Task 1: Analytical Reading and Writing
This examination is based on Reading Selection A, "The Central Puzzles of Learning" and "The Difficulties Posed by School" by Howard Gardner, which you were given to read and study in advance and on Reading Selection B, "To Err Is Human" by Lewis Thomas. The readings are printed below. Read "To Err Is Human" and review the Gardner readings in light of the writing assignment, which is printed following Reading Selection B below.
Reading Selection A
In these two excerpts from his book, The Unschooled Mind, Howard Gardner first introduces an important question that he will explore and then begins to find an answer to it.
The Central Puzzles of Learning
Many a person who has tried to master a foreign language in school has thought back wistfully to his (or her*) own learning of his native tongue. Without the help of a grammar book or a trained language instructor, without the sanctions of a course grade, all normal children readily acquire the language spoken in their vicinity. More remarkably, children who are too young to sit at a school desk but who happen to grow up in a polyglot environment can master a number of languages; they even know under which circumstances to invoke each tongue. It is humbling to realize that language learning in early life has operated exquisitely over the millennia, yet linguists are still unable to describe the grammar of any naturally occurring language in a completely satisfactory way.
One can, of course, attempt to dismiss language as a special case. After all, we are linguistic creatures, and perhaps we have special dispensation to speak, just as warblers and chaffinches sing as part of their avian birthright. Or one can stress the immense importance of language in all human intercourse; perhaps therein lies the solution to the question of why all children successfully master language within a few years of their birth.
Upon examination, however, language turns out to be unexceptional among human capacities. It is simply the most dramatic instance of one puzzle in human learning‑the facility with which young humans learn to carry out certain performances that scholars themselves have not yet come to understand. During the first years of life, youngsters all over the world master a breathtaking array of competences with little formal tutelage. They become proficient at singing songs, riding bikes, executing dances, keeping scrupulous track of dozens of objects in their home, on the road, or along the countryside. In addition, though less visibly, they develop powerful theories of how the world works and how their own minds work. They are able to anticipate which manipulations will keep a machine from functioning properly; they can propel and catch balls hurled under various conditions; they are able to deceive someone else in a game even as they can recognize when someone is trying to play a trick on them. They evolve clear senses of truth and falsity, good and evil, beautiful and ugly‑senses that may not always be consistent with communal standards but that prove remarkably serviceable and robust.
Intuitive Learning and Scholastic Learning
We are faced with another puzzle. The very young children who so readily master symbol systems like language and art forms like music, the same children who develop complex theories of the universe or intricate theories of the mind, often experience the greatest difficulties upon their entry in school. Speaking and understanding language have proved unproblematic, but reading and writing may pose severe challenges; counting and numerical games are fun, but learning mathematical operations can prove vexing, and the higher reaches of mathematics may remain forbidding. Somehow the natural, universal, or intuitive learning that takes place in one's home or immediate surroundings during the first years of life seems of an entirely different order from the school learning that is now required throughout the literate world.
So far, this puzzle is not unfamiliar and has been commented upon often. Indeed, one might go so far as to claim that schools were instituted precisely to inculcate those skills and conceptions that, while desirable, are not so readily and naturally learned as the intuitive capacities cited above. Accordingly, most of the recent raft of books and reports about the "educational crisis" perseverate on the difficulties students have in mastering the overt agenda of school. Such a description of the failings of school may be accurate as far as it goes, but in my view it does not go nearly far enough. In this book I contend that even when school appears to be successful, even when it elicits the performances for which it has apparently been designed, it typically fails to achieve its most important missions.
Evidence for this startling claim comes from a by now overwhelming body of educational research that has been assembled over the last decades. These investigations document that even students who have been well trained and who exhibit all the overt signs of success‑ faithful attendance at good schools, high grades and high test scores, accolades from their teachers‑typically do not display an adequate understanding of the materials and concepts with which they have been working.
Perhaps most stunning is the case of physics. Researchers at Johns Hopkins, M.I.T., and other well‑regarded universities have documented that students who receive honor grades in college‑level physics courses are frequently unable to solve basic problems and questions encountered in a form slightly different from that on which they have been formally instructed and tested. In a typical example, college students were asked to indicate the forces acting on a coin that has been tossed straight up in the air and has reached the midway point of its upward trajectory. The correct answer is that once the coin is airborne, only gravitational pull toward the earth is present. Yet 70 percent of college students who had completed a course in mechanics gave the same naive answer as untrained students: they cited two forces, a downward one representing gravity and an upward one from "the original upward force of the hand." This response reflects the intuitive or common‑sense but erroneous view that an object cannot move unless an active force has somehow been transmitted to it from an original impelling source (in this instance, the hand or arm of the coin tosser) and that such a force must gradually be spent.
Students with science training do not display a blind spot for coin tossing alone. When questioned about the phases of the moon, the reasons for the seasons, the trajectories of objects hurtling through space, or the motions of their own bodies, students fail to evince the understandings that science teaching is supposed to produce. Indeed, in dozens of studies of this sort, young adults trained in science continue to exhibit the very same misconceptions and misunderstandings that one encounters in primary school children‑ the same children whose intuitive facility in language or music or navigating a bicycle produces such awe.
The evidence in the venerable subject of physics is perhaps the "smoking gun" but, as I document in later chapters, essentially the same situation has been encountered in every scholastic domain in which inquiries have been conducted. In mathematics, college students fail even simple algebra problems when these are expressed in wording that differs slightly from the expected form. In biology, the most basic assumptions of evolutionary theory elude otherwise able students who insist that the process of evolution is guided by a striving toward perfection. College students who have studied economics offer explanations of market forces that are essentially identical to those preferred by college students who have never taken an economics course.
Equally severe biases and stereotypes pervade the humanistic segment of the curriculum, from history to art. Students who can discuss in detail the complex causes of the First World War turn right around and explain equally complex current events in terms of the simplest "good guy‑bad guy" scenario. (This habit of mind is not absent from political leaders, who are fond of portraying the most complicated international situations along the lines of a Hollywood script.) Those who have studied the intricacies of modem poetry, learning to esteem T. S. Eliot and Ezra Pound, show little capacity to distinguish masterworks from amateurish drivel once the identity of the author has been hidden from view.
Perhaps, one might respond, these distressing results are simply a further indictment of the American educational system, which has certainly experienced (and perhaps merited) its share of drubbing in recent years. And in fact the majority of the research studies have been carried out with the proverbial American college sophomore. Yet the same kinds of misconceptualizations and lack of understanding that emerge in an American setting appear to recur in scholastic settings all over the world.
What is going on here? Why are students not mastering what they ought to be learning? It is my belief that, until recently, those of us involved in education have not appreciated the strength of the initial conceptions, stereotypes, and "scripts" that students bring to their school learning nor the difficulty of refashioning or eradicating them. We have failed to appreciate that in nearly every student there is a five‑year‑old "unschooled" mind struggling to get out and express itse6r Nor have we realized how challenging it is to convey novel materials so that their implications will be appreciated by children who have long conceptualized materials of this sort in a fundamentally different and deeply entrenched way. Early in the century, the work of Freud and other psychoanalysts documented that the emotional life of the young child strongly affects the feeling and behavior of most adults. Now the research of cognitive scientists demonstrates the surprising power and persistence of the young child’s conceptions of the world.
Consider examples from two quite different domains. The changing seasons of the year come about as a function of the angle of the earth on its axis in relation to the plane of its orbit around the sun. But such an explanation makes little sense to someone who cannot shake the deeply entrenched belief that temperature is strictly a function of distance from a heating source. In the domain of literature, the appeal of modem poetry resides in its powerful images, its often unsettling themes, and the way in which the poet plays with traditional formal features. Yet this appeal will remain obscure to someone who continues to feel, deep down, that all poetry worthy of the name must rhyme, have a regular meter, and portray lovely scenes and exemplary characters. We are dealing here not with deliberate failures of education but rather with unwitting ones.
Unwitting, perhaps, but not necessarily unnoticed. That some of us may be at least dimly aware of the fragility of our knowledge was brought home to me powerfully in a conversation with my daughter, then a sophomore in college. One day Kerith phoned me, quite distressed. She voiced her concern: "Dad, I don't understand my physics course." Ever eager to assume the role of the patient and sympathetic father, I replied in my most progressive tone, "Honey, I really respect you for studying physics in college. I would never have had the nerve to do that. I don't care what grade you get‑it is not important. What’s important is that you understand the material. So why don’t you go to see your teacher and see if he can help?" "You don’t get it, Dad," responded Kerith decisively. "I've never understood it."
Without wishing to burden these words with cosmic importance, I have come to feel that Kerith's comment crystallizes the phenomenon I seek to elucidate in these pages. In schools‑including "good" schools‑all over the world, we have come to accept certain performances as signals of knowledge or understanding. If you answer questions on a multiple‑choice test in a certain way, or carry out a problem set in a specified manner, you will be credited with understanding. No one ever asks the further question "But do you really understand?" because that would violate an unwritten agreement: A certain kind of performance shall be accepted as adequate for this particular instructional context. The gap between what passes for understanding and genuine understanding remains great; it is noticed only sometimes (as in Kerith's case), and even then, what to do about it remains far from clear.
In speaking of "genuine understanding" here, I intend no metaphysical point. What Kerith was saying, and what an extensive research literature now documents, is that even an ordinary degree of understanding is routinely missing in many, perhaps most students. It is reasonable to expect a college student to be able to apply in a new context a law of physics, or a proof in geometry, or the concept in history of which she has just exhibited "acceptable mastery" in her class. If, when the circumstances of testing are slightly altered, the sought‑after competence can no longer be documented, then understanding‑in any reasonable sense of the term‑ has simply not been achieved. This state of affairs has seldom been acknowledged publicly, but even successful students sense that their apparent knowledge is fragile at best. Perhaps this uneasiness contributes to the feeling that they‑‑or even the entire educational system‑are in some sense fraudulent.
The Difficulties Posed by School
Going beyond simple literacy, a further mission of the schools is to transmit concepts, networks of concepts, conceptual frameworks, and disciplinary forms of reasoning to their students. These topics generally bear some relation to the areas in which students are ordinarily interested and about which they have already developed intuitive theories, schemes, and kindred explanatory constructs; after all, science treats the natural world, even as history relates the story of one's group and of other relevant friendly or hostile groups.
To the extent that these materials are presented simply as lists or definitions to be memorized, they can usually be mastered by students who apply themselves to the task at hand. The curriculum of school ought to go beyond a rehearsal of facts, however, and introduce students to the ways of thinking used in different disciplines. Such an introduction would involve exposing students to new ways of conceptualizing familiar or unfamiliar entities, be they the laws that govern objects in the physical world or the ways in which events are conceptualized by historians.
The content of the various disciplines is typically encountered in forms quite remote from the conceptions the student brings to the class. The student learns about the laws of physics or the causes of war by reading a textbook or by hearing the teacher lecture. Hence the challenge for the educator is threefold: (1) to introduce these often difficult or counterintuitive notions to the students; (2) to make sure that this new knowledge is ultimately synthesized with earlier ideas, if they are congruent with one another, (3) to ensure that the newer disciplinary content supplants previously held conceptions or stereotypes that would in some way collide, with or undermine the new forms of knowledge.
At last we can confront directly the primary reasons why school is difficult. It is difficult, first, because much of the material presented in school strikes many students as alien, if not pointless, and the kinds of supporting context provided for pupils in earlier generations has become weakened. It is difficult, second, because some of these notational systems, concepts, frameworks, and epistemic forms are not readily mastered, particularly by students whose intellectual strengths may lie in other areas or approaches. Thus, for example, students with strengths in the spatial, musical, or personal spheres may find school far more demanding than students who happen to possess the "text‑friendly" blend of linguistic and logical intelligences. And it is difficult, in a more profound sense, because these scholastic forms of knowing may actually collide with the earlier, extremely robust forms of sensorimotor and symbolic knowing, which have already evolved to a high degree even before a child enters school.
Education for understanding can come about only if students some how become able to integrate the prescholastic with the scholastic and disciplinary ways of knowing and, when such integration does not prove possible, to suspend or replace the prescholastic ways of knowing in favor of the scholastic forms of knowing. Finally, students need to be able to appreciate when a prescholastic form of knowing may harbor a different or even a deeper form of understanding than the discipline‑related form of knowing learned in school.
Up to this point I have spoken of the difficulties of school primarily in terms of the problems experienced by students as they are asked to think in new kinds of ways about new kinds of concepts and forms. Even in the happiest scholastic environment, such a regimen may pose problems. Yet, human constraints on learning are magnified by the equally burdensome constraints under which schools themselves must operate. Although it would be desirable for teachers to work directly with small and well‑motivated groups of students, most schools are burdened with large classes, onerous rules and regulations, disruptive demands for accountability, and students who have many personal problems. It is not surprising that an education geared toward understanding is a low priority in such schools; by their nature, bureaucratized institutions have difficulty in dealing with ends that cannot be readily quantified.
In fact, what seems to have evolved in most parts of the scholastic world is an uneasy kind of detente. Teachers require students to answer preset kinds of problems, to master lists of terms, and to memorize and then feed back definitions upon request They do not ask students to try to reconcile their earlier, partial forms of understanding with the notations and concepts of school; instead they deal only with the latter forms of knowing, hoping that students can later develop the reconciliations on their own. Nor do teachers pose challenging problems that will force their students to stretch in new ways and that will risk failures that might make both students and teacher look bad.
As I have come to express it, neither teachers nor students are willing to undertake "risks for understanding"; instead, they content themselves with safer "correct‑answer compromises." Under such compromises, both teachers and students consider the education to be a success if students are able to provide answers that have been sanctioned as correct. Of course, in the long run, such a compromise is not a happy one, for genuine understandings cannot come about so long as one accepts ritualized, rote, or conventionalized performances.
No doubt educators have arrived at this compromise for many reasons, not least because the distance between students' intuitive understandings and the understandings exhibited by disciplinary experts is so vast. Scholastic responses‑correct‑answer compromises‑seem a viable midpoint between these disparate forms of understanding. But just how great is the disjunction between scholastic and nonscholastic forms of understanding has become apparent only in recent years. This area has been the major concern of a number of scholars who call themselves "cognitive scientists interested in education" or "educators interested in cognitive‑scientific research." The names of many of these researchers are found in the notes keyed to the relevant studies, but it is appropriate to pay special tribute to the work of Michael Cole, Jean Lave, Lauren Resnick, Sylvia Scribner, and their associates. Their work has much influenced my own thinking and informs much of the ensuing discussion.
As I have already suggested, each discipline, and perhaps each subdiscipline, poses its own peculiar forms of difficulties, its own constraints that must be tackled. The disjunctions between intuitive understandings of history and the formal versions encountered in school are not directly comparable to the disjunctions encountered in physics, mathematics, or the arts. These distinctions should not be in any way minimized but it will be useful from here on to group these disjunctions under three principal headings. In the case of science and science‑related areas, I will speak of misconceptions that students bring to their studies. In the case of mathematics, I will speak of rigidly applied algorithms. ‑ Finally, in the case of nonscientific studies, particularly those in the humanities and arts, I will speak of stereotypes and simplifications.
I must underscore two points. First, I must stress that there exists no sharp line between misconceptions and stereotypes. Indeed, difficulties in mathematics and in certain of the social sciences seem to fall about midway between the prototypical misconception in physics and the prototypical stereotype in history or the arts. It is mostly for pragmatic reasons that I have divided the evidence on these difficulties into two large chunks.
I must also concede that use of the terms "misconceptions" and "stereotypes" entails a risk; these terms may imply that the views of young students are completely inadequate and that the views of older children or disciplinary experts are entirely superior. In fact, however, the situation proves far more complex. There are positive rationales underlying the views held by young children, and often these perspectives harbor important insights, which may be lost by older children and may seem obscure or remote to beginning students. By the same token, there is no smooth road from misconceptions to correct conceptions, from rigidly applied algorithms to flexible trafficking between formalisms and their referents, from stereotypes to rounded, multiply nuanced views. All understandings are partial and subject to change; far more important than arrival at a "correct view" is an understanding of the processes whereby misconceptions are reformulated or stereotypes dissolved. Because of their vividness and suggestiveness, I continue to use the terms "misconceptions" and "stereotypes" here; however, it would be more accurate to speak of "earlier understandings" and "more elaborated forms of understanding."
(*For expositional ease, I vary the gender forms from now on.)
Next Page (Reading Selection B)