While student persistence models remain useful in illustrating the problems and processes relating to student persistence, the relationship between college and student is lost be-tween the simplicity and complexity of the various models. Without a clear explanation of what the model represents, it is difficult for administrators and practitioners to fully com-prehend the significance of the model and how it relates to campus policy.

The Geometric Model of Student Persistence and Achievement provides a user-friendly method for discussion and focus on (a) the cognitive and social attributes that the student brings to campus; and (b) the institutional role in the student experience. The geometric model differs from others by placing the student at the center of the model, rather than an indifferent element to a flow chart or structural equation model.

The Geometric Model of Student Persistence and Achievement

The model also allows us to discuss the dynamics between cognitive, social, and institu-tional factors, all of which take place within the student. These three forces must combine to provide a solid foundation for student growth, development, and persistence. When sta-bility is lost, students risk reducing their academic and social integration with the institution, and therefore risk dropping or stopping out. This model works to help describe the persistence process, and the delicate balance between student resources (what the student brings to campus) and institutional resources (what the institution provides for the student).

The strength in the model and the following conceptual framework is in their ability to help institutions work proactively to support student persistence and achievement. Diagnostic and supplementary knowledge of the student is a vital component of the geometric model, because without knowledge, the institution is incapable of making prudent decisions on whom to admit.

Three Forces Affecting Student Persistence and Achievement
In terms of college persistence and achievement, three particular forces account for the entire spectrum of student outcomes: cognitive, social, and institutional factors. Briefly stated, the cognitive factors form the academic ability—the strengths and weaknesses—of the student, such as the level of proficiency in reading, writing, and mathematics. Social factors, such as the ability to interact effectively with others persons, personal attitudes, and cultural history, form a second set of external factors that characterize the individual. The third set of factors, institutional, refers to the practices, strategies, and culture of the college or university that, in either an intended or unintended way, impact student persis-tence and achievement. Examples include faculty teaching ability, academic support programming, financial aid, student services, recruitment and admissions, academic ser-vices, and curriculum and instruction.

Cognitive Factors
The cognitive factors relate to the intelligence, knowledge, and academic ability a student brings with him or her to the college environment. These factors may be measured by such variables as course selection and completion in high school, aptitude, or extracurricular involvement in academic-related areas. Cognitive factors are important because they di-rectly relate to the student’s ability to comprehend and complete the academic portion of the college curriculum.

An important element of the cognitive factors relating to student persistence and achieve-ment is the student’s decision-making and problem-solving ability. The decision-making process is an important part of the models described earlier. Tinto (1975, 1993) describes the decision-making process regarding goal commitment and dropout, Bean (1982) de-scribes an intent to leave, and Anderson (1985) identifies value conflicts and career indecision among the important variables that a student controls through the set of social and cultural values instilled in him or her. The student’s decision-making process occurs within the confines of the geometric shape represented in the model presented above. It is here that the social and cognitive factors interconnect to form the decision-making proc-ess.

Social Factors
The second factor related to student persistence and performance is the set of social fac-tors impacting on students. Such factors include parental and peer support, the development or existence of career goals, educational legacy, and the ability to cope in social situations. The social issues facing college students are of ever-increasing interest to higher education personnel. The research field generally agrees about the importance of social integration with regard to student retention and the fact that students have a diffi-cult time persisting when they are not socially integrated into campus life. Thus, the factors identified on the social side of the geometric model are uniquely important to students’ stability.

A student’s social underpinning and opportunities have obviously crossover impact on his or her cognitive development. A student who is brought up in a culturally and education-ally rich environment will develop skills critical to postsecondary, career, and personal success. Students hailing from less supportive environments may bring with them defi-ciencies in their self-esteem and efficacy, especially as they relate to academics when compared with students from more advantaged backgrounds.

Institutional Factors
College is undoubtedly the biggest social change a traditional-age student has ever under-taken. College presents stresses, at some level, to all students. Substantial research exists on the stresses of freshman year, especially on minority and low-income students. Regard-less of one’s subscription to either Gennep’s social anthropology theory (Tinto, 1988) or to Valentine’s biculturation theory (Rendon, Jalomo, and Nora, 2000; Valentine, 1971), how the institution reacts to students is of primary importance to retention, persistence, and completion.

The institutional side of the triangle relates to the ability of the institution to provide ap-propriate support to students during the college years, both academically and socially. Issues related to course availability, content, and instruction affect a student’s ability to persist, as do support mechanisms such as tutoring, mentoring, and career counseling. Although this axis has a direct effect on a student’s stability during college, it also can be seen as a flexible set of programs or conditions that the college can mold to meet the diverse needs and attributes of individual students.

The significance of setting institutional factors on equal ground with cognitive and social factors is to illustrate the importance of campus participation and knowledge in students’ social and academic development. The geometric model places this set of factors at the base of the triangle because it is the college that forms the foundation for college success. It is here that the institution can identify and match the needs of individual students, a student cohort group, or the student body as a whole.

The Model in Practice
The strength of the geometric model is that it allows users to move from a theoretical con-versation to a study of practice in the present and over time. On the theoretical level, using the geometric nature of this model helps us understand persistence, how various factors may interact, and how the institution is involved in the persistence process. Only through the collection of data to further understand the cognitive and social experiences of stu-dents can the institution know how to act on these theoretical structures. Thus, we begin with the theoretical and move toward the practical, starting with a discussion of equilib-rium.

Achieving Equilibrium
The geometric model allows us to discuss the dynamics between cognitive, social, and in-stitutional factors, all of which take place within the student. We use the word equilibruim to define the status of a student when he or she is in a mode to persist in college. That is, the forces of cognitive, social, and institutional factors must combine from some type of equilibrium, or balance, to provide a solid foundation for student growth, development, and persistence. When equilibrium is lost, students risk reducing their academic and social in-tegration with the institution and therefore risk dropping or stopping out (Spady, 1970; Tinto, 1975). This process is described in the following paragraphs.

Stage One. Each side of the geometric model represents a series of variables that define the cognitive, social, and institutional structure of the student experience. Each variable, in its own right, has an impact on the persistence process. In fact, each variable has one of three consequences for the student: it can positively, negatively, or neutrally impact stu-dent persistence and growth. As illustrated below, the net result is a series of plus and minus experiences that mold the behavior and characteristics of the student. It is impor-tant to note that each force or impact on the student is distinct and different. Thus, one should not infer that the effect of one variable can be equally neutralized by another. It is reasonable to assume, however, that certain variables can alter the effect of other vari-ables. Thus, the individual impact of variables can combine and work with or against other variables, known as reciprocity. If we could algebraically calculate the impact of these variables, we would end up with a beta value to describe the cognitive, social, and institu-tional value. Although theoretically possible, it would be a massively challenging practice to equate all inputs to a singular coefficient.

An example of reciprocity is the combination of academic motivation, appropriate learning environments, and academic support. The net effect of these three variables (and surely dozens of others) could have a dramatic effect on student achievement and ultimately per-sistence in college. This combination of forces—the reciprocity of variables effect—gives us a net effect for each of the three planes of the geometric model.

Stage Two. The second stage refers to the continuation of our reciprocity theory to the entire spectrum of variable interaction, that is, between cognitive, social, and institutional variables. The force generated by all variables—either individually or across axes—accounts for the stability or instability of student persistence and achievement and ultimately the achievement of equilibrium.

Although balance may be achieved on each axis of the triangle (as shown in the prior fig-ures), it is naive to suggest that an equal balance exists among the three sides of the model, even if we could define what that balance would look like. In other words, rarely would the triangle be truly equilateral. The complexity of human behavior and learning theory suggests that there is an infinite combination of variables from each of the three axes that can result in an outcome measurable through student persistence and achieve-ment. As previously stated, however, we use the word equilibrium to define the status when the cognitive, social, and institutional forces combine in a manner that supports stu-dent persistence and achievement—that is, the model is stable and supports persistence and achievement.

Moreover, a seemingly perfect, equilateral polygon (that is, equal effect from each re-source) does not necessarily constitute the best model of stability for a student. Not only is this effect seemingly impossible, but it is illogical to assume that an equilateral model is a reasonable description of human ability and behavior. Rather, the individuality of the stu-dent necessitates that the model must shift and sway and evolve in a variety of ways and still provide a model of stability. The human condition is very much an ebb-and-flow, far-from-static situation, where shifts in one social or cognitive area prompt a protective re-sponse to counterbalance that shift. To illustrate this point, the illustrations below introduce four variations of model stability, all of which are in a state of equilibrium, there-fore supporting student persistence. Illustration A represents the so-called “perfect” situation where the student has relatively equivalent levels of cognitive and social re-sources and requires a similar level of institutional commitment to aid his or her persistence and performance. The bar chart to the side of the illustration helps to define the relative force of each axis apart from the illustration. In this case, the three levels, cog-nitive, social, and institutional, are similar.

Illustration B represents a student with low academic resources but excellent social skills, with the requisite institutional intervention and support. Through social networks, strong will, and the appropriate assistance from the institution, the student may be able to apply the necessary cognitive skills while also developing new skills to succeed in college. An example is a good-natured student who lacks the academic fortitude, perhaps because of a below-average education during middle and high school. With diagnosis from the institu-tion and the implementation of appropriate support programs, the student could persist in college and build up his or her cognitive resources.

Illustration C represents a student with high cognitive resources and low social resources. The cognitive ability of the student is so strong that even the institutional forces are below average level. A person who may fit this model could be the stereotypical brilliant thinker whose social skills leave something to be desired. In most cases, we would think that this type of student will persist to graduation, but because the college experience is about more than completion and about developing the individual to his or her full social and aca-demic potential, it is important for the institution to consider interventions to help that student develop social skills that will be beneficial throughout his or her life.

The last example, Illustration D, illustrates a student with extremely high cognitive and so-cial ability, therefore negating much of the need for institutional support beyond those related to basic instruction. In fact, it is likely that the institution acts more as a barrier than a conduit to goal attainment for students fitting this mold. With such strong academic and social skills plus related resources, these students probably tear through the curricu-lum (the classic distance education student).

As described, the graphic representations illustrate four different student models; all are considered in equilibrium because of the ability of the institution to deliver the appropriate level of support services to counter the strengths and weaknesses of the student. If one component of the model is forced to overcompensate for too many negative factors attrib-uted to the other two sides of the triangle, then the student is likely to run into problems.

Thus, a student with low net cognitive resources and low net social resources is unlikely to persist in college, regardless of what the institution may provide in terms of support services.