# An Equation for Equity

### by Jay HillJuly 1, 1998

The question of equity in the education system is one of great concern and great difficulty. Differing views of how to bring about equity or even what equity means create a morass of political and pedagogical quandaries in which the students themselves are ultimately mired. Creating a formula describing the influences of various factors upon equity issues is an extremely subjective act (despite the objective appearance of formulas themselves). In order to understand such a formula, the reader must understand the creator's view on equity. For the purposes of this paper, equity in education is confined to the school system, without taking into account future job opportunities. Equity is the equal understanding and appreciation of the various cultures from which the students come (by both the students and the teachers), the development of knowledge within those cultural frameworks, and an understanding of mathematics within varying cultural frameworks. Achievement is, thus, a measure of the mastery of mathematics within the student's own culture and an understanding of mathematics within cultures outside of the student's culture. This being said, assessment of equity (equality of achievement under the aforementioned constraints) is another issue which must be taken into account, but not within the confines of this paper.

With this definition of equity in mind, I propose that the following equation best describes equity within the classroom:

Lall = (0.1)S + (0.3)P + (0.2)C + (0.4)T

where

Lall = equitable learning for all students
S = student input (e.g.: knowledge, ability, motivation, home experiences)
P = political factors (e.g.: busing, desegregation, national and state standards)
C = mathematics curriculum (e.g.: content, image, assessment)
T = teacher input (e.g.: knowledge, beliefs/expectations, pedagogical style, cultural knowledge and understanding)

Within the classroom, everyone has certain responsibilities for creating an atmosphere of equity. The student is certainly not exempt from these and must put forth the effort to understand both the material and the context in which the material is learned. However, it cannot be expected that students will understand the impact of learning (or not learning) the material discussed, presented, and/or discovered. It is the teacher's responsibility to provide the impetus (through activity or through explanation) for learning materials where application is not immediately evident.

Each student brings a repository of cultural knowledge and everyday uses of mathematics. Once again, it is the teacher's job to help the students recognize their own understandings of mathematics and facilitate their discovery and creation of mathematical truths. This belief is a synthesis of what Ernest identified as "Platonist" and "problem-solving" approaches to teaching mathematics. It is also consistent with Kay's view that there is "no single most effective method to teach mathematics" (Thompson, p. 115). It also points out that, although the student brings much to the table, the teacher is the one who must help sort and develop the students contributions.

However, the teacher is limited in what he or she can do with the students by what kind of students are in her classroom (demographics), what constraints are placed upon him or her by the curriculum and the surrounding political climate (among other things). Politics plays a major role in the atmosphere of the classroom and the level of equity in the schools. Possibly the greatest single effect politics has played in educational equity is the desegregation of schools. However, politics continues to play a major role in educational equity. One need only look at the current political antagonism toward bilingual education to see how politics can influence curricula and pedagogy (for good or for ill). It is through political means that curricula are developed, standards are set, and teachers are promoted, hired or fired. These political pressures can serve to promote or (more often than not) hinder equity in schools and, outside of teachers, probably most strongly affect the level of equity found in the school system.

As mentioned earlier, the curriculum also plays a major role in the level of equity found in schools. It serves as a guide for teachers as well as a measuring tool against which teachers and schools are evaluated. By manipulating the curriculum, political powers are able to manipulate the classroom, but, due to the necessary input of teachers in the development of curricula, the classroom does not become a purely political arena. In many ways, the curriculum serves as a mediator between the wants and needs of the power structure and the wants and needs of the teachers and students. In its role as mediator, the curriculum goes a long way toward setting the tone for educational equity, but, ultimately, the teacher is the one who deals with the students directly and mediates the subject and the students.

It has been my experience that teaching styles contribute to (or detract from) equity according to the individual teacher and the individual classroom. As Kay mentioned in Thompson's study, "appropriateness of a method [is] highly circumstantial and generally unpredictable" (p. 115). The curriculum and politics used to create it seek to provide pedagogical guidelines on which teachers are to base their classroom activities. The usefulness of such materials is that they act as a reference point for teachers to look to in times of doubt. Yet, if Kay's assertion that the appropriate method is based on circumstance and is "unpredictable," the power of such materials is quite limited and, once again, the teacher is left as the primary arbiter of equity in the classroom.

It is clear that, despite the influences of other forces in education, the teacher holds the banner when it comes to equity. The teacher must deal daily with the students, their needs, their cultures, their ideas. The teacher must provide an atmosphere within which students can explore their own cultural understanding of mathematics and get a glimpse of other perspectives on that same subject. Studies such as those cited by Gutierrez show that, despite such negative curricular tools as tracking, students can essentially achieve equally under differing curricula given that the teacher resources are equally distributed (p. 510).

This may seem to be yet another addition to the long list of duties held by the teacher. In today's society the teacher acts as parent, disciplinarian, psychologist, politician, and now arbiter of equity, but all of these are merely different facets of the student's educational experience. The more we get away from seeing teaching as the dissemination of information, the more obvious the need for teachers skilled in these other areas. In the formula given above, it is key to remember that, despite the primary influence of teachers, they are not the sole measures of equity in the classroom. All factors must be considered and adjusted to create the equitable atmosphere for which we strive.

## Bibliography

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In Ernest, P. (Ed.), Mathematics Teaching: The State of the Art, pp. 249-254. New York: Teachers College Press.

Gutierrez, R. (1996). Practices, beliefs, and cultures of high school mathematics departments: Understanding their influences on student advancement. Journal of Curriculum Studies, 28 (5), 495-530.

Thompson, A. G. (1984). The relationship of teachers' conceptions of mathematics and mathematics teaching teaching to instructional practice. Educational Studies in Mathematics, 15, 105-127.