place in the classroom in which the curriculum was developed through an ethnomathematical lens. Ethnomathematics is grounded in the Freirean model of valuing the intellectual contributions of marginalized cultures and using these contributions to teach for liberation. This study introduces the culturally responsive strategy of teaching as the “Tribal Elder.” A Tribal Elder is one who is a leader in the community, who knows how to navigate the outside world to ensure survival, is related to the students by kin, and is trusted by the students and their parents. How these relations were built, while at the iii same time engaging the students in high-level mathematics is reported. It was hoped that unpacking my teaching and investigating from the inside would lead to further development of the theory of the mathematics teacher as Tribal Elder in the classroom and could then be emulated by others. iv APPROVAL PAGE The faculty listed below, appointed by the Dean of the School of Graduate Studies, have examined a dissertation titled “The Role of the Tribal Elder in Teaching Calculus through an Ethnomathematics Lens,” presented by Robert Riggs, candidate for the Doctor of philosophy degree, and certify that their opinion is worthy of acceptance. Supervisory Committee Rita Barger, Ph.D., Committee Chair Department of Curriculum and Instruction Elizabeth Stoddard, Ph.D. Department of Physics Jie Chen, Ph.D. Department of Mathematics and Statistics Eric Hall, Ph.D. Department of Mathematics and Statistics Omiunota Ukpokodu, Ph.D. Department of Curriculum and Instruction Dr. Louis Odom, Ph. D. Department of Curriculum and Instruction v CONTENTS ABSTRACT ..................................................................................................................... iii LIST OF TABLES .............................................................................................................. xi ACKNOWLEDGEMENTS ............................................................................................... xii Chapter 1. INTRODUCTION ..........................................................................................................1 Statement of the Problem .......................................................................................15 Purpose of the Study ..............................................................................................20 Research Questions ................................................................................................27 Theoretical Background .........................................................................................29 Critical Theory and Paulo Freire................................................................29 Critical Race Theory ..................................................................................30 Constructivist and Sociocultural Theory ...................................................31 Culturally Relevant Pedagogy ...................................................................32 Ethnomathematics ......................................................................................34 Significance of Study .............................................................................................34 Definition of Terms................................................................................................37 2. REVIEW OF LITERATURE .......................................................................................39 Critical Theory and Paulo Freire............................................................................39 Freirean Ideals in Critical and Culturally Relevant Pedagogy.....................................................................................42 Robert Moses and the Algebra Project ......................................................42 vi Eric Gutstein and Reading and Writing the World With Mathematics ...............................................................45 Critique of Mathematics for Social Justice ............................................................49 Ethnomathematics Framed by Culturally Responsive Teaching .................................................................................52 Critical Race Theory and the Achievement Gap ...................................................56 Critical Race Theory ..................................................................................56 Achievement Among African Americans..................................................60 W. E. B. Du Bois .......................................................................................67 Asa Hilliard ................................................................................................73 Pedagogical Frameworks .......................................................................................80 Teacher Preparation and Practice in the Urban Classroom........................................................................................90 Sociocultural Aspects of the Mathematics Classroom...................................................................................................93 Graphing Calculators .............................................................................................98 Summary ..............................................................................................................100 3. METHODOLOGY ..................................................................................................104 Restatement of Purpose and Research Questions ................................................104 Purpose of the Study ................................................................................104 Research Questions ..................................................................................106 Action Research ...................................................................................................108 Research Perspective............................................................................................110 Participants and Context of the Study..................................................................117 vii Gaining Entry and the Researchers Role .................................................118 Data Sources and Collection Procedure...................................................118 Data Collection ....................................................................................................119 Data Analysis .......................................................................................................122 Field Dependent Teaching ...................................................................................123 Identity .....................................................................................................124 Security ....................................................................................................124 Validity.....................................................................................................125 Teacher Competence............................................................................................126 Student Achievement ...............................................................................126 Cultural Competence................................................................................127 Sociopolitical Competence ......................................................................127 4. DISCUSSION ..........................................................................................................129 Overall Pedagogy, Curriculum Used, and Mathematics Objectives ....................................................................132 Mathematical Stories of the Students ..................................................................136 High Self-esteem and Confidence Toward Mathematics..........................................................................136 Negative Experiences...............................................................................140 Negative Experiences Turned Around By a Caring Teacher ..........................................................................145 “Not Until Everybody Gets It” and “Breaking it Down” ...........................................................................149 Actions of the Tribal