It is no secret that United States students rate very low in mathematics in international standardized testing. We hear many practical suggestions for changing this. We suggest that although practical suggestions will eventually be needed, first we need a philosophic shift in the way we view the mathematics classroom, the mathematics student, and how mathematics is learned. This philosophic shift must precede the practical if we are to see the degree of change that is needed. In essence, the shift is from an absolutistic view of mathematics to one of a sociological view of mathematics.

Mathematics itself is predominately viewed as a static subject with students viewed as individually struggling with learning concepts lectured on by the teacher, and mathematical communication as asking the student to circle his or her answer upon completing a calculation. Many individual students are lost in this process.

In the new philosophic view that we are suggesting, mathematics is viewed as a process with students conceptualized as apprentices grappling with the concepts of mathematics that emerge as communities of mathematicians (the students and the teacher) immerse themselves in the subject matter collaboratively.

Mathematics education is a relatively new field. Since its beginnings it has struggled with issues such as how best to prepare teachers and eventually such questions as: What mathematics should be taught? How should mathematics be taught? What are the goals of mathematics education? Who should take mathematics?

Certainly different philosophies in vogue at a particular time shape the way these questions are answered. For example, the practical needs of society once drove the answers to the questions. But as technology advanced, it (as well as philosophical changes) modified the responses to the "what," "how" and "who" questions of mathematics. Although the practical needs of society still dominated in directing the energies of mathematical education, those needs were not the only concerns of educators and the public.

The nature of students and how they learn emerged as another concern. The field of mathematics education was thus profoundly affected by the field of psychology. Learning theories about what goes on in a student’s mind as he or she is learning mathematics led to the question of how mathematics can best be taught. Behavioral learning theory, social learning theory, and, especially, cognitive approaches became relevant and applicable in better understanding the math student. For example, behavioral learning theory might suggest that in order for a student to learn mathematics, a system of rewarding the student for correct answers needs to be implemented. Or perhaps a cognitive approach would be to determine the cognitive processes that occur in an individual’s mind as she or he adds two fractions, and then promote those cognitive processes.

Mathematics educators today are especially interested in situated cognition (i.e., we learn in a particular situation; we are affected by our surroundings). Mathematics educators realize that our learning may be specific to the setting in which it is learned. In fact, mathematics educators have found that the mathematics that students learn in classrooms is not the mathematics that students use in everyday life. Everyday life occurs in an environment—a cultural environment. Yet, the way that mathematics is taught in the schools is in a very different cultural environment. Some might say it occurs in a vacuum, but sociologists know that this is not possible. Regardless, researchers have found that this school mathematics will not transfer to the mathematics of everyday life. Lave (1988) states that researchers should be "social anthropologists of cognition" in order to decide how best to teach mathematics. The principles of sociology have been ignored in the teaching of mathematics, and a price has been paid. In many cases, students who are able to solve mathematical problems in the classroom are not able to solve the same mathematical problems on the job or even in the grocery store.

Some mathematics educators have become sociologists when attempting to answer the questions of how to best teach mathematics and how mathematics is learned. Perhaps mathematical knowledge is not transmitted from the teacher to the student, but rather mathematical knowledge is constructed while a student is being enculturated within a mathematical community. The former view of mathematics as an absolute, certain, static discipline is being challenged. The sociological perspectives that have entered the field of mathematics are not exclusive to mathematics. They are part of a trend in postsecondary education to enculturate students to the language and approaches of each field, whether it be biology or business, physiology or physics.

This view of mathematics as a social practice is consistent with the "sociology of knowledge," which is concerned with the production of knowledge. The claim is that all human knowledge is socially constructed. Thus, we must consider the role of the social environment. Looking hermenuetically at the field of mathematics, then, important questions include:

• What is the social genesis of mathematical knowledge?
• Because knowledge is value-laden, what social groups’ purposes and interests are being served?
• Of the types of mathematical knowledge which could have been selected, why is it that other types did not predominate?
• How is what we know and how we know it a function of the socio-historical times in which it originated?
• How do mathematicians decide what counts as mathematics?

The sociology of knowledge studies the social sources and social consequences of knowledge. The organization of a society shapes the content and structure of knowledge (Kearl, 2000). Thus, social, cultural, political, and practical considerations influence the knowledge that a society of people has in a given socio-historical time. Applied to mathematics, then, mathematical knowledge may be seen as a product of ongoing social processes and a reflection of cultural, political, and practical norms and values.

The converging of mathematics with sociology’s more relativistic approach reflects the influence of Postmodernism. Mathematics’ absolutism is being deconstructed. Postmodernism revels in ambiguity and fragmentation, and is reluctant to embrace totalizing, absolute ideas. "Grand narratives" are stories a culture tells itself about its practices and beliefs (Klages, 1997). Every belief system or ideology has its grand narratives. The field of mathematics, then, has a grand narrative. In the postmodern era, these grand narratives are rejected; it is suggested that such narratives hide the contradictions and instabilities inherent in a given social organization or practice.

This deconstructionist approach actively challenges the traditional boundaries between oppositions — e.g., between reason and emotion; self and other; subject and object. The implications of this deconstruction of the grand narratives are far-reaching as applied to the teaching and learning of math. For example, an obvious implication is that it will affect how math educators view the learning of math and how they set out to teach it. A teacher’s (and a student’s) view or perspective of the subject matter is not a small detail. Both the content and the form of learning are affected. While we do not necessarily accept all of the philosophical underpinnings of Postmodernism (or social constructivism, as it is known in mathematics education), we do see how aspects of this school of thought can be used in helping to better understand and, indeed, facilitate the learning of math.

Learning does not occur in a vacuum. The social environment needs to be considered. This may mean, for example, looking at:

• the background of mathematics teachers, their training and their view of the discipline.
• the socialization process—whether math teachers and students have been socialized with messages that males are better than females at math.
• the disparity between what we believe and how we teach.

The idea of students as apprentices is consistent with social learning theory’s emphasis on learning by observation. A "master" (the teacher) demonstrates a behavior that the apprentice (the student) models, receiving feedback and monitoring throughout the process. The realization that mathematics can be learned in a more participatory, interactive way is reflected in classrooms where group work and other innovative teaching approaches are being used. It is through the merging of mathematics with sociology that we recognize that learning by doing complements learning by watching.

The sociologist speaks to the mathematician with the words "We do not learn in isolation." This might run contrary to how we have conceptualized people learning mathematics in the past. But, just because we do not acknowledge nor recognize the influence of culture does not mean culture does not have its influence. For surely, there does not exist an example of someone learning in isolation. The traditional model of teaching with the teacher lecturing and the students taking notes and studying is not isolation. At the very least, the teacher is in the process. Even if we take the student studying a textbook on his or her own, the textbook is a tool of the culture. Again, we see that the student is not isolated. The bottom line in the classroom is that the teacher is able to understand what it is to "do mathematics" and that in fact mathematics is not a solitary sport, and certainly not a spectator sport. Rather, to do mathematics is to be able to be a mathematician in the company of other mathematicians and to be able to mathematics comfortably and skillfully as situations necessitate.

The converging of hard science with social science reflects the interdisciplinary work that is being done across college campuses today. While mathematics and sociology may seem, in many ways, to be strange bedfellows, their connection is both intriguing and significant. Sociological considerations in the field of mathematics raise a productive host of new issues, questions, and concerns. We find it exciting to be talking across fields and colleges, in a language that we both understand. The dialogue has begun.

We encourage others to reap the benefits to themselves and their students of this type of collaboration. By bringing disciplines together, we create a richer, more holistic, seamless educational experience for our students. And, we enhance our own perspectives. Specific to mathematics education, a partnering with sociology is the only way that mathematics will return to the people something that we all can do again, not just something done by the select few. Specific to sociology, partnering with mathematics education is one way for sociology’s practical side to be seen and increases the chance that education will look to sociology as a legitimate resource for all kinds of disciplines.

Kearl, M. C. (2000). Sociology of knowledge. [On-line]. Available: http://www.trinity.edu/~mkearl/knowledg.html.

Klages, M. (1997). Postmodernism. [On-line]. Available: http://www.colorado.edu/English/ENGL2012Klages/pomo.html.

Lave, J. (1988). Cognition in practice. Cambridge England: Cambridge University Press.