Determining the Extent to Which Program Structure Features and Integration Mechanisms Facilitate or Impede Doctoral Student Persistence in Mathematics

Introduction Mathematics, as a discipline, is faced with a number of concerns. Over the last twenty years, academic commentators have voiced disquiet over, 'the supply, quality, and composition of the U.S. talent pool in scientific and mathematics fields' (Stage & Maple, 1996, p. 24). A recent survey indicates that throughout the 90s the number of full-time mathematics doctoral students decreased and looks set to continue declining albeit at a slower rate (American Mathematical Society [AMS], 2003). In addition, women and some ethnic minority groups remain under-represented at doctoral level (Herzig, 2002), despite initiatives and resources aimed at recruiting minorities into mathematics. Moreover, the number of doctorates awarded to U.S. citizens is declining (Herzig, 2002). Finally, studies show that as many as fifty percent of all doctoral students depart from their studies (Lovitts, 2001) and mathematics is no exception; attrition rate estimates vary from 30% to 70% (Bowen & Rudenstine, 2002). Attrition is not only a cause for concern in terms of faculty time expended, institutional costs and public resource investment (MLA Committee, 1998), but the individual cost to the student is staggering in terms of financial, personal and professional consequences (Lovitts, 2001). Past research has identified a constellation of factors leading to attrition and, while the following section outlines a number of these factors, it is by no means exhaustive. Some faculty and administrators view doctoral departure as a function of the idiosyncrasies of individual students, such as lack of academic ability, motivation, or commitment. This discourse tends to place responsibility on the shoulders of the student, the so-called 'drop-out'. Yet research indicates that students who withdraw from their doctoral studies and students who persist share a similar grade point average (Lovitts, 2001). In addition, evidence suggests that several pre-entry factors are associated with high attrition such as delayed entrance into a doctoral program, a change of institution and/or discipline of study (Baird, 1993). Other external factors that may impede Ph.D. completion include marriage, having children or caring for elderly parents (Lovitts, 2001). Nonetheless, there are those who argue that the rationale underpinning student departure is partly a function of what occurs post entry to a graduate program (Tinto, 1987) and, as such, high attrition cannot be understood independent of institution context. It is suggested, for instance, that the greater the extent to which students are integrated into the academic and social life of an institution, the more likely doctoral persistence (Lovitts, 2001; Tinto, 1993). As such, there are a number of mechanisms that serve to facilitate integration into a department such as availability of office space, effective mentoring schemes, type of financial support, teaching opportunities, and a good working relationship with advisor (Golde, 2000; Herzig, 2002). In addition, department features such program structure may also assist participation in the social and professional life of the department. Program Structure Features: the Preliminary and Qualifying Examinations A mathematics doctoral program in the U.S. takes the form of two stages. The first stage typically extends over a period of about three years and involves the student taking a number of courses culminating at the University of California with the sitting of a preliminary examination. The preliminary examination is a six hour written examination predominantly covering undergraduate material (UC Berkeley Mathematics website, 2004). The examination is sat before the start of each semester and doctoral students are required to pass it within their first three semesters of entering the mathematics program. The second stage of the doctoral program commences with the qualifying examination which is a three hour oral examination that places emphasis on the students' area of specialization (UC Berkeley Mathematics website, 2004) and this must be attempted within the first two years of entry. …