The following paper was originally presented as a weekly Learning Agreement Themes application in my Walden University Applied Management and Decision Sciences: Finance PhD course requirements.
Having a strong foundation of background knowledge upon which to build helps understand relationships between concepts and identify the most efficient methods to solve problems using the most compelling tools from a diverse skill set. Having a teacher guide students through a formal curriculum helps ensure that all students are given the opportunity to benefit from epiphanies during learning, which cement problem-solving techniques and concepts for the remainder of their practical lives. While being self-taught certainly attests of a student’s motivation, it also alerts that the student likely has glaring shortfalls in knowledge base; without a teacher to point out superficially-unrelated applications for a concept, the student has no reason to investigate those paths and knowledge becomes fragile. In appendix 1, I illustrate this fragility of knowledge. In one application, a qualified engineer solves a basic mathematical problem using the most complex route possible, thus introducing errors and missing the point of the exercise, which was to help identify a basic problem disguised as a more complex one. I solve the same problem using a well-known identity and factoring method, reducing the chance of error; further, in many differential equations, it is impossible to integrate some expressions systematically without looking up a solution, and sometimes recognizing identities to simplify a problem is the only way to find a solution. Such is the fault in some predicates of radical philosophies; for example, Illich (1970) erroneously implies that a motivated student can mechanically, without guidance toward developing insights, “master in a few months…equally of special languages, such as algebra…” as if he, himself, lacked the knowledge of mathematics he needed to make this philosophical argument compelling—a prime supporting example of a tenet of liberal philosophies that students are ill-prepared to decide what courses they would best benefit from (Adler, 1982); a true elective system deprives students of the guidance needed to form a strong foundation from which to draw. Paradoxically, Illich would have made a more compelling argument had he benefitted from this liberal system.
Adler (1982) exemplifies this type of liberal thinking in his radio address, “Freedom through discipline.” He points out that freedoms exist not solely as discretionary license but as necessary measures; that is, that an individual has not been oppressed does not imply freedom, but that the “ability to exercise will” must be express and not inferred: “If he did not recognize the authority of what ought and ought not to be done, his freedom would be empty; or worse, it would be mere license.” Dewey, an archetypal Progressive theorist, points out that, “people do not think about or go in search of freedom ‘unless they run during action against conditions that resist their original impulses’” (Greene, 1988). Greene (1988) agrees with Adler and Dewey in this respect: “When people cannot name alternatives, imagine a better state of things, share with others a project of change, they are likely to remain anchored or submerged, even as they proudly assert their autonomy.” In this way, Greene proposes that education for freedom must operate as empowerment rather than indoctrination.
Illich (1970), however, points out faults in implementation rather than core philosophy as an argument against formal schooling: “But most people acquire most of their knowledge outside school, and in school only insofar as school, in a few rich countries, has become their place of confinement during an increasing part of their lives.” Such cynicism encourages abolishing rather than improving a system that ideally should strive to foster insightful problem-solving drawing on a diverse problem-solving skill-set and instead encourages problem-based learning at all skill levels without regard to a student’s abilities to think critically and what kind of foundational skill-set students have to draw from.
While Greene (1988) supposes that education is necessary to identify freedom: “These resistances and obstacles have meaning only in and through the free choice which human reality is.” Adler (1982) qualified this idea by stating that this individual freedom must be subordinate to justice in order to assure freedom to a society: “Since the desires and wants of individual men will bring them into conflict, freedom from laws necessarily means subjection to the war of each man against every other.”
While Greene and Adler clearly share some views on educational philosophies, it is clear that while Adler is predominantly Liberalist, Greene is predominantly Radical. In Greene’s The Dialectic of Freedom (1988), points out education in terms of Marxist ideals and enlightening society in order to overcome oppressive indoctrination: “Little is done to counter media manipulation of the young into credulous and ardent consumers—of sensation, violence, criminality, things. They are instructed daily, and with few exceptions, that human worth depends on the possession of commodities, community status, a flippant way of talking, good looks. She decries the imbalance of ownership by the bourgeoisie and how “the wealthy, the advantaged, benefit from this new attention to freedom” (Greene, 1988).
While Greene parallels elements of both Traditionalist and Pragmatic theorists, that she nonetheless is flavored by an overarching Critical flavor makes her predominantly a Radical theorist. A view that more appropriately balances the philosophical and pragmatic approaches would be to consider that all three schools have merit, but that they apply not only differentially by situation, but by level of abstraction. While the Traditionalist approach to fostering a strong, wide, stable foundation as a base of knowledge is most applicable to earlier education. Problem-based contextual learning most effectively leverages the freedom a learner has to select how to study what must be guided by a modicum of proficiency in the basics of a diverse set of disciplines. In all cases, critical thinking retains the benefit of content while avoiding the prejudice of indoctrination.
References
Adler, M. J. (1982). The paideia proposal. New York: Macmillan.
Greene, M. (1988). Freedom, education, and public spaces. In The dialectic of freedom (pp. 1–23). New York: Teachers College Press.
Illich, I. (1970). Why we must disestablish school. In Deschooling society (pp. 1–24). New York: Harper and Row.
Appendix I: Differentially-solving non-differential expressions
Figure 1.1 Solution by aerospace engineer using “brute force” generic approach
Figure 1.2 Author’s solution using identity and difference of squares