The Doctorate Is Part of the Infrastructure of Our Research Field (2024)

The Conference on Doctoral Programs and the Survival Problem

A year ago, toward the end of October 2022, some 80 mathematics education faculty members from universities across the U.S., including myself, met in Las Vegas for a third conference on doctoral programs in mathematics education in the U.S. The prior conferences, organized by the pioneering efforts of Bob Reys, happened in 1999 and 2007 and resulted in important reports (respectively, , and ) and a set of standards for doctoral programs in mathematics education that received the endorsem*nt of the Association of Mathematics Teacher Educators (AMTE).² An important component of these standards is the core knowledge of mathematics education that doctoral programs are expected to impart, often through mathematics-education-specific coursework. The avowed goal for the 2022 conference was to review and revise these standards. Whereas at the end of the conference we were left unclear about the existence of enough available energy and will to revise those standards, more fundamental questions were also raised that, in my view, may need to be addressed regardless. These questions included the following:

• Are doctorates in mathematics education going to survive in the U.S.?

• Is mathematics education research going to survive?

In case these questions, which were endorsed by a few of us, may seem a bit alarmist at first glance, let me give a bit of context to explain my logic.

Two decades ago, some in our field perceived that we had a broad landscape in which our field could make its mark. A growing number of tenure-line faculty positions in mathematics education were available for individuals with doctorates to aspire to occupy. Many also had a sense that, even if our field were still young, the knowledge developed in mathematics education research should, among other goals, support the development of prospective mathematics teachers and mathematics curricula for use in schools. And much energy and resources seemed to be available to dedicate to doctoral preparation in a context of generous support from the National Science Foundation for the development of capacity to accomplish those tasks.³ The standards for doctoral programs and the later emergent ideas that niches of specialization could be fostered or accreditation of doctoral programs in mathematics education in the U.S. might be advisable were, in my view, a response to such a sense of abundance (). That sense of abundance has, however, been changing.

A Changing Landscape

Some of us are perceiving much less abundance of riches these days, to the point that, even if the survival questions bulleted earlier may read literally as alarmist, they should be seen as an invitation to think proactively and engage in conversations about how to steward our field in a changing landscape. And the landscape is indeed changing. Across academia, tenure-track jobs, for which doctorates are necessary, have been losing ground with respect to contingent faculty jobs. Some of us have faced difficulties offering doctoral courses in mathematics education in our own institutions, as expectations about the minimum number of students registering to take courses threaten their viability and the numbers of students available to take those classes have decreased. In some cases, department chairs (including myself, when I was in that role at my university) have suggested that instructors of courses that had previously focused on a particular range of phenomena in mathematics education (e.g., students’ thinking and learning) should make such courses appealing to all areas of science, technology, engineering, and mathematics (STEM) by including readings from research in those other content areas. In other cases, instructors have been able to maintain a focus on solely mathematics education research but have been expected to enroll students aspiring to master’s degrees. In yet other cases, faculty members have been asked to sponsor independent reading seminars in lieu of offering courses. Insofar as doctoral programs are embedded in single university institutions and the viability of doctoral courses depends on registration numbers, we may soon be entering a reality in which many doctoral programs cannot guarantee the availability of the courses that cover the material recommended by the doctoral program standards. In my own institution, the mathematics education specialization is fading away alongside most others and being replaced by a program in Educational Studies in which courses are expected to attract people focused on all content areas. This tendency seems common at least across programs housed in leading schools and colleges of education, where the sizes of entering doctoral cohorts have been decreasing. One reason for such reduction is the increasing cost of attendance and the increased expectation that financial support for the cost of attendance and living expenses be provided for all doctoral students.

To complement those impressions, consider what we can glean from the Survey of Earned Doctorates of 2021 (SED; National Center for Science and Engineering Statistics, 2022). The survey compared the changes in the number of doctorates per field between 2001 and 2021. Whereas the total number of doctorates each year has increased by 28% during those 20 years, the fields that have increased the most are science and engineering, a category that includes psychology and social sciences in addition to the STEM disciplines, but not mathematics or science education specializations of doctorates in education. The largest increases are in STEM fields themselves: computing and information sciences (184%), mathematics and statistics (99%), and engineering (85%). In contrast, the numbers and change percentages for doctorates in education have experienced a marked and consistent decline in the last 20 years—from 6,356 in 2001 to 4,252 in 2021, or an accumulated decrease of 33%. The data in mathematics education present an exception, as reported by Reys and Reys (2016): The number of graduates was still increasing in 2014 (681 in 2010–2014, compared with 607 in 2005–2009 and 429 in 2000–2004). Also, according to Robert Reys (personal communication, June 12, 2023), 1,422 doctorates in mathematics education were conferred between 2011 and 2020, compared with 1,092 between 2001 and 2010.

Though a small number of universities offer doctorates in mathematics education within mathematics departments, the majority of doctoral degrees in mathematics education in the U.S. are conferred by schools and colleges of education (). Because most mathematics education scholars on faculty in schools and colleges of education in the U.S. are gathered in departments more broadly named (e.g., curriculum and instruction, educational studies, teacher education), doctoral degrees in mathematics education often are officially specializations of doctorates in education. One of the ways in which schools and colleges of education have been responding to the decrease in the number of doctoral students is by reducing the number of specializations within the larger field of education research, conceivably combining mathematics education with other disciplines into specializations such as STEM education, teacher education, or the learning sciences, or by looking for interdisciplinary themes of contemporary interest, such as equity and social justice or instructional improvement, to form specializations that are better subscribed. Thus, whereas the number of doctorates in mathematics education may not (yet) be decreasing as much as those in education as a whole are, the preparation that those students receive in coursework in schools and colleges of education seems to be increasingly less specific to our field of scholarship.

Much has happened in the two decades covered by the SED report that may have caused these changes, and I do not intend to analyze those possible causes—such an exercise is likely to exceed my expertise and the space available here (but see Gumport, 2023, for a quick recent history of graduate education). Furthermore, whether those institutional changes are seen as positive or negative depends on the perspective one takes. I have the privilege now of not having to think as an administrator in an institution and, instead, have the obligation to think as a steward of our research field. Thus, my intention is to highlight and address the questions that arise for us as a field as a result of those institutional responses. Whereas such institutional responses to the circ*mstances are reasonable within the frame that has been used in the U.S. to confer doctoral degrees, as a field of scholarship we must also question whether such a frame is still serviceable to provide for the needs that doctoral degrees have been expected to serve.

In the next two sections, I elaborate on those two issues. First, I identify what I call the schooling of the doctorate as the frame of reference that has enabled the pursuit of doctorates in the U.S. Second, I identify three important functions that have been served by the pursuit of doctorates. After those two sections, I come back to the question of how we as a knowledge production field can react to the present challenges to doctoral programs in mathematics education in the U.S.

The Schooling of the Doctorate in the U.S.

Whereas the conferring of doctoral degrees has existed for centuries and across countries, large variability exists across time and place in what it takes for doctoral degrees to be awarded, with the oral defense of theses being the consistent element among much variability otherwise (W. Clark, 2006). Scholarship in higher education has accounted for this variability historically and internationally (B. R. Clark, 1993; W. Clark, 2006; Gumport, 2023). Our international readers may benefit from learning how American universities have organized to confer doctoral degrees, and this description may also underscore for those of us working within the U.S. how the contexts in which doctorates are conferred contribute to frame the ways in which we initially tend to respond to the challenges to and changes in doctoral education.

Doctoral pursuit in the U.S. has been associated with the concepts of a “doctoral program” and “doctoral student,” which allow American universities to incorporate doctorates within their teaching operations by establishing similarities of expectations with other programs of study. Like undergraduate and master’s degree programs, American doctoral programs entail acquiring a number of instructional credits from courses taken. Additionally, doctoral programs also require receiving instructional credit from other experiences unique to doctorates such as apprenticeships, passing qualification exams, and the writing and oral defense of a dissertation. Thus, in speaking of a “doctoral program,” one applies to the awarding of doctoral degrees a similar institutional frame as that with which the higher education sector organizes itself to develop individuals and create social expertise: One frames doctorates as another round of schooling, epitomized in how some scholars write about PK–20 (meaning prekindergarten to 20th grade!) as a schooling continuum. In such a frame, universities compete with one another for the most desirable students and use their doctoral programs, like other degree programs, as vehicles for their brand. The concepts of “doctoral program” and “doctoral student” make the awarding of doctoral degrees a consequence of a form of schooling that I refer to as the schooling of the doctorate. By this I mean that doctorates are framed as educational programs owned and offered by single institutions.

Could it be different? Reys and Dossey (2008) included concrete examples of how other countries confer doctorates in mathematics education. I am not necessarily advocating for this alternative, but asking you to consider that doctoral degrees could be conferred to individuals who have spent time learning from more experienced researchers and producing scholarship with them. When that scholarship reaches critical mass, the novice scholar might present it to a group of more experienced scholars (e.g., a faculty) and receive a doctoral degree in recognition. That is, doctorates could be seen, alternatively to a form of schooling, as one of the outputs of the research operations of a scholarly community that relies on members of university faculties for final evaluation: Promising scholars might be offered the opportunity to work within a lab or center and learn from the work in which they are engaged, as well as from research seminars, bibliographic resources, consultations with more senior researchers, and minicourses offered by professional associations. This is how the doctorate in mathematics at Universidad Nacional de Córdoba in Argentina was structured when I was there in the early 90s. Imagining this alternative can serve as a comparison backdrop when cost is used to argue for why mathematics education specializations are not viable.

The location of doctoral studies within the education function of universities frames it within similar considerations as those of other degrees, which have the dual function of individual development and workplace preparation and which usher considerations that are individually centered (e.g., personal responsibility, personal fulfillment, career development, customer satisfaction, cost of attendance, return on investment, etc.). But the alternative possibility of considering the doctorate as an output of research operations brings with it considerations of a communitarian nature (with community meaning the scholarly community of a field of studies, and possibly also the national community or the human community).

Schooling the doctorate as a way of organizing for the pursuit and awarding of doctoral degrees has made some sense for a long time in the U.S., but it has also been limiting. In the following section, I discuss three functions of the doctorate and how they have been served by the schooling of the doctorate. Because the schooling of the doctorate has been neither eternal nor universal, we should think about whether the current challenges it faces not only force us to consider changes but also give us an opportunity to reform its structures to better serve all these functions; indeed, to turn those functions into purposes that we strive to accomplish.

The Functions that Have Been Served by Schooling the Doctorate

Doctoral degrees satisfy, at least in principle, three different functions: Marking accomplished individual development, credentialing social expertise, and enabling knowledge production. The schooling of the doctorate has been a useful frame for achieving those three functions in some ways. Yet, the present challenges to our capacity to offer mathematics education courses and whole specializations means that the possibility that institutionally contained programs will continue to satisfy all three of those functions needs to be questioned and such organization revisited.

Recognition of individual accomplishment is historically at the root of the PhD degree. According to W. Clark (2006), the rise of the PhD is connected to the efforts of German humanists to have their scholarship merit social recognition equal to that given to jurists, physicians, and theologians, who had previously been the only ones who availed themselves of the “doctor” title. An important virtue of the schooling of the doctorate is that it infuses an institutionally regulated, and hence more predictable, sense of time for an individual’s pursuit of the scholarship that can be recognized with a doctorate. Instead of individuals chipping away at a dissertation problem for many years, individuals may start their doctoral pursuit even before they know anything about the problems they will investigate. Indeed, aspirants can develop intellectually over time, from someone who may not yet be a scholar to someone who has become a scholar. In this sense, schooling the doctorate has contributed to the democratization of both the degree and of scholarship as a whole because it has provided a path toward the doctorate for people who can potentially come from diverse prior exposure to scholarship. The schooling of the doctorate brings with it the familiar ways of passing the time in higher education (e.g., doing course assignments, attending classes) and uses them to usher novices into scholarly work. If individual development were the single function of the doctorate, a way to respond to the decrease in numbers of available doctoral admissions could be to make doctoral programs purposefully tailored to the needs and goals of the individual student, for example, as recommended by Michael Solomon, the Dean of the Graduate School at the University of Michigan, whose initiative “Advancing New Directions in Graduate Education” seeks to shape doctoral programs across the board to be more student centered. This possibility seems sufficiently widespread that Gumport (2023) also recognized it as reasonable. But individual development is not the only function that doctorates serve; turning that into the purpose of doctorates ignores other important functions.

The doctoral degree has also served as a credential of socially valued expertise—that is, as a source of workforce training. Specific courses and experiences, beyond the impact they make on individual development, have contributed to certifying the holder of a doctorate as an expert in a field of scholarship. For a long time, at least in the U.S., obtaining stable faculty positions in universities depended on having a doctorate. This was not just because the degree offered a mark of individual accomplishment, but also because the degree attested to some amount of knowledge and capacity of social value—knowing enough of a subject to be able to teach it to undergraduates. The possibility for doctoral aspirants to take courses in mathematics education has been particularly serviceable to the preparation of experts who would engage in mathematics teacher education, usually as professors in teacher education programs or teaching undergraduate mathematics courses taken by prospective teachers.⁴ This can explain why AMTE got involved in sanctioning standards for doctoral programs in mathematics education: To educate mathematics teachers, the expectation that the educator have expertise in the field of mathematics education is reasonable. Although this is by no means the only function of doctoral courses in mathematics education, the course-taking aspect of the schooling of the doctorate affords structures that permit doctoral aspirants to cultivate expertise that serves this and other future work (e.g., curriculum development). This function of the schooling of the doctorate can be seriously undermined by initiatives to make doctoral programs more student centered or by turning diverse specializations into programs of wider appeal with courses that have more general foci. Yet, the need for this socially valued expertise seems to have been on the decline, considering the reduction in available tenure-track faculty jobs. And yet the doctorate also serves as more than the certification of expertise.

A third function of the doctorate is to assist in the production of public knowledge by preparing people to do research and expecting them to produce original scholarship. Because newly minted doctorates are expected to have written a dissertation reporting on original research—a development that W. Clark (2006) dated to the middle third of the 19th century—the conferring of doctoral degrees is associated with what I would like to describe as the reproduction of the conditions of production of knowledge and of fields of knowledge.⁵ Through both the activities done in pursuit of their doctoral dissertations and the experiences gained through other research work in which candidates get involved during their time in doctoral programs (e.g., working in research labs), the schooling of the doctorate has enabled fields of knowledge to generate more knowledge and more capacity for knowledge creation. The conditions of production of knowledge include, especially, the skills and dispositions to engage methodically and inquisitively with the world, with the goal of contributing to the knowledge of humankind.

Though courses and the expectation of a doctoral dissertation have been important for doctoral programs to contribute to knowledge production, the facts that doctoral programs exist within research universities, which are sites for the production and cultivation of knowledge (and not only developers of individuals or purveyors of workforce training), and that many doctoral programs have been configured as requiring full-time attendance have been even more important: They have enabled doctoral aspirants to be apprenticed into research by working next to researchers who advance the production of knowledge. At a time in history in which generative artificial intelligence promises to revolutionize the more mundane tasks of knowledge retrieval and dissemination, the apprenticeship into the creative aspects of research that doctorates have made possible can make a real difference not only for our knowledge field but also for individuals and society.

That the U.S.’s schooling of the doctorate has been able to fulfill these three functions—individual development, creation of social expertise, and knowledge production—has been a matter of admiration by some scholars overseas. Still, although the schooling of the doctorate in mathematics education has done so, it has not done so optimally, equitably, or efficiently.

The Present Challenges to the Schooling of the Doctorate

The three functions of doctoral training have been maintained in a delicate equilibrium that is not without strain to the parties involved. For example, the schooling of the doctorate entails expensive investments for everybody involved, especially in this day and age when bottom-line considerations are the coin of the realm in higher education (Gumport, 2023). Even in the best-case scenario—when doctoral students are supported by research assistantships that pay their tuition to study and wages to apprentice in research next to active scholars—individual students often invest years of meager income without being sure that they will find gainful employment at the end. Universities that offer doctoral programs spend thousands of dollars subsidizing students’ tuition and allocating faculty time to teach courses that do not generate as much revenue as more robustly enrolled undergraduate and master’s courses. And research sponsors spend thousands of dollars in work wages that may not always be the most efficient way to get research work done (as compared, for example, with paying for research staff who work full time).

Other challenges have been mounting from all sides. Faculty have been experiencing challenges in recruiting doctoral students to enroll in doctoral courses in mathematics education. Universities have been challenged in their capacity to offer those courses, and hence maintain specializations, given the expense of offering courses that are undersubscribed. Doctoral students have been increasingly challenged by the reduction in tenure-track employment prospects and programs have not always prepared them well to take jobs in the growing education research sector. And research sponsors (e.g., faculty members who have research grants), already working in a context of more competitive grant-getting and limited budgets, have found it increasingly difficult to fundraise for, recruit, and retain individuals who want to apprentice into research assistant positions.

The schooling of the doctorate has fulfilled the three functions by shaping programs that, by being contained within single institutions, are also unlikely to be optimal in meeting the needs of all parties involved. A single institution does not have the resident expertise or availability to teach all the courses that would build capacity for all possible job prospects requiring a doctorate; the manifold of available research apprenticeship experiences that can use the skills and interests of all available apprentices; or even the appropriate match of financial support, social context, and mentoring capacity for the needs and goals of all individual students. Even if students are financially well supported, institutions do not often match the needs and potential of doctoral aspirants with the mentoring that will help them thrive or the research apprenticeships that build on their strengths; some doctoral students do not get serious apprenticeship into research even if they are well mentored to complete the requirements of their doctoral program. That is, the challenges of the schooling of the doctorate are related not only to efficiency, but also to equity. As Hiebert et al. (2008) noted as a summary of their reflection:

The U.S. system of mathematics education doctoral studies severely underestimates the depth of training required to do the work of a mathematics educator. If the system is to improve, it must . . . adopt strategies for improvement that identify the major work areas or specialties for mathematics educators and then provide authentic and extensive preparation in just these areas. (p. 250)

Because we experience these challenges within each university, our first, inertial, response may, understandably, be an intramural or intrainstitutional one: If we cannot afford to offer a doctoral program specifically in mathematics education, what doctoral program could we afford to offer instead? In those questions, “we” is often interpreted as the members of a faculty in a given institution. But we can, and I invite us to, think of “we” as all of us mathematics education scholars committed to stewardship of our research field, and ask instead: Is a series of distinct intramural or intrainstitutional responses the best way to respond to the challenges of the schooling of the doctorate? Can we, as workers in a research field, design ways of conferring doctorates that will purposefully aim at satisfying the three functions of a doctorate efficiently and equitably?

The Doctorate Is Part of the Infrastructure of the Research Field

From my vantage point as editor of JRME, I see a lot more cooperation and collaboration across institutions: Reviewers mentor authors through their reviews, even though they necessarily work in different institutions; authors from different institutions collaborate in coauthoring papers that report about joint projects. As a component of our field’s research infrastructure, the journal not only provides a cooperative resource for our field but also receives collaborative stewardship efforts from our field’s citizens—authors and reviewers. The same can be said about other components of our field’s research infrastructure, such as conferences and professional associations.

The doctorate is another element of that infrastructure. As producers of knowledge, we look to emerging scholars as those who might continue and improve our knowledge production. Moreover, our research field relies on new scholars to continue to expand its focus and its gaze (Herbst et al., 2022). We rely on the production of doctorates across all institutions to prepare people for this work. At this moment in which the schooling of the doctorate runs the risk of failing to commit to the purpose of knowledge production, could we muster enough strength and vision to rethink doctoral preparation for research in mathematics education not as an intramural teaching operation but as a cooperative, interinstitutional professional service that builds on our aggregate research operations? By virtue of serving to mark individual accomplishment, identify social expertise, and foster knowledge production, doctorates are key elements of our field’s human infrastructure. As a research field, we draw on doctorates to recognize and promote our field’s workers, to disseminate our expertise through education and service, and especially to grow our capacity to produce new knowledge. Could we, for a moment, set aside the thought that, as faculty members, we are employed by different institutions, and instead encourage the thought that, as scholars, we serve a common field of knowledge production? Could we come to think of a response to the challenges the schooling of the doctorate is facing in a way that is not subservient to schooling but that complements and improves on schooling so as to ensure that all three functions of the doctorate are held as purposes? What could that look like? The next editorial will propose some ideas, but until then I hope we can begin to engage in this conversation.