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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 II: Reflective Assessment Solution
An assessment approach to this problem and potential solutions will need to assist educational policy makers, educational leaders, and community leaders to discriminate and define the differences between the mathematical reasoning required in various workplace venues from the study of classic mathematics taught in academic settings (Hacker, 2012). Consider that the Summary Report for Industrial Engineering Technicians (17-3026.00 of the O*Net Online, a partner of the American Job Center Network) states under the Knowledge category that the following mathematical skills are needed for the position: Arithmetic, algebra, geometry, calculus, statistics, and their applications (Workplace System Support," 2010). The job preparation guidelines are general and considerably more inclusive than they are detailed. The natural response of a curriculum planning team to this level of information is to require that students planning to major in engineering take course in each and every one of these advanced mathematics courses -- in fact, this is precisely the institutional response that is currently evoked.
Fundamental to this assessment is the development of a deep understanding of jobs and careers that are based on what are commonly referred to as STEM credentials -- degrees obtained from majors in science, technology, engineering, and math (Hacker, 2012). Research conducted over the past several decades indicates that considerable training occurs after employees are hired for STEM-based positions; this on-the-job training is designed to bring employees up to speed with regard to the types of computations needed for the work they have been hired to do (Hacker, 2012). A notable example can be found in Toyota's initiative in a manufacturing plant located in remote Mississippi county: here -- despite the fact that outcomes from the local public school system leave much to be desired -- Toyota has developed a community outreach program that works with the community college to provide instruction in machine tool mathematics that is customized to the work that takes place in the Toyota plant (Hacker, 2012). International models of this type of community-enterprise collaboration have a long history (Hacker, 2012). In Germany, for instance, apprenticeship programs provide high-tech knowledge to workers entering an industry through the in-house apprenticeship experience and associated coursework in community-based institutions (Bosch, 2000; Hacker, 2012). One aspect of the problem that needs to be accurately assessed is how well non-academic resources can provide the knowledge and skills needed by America workers to contribute innovations to and sustain an advanced industrial economy" (Hacker, 2012, SR6).
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…[continue]
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