Advanced mathematics requirements and organizational health in secondary education

Organizational Health

Educational institutions generally approach organizational improvement by addressing the performance standards to which students, educators, and administrators are held. The standards movement has been a dominant theme in educational policy arenas and in the public eye. With roots in the 1950s Cold War mentality, the thrust of educational improvement has been prodded by perceptions of international industrial and scientific competition. If the rigor of educational standards in the nation -- according to the logic of this argument -- falls below that of other countries, our economy will falter and the balance of trade will be compromised, perhaps beyond the point of recovery.

Fears for the future of the country and our citizens run deep; these fears propel a course of action that is not particularly based on rational thinking and lacks a base of evidence. The course of action adopted by educational policy makers and educational leaders in the country is this: Advanced mathematics and science are necessary if students are to be disciplined learners with refined capacity for scientific analysis and application of their learning once they enter the world of work. In this paper, I discuss this premise, its effect on the establishment of curricula, and the ramifications for students. An exploration of other educational models that take a different tack with regard to requirements for advanced math and science follows. The paper is articulated within a frame that assumes alignment between organizational goals and organizational practice is a strong indicator of organizational health. Specifically, instruction in advanced mathematics -- with an emphasis on algebra -- is the unit of analysis by which the argument is advanced.

Section I: Instructional Problem Description

Advanced mathematics is requirement for students enrolled in secondary education and post-secondary educational programs. According to a minority of experts, this is completely wrong-headed. One of the opponents of the broadly applied requirements for advanced mathematics is Andrew Hacker, a professor emeritus of political science at Queens College, City University of New York, and the co-author of Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids -- and What We Can Do About It? According to Hacker, the defenses for requiring advanced mathematics -- from geometry through calculus -- are "largely or wholly wrong -- unsupported by research or evidence, or based on wishful logic" (Hacker, 2012, p. SR1).

Hacker argues that the requirements for advanced mathematic in secondary schools takes an unnecessary and unwarranted toll on students, as well as an ancillary toll on society and the national welfare. In the United States, the average failure rate for ninth graders is one in four. Consider that national dropout rate is an average and certain areas of the country have substantively higher failure rates (Hacker, 2012). For instance, during the 2008-2009 academic year in South Caroline, 34% of the students enrolled in high school failed, and in Nevada for that same period, the failure rate reached 45% (Hacker, 2012). When close to half of the high school students in America are failing, something is very wrong with the system (Hacker, 2012). A corpus of secondary educators, parents, and students argue that the high failure rates are predominantly a result of the requirements for passing algebra in order to graduate (Hacker, 2012).

As a subject, algebra is found to be a difficult area of study for students from all backgrounds and from all types of schools. In most states, students are required to at least achieve the rank of "proficient" in algebra -- 43% of the white students in New Mexico and 39% of the white students in Tennessee fell below a proficient rank (Hacker, 2012). The problem is compounded by the entrance requirements of colleges and universities across the country (Hacker, 2012). The two university systems in California only consider applications from students who have three years of mathematics to their credit (Hacker, 2012). Given that these two university systems do not offer exclusively science and technology curricula, an artificial barrier has been erected that prevents students who are unlikely to successfully complete all of the required advanced mathematics courses -- but who certainly could complete liberal arts programs -- from effectively applying to these institutions of higher education (Hacker, 2012). Students who are enrolled in community colleges face the same apparently non-scalable wall imposed by the requirement for algebra (Hacker, 2012). Less than 25% of the students enrolled in two-year schools were able to pass the required algebra classes (Hacker, 2012). In addition, the bar is often set very high for mathematics scores. Colleges and universities -- and not just Ivy League colleges -- may require SAT math scores of 700 or better for admission (Hacker, 2012). With only about 9% of the men and only 4% of the women who take the SAT's achieving a math score of 700 or better, the selection process is heavily skewed to accept students who are naturally inclined to perform well in mathematics (Hacker, 2012). How this meets the needs of students whose talents lie in other legitimate areas of academic study is never clearly explained.

Colleges and universities frequently set up a system of pre-requisites that permit students to take difficult courses two, three, four, and five times in order to pass (Hacker, 2012). Repeating courses is common for mathematics classes that are required for a major, as well (Hacker, 2012). The outcome of imposing advanced mathematics coursework indiscriminately on all majors offered in an institution of higher education is three-fold: 1) Many students drop out of secondary education and post-secondary education when they are unsuccessful in the mathematics courses they take; 2) some students are so daunted at the prospect of taking advanced mathematics that they never attempt coursework that can lead to college entrance; and 3) the limited resources available to colleges and universities brings about a focus on coursework that community partners clamor for, even when that focus is ill-advised (Hacker, 2012).

Section III: A Critical Review of the Research

The idea that a uniform curricula might not be desirable for all students is not new. Importantly, because of the association of differentiated curricula with tracking students or "dumbing down" education in response to high numbers of failing students, standards-based education has gained in popularity (Barth, 1997; Hacker, 2012; Halliman, 2002). The Leave No Child Behind Act is a strong testimony to the widespread acceptance of the yoked tenets of standardized testing and high performance standards.

Proponents of the extant educational systems argue that mathematics are critical to the development of conceptual understanding and use of the quantitative tools that are regularly used in high tech fields (Hacker, 2012). The refrain is often heard that not enough students graduate with degrees in STEM majors, and that students in America are not able to compete with students in Canada, Finland, and South Korea who score higher on their mathematics tests than do students in the U.S. ("Business Coalition," 1998; Hacker, 2012).

Section IV: A Learning Solution Proposal

The expectation that people should have a solid grounding in arithmetic and basic numerical skills, such as ratios, decimals, and estimating, is both fair and prudent (Association of Manufacturers," 1998; Teachers of Mathematics," 1989). Yet the changing workforce is likely to alter the skillsets needed by employees in manufacturing-relevant positions. In fact, the Georgetown center on Education and the Workforce has provided a definitive analysis that indicates only about 5% of entry-level workers will be required to be proficient in algebra or mathematics above that level. One question that the Georgetown Center on Education and the Workforce has presented is just how many positions are actually available for graduates from STEM-based course -- a perspective that flips the conventional concern on its head. Typically, the question of interest is directed toward the shortages of skilled workers rather than asking how many positions are actually available that required the STEM-based skills. Not asking the right question at the right time about the nexus between the labor force and higher education contributes to surplus graduates with a particular major, a phenomenon that has variously happened with nurses, teachers, and is currently impacting engineers. A study completed in January 2012 by the Georgetown center found that the unemployment rate for engineering graduates is 7.5%, and for computer scientists, the unemployment rate is 8.2%.

By adapting a tripartite technical education and job training program similar to the apprenticeship programs in Germany, issues about the actual skills that are needed on the job and the education that students are required to obtain will be aligned. The model is entirely collaborative and requires that policy makers / public authorities, organizations and associations of employers, and trade unions work together to articulate meaningful curricula and educational programs (Bosch, 2000). For instance, according to the German national Vocational Training Act, technical and vocational training needs to emphasize "broad basic vocational knowledge and the knowledge and technical skills required to perform an occupational activity" (Bosch, 2000). Clearly, a system that focuses on the skills actually needed in a particular job precludes a focus on the needs that serve the purpose of the training firms (where apprentice placements are located) and on the specified standards of the educational institutions (Bosch, 2000).

Conclusion

Conventional wisdom and crowd-sourcing have led to a uniform approach to educational preparation that strongly emphasizes the STEM-based skillsets. The pressure to yield ever higher performance scores in engineering, mathematics, science, and technology regardless of students' intentions for college majors and courses of study has led to a growing body of discouraged students. The talents of these students may lie in areas outside of STEM majors. In much the same way that Marcus Buckingham-in his research on managerial effectiveness for the Gallup organization -- argues that managers must develop workers' strengths rather than focusing on the weaknesses, the American educational system must establish performance standards that mesh with the diversity of talents and interests of students who are attending or hope to attend institutions of higher education. The first step in this direction is to ensure that robust workplace-based instruction is available to students through collaborative arrangements with employers and apprenticeship programs. The efficiency of this process -- which borrows from inventory control just-in-time principles -- will help to ensure that training is current and reflects true employment skill demands.