Module 10: Discussion 10: Becoming Quantitative

Drawing on the work of several prominent scholars, the author describes the evolution of quantitative critical inquiry and compares this perspective to traditional research paradigms.

Answering Critical Questions Using Quantitative Data

Frances K. Stage

With this volume we seek to demonstrate the ways that we as scholars turn our quantitative skills toward asking and answering critical questions in higher education research. We examine a variety of higher education issues from a critical stance, using quantitative methods. Collectively, our work demonstrates ways of moving beyond traditional conceptualizations of quantitative research. We use our scholarship to push the boundaries of what we know by questioning mainstream notions of higher education through the examination of policies, the reframing of theories and measures, and the reexamination of traditional questions for nontraditional popula- tions. Although the work presented here is divergent, the commonality of the presentations lies in each scholar’s critical approach to conventional quantitative scholarship.

In the following chapters the authors focus on research questions rather than methods or findings. They describe the ways conventional research drove them to the questions of their studies, and then tell how those results challenged the status quo. Because the perspective of this vol- ume is on the framing of the research questions, methods and results are secondary and are presented only to illustrate various applications of crit- ical quantitative inquiry. We hope to demonstrate that being a quantitative criticalist comes with the questions we ask, not with the methods we use to answer them.

In this chapter, I invoke various scholars’ definitions of critical inquiry, and relying primarily on Kincheloe and McLaren (1994), provide arguments

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NEW DIRECTIONS FOR INSTITUTIONAL RESEARCH, no. 133, Spring 2007 © Wiley Periodicals, Inc. Published online in Wiley InterScience (www.interscience.wiley.com) • DOI: 10.1002/ir.200

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to justify taking the discourse beyond discussions of method. Next I pro- vide examples of the work of several prominent quantitative criticalists in higher education, and then describe more fully the characteristics of this approach vis-à-vis current dominant research paradigms. Finally, I provide a brief overview of my own research on students’ participation in mathemat- ics and science-based majors as I’ve moved from being a postpositivist to a quantitative criticalist.

Critical Theory

Critical theory evolved from the German Frankfurt school and was described by Habermas (1971) as differing in aim, structure, and justifica- tion from “quantitative” (described as empirical-analytic) science, which is designed to predict and control natural events. Tierney and Rhoads (1993) described critical theorists as those who (1) seek to understand the experiences of individuals and groups in light of cultural constraints and societal prescriptions; (2) recognize the importance that power plays in structuring human subjectivity; (3) give credence to the importance of cul- tural difference; (4) investigate how science and knowledge get defined and changed; and (5) extend theory into the arena of action.

Schwandt (1997) described critical social science as characterized by five general themes. First, it aims to integrate theory and practice so that individ- uals are aware of inconsistencies and contradictions between their belief sys- tems and social practices. Second, critical social science rejects the idea of a detached social scientist and “is oriented toward social and individual trans- formation” (p. 24). Third, critical social science rejects traditional empirical research schemes, which aim to eliminate crises, conflict, and critique. Criti- cal social science embraces practical, moral, and ethically and politically informed research. Fourth, critical social inquiry requires enlightened self- knowledge and effective social political action. Finally, critical social research examines possibility and transformation as outcomes of the research.

Kincheloe and McLaren (1994) present the project of critical research as interrogation “in order to uncover the contradictions and negations embodied in any objective description” and to discover the “hidden assump- tions . . . the critical researcher must dig out and expose” (p. 144). The other authors in this volume and I claim that such descriptions do not pre- clude the possibility of quantitative approaches. In addition, we believe that as quantitative researchers we are uniquely able to find those contradictions and negative assumptions that exist in quantitative research frames.

Although the majority of critical work in higher education is conducted by scholars who apply naturalistic and qualitative techniques to answer questions, well-known scholars outside higher education promote the use of data and numbers in critical work, such as Carspecken (1996) and Com- stock (1982 ). Even Karl Marx (1999) employed quantitative analysis in his socialist arguments (see Das Kapital). As a group, the authors in this vol-

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ume hope to refute claims that quantitative analysis is always formulaic, reductive, and instrumental in approach. Rather, we demonstrate that work- ing with data in the form of numbers can make a contribution to critical inquiry in higher education.

To structure the argument, I chose Kincheloe and McLaren’s (1994) definition of critical theory. Their definition stresses underlying common- alities of definitions that they caution should not imply consensus. For example, Lather’s (1992) definition of critical inquiry most often includes inquiry into how lives are mediated by classism, racism, sexism, and het- erosexism but assumes qualitative approaches to those questions. Kinche- loe and McLaren’s definition is appealing because they avoid methodological assumptions that would preclude the reason for this volume, and they seek a consensual definition of critical theory.

Briefly, Kincheloe and McLaren (1994) describe as critical a researcher or theorist who attempts to use his or her work as a form of social or cul- tural criticism and who accepts the following paraphrased assumptions:

• Thought is mediated by socially and historically created power relations. • Facts cannot be isolated from values. • The relationship between concept and object is never fixed and is often

socially mediated. • Language is central to the formation of subjectivity. • Certain groups in society hold privilege over others that is maintained if

subordinates accept their status as natural. • Oppression has many faces that must be examined simultaneously. • Mainstream research practices generally reproduce class, race, and gen-

der oppression.

The seven elements of Kincheloe and McLaren’s (1994) definition, although broad and consensus seeking, do not preclude quantitative inter- rogations of these issues.

In fact, many researchers in higher education use quantitative means to “attempt to confront the injustice of a society or a sphere within the soci- ety” (Kincheloe and McLaren, 1994, p. 140) and to demonstrate class, race, and gender oppression using numbers. For example, Glazer-Raymo (2005) used numbers to demonstrate inequities for women in academe, and Slaughter and Rhoades (2004) used quantitative approaches to illuminate the monetary buildup of technology and “big science” at the expense of the social sciences and the humanities in higher education.

Further, Kincheloe and McLaren enjoin researchers to become self- conscious, a noble aspiration for quantitative researchers. With heightened awareness, who better to discover “ideological imperatives” and “epistemo- logical presuppositions” as well as “subjective, intersubjective, and norma- tive reference claims” than those who see the direct results of those claims in their everyday work (Kincheloe and McLaren, 1994, p. 140).

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Recently scholars have written in more inclusive terms across the quan- titative and qualitative paradigms. For example, Tashakkori and Teddlie (1998) write of a pragmatist paradigm that argues against dominant philoso- phies and rejects the “forced choice” between qualitative and quantitative approaches. They acknowledge the value-laden nature of research, that fact is theory-laden, and that the nature of reality is constructed. Research approaches are viewed as part and parcel of an eclectic tool kit, wherein the researcher hunts for the tool to fit the question.

In contrast, the quantitative criticalist, rather than confirming con- ventional wisdoms and seeking consensus, adapts a proactive stance by consciously choosing questions that seek to challenge. The quantitative criticalist seeks to forge challenges, illuminate conflict, and develop critique through quantitative methods in an effort to move theory, knowledge, and policy to a higher plane.

Quantitative Possibility

According to critical theorists, the project of critical theory is not merely the rewriting of the world but also “posing the research itself as a set of ideo- logical practices” (Kincheloe and McLaren, 1994, p. 144). Indeed, without broad questioning of ideological practices, the need for rewriting would be an endless duplicitous task. One group of theorists and researchers would continually produce work that the second group of theorists would then examine for flaws and refutations.

Kincheloe and McLaren (1994) enjoin that “[e]mpirical analysis needs to be interrogated in order to uncover the contradictions and negations embodied in any objective description” (p. 144). But who better to help uncover the “ideological inscriptions” in quantitative research than quanti- tative analysts themselves? As an example, recently John Braxton (2000) edited a book focused on challenges and revisions to a widely used theoret- ical model in higher education, the Tinto model of college student persis- tence. Two dozen scholars with years of research suggested additions and modifications based on their successes, failures, and discoveries using that model. This book can serve as an example for future conference symposia, reports, and books questioning assumptive practices and generating possi- ble alternatives .

Consider the following possibilities:

• A graduate student observes underlying assumptions in sociological causal models. She notices that by failing to take into account family income, empirical research consistently problematized (stigmatized?) sin- gle motherhood. Her quantitative dissertation controls for income to examine the relationships of single motherhood and single fatherhood to various educational and social benchmarks for children.

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• Two researchers notice in their own research that traditional causal mod- els of college student satisfaction and retention do not help explain the college experiences of immigrant students. In interpretive studies of immigrant college students’ experiences, they read about the demoraliz- ing effects of campus racism. They design a quantitative study that includes indicators of racism resulting in a more clear understanding of immigrant students’ satisfaction and persistence.

These hypothetical examples are not unlike the origins of some quan- titative research being conducted today. Increasingly, researchers do not need to have a personal sociocultural stake in outcomes (although they some- times do) in order to recognize erroneous assumptions and ideological traps. Enlightened quantitative researchers are often better able to uncover the “hidden assumptions” and “ideological inscriptions” in their own work, as well as in the quantitative work of others. Researchers inexperienced in quantitative approaches might not recognize or understand the detailed measurement of some variables, the effects of ignoring other variables, and the implications of positional placements of variables in causal models.

This volume describes an increasingly evident way of conducting quan- titative research. This approach does not seek merely to verify models. Rather it focuses on questioning and then modifying models or creating new models that better describe the ever-differentiating individuals who are the focus of educational research. When models do not accurately reflect a given population’s experiences, the task is to pose alternatives to those models. Rather than focus on explanation, or fairness, it focuses on equity concerns that can often be highlighted through analysis of large data sets—for exam- ple, by focusing on differences by race, class, and gender.

Table 1.1 depicts a familiar comparison between critical and positivist approaches. As we can see, critical quantitative research falls between the two. If we focus solely on research methods—arguably the less interesting of a researcher’s concerns—we see little difference between the positivistic approach and the critical quantitative approach. However, the second part of the table, the most interesting part, rests with the motivation for the research.

For the critical quantitative researcher, characteristics of method, the top half of the table—scope, findings, focus, data, and kinds of results reported— resemble typical positivistic research. The scope is broad rather than in-depth, the findings are generalizable using aggregated data, and the results are inde- pendent of context. However, it is in the motivation for the research, as illus- trated in the lower half of the table, that the questions, goals, and outcomes of the research more closely match those of the critical researcher.

The critical researcher calls into question models, assumptions, and mea- sures traditionally made under the positivist perspective. By using techniques such as interviews and observations, traditional critical researchers demon- strate situations and populations for whom the assumptions and models are

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Table 1.1. Methods and Motivations for Research Paradigms

Critical Positivist- Critical Quantitative Postpositivist

Research methods

Scope In-depth Broad Broad

Findings Interpretive Generalizable Generalizable

Focus Individual Group Group

Data Idiographic Aggregate Aggregate

Results Context Context Context dependent independent independent

Research motivation

Questions Model questioning Model questioning Model verification modification confirmation

Goals Description Investigation Explanation

Outcomes Equity Equity Fairness

fallacious. The critical quantitative researcher also questions models and assumptions but uses analysis of sociological and economic processes to demonstrate that for particular population groups, some widely accepted models and assumptions are inaccurate.

A positivistic researcher seeks models that nearly completely explain phe- nomena of interest, aiming for confirmation and verification to explain universal human behavior. But because much of positivistic research is based on previously developed models, the outcomes tend to replicate the status quo and verify meritocratic fairness. In contrast, the goal of the critical researcher is exploration or investigation. Does the model hold for a new population of interest—for example, students at urban institutions or rural, working-class students? The outcomes for any critical researcher, no matter the method, center around equity.

The critical quantitative researcher has two tasks:

• Use data to represent educational processes and outcomes on a large scale to reveal inequities and to identify social or institutional perpetuation of system- atic inequities in such processes and outcomes. This work has become increas- ingly possible during the past two decades as a result of the proliferation of large representative databases, both national and institutional, broad- ened access to them, and the development of myriad analysis approaches.

• Question the models, measures, and analytic practices of quantitative research in order to offer competing models, measures, and analytic practices that bet- ter describe experiences of those who have not been adequately represented.

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This task focuses on professional self-regulation and requires that quan- titative researchers become less polite and more critical of themselves and their colleagues. It requires the development of inquiry focused on all aspects of quantitative research, questioning the status quo on approaches to problems and actively seeking to constantly improve the state of the art, including models, measures, and the application of analytic methods.

Some Examples

Amaury Nora and Alberto Cabrera have spent most of their careers working on expanded models of college student success. One joint effort included stu- dents’ perceptions of prejudice on the parts of faculty and staff, and incidents of being singled out as different in a specific class. Their model demonstrated the importance of these new factors in persistence models for both minority and nonminority students in college (Nora and Cabrera, 1996). Among other contributions they have made are the alteration of traditional models of per- sistence to include ability to pay (Cabrera, 1987) and specific campus-based financial aid factors (Nora, 1990).

After exploring aspects of Latino students’ sense of belonging and cam- pus involvement through causal modeling, Sylvia Hurtado and Deborah Carter (1997) found that important aspects of involvement differed from those typically described for mainstream students. They cited the impor- tance of transitions to college and perceptions of campus racism and sug- gested more careful attention to the meanings of campus involvement as modes of college attendance evolve, such as service learning, part-time attendance, and distance education. In addition, Hurtado (2001) has ex- plored the influence of diverse classrooms on the academic development of all students, and Carter (1999) has studied the effect of institutional envi- ronments on college students’ aspirations and degree expectations.

David Drew’s (1996) Aptitude Revisited examined educational issues surrounding mathematics and science education in the United States. Along with his discursive evaluation, he provided examples of what might be con- sidered critical quantitative analysis to help us understand what seems to be a predominantly U.S. emphasis on aptitude that systematically screens women and minorities from careers and educational opportunities.

Finally, Bensimon, Polkinghorne, Bauman, and Vallejo (2004) describe a “practitioner-as-researcher” approach that distances the research process from the academic sphere and situates it in the surroundings being studied. In their model, practitioners in the institutional environment of interest (faculty and administrators) develop research questions, decide on data to be collected, and provide analysis of results, with the advice of professional researchers. Research conducted in this fashion is certainly critical and often quantitative; it provides the data deemed most relevant in answering the questions asked in the context being studied.

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These researchers described above did not merely seek to explain and predict. They studied college students knowing that college programs, coun- seling and advising, and even faculty behaviors were guided by quantitative research of the past. They attempted to show that by basing work in the col- lege setting on research conducted on the students of the past, scholars may have ignored critical elements of the college experience that would promote equal educational opportunity for all students on campus.

In using quantitative methods to examine issues surrounding mathe- matics during the transition from high school to college, to examine nuances of college choice for low-income students, or to explore experi- ences of students of color in nonselective institutions, researchers can show pervasive negative effects that result from assumptions about students and about access to college and to education. The qualitative studies provide details on how subtle experiences color students’ lives; the quantitative studies provide the persuasion of numbers. When the two are taken together, the critical work of educational researchers is more complete.

One Researcher’s Evolution

My own earliest quantitative critical work began in the late 1980s with stud- ies of students’ participation in mathematics and science-based majors. A common practice at the time was to include the predictor variables gender and ethnicity in models of student experiences. As predictors, those vari- ables, when significant, signaled a difference, but they did not really provide a picture of that difference. Several results led me to ask what exactly were the different experiences that caused race and gender to be significant? By separating groups by race and gender for analysis, my colleagues and I were able to describe patterns of experiences for specific groups of students that led to the outcomes on which we were focused—in this case participation in mathematics and science majors.

We discovered that models for predicting participation worked better for some students than others (Maple and Stage, 1991). In other words, for some student groups there were a greater number of significant predictors and greater amounts of variance explained even when we controlled for sample size. However, with our complicated models, we did not always get the results we expected and often were unable to explain our findings.

In the mid-1990s we used the National Educational Longitudinal Study of 1988 (NELS:88) database and focused on some standard college choice models widely used at the time (Hamrick and Stage, 1998). Here we first examined a conventional model for eighth graders in all schools; then for eighth graders at urban, low-income schools; then for white, Hispanic, and African American students at those low-income schools. Controlling for sample size, we were able to demonstrate that the model described college choice best for students who did not attend urban low-income schools and least well for African American students at the urban low-income schools.

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We modified the college choice model based on literature from our col- leagues (Attinasi, 1989; Levine and Nidiffer, 1996; McDonough, 1997; Terenzini and others, 1994). The new model included the influence of school activities and educational mentors outside the school context. The modified model actually showed improved fit for white students but little difference for students of color (Hamrick and Stage, 2004). A limitation may be the way those variables were measured and a tentative conclusion was that if such models of college choice continue to be used, they be reconcep- tualized independently by racial-ethnic and class groups.

Work in the late 1990s refocused on student participation in math and science-based majors (Kinzie, Stage, and Muller, 1998). This time a logistic regression model combined conventional predictors with measures of social capital. Using male and female African American, and white subgroups, we found that four of five conventional predictors were significant for white males and females and none were significant for African American males. For other African American female, Asian American and Hispanic subgroups, conventional predictors were significant until the social capital predictors were added to the model. In other words, family background was more important than prior educational experiences in explaining student success.

More recently, my work with colleagues focused on tracking of students into academic or nonacademic course work in high school. Counseling high school students into academic, vocational, or general course tracks has been practiced for decades, despite controversy (Oakes, 1988). Some defend tracking, whereas others believe it promotes systematic discrimination. Researchers have found that underrepresented minorities, low-income stu- dents, and women are less likely to study college preparatory mathematics than are white men with the same levels of high school achievement (Drew, 1996; Harris, 2000). Furthermore, these discrepancies can be the result of persuasion on the part of influential teachers and counselors or simply because of the provision of narrower curricular choices (Drew, 1996; Oakes, 1988). We explored the question: Is academic tracking in high school math- ematics courses useful in helping students succeed?

In our initial study we examined relationships among students’ ethnic- ity, course-taking patterns, and academic achievement in mathematics (Stage, Carter, and Musoba, 2003). Using data from the National Education Longi- tudinal Study of 1988, we divided students by racial-ethnic grouping and by quartiles according to their mathematics achievement in eighth grade. Lev- els of rigor in mathematics curriculum and achievement in twelfth grade were then examined. Between ethnic groups, we found significant differences in placement for students of similar levels of initial achievement. For all eth- nic groups, regardless of initial mathematics achievement, a more rigorous academic curriculum resulted in significantly higher gains in achievement scores from the eighth grade to the twelfth grade. The differences were most dramatic for students with the lowest initial achievement. Current work includes foci in two directions: an analysis of the effects of tracking across

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racial-ethnic groups controlling for gender and socioeconomic status and an in-depth focus on the effects of academic tracking on mathematics achieve- ment for African American men and women.

Beginning in the late 1990s I joined with other colleagues, including several of the authors contributing to this volume, at annual meetings of the Association for the Study of Higher Education to begin exploring crit- ical quantitative possibilities and implications for our collective work (Stage, Rhoads, Bensimon, and Creswell, 1997; Stage, Hurtado, Braxton, and St. John, 2001; Stage and others, 2002). In her 2006 address to the Association for the Study of Higher Education, President Estela Bensimon enjoined scholars to question their assumptions and to conduct research that is relevant to their stakeholders. We have continued our evolution as quantitative criticalists and some of that work is detailed in the chapters of this volume.

I persist in this line of study despite a bias with which some view quan- titative work. By default, as a quantitative researcher, we are sometimes viewed as theory confirmers, believers in a grand plan, incrementalists. But although I generally value quantitative inquiry, I view it with the healthy skepticism it deserves. All our approaches and our variety of conceptualiza- tions have a contribution to make in critical higher education work. I hope you join me in incorporating critical perspectives into your own work, whether it is quantitative or qualitative.

References

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nity. Albany: State University of New York Press, 1997. Nora, A. “Campus-Based Aid Programs as Determinants of Retention Among Hispanic

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Stage, F. K., and others. “Using Quantitative Data to Answer Critical Questions.” Paper presented at the Association for the Study of Higher Education, Sacramento, Nov. 2002.

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FRANCES K. STAGE is professor of administration, leadership, and technology in the Steinhardt School at New York University and a former Senior Fellow at the National Science Foundation.