published_or_final_version / Chinese / Master / Master of Philosophy

This dissertation examines the interactions of mathematicians, mathematics educators, and teachers with a set of 12 algebra problems. The data are from two Making Connections workshops (2006 and 2008) which included members of these three professional groups; each workshop was comprised of 13 participants. The primary analytical focus was a task in which each professional group separately discussed and categorized the 12 algebra problems; interviews were conducted with the participants from the 2008 workshop. The methods and analysis of this study were framed by research on the teaching and learning of algebra, on curriculum use as a participatory relationship, and on the dispositions and beliefs of members of the three professional groups.The study indicated that teachers, as compared to the other two groups, drew more heavily upon their knowledge of students as they made sense of the algebra problems. Teachers were at times concerned with the wording of questions as an obstacle for students. The mathematicians and mathematics educators put a greater focus on algebraic structure as they discussed the problems whereas the teachers put a greater focus on graphing. I connect these findings to the workshop participants' views of algebra.

Thesis (Ph. D.)--Harvard University, 1970. / Includes bibliographical references (p. 286-319).

Thesis (Ph.D.)--City University of New York, 1991. / Includes bibliographical references.

This thesis is principally concerned with George Chrystal's life and his work, mainly in three directions viz., as an experimentalist, a mathematician, and an educationist. The main object is to bring to light the work of a personality who is representative of many more who are always forgotten. The majority of historians of science consider the works of the giants in science, ignoring totally the contributions made by the less prominent people like Prof. George Chrystal. In fact their contributions serve as one of the most important factors in propagation of scientific knowledge. His main contributions: verification of Ohm's Law experimentally; Non-Euclidean geometry; differential equations; text books on algebra; theory of seiches; institution of leaving certificate examination in Scottish education and many more have been discussed in detail. A survey of Chrystal's general thought is given in so far as it may be gathered from his scattered remarks. The references are mentioned by numerals in the superscript, details of which are given at the end of each chapter. The main text consists of six chapters. There are three appendices at the end,' Appendix 'A' consists of his correspondence with different scientists, most of which is still unpublished. Appendix 'B' contains a bibliography of his contributions in chronological order, and Appendix 'C contains his three Promoter's addresses. Tables and figures are attached at their proper places, including some rarely available photographs.

A growing body of literature seeks to challenge the deficit-oriented narratives around Black students in mathematics by exploring the perspectives and experiences of successful Black students and professionals in the field—in doing so, aiming to provide counternarratives to the dominant discourse that center their participants’ voices, as well as to understand the factors that may influence Black students’ decisions to pursue advanced mathematics degrees and careers. Many such studies highlight racialized mathematics identity as a crucial factor for their participants’ long-term mathematics engagement; such studies seek to identify the sociostructural factors that contribute to its development, but generally do not examine the roles of different psychological factors. Despite evidence of the existence of relationships between mathematics identity development and specific cognitive factors such as mathematics conceptions, as well as affective factors such as mathematics self-efficacy, few studies have examined how these various constructs interact with identity development, and in turn, students’ mathematics engagement and learning outcomes. Fewer have examined these factors’ interactions for Black participants. A comprehensive understanding of how and why Black students decide to persist in mathematics necessitates an integrated approach that simultaneously examines the connections between participants’ psychological and sociostructural factors. In light of past findings around the significant role of mathematics self-efficacy in shaping students’ long-term mathematics engagement; prior findings around relationships between mathematics self-efficacy and identity; and the influences of mathematics conceptions on other affective mathematics beliefs, I chose for the present study to investigate the contributing factors for and interactions between mathematics self-efficacy, identity, and conceptions throughout the academic trajectories of several contemporary Black mathematicians. In doing so, I hoped to amplify my participants’ perspectives in the broader conversation around how to support Black students and students belonging to other historically excluded groups as they navigate mathematics learning environments that, at times, fail to stimulate, nurture, or uplift them. Using thematic analysis of several extensive semi-structured interviews, this narrative inquiry investigated these questions through the narratives of five contemporary Black mathematicians who were selected from a prior study on the impacts of sharing diverse mathematicians’ stories with students. Data sources included participants’ extant interview transcripts from both this study and other prior studies; as well as extensive follow-up interviews, online public engagement materials such as lectures and media publications, and my own memos. Data was coded using thematic analysis for both deductive themes related to the conceptual framework for this study, as well as emerging themes suggesting the existence of potential interactions between these constructs. Findings, which are reported in narrative form, suggest the importance of early and ongoing engagement with open-ended and reasoning-based mathematics tasks as a means of promoting broad conceptions of mathematics, self-efficacy for completing more challenging nonroutine tasks, as well as robust mathematics identities. Additionally, and in contrast to much of the literature around self-efficacy sources, findings from the present study highlight the particular importance of vicarious experiences of success by other Black mathematicians in shaping not only participants’ mathematics self-efficacies but their conceptions of mathematics, and accordingly, their dispositions toward mathematics.

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This paper is directed toward helping the new graduate student in mathematics to acquire a feeling for the literature of his field and thus carry out a more efficient literature search. As the field of mathematics developed, the number of journals carrying mathematical articles grew. Today there are over 120 journals devoted in whole or in part to mathematics. This vast amount of literature presents a problem common to beginning graduate students initiating a research project. As an introduction, a discussion is given of the development of mathematics from the time of the first learned academies to the time of Crelle's Journal, with emphasis being placed on some of the outstanding mathematicians of the period. The years covered constitute the pre-birth era of modern mathematical literature. The second section concerns the growth of the literature and contains a partial listing of the major mathematical research journals of the world. Also in this section, there is a discussion devoted to the use of the literature with hints for organizing a systematic literature search. The remainder of the thesis is devoted to some of the major mathematical societies and journals of the world. In these letter sections there is information concerning 23 societies from 11 different countries. Particular emphasis is placed on the American Mathematical Society and its publications as it is one of the foremost organizations of its type in the world today. Much of the information for the sections concerning the societies was obtained by personal correspondence, on the part of the author, with persons directly associated with the various societies. / Master of Science

This research investigated the career trajectories of mathematics professors of African heritage. The principal objective was to determine the factors that promoted self-efficacy, which made them complete a PhD in mathematics or an EdD in mathematics education regardless of the obstacles they encountered. I investigated 10 professors, males and females, of African heritage at the City University of the Northeast by using open-ended biographical questionnaires and individual interviews Several themes emerged from the data collected. The major themes that impacted the career trajectories of African American male and female mathematics professors were (a) family influence; (b) teacher influence; (c) peer influence; (d) problem solving approach; (e) perceptions of mathematics; (f) prior experience; (g) and individual perseverance (determination) and commitment (obligation). The findings of this research suggested that there are opportunities for young men and women of African heritage to develop into successful mathematicians (the term successful mathematicians is used to denote those men and women of African heritage who have completed their terminal degree, in mathematics or mathematics related subjects) provided that parents, teachers, and peers act their part.