Discourse regarding the “gatekeeper” concept in mathematics can be traced back over 2300 years ago to Plato’s (trans. 1996) dialogue, The Republic. In the fictitious dialogue between Socrates and Glaucon regarding education, Plato argued that mathematics was “virtually the first thing everyone has to learn…common to all arts, science, and forms of thought” . Although Plato believed that all students needed to learn arithmetic—”the trivial business of being able to identify one, two, and three” —he reserved advanced mathematics for those that would serve as philosopher guardians2 of the city. He wrote: We shall persuade those who are to perform high functions in the city to undertake calculation, but not as amateurs. They should persist in their studies until they reach the level of pure thought, where they will be able to contemplate the very nature of number. The objects of study ought not to be buying and selling, as if they were preparing to be merchants or brokers. Instead, it should serve the purposes of war and lead the soul away from the world of appearances toward essence and reality.
Although Plato believed that mathematics was of value for all people in everyday transactions, the study of mathematics that would lead some men from “Hades to the halls of the gods” should be reserved for those that were “naturally skilled in calculation” ; hence, the birth of mathematics as the privileged discipline or gatekeeper. This view of mathematics as a gatekeeper has persisted through time and manifested itself in early research in the field of mathematics education in the United States. In Stanic’s review of mathematics education of the late 19th and early 20th centuries, he identified the 1890s as establishing “mathematics education as a separate and distinct professional area” , and the 1930s as developing the “crisis” in mathematics education. This crisis—a crisis for mathematics educators—was the projected extinction of mathematics as a required subject in the secondary school curriculum. Drawing on the work of Kliebard , Stanic provided a summary of curriculum interest groups that influenced the position of mathematics in the school curriculum:
(a) the humanists, who emphasized the traditional disciplines of study found in Western philosophy;
(b) the developmentalists, who emphasized the “natural” development of the child;
(c) the social efficiency educators, who emphasized a “scientific” approach that led to the natural development of social stratification;
and (d) the social meliorists, who emphasized education as a means of working toward social justice.
Stanic noted that mathematics educators, in general, sided with the humanists, claiming: “mathematics should be an important part of the school curriculum” . He also argued that the development of the National Council of Teachers of Mathematics (NCTM) in 1920 was partly in response to the debate that surrounded the position of mathematics within the school curriculum. The founders of the Council wrote: Mathematics courses have been assailed on every hand. So-called educational reformers have tinkered with the courses, and they, not knowing the subject and its values, in many cases have thrown out mathematics altogether or made it entirely elective. …To help remedy the existing situation the National Council of Teachers of Mathematics was organized.
The question of who should be taught mathematics initially appeared in the debates of the 1920s and centered on “ascertaining who was prepared for the study of algebra” . These debates led to an increase in grouping students according to their presumed mathematics ability. This “ability” grouping often resulted in excluding female students, poor students, and students of color from the opportunity to enroll in advanced mathematics courses . Sixty years after the beginning of the debates, the recognition of this unjust exclusion from advanced mathematics courses spurred the NCTM to publish the Curriculum and Evaluation Standards for School Mathematics (Standards, 1989) that included statements similar to the following:
The social injustices of past schooling practices can no longer be tolerated. Current statistics indicate that those who study advanced mathematics are most often white males. …Creating a just society in which women and various ethnic groups enjoy equal opportunities and equitable treatment is no longer an issue. Mathematics has become a critical filter for employment and full participation in our society. We cannot afford to have the majority of our population mathematically illiterate: Equity has become an economic necessity.
In the Standards the NCTM contrasted societal needs of the industrial age with those of the information age, concluding that the educational goals of the industrial age no longer met the needs of the information age. They characterized the information age as a dramatic shift in the use of technology which had “changed the nature of the physical, life, and social sciences; business; industry; and government” . The Council contended, “The impact of this technological shift is no longer an intellectual abstraction. It has become an economic reality” . The NCTM believed this shift demanded new societal goals for mathematics education:
(a) mathematically literate workers,
(b) lifelong learning,
(c) opportunity for all,
and (d) an informed electorate.
They argued, “Implicit in these goals is a school system organized to serve as an important resource for all citizens throughout their lives” . These goals required those responsible for mathematics education to strip mathematics from its traditional notions of exclusion and basic computation and develop it into a dynamic form of an inclusive literacy, particularly given that mathematics had become a critical filter for full employment and participation within a democratic society. Countless other education scholars have made similar arguments as they recognize the need for all students to be provided the opportunity to enroll in advanced mathematics courses, arguing that a dynamic mathematics literacy is a gatekeeper for economic access, full citizenship, and higher education. In the paragraphs that follow, I highlight quantitative and qualitative studies that substantiate mathematics as a gatekeeper.
The claims that mathematics is a “critical filter” or gatekeeper to economic access, full citizenship, and higher education.In the today context, mastering mathematics has become more important than ever. Students with a strong grasp of mathematics have an advantage in academics and in the job market. The 8th grade is a critical point in mathematics education. Achievement at that stage clears the way for students to take rigorous high school mathematics and science courses—keys to college entrance and success in the labor force.
Students who take rigorous mathematics and science courses are much more likely to go to college than those who do not. Algebra is the “gateway” to advanced mathematics and science in high school, yet most students do not take it in middle school. Taking rigorous mathematics and science courses in high school appears to be especially important for low-income students. Despite the importance of low-income students taking rigorous mathematics and science courses, these students are less likely to take them. The report, based on statistical analyses, explicitly stated that algebra was the “gateway” or gatekeeper to advanced (i.e., rigorous) mathematics courses and that advanced mathematics provided an advantage in academics and in the job market—the same argument provided by the NCTM and education scholars. The statistical analyses in the report entitled, Do Gatekeeper Courses Expand Educational Options? presented the following findings:
Students who enrolled in algebra as eighth-graders were more likely to reach advanced math courses (e.g., algebra 3, trigonometry, or calculus, etc.) in high school than students who did not enroll in algebra as eighth-graders. Students who enrolled in algebra as eighth-graders, and completed an advanced math course during
high school, were more likely to apply to a fouryear college than those eighth-grade students who did not enroll in algebra as eighth-graders, but who also completed an advanced math course during high school. The summary concluded that not all students who took advanced mathematics courses in high school enrolled in a four-year postsecondary school, although they were more likely to do so—again confirming mathematics as a gatekeeper.
The concept of mathematics as providing the key for passing through the gates to economic access, full citizenship, and higher education is located in the core of Western philosophy. The school mathematics evolved from a discipline in “crisis” into one that would provide the means of “sorting” students. As student enrollment in public schools increased, the opportunity to enroll in advanced mathematics courses (the key) was limited because some students were characterized as “incapable.” Female students, poor students, and students of color were offered a limited access to quality advanced mathematics education. This limited access was a motivating factor behind the Standards, and the subsequent NCTM documents. NCTM and education scholars’ argument that mathematics had and continues to have a gatekeeping status has been confirmed both quantitatively and qualitatively. Given this status, I pose two questions:
(a) Why does our education system not provide all students access to a quality, advanced (mathematics) education that would empower them with economic access and full citizenship?
and (b) How can we as mathematics educators transform the status quo in the mathematics classroom?
To fully engage in the first question demands a deconstruction of the concepts of democratic public schooling and an analysis of the morals and ethics of capitalism. To provide such a deconstruction and analysis is beyond the scope of this article. Nonetheless, I believe that Bowles’s argument provides a comprehensive, yet condensed response to the question of why our education remains unequal without oversimplifying the complexities of the question. Through a historical analysis of schooling he revealed four components of our education:
(a) schools evolved not in pursuit of equality, but in response to the developing needs of capitalism (e.g., a skilled and educated work force);
(b) as the importance of a skilled and educated work force grew within capitalism so did the importance of
maintaining educational inequality in order to reproduce the class structure;
(c) from the 1920s to 1970s the class structure in schools showed no signs of diminishment (the same argument can be made for the 1970s to 2000s);
and (d) the inequality in education had “its root in the very class structures which it serves to legitimize and reproduce” .
He concluded by writing: “Inequalities in education are thus seen as part of the web of capitalist society, and likely to persist as long as capitalism survives” . Although Bowles’s statements imply that only the overthrow of capitalism will emancipate education from its inequalities, I believe that developing mathematics classrooms that are empowering to all students might contribute to educational experiences that are more equitable and just. This development may also assist in the deconstruction of capitalism so that it might be reconstructed to be more equitable and just. The following discussion presents three theoretical perspectives that I have identified as empowering students. These perspectives aim to assist in more equitable and just educative experiences for all students: the situated perspective, the culturally relevant perspective, and the critical perspective. I believe these perspectives provide a plausible answer to the second question asked above: How do we as mathematics educators transform the status quo in the mathematics classroom?
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