The Hierarchy of Knowledge: The Most Neglected Issue in Education
By Lisa VanDamme
The dismal state of many American schools—especially public schools—is almost universally acknowledged. If you browse the education section of any major bookstore, you will find popular titles such as Why Johnny Can't Read, The Schools We Need: And Why We Don't Have Them, and Dumbing Down Our Kids. These books document the borderline illiteracy, the nonexistent math skills, the vast ignorance of history, and the lack of basic reasoning ability that characterize millions upon millions of students today.
Less acknowledged is that even those who attend the reputedly “good” schools emerge basically uneducated. While they dutifully pursue A's and high standardized test scores to get into prestigious colleges—with as much memorization, homework, and test preparation as that requires—the amount of real, usable knowledge these students possess upon graduating from high school is pitiful. While they may have passed Advanced Placement history exams, they are radically ignorant of the basic progression of history from antiquity to the present—an ignorance reflected in our public discourse, in which all political events and questions are treated as unprecedented, and history is rarely cited. While they may have read many classics of literature, few have developed an appreciation of the value of great literature; rarely do they develop into lifelong readers who harness the power of classic literature to enhance their lives. While they may have passed advanced math and science courses, most have no understanding of the milestones of science or the nature of scientific discovery. While they have been doing homework and taking tests for a dozen years by the time they reach college, most write and think so poorly that college professors—and later, job recruiters from writing-intensive professions such as law—are aghast upon reading their work. And while they have been told their whole lives of the importance of education, it is rare to find a student among them with a genuine love of learning—a student who seeks to understand the world around him, and embraces with excitement the prospect of learning all about it from his teachers.
Do I demand too much of schools and students? My experiences and successes, first as a homeschooler and then as the founder and director of VanDamme Academy, a small elementary and junior high school, prove otherwise. When parents visit my school, they are awed by the students, who demonstrate great accumulated knowledge, sharp thinking skills, and genuine enthusiasm for learning.
Visitors to VanDamme Academy often comment on the total engagement of the students. It is typical for every student in the class to be completely attentive and actively involved in class discussion. Conversations about the day's material will often continue after class. A while ago, while sitting at my desk, I heard a heated argument between two eighth-grade boys in the hallway. One of them yelled, “It's not that kind of love!” You might think they were having a spat about a teenage crush, but in fact, they were discussing the relative vices of the villains in The Count of Monte Cristo, and whether Dantes's rival Fernand was really in love with Mercedes.
Discussions of their work also continue at home. A seventh grader in my grammar class recently came to me after school and asked, “In the sentence 'He said Go,' isn't “go” a noun clause with the understood “you” serving as the direct object of 'said'?” I said “yes” and then naturally asked “why?” to which he responded, “Oh, I just had an argument about it with my dad.” When one of my students was asked on a high school application to describe his favorite activity, he asked his parents, “Can I say school?”
Last year, VanDamme Academy sent its first group of eighth-grade graduates on to local high schools. Two will be entering ninth grade having finished calculus and a college-level physics course. Most have completed high school grammar, mastered the art of diagramming sentences, and studied techniques of style in Foerster and Steadman's Writing and Thinking, an outstanding college textbook.1 Some have become such clear and articulate writers that a law professor visiting the school asked whether she could borrow some of their essays to show her students what it means to write well. All have studied the history of the Western world, and have read and analyzed dozens of plays and novels by such authors as Sophocles, Rostand, Ibsen, Sinclair Lewis, Victor Hugo, and Ayn Rand. And best of all, they have retained the essentials of this knowledge, and cultivated a genuine love of learning along the way.
A recent experience I had at one of the most prestigious high schools in California, to which many of my students applied, reveals just how uniquely well educated the graduates from VanDamme Academy are. The principal called a meeting with me to discuss my students' placement in particular classes, because most of them had surpassed the ninth-grade curriculum. He suspected that the students were not as mature and academically advanced as they claimed. He pulled out the file for Troy, one of my most talented students, and said, “This kid claims to be exceptionally advanced in the sciences and exceptionally advanced in the humanities. I've never seen that.” I explained that Troy had completed a two-year history of physics course and a college-level technical physics course; I described the grammar, writing, literature, and history curriculum he had mastered; and I pointed to the scores on the test that this school itself had administered, which were in the 99th percentile across the board. Not satisfied, he then looked at me, and—on the premise that a child so educated and intelligent would have to be a social misfit—asked, “What about his personality?” I explained that he was friendly, funny, social, a good basketball player—a generally well-rounded teenager. The principal, unable to believe this, asked the admission's director, “Is that consistent with the interview file?” The director pulled out the file, looked under the heading of “personality” and read the interviewer's first comment, which was: “I can't say enough good things about Troy.”
What explains the vast difference between the knowledge and enthusiasm of students at VanDamme Academy and those of other schools? It is not that we recruit only ultra-motivated geniuses; most of our students come in ignorant and disillusioned with school. It is, rather, a consequence of factors that are replicable, in principle, by any school. The primary difference is in our basic educational philosophy—and above all, our view of the nature of the knowledge that students are to be taught.
To understand that difference, consider the following hypothetical scenario.
Imagine what would happen if a first-grade teacher, instead of teaching her students addition and subtraction, attempted first to teach them algebra—or, even worse, in the name of intellectual rigor and in an effort to offer a program of exceptional quality—decided to dive right into calculus. Obviously, the students would learn nothing. Being unable to grasp the basic operations of mathematics with specific numbers, they would be completely unable to grasp the idea of a variable that abstracts away from any particular number—let alone advanced equations involving complex algebraic calculations.
Fortunately, few schools would attempt to teach math in this way. But they commit the same error, in less extreme and far less noticeable form, throughout all subjects—that is, the error of teaching certain content before students have the context necessary to grasp it.
All abstract knowledge depends, for its meaning and validity, on other knowledge that sets the context for it. For example, algebra depends on addition, and calculus depends on algebra. The more complex the knowledge, the more extensive the knowledge that must precede it.
One major aspect of the fact that knowledge depends on other knowledge—the aspect most relevant to and most violated in education—is that more abstract knowledge depends on less abstract knowledge. This is the principle of the hierarchy of knowledge.
All abstract knowledge of reality begins with our only direct point of contact with reality: perceptual observation. For example, the first concepts formed by a child are those formed directly from perceptual data; they are what philosopher Ayn Rand, the first philosopher to fully identify the hierarchical nature of knowledge, called “first-level concepts.” A child looks out at the world, perceives entities, and integrates his perceptions into these first-level concepts—concepts such as “cat,” “dog,” and “horse.”
Using these first-level concepts, a child is able to form simple generalizations such as “cats meow” or “dogs bark.” From these early concepts and generalizations, and with further observation, he is then able to form more abstract concepts (concepts further removed from the perceptual level) and to make more abstract generalizations. For example, noting the essential similarities between cats, dogs, and horses, he is able to form the concept “animal.” He does not look at the world and see “animals”; he looks and sees cats and dogs and the like—from which observations he is able to form the corresponding first-level concepts. Then, having formed these abstractions, he is able to form the broader abstraction of “animal.” Eventually, having made countless observations, and having grasped a complex range of concepts and relationships on various levels of abstraction, he is able to form generalizations such as: “All animals are mortal.”
A concept or generalization is more or less abstract according to its cognitive distance from the perceptual level. Concepts and generalization exist in a hierarchy, from the perceptual level to the highest level abstractions.
Highly abstract concepts presuppose a very long chain of prior conceptualizations. This is why, for example, so much knowledge must be gained for students to learn calculus.
Knowingly or not, parents encounter the issue of hierarchy all the time. When my daughter Lana was 2 1/2 years old, I took her to the hospital to visit a friend of mine who had given birth that day to a baby girl named Talia. I told Lana, “Today is Talia's birthday!” She looked at me with a puzzled expression and said, “She's having a party?” I said, “No, it's her birthday,” and stumbled my way through an explanation of what it meant for this to be Talia's “birth day” and what the connection was between a “birth day” and a “birthday party.”
I quickly realized that it was impossible for Lana to grasp the connection between the birth of a baby and the cake, presents, and balloons, which to her were the essence of a birthday party. To do so, she would have to grasp, among other things, the concept of “birth,” which she did not yet really understand, the concept of a “year,” so that she could learn that the passing of a year marked the anniversary of a person's birth, and the concept of “celebration,” so that she could understand why the anniversary of one's birth is celebrated with a party, and so on. It was impossible for me to teach Lana a more advanced understanding of the concept of “birthday” given her context of knowledge—she had not formed and could not yet grasp the prerequisite concepts.
There is a necessary order to the formation of concepts and generalizations. A child cannot form the concept of “organism” until he has first formed the concepts of “plant” and “animal”; he cannot grasp the concept of “animal” until he has first formed concepts such as “dog” and “cat”; and so on. The pedagogical implication of the fact that there is a necessary order to the formation of abstract knowledge is that you must teach concepts and generalizations in their proper order. An abstract idea—whether a concept, generalization, principle, or theory—should never be taught to a child unless he has already grasped those ideas that necessarily precede it in the hierarchy, all the way down to the perceptual level.
Let us explore and elaborate on the principle of hierarchy in education, by investigating its abuse and proper use in the teaching of science, history, and literature.
Science
Several years ago, a teacher from my school was tutoring Kevin, then a freshman in high school. One day, Kevin came to their session asking for help in preparing for a test on protein synthesis. The tutor went over the information Kevin had been presented, helping him to memorize the following: “Messenger RNA is synthesized by complementary base pairing with deoxyribonucleotides to match a portion of one strand of DNA called a gene. Subsequently, ribosomal subunits attach to the messenger RNA and amino acids are joined to form a polypeptide or a protein through a process called translation . . .” and so on. After Kevin had successfully memorized this highly complex process by which a protein is produced, the tutor asked him an insightful question: “Kevin, what is a protein?”
Kevin had no idea.
This type of “learning” is typical of nearly every science class and every textbook in every school I have ever seen or heard about, whether a public school, a Catholic school, or a Montessori school. A student is expected to learn about a highly technical, highly abstract scientific topic, such as the production of a protein, without any of the preceding context that would make it intelligible.
Kevin had not first learned the observations that led Darwin to believe that traits could be inherited, or the simple experiments of Mendel and the theory of genes, or the process by which DNA was discovered. Since the understanding of the production of a protein depends on this (and much, much more) knowledge, Kevin's memorization feat was not real understanding—he was not gaining real knowledge. Instead, he was performing a fleeting recitation of what in his mind amounted to a fairy tale with a lot of technical scientific jargon.
Tragically, much of mankind's brilliant accumulation of scientific knowledge has this standing in the minds of today's students.
Consider the way you were taught Newton's Laws of Motion. If your education was typical, the teacher came into class one morning, stood at the board, and declared that Newton identified three laws of motion—which you dutifully wrote down and later committed to memory. No context had been established for these discoveries. No information had been given as to what earlier observations and theories were made by other great scientists, what further discoveries were made by Newton, and how Newton's incomparable genius enabled him to integrate all this information into three fundamental, universal laws governing the behavior of every object in the universe.
Pick up any grade school science textbook and you will see the same problem. Page one usually displays in vivid color a diagram of the structure of an atom. The chapter tells the students that an atom is a tiny unit of matter, that it has a nucleus made up of protons and neutrons, that the nucleus is surrounded by electrons, and so on. The question that such books make no attempt to answer is: Why should a child believe this drawing any more than he believes the Saturday morning cartoons? He has never seen an atom, or a nucleus, or an electron; he has not been told how scientists discovered the existence and properties of this thing that cannot be seen; nor can he possibly understand the implications of the existence or nature of atoms. Thus, all of the material stands as meaningless gibberish he has been asked to accept on faith.
The vast majority of today's science teachers simply do not understand what it means to learn. They do not understand that there is a necessary order to learning, and that adhering strictly to this order is the only way to ensure that the student has a clear, independent grasp of the material. Today's teachers seem more concerned with enabling their students to parrot impressive-sounding words than they are with fostering their ability to think. That is why a high school chemistry teacher of Kira, one of my former students, said the following when he began a section on quantum theory: “This material is far too complex for any of you to really understand—but don't worry, we'll only spend a few days on it.”
Such “teaching” is a betrayal of the purpose of education, which is to give children the essential knowledge and cognitive powers necessary to be independent, productive, happy adults. In terms of content, to the extent that the hierarchy of knowledge is violated in students' education, they learn nothing of the material they are being taught; they learn only to repeat what they are told. In terms of method, to the extent that the principle is violated, students fail to learn what it really means to come to know something; this is replaced with the deadly lesson that knowledge of complex, abstract scientific issues is gained by parroting the words of an authority.
Students who have no true concept of scientific knowledge are ripe for pseudo-scientific propaganda. In today's schools, the leading propagator of such propaganda is the environmentalist movement. For example, it is routine for seven-year-olds to be taught that catastrophic global warming is imminent, that it is caused by man, and that industry and Republicans are “selfishly” leading us toward an apocalypse for their own short-term gain. In talking to these children and seeing them interviewed, what is most disturbing is the certainty they project in taking a position on as complex an issue as long-term climate change—when they have no knowledge of the principles of chemistry, physics, or meteorology. Many parents understandably object to such indoctrination because of its anti-capitalist, pseudo-scientific content; the more fundamental objection to make, however, regards the anti-hierarchical method that it exhibits—a method that makes all learning, even of the truth, a form of indoctrination.
Another consequence of the rampant violation of hierarchy in science education, available to both teachers and students alike, is that students find learning about science boring.
When I ask people about their experience studying science in school, particularly physics, the answer is almost always the same, “It was boring and a lot of memorization.” If taught the way Kevin was taught protein synthesis, this is inevitably true. If you do not attain a genuine grasp of the material you are being taught, because you do not have an understanding of the conceptual context it presupposes, all you can do is memorize it and parrot it back. Memorizing technical jargon that has no cognitive standing in your mind can be nothing but boring.
To compensate for this, many science teachers use artificial means to motivate their students. Some make science a trivia game. They play Jeopardy or Science Bingo or other games contrived to make their students enthusiastic about the passive acceptance of a bunch of information these students do not really understand. I have no objection to the occasional use of games in the classroom, but if a teacher depends too much on these contrived attempts at motivation, it is a good indicator that the children are not fulfilled by the work itself. That is usually because they do not understand it.
Other science teachers have turned to more grotesque methods of motivating their students. The Wall Street Journal reported several years ago on the growing popularity of criminal forensics classes for ninth- and tenth-graders. Here is a description of a federally-funded forensics program at a high school in Minnesota:
Last summer, Minneapolis teacher Bobbie Rush led 22 ninth-graders to a deserted stretch of Mississippi River shoreline. There, they came upon a mock crime scene: a dismembered mannequin in a car trunk, a severed arm in a grocery bag and a bloody hacksaw. That wasn't the only macabre scene the teenagers encountered. During a separate field trip to the city morgue, they saw a decomposed cadaver crawling with maggots and a mutilated corpse being boiled so the bones could be examined for signs of foul play. “Another guy got buried alive while working in a ditch,” recalls fifteen-year-old Heather Callahan, who thought the trip was fun. “He was already cut open and everything.”2
According to the article, the goal of classes in forensics—a highly specialized branch of applied science—is to make science appealing to today's teenagers, who are growing up in a world of “fast-paced and reality based entertainment.”
The purpose of science education, however, is not to make science appealing to children (although that is important). The purpose is to convey crucial scientific knowledge to a child and to ensure that he actually understands the material being taught. Motivation is one of the means to that goal, and as such, it must not be separated from the goal; it must be integrated with it. Motivation flows from the right content taught the right way—both of which are dictated by the hierarchy of knowledge.
Properly taught—that is, hierarchically taught—science unlocks important facts about the physical world and demonstrates the intelligibility of the universe. It shows students the power of man's mind to discover these facts and to use them to improve his life—to create the wondrous world of technology that surrounds us—which instills in students a strong, implicit respect for the power of reason. Properly taught, science is anything but boring—because it is anything but meaningless and purposeless.
It should be a fundamental rule in science education, and in education in general, that students are always taught material they can thoroughly grasp for themselves. If a teacher is presenting a principle about the physical world, the students should either be able to point to the evidence in reality—or to recreate the process of observation, reasoning, and generalization—that supports the principle. This means that science should be taught in a proper order: beginning with the simplest, most easily observable facts about the physical world, and proceeding systematically to more complex, abstract theories. It demands that the approach to science be essentially historical in progression, since the simplest discoveries are necessarily the earliest. This is the approach we take at VanDamme Academy.
The science curriculum for the elementary students at VanDamme Academy is taught primarily through experiments. These students are learning principles that are very close to the perceptual level, so we always demonstrate the principle in carefully designed hands-on experiments, so that they see it for themselves.
Let me give you a few examples of this approach from science lessons I taught when I was a homeschooler. My class spent several weeks studying simple machines. Simple machines were discovered very early in history, and the principles behind them are not difficult to grasp. In one class, we studied friction and the effects of friction on motion. We dragged a brick across a board with a spring scale and measured the amount of force it took. Then we placed waxed paper over the board and dragged the brick across the wax paper, again observing how much force was necessary. We did many other related experiments, learning, for example, about lubricants and their ability to reduce friction.
I was always very careful to isolate the principle being studied, so that the hands-on activity did not degenerate into a pointless game. The students were required to write up the experiment, to explain the principle behind it, and to identify examples of the principle from their own day-to-day experience.
If students have a clear, first-hand grasp of the material, finding examples in everyday life is easy and exciting. Two of my students spent a car ride identifying all the simple machines they could find. “This knob on the radio is a wheel and axle, this handle to recline the seat is a lever . . .” and so on.
Here is another example of the lessons I would give to students of this age. We studied air pressure, the existence of which is easy to identify with some simple experiments. In one experiment, we placed a piece of paper over a ruler on a flat table, with the end of the ruler extending over the edge of the table. Then we pressed on the ruler, and felt a great deal of resistance, because there was air pressure from the top holding the paper down, but none from underneath to counteract the pressure from above. Then we put things under the paper to hold it up, so that it was not flat against the table, and pushed on the ruler again. This time, very little force was necessary to lift the paper, because there was air pressure from both sides.
A student taught in such a way will have a solid, independent understanding of the principle. One important consequence and reward of this is that he will be able to integrate what he learns with other things he knows and learns; he will notice its relation to other facts about the world, thus contributing to his ever-growing network of knowledge. If, by contrast, a student cannot grasp a principle first hand, he cannot see its connection to anything else—and his “knowledge” will take the form of disparate bolts from the blue, disconnected from each other and from reality.
Let me give you an example of an integration made by one of my students. We had just finished a series of air pressure experiments, and I came into class one day with a plunger and a step stool. I wet the rim of the plunger, pushed it on the step stool, and lifted the step stool in the air. I asked my students, “Why did that happen?” They thought for a minute, and then one explained that the plunger stuck to the stool because of air pressure. He explained that I had forced air out of the cup, so there was air pressure from the outside holding it on to the step stool, but little from inside pushing them apart. Then I asked, “Why did I wet the rim, of the plunger?” One of my students, thinking back to our unit on simple machines, raised his hand and said the following, “The water works like a lubricant, filling in the bumps and crevices on the surface of the plunger. So wetting the rim of the plunger helps to keep air from getting inside the plunger cup.” Such independent connections and observations can come only from real understanding. If taught in this way, children become enthusiastic about science.
One day, I taught my students the principle that water pressure increases only with depth. I gave them a powerful demonstration by poking holes at the same depth in two vessels of dramatically different diameters, and observing identical jets of water coming out of the holes. They were shocked and fascinated, and when one student's mother came to pick him up, he immediately went to the board and started drawing diagrams and testing her about this principle to see if she understood it as well as he did. Such enthusiasm springs from a first-hand grasp of relevant principles, which can be achieved only by means of a hierarchy-driven curriculum.
The principle of hierarchy is just as crucial in teaching more abstract scientific knowledge to older children as it is in teaching the simplest scientific knowledge to younger children. Consider the subject of physics.
Most science teachers present the highly abstract laws of physics as if they are self-contained truths, unrelated to the long history of scientific development. For example, Newton's discovery of universal gravitation, one of the most extraordinary discoveries in the history of thought, is usually presented as an out-of-context commandment to be memorized—as knowledge that, along with Newton's apple, fell from the sky.
A proper science teacher, by contrast, recognizes what the students must know for this law to be intelligible. He explains the steps in Newton's reasoning, and ensures that the students have already learned the discoveries leading up to Newton's theory, the principles they must know if they are to follow his reasoning.
In the famous incident with the apple, Newton asked himself if the same attractive force from the Earth caused both the apple's descent and the moon's orbit. In order to check the idea, Newton needed to know the acceleration of the apple (which he learned from Galileo), the size of the Earth (which had been measured by Eratosthenes), and the distance to the moon (which was calculated by Aristarchus). If the students are to grasp the law at hand, they must first grasp these facts—as did Newton.
Further, in arriving at this hypothesis, Newton was relying on Galileo's principle of inertia, Kepler's laws of planetary motion, and the law of circular acceleration (which Newton himself had discovered a few months earlier). Without this knowledge, Newton could not even have raised the question. Therefore, without this knowledge, the students cannot grasp the question and they certainly cannot understand Newton's final answer.
Having been taught physics as it progressed historically, the students at VanDamme Academy know the discoveries of Aristarchus, Eratosthenes, Kepler, and Galileo. When guided through the ingenious process by which Newton integrated this knowledge and built upon it, the students thoroughly grasp the principle of universal gravitation: They see that it is true and why it must be true. The law of gravitation is, in their own minds, connected to reality. It is real knowledge.
Does the hierarchical approach to teaching science require that students be taught the entire history of science, including every detail of every experiment ever performed? No. A crucial part of teaching in accordance with the principle of hierarchy is to select only the essentials. This is in contrast to the common view, expressed in a local newspaper by a high school biology teacher, that the hardest part of his job is keeping up with all the latest discoveries in his field. The latest developments in biology are properly the concern of Ph.D. biologists who have the context to understand them and the need to apply them.
High school students should be taught a carefully selected list of the most essential discoveries in the field, and should be taught them in hierarchical order. Only if they are taught by this method will they emerge with a sound understanding of the fundamental concepts of science and a genuine ability to think. Anything else deprives them of independently grasped, real knowledge, in favor of passively accepted pseudo-knowledge.
The entire field of science education needs to be reconceived—reconceived with respect for the hierarchy of knowledge.
History
One day, Kevin, the same unfortunate student forced to memorize the process of protein synthesis, arrived at his tutoring session asking for help with a similarly inappropriate writing assignment for history class. As background for this writing assignment, he was asked to read four arguments for and four arguments against laissez-faire capitalism. He was then supposed to make his own judgment about capitalism, and to write a paper defending his view.
Kevin's tutor read through and discussed each of the arguments with Kevin. At the conclusion of their discussion, Kevin asked, “Didn't they try laissez-faire capitalism once, and it didn't work?” His tutor—knowledgeable about history and well aware that laissez-faire has never been fully implemented anywhere—asked, “When?” and Kevin said, “I don't know, in France some time?” The tutor could not restrain his response: “Under which king or emperor did they try laissez-faire capitalism in France?”
Like most students today, Kevin was being asked to make a highly abstract political evaluation without any knowledge on which to base his evaluation. Like Newton's laws or atomic theory, political principles are treated as coming from out of the blue, and the students have no means by which to understand them, much less validate them. This method—insofar as a student does not himself heroically reject it—can have only two results: dogmatism or subjectivism—ideas are accepted on the authority of the teacher or on the whim of the student.
Without the knowledge to make an informed judgment, the average student tends to go along with the usually obvious leaning of the teacher. In place of a strong conviction based on a clear understanding of the principle and its foundation in the facts of history, the student has a woozy feeling that he is supposed to hold a certain belief and that his peers and authorities will condemn him if he does not. In one of my former student's history classes, the teacher lectured for an hour on the virtues and successes of the U.N.—how much it has contributed to the relief of hunger and world peace. The student's assignment the following day was to write a one-page paper on her own opinion of the U.N.
High school freshmen have no business discussing and offering opinions on politics. Before they can form broad principles about what men should do, they must first know what men have done—and what the results have been—so that they are equipped with a vast store of knowledge about human nature, causal relationships, and human institutions. In a word, they must study history.
Students need to learn the history of Greece and Rome; of the Dark Ages and the Renaissance; of the wars, monarchies, empires, and revolutions of Europe; and of the United States. When they reach adulthood, they can integrate their knowledge of the major events and trends of history with knowledge from other fields and a wide range of personal experiences. Only then will they be able to form rational, meaningful convictions about politics.
Many parents are understandably disgusted by the barrage of leftist political propaganda children receive from the time they set foot in most schools. From preschool on they are taught that nuclear power is lethal, that the peaceful “Native Americans” were exploited by evil white settlers, and so on. In responding to such indoctrination, what you who are parents and I as a teacher have to remember is that you do not fight propaganda with propaganda. As hard as it can be sometimes, you have to refrain from trying to give children the “right answers” before they are capable of grasping them. If a child does not understand the reasons for a position, then the position, in his mind, is not right but meaningless; it is not grounded knowledge, but a floating abstraction.
The terrorist attacks of September 11 drew everyone into politics. Many parents wondered how to explain this horrific event to their children. The reaction of many schools, especially public schools, was outrageous. Alan Bersin, superintendent of the San Diego school district, took over the history classes in a San Diego school just after the attacks. His assignments to the students included: “Compare the bombing of the World Trade Center to our bombing of Hiroshima,” and, “Consider this event from all points of view, including that of a Palestinian”—this, after we had witnessed footage of Palestinians on camera, gleefully celebrating the deaths of thousands of innocent Americans.
To counter the moral relativism that dominated the response to 9/11 in many schools, concerned parents felt the need to offer their children a rational, pro-America perspective on terrorism. They were understandably horrified by the nonsense that was being pushed on their children, and wanted to arm them with defenses against this irrationality. I know many thoughtful, intelligent parents and teachers who attempted to explain to young children such issues as why it is morally justified to kill innocents in war and why the United States has every moral right to take military action against supporters of Islamic terrorism such as Afghanistan and Iran.
This is an understandable mistake, but a mistake nonetheless. Handing a child these preformed conclusions gives him the message that he can hold complex and abstract judgments without the first-hand knowledge from which to draw them. If he accepts ideas without understanding them, it makes no difference what they are; the ideas will be floating articles of faith. You do not fight dogma with dogma; you fight it with a real education. If, across many years, children are systematically taught the relevant facts—and to draw conclusions only on the basis of such facts—then they will not become victims of propaganda. They will acquire the ability to think independently about complex issues and to make informed, rational judgments. If your views are valid, then a child so educated will likely come to agree with you independently, which is the only meaningful form of agreement.
The worst schools violate hierarchy, not by failing to teach history before delving into questions of political philosophy, but by dropping the teaching of history altogether.
Many schools have done away with history and replaced it with something called “social studies,” in which students learn a random assortment of facts—from crucial events to the most insignificant minutiae—about wars, imports and exports, physical geography, art, government, eating habits, and so on. Major events of history, to the extent that they are mentioned, appear to be causeless and inexplicable—because they are presented without the essential context of the events that preceded them and had a causal influence on them.
For example, when I began homeschooling, I asked one of my students, who had just finished a year of a social studies class focused on America, a simple question about the Civil War. She told me that she did not know the answer because her class had spent most of their time studying the specific role of women and blacks in the war.
A hierarchical presentation of history is one in which events are presented in the context of the ideas and events that preceded and gave rise to them. Students can understand the events and significance of the American Revolution, for example, only if they are able to compare and contrast it in their minds with the democracy of Greece, the empire of Rome, and the monarchies of Europe—all of which were major objects of study by the Founding Fathers. Students can grasp the origin of America only if they have studied the historical development of freedom, from representative government in Greece, to law in Rome, to the Magna Charta in England, to the Declaration of Independence.
At VanDamme Academy, the students view history as an intelligible and fascinating story filled with drama and heroes and lessons about life. If you talk to my former students, one comment you will hear frequently is that they always felt they knew why they were learning the things they were learning. Before I started teaching, I was intimidated by the idea of having to motivate the students. I thought I was going to have to bend over backward trying to show my students how the knowledge they were learning was relevant. I thought I would have to give convoluted and contrived examples to connect the Thirty Years' War to the life of a ten-year-old child. What I learned was that, taught properly, history is inherently motivating. If your curriculum focuses only on the most world-changing events of history, and you teach students what happened, why it happened, and what consequently followed, their reaction is always, “Now I see why that is important!”
One of my students was out sick and missed a lecture on the Industrial Revolution from Andrew Lewis, whom I am fortunate enough to have as a history teacher at my school. At the first opportunity, he cornered Mr. Lewis and made him repeat the lecture, pressing him with thoughtful questions, because he wanted to be sure he did not miss a chapter in the story. He wanted to be sure he understood what happened next and why; he knew that whatever he missed, it mattered.
Let me briefly describe our overall approach to history. We teach history chronologically, in a three-year cycle—with each cycle being more abstract, and involving deeper causal relationships, than the last. In the first year of the cycle, students study Greece and Rome; in the second year, they study the history of Europe; and in the third, they study American history. We then repeat the cycle, and they learn about the same periods again, but at a more abstract level.
In our teaching of history, we emphasize causes, so that students see that the events of history are not random or inexplicable. And we stress connections—comparing and contrasting historical figures or events, so that students will one day be able to come to informed, rational conclusions about politics by means of their own independent thinking.
As in science, a consequence of teaching history by the right method and at the right level is that the students make their own integrations. One day, when I was teaching history as a homeschooler, I gave my students a lecture about Oliver Cromwell and his establishment of a dictatorship in England. At the conclusion of my lecture, Kira, who was then in sixth grade said, “Isn't he just like Martin Luther? At first he appears to be fighting for liberty against an oppressive power, and then he turns around and establishes his own oppressive regime.” That was an excellent integration, and because she possessed the context of knowledge with which to make it, the integration was thereby stored in her memory so that she could later contrast these revolutions with the American Revolution. Such integrations are what enable students to eventually come to valid abstract political conclusions.
Let us turn to literature.
Literature
Literature is all but forgotten in education today, and those few schools that even attempt to teach the subject routinely violate the necessary order of knowledge in two crucial respects: in the novels they select, and in the means by which they analyze them.
In an effort to offer an alternative to the “dumbing down” that goes on in today's public schools, prestigious private schools and ambitious homeschoolers are having young children read the “classics.” This approach is encouraged in The Well-Trained Mind , a popular book among homeschoolers.3 The book has value in that it takes the potentially overwhelming task of creating a complete curriculum at home and makes it a reasonably simple and manageable process. The book recommends many excellent resources and offers some good advice on how to structure a child's education from kindergarten through twelfth grade. I recommend The Well-Trained Mind to those interested in education, but with the qualification that it often flagrantly violates the hier≠archy of knowledge. One of the ways it does so is in its selection of literature. For first- through fourth-graders, The Well-Trained Mind recommends, among other things: Gulliver's Travels, a satirical commentary on 18th-century English society; Les Miserables, whose theme is, “The injustice of society toward its lower classes”; and the poems of Wordsworth, which denounce selfish materialism and encourage a retreat to the simple purity of nature.
These works of literature, because of the abstractness of their themes, are not accessible to young children. A fourth-grader does not have the knowledge and range of experiences that would enable him to grasp whether society is just or unjust, or even what “society” is. He has not considered such broad philosophical issues as self-interest and self-sacrifice or materialism and spiritualism. The classics assume the cognitive context of an adult. They are filled with romance, psychological insights, philosophical principles, and other content that makes them remote from the knowledge and experience of a child.
Those pushing the classics usually recognize that the novels in their original and unabridged form are too daunting for children—and thus recommend simplified, children's versions of the works. This is a mistake.
It is impossible to simplify the plot of a great novel to a story that can be followed by a nine-year-old and still retain the same theme; the plot is complex because the theme is abstract. Consequently, children's versions of the classics bear little resemblance to the originals.
When I first started teaching, I was asked to give my students a lesson on a children's version of the Hunchback of Notre Dame. This complex novel includes a devout priest tortured by sexual passion for a Gypsy girl, and a hunchback torn between loyalty to the priest, who saved his life, and devotion to the Gypsy girl, whom he desperately loves. In the children's version, the story had no more complexity than Beauty and the Beast. Its theme was, “Beauty is only skin deep.” This is not an abbreviation of the theme, but an annihilation of it.
Because the children's versions of the classics fail to convey the meaning and depth of the originals, they are of no real value to children; indeed, they are a disvalue. The classics of Romantic fiction have unique, dramatic, and gripping plots that are an irreplaceable thrill to read for the first time. To the extent that the children's versions do resemble the originals, they spoil the plot, and deprive the child of the experience of being swept away by an exciting and unfamiliar story when he reaches the age that he can appreciate it. Those of you who remember and appreciate the dramatic endings of novels such as The Hunchback of Notre Dame, A Tale of Two Cities, or The Scarlet Pimpernel should understand why it would be a crime to rob the child of first discovering them when he is old enough to experience their emotional power.
Rather than reading bastardized versions of great novels, children should read great children's novels. Children's novels are written for children: They have plots that enthrall children, characters to which children can relate, and themes that children can understand.
My favorite novel for children is Anne of Green Gables. Anne, the main character, has a passionate, independent spirit that makes a lasting impression on children and adults alike. Her adventures are delightful to every child, and the theme of the novel, which concerns the importance of pursuing your values with passion, is one that children can understand. (Others novels at the top of my list include: The Secret Garden, An Indian in the Cupboard, The Witch of Blackbird Pond, and From the Mixed-Up Files of Mrs. Basil E. Frankweiler.)
Introducing students to the great novels for children ignites in them a sincere passion for reading. Several years ago, some of my students read The Secret Garden, a story about a lonely, sickly orphan girl who discovers an abandoned flower garden and works to bring it back to life. They loved the story itself, but they also enjoyed being able to identify the theme and to see its relation to the characters and events in the story. They recognized that as the garden was brought to life, so was the orphan girl; they saw that it gave her an opportunity to form friendships, to gain physical strength, and to have strong values for the first time in her life. They loved this novel because it has a beautiful plot and a clear theme that they can thoroughly understand.
Eventually, of course, students are ready to make the transition to adult literature. One means of helping them to do so is by introducing them first to great plays. I have found that reading plays helps students to segue from the simple plots and themes of children's novels into the deeper themes of adult novels.
Plays are inherently simpler than novels, because the author must convey his theme in a very short text. The plot has to be fairly simple, the characters have to be ruthlessly essentialized, and the theme has to be simple enough to convey in a few hours on stage. This makes plays typically easier for children to digest and analyze.
Some of my favorite plays for children at this stage of transition are An Enemy of the People, The Miracle Worker, Inherit the Wind, Twelve Angry Men, Pygmalion, and The Winslow Boy. Another gem of a play is The Admirable Crichton, by J. M. Barrie, the author of Peter Pan. It is a comedy about a stupid and haughty aristocratic family and their highly competent but very humble servant. They get lost on a desert island and, in the face of practical necessity, find the social hierarchy turned upside down. (This is one reversal of hierarchy that I entirely approve of.)
When I first introduce plays, at about fifth or sixth grade, depending on the maturity of the class, the students struggle through them. They are being asked to make more complex integrations than they are accustomed to making. But after they analyze a few plays together, I see them blossom before my eyes. They mature from potential literary scholars to junior literary scholars, able to delve into the classic novels, to understand them, and to benefit from the experience.
Several years ago, my class read An Enemy of the People and The Winslow Boy. There is a strong parallel between the characters of these two plays: the independent man standing up for what is right in the face of opposition, the wife who initially opposes him because she is afraid he will compromise the family's future, and the strong and loyal daughter who comes to her father's defense. My students noted these similarities, and each wrote an essay comparing the characters. One of my students, in the course of writing his paper, approached me and said he thought that though the daughters were very similar in some respects, they were quite different in one crucial respect. Petra, in An Enemy of People, stood behind her father because she believed, on the same grounds as did he, that he was right. Catherine, in The Winslow Boy, supported her father's actions but for a reason different from his. He was fighting for his son's honor; she was fighting for a political principle. This student had such a clear understanding of these plays that he was able to notice an aspect of them that I myself had never considered.
That kind of understanding is made possible by a proper selection of novels—a selection that accounts for the hierarchical nature of knowledge—and by a proper method of analyzing novels—a method that respects the principle that there is a necessary order to learning.
Students today are usually taught to analyze literature, not by reading it and trying to grasp it as a whole, but by dissecting it into disconnected fragments. Usually, the analysis focuses on issues of style, such as similes and metaphors, narrative voice, foreshadowing, irony, and symbolism. Each of these elements is examined in isolation and interpreted independent of the work as a whole. To teach literature in this way is like bringing a child to the Sistine Chapel and—in the name of “analyzing” and “understanding” it—making him look at the ceiling through binoculars, so that all he sees are individual brush strokes and never the work as a whole.
The teaching of style before content, though not strictly an issue of hierarchy, is a closely related error. It is another way in which educators violate the necessary order of knowledge—the severing of an item of knowledge from the lateral context that makes it graspable. It is impossible to analyze the symbols of a novel without the context of the novel's plot, characterization, and theme. The purpose of any single element in a work of fiction can be interpreted only by integrating it with all the other elements.
Take for example, a prominent symbol in Ayn Rand's novel Atlas Shrugged—the hollow tree. This symbol, which in Ayn Rand's novel represents the decay of industrial society under collectivism, could be used to express any of a number of things, depending on the context in which it is found. Victor Hugo could have used the same image in The Man Who Laughs as a metaphor for Josiana's beautiful body and empty soul. Tolstoy could have used it in Anna Karenina as a symbol for the individual's inflated sense of self, and his true weakness apart from society. Margaret Mitchell could have used it in Gone With the Wind to represent the collapse of the old, aristocratic South. The point is, there are no grounds on which to choose any given interpretation over another, except by reference to other elements of the story and the theme conveyed by the integration of all those elements.
Literature, like science and history, should be taught in a logical order. This means that the teacher should strive first to help the students integrate the events of the story into an essential understanding of the plot, the basic nature of the characters, and the work's theme. Then, in relation to these basic elements, the finer points of style should be discussed insofar as they help to illuminate the whole.
When students are taught to understand a work of literature as a whole—the sequence of events and their logical relationships, the essential natures of the characters and how their natures relate to those events, and the abstract meaning conveyed by the events and characters—students come to deeply appreciate the value of literature. They develop an ability to see meaning behind a story, and to apply that meaning to their own lives.
When my students read the play Antigone, we discussed the important differences between Antigone, who is passionately and proudly devoted to her own independent values, and her sister Ismene, who is meekly subservient to authority. I reminded my students that though they were not likely to encounter the specific decision of whether to bury their brother against a king's decree, they would within the next week be confronted with a decision that demanded they choose whether to be like Antigone, and stand on their own reasoned conviction, or like Ismene, and bow to arbitrary outside opinion. Accustomed to such discussions, my students clearly grasped this point.
The next day, a student likened Ismene to Javert, of Les Miserables, saying both were faithful to the law. I quickly pointed out that the similarity was superficial: that Javert was devoted to the law passionately and on principle, while Ismene conformed to the law from a lack of conviction and fear of negative consequences. One of my students then raised her hand and said, “This is the value of literature. You see important similarities and differences among characters, and that helps you understand the people you meet in your life.” That is the power of literature. And had this student spent her time musing about disparate, out-of-context symbols and literary devices that were therefore impossible to interpret, she would never have made this connection.
Given a proper, hierarchical education in literature, students will become lifelong readers, eager to enter each new universe and to be exposed to new characters and ideas that will help them better understand and enjoy their own lives.
Hierarchy and Montessori
Maria Montessori was one of the few true scientists of education. Montessori created an ingenious system for educating children from the ages of three to six. A thorough understanding of the developmental needs of preschool-aged children, careful observation of their interests and responses to various educational materials, and a deep respect for the autonomy of the individual led her to identify principles for setting up an ideal classroom environment for preschoolers. Montessori studied children carefully to determine what they were ready to learn and when. She gauged the success of a given material by the child's response to it. She found that if the materials fail to meet the child's developmental needs, he will flit from one thing to another, never becoming deeply engaged in any activity. If the materials are developmentally appropriate, the child will seem to have a limitless attention span.
Because she based her work on observations of what is actually required for young children to learn, one important quality of the materials developed by Montessori for the ages three-to-six classroom, whether she thought of it in these terms or not, is a respect for hierarchy. At this age, children do not learn primarily from instruction, but from observation and experience. They are learning first-level concepts. These concepts cannot be taught; they must be formed by direct perception of differences and similarities among things. A child does not learn about gradations in color, differences in size and shape, or variations in sound and texture by listening to a lecture. He learns them by “hands-on” experience.
Montessori developed brilliant materials that encourage a child to focus his attention on such things and thus to form the corresponding first-level concepts. The Montessori child does not roam aimlessly around a chaotic playroom, picking up one toy and then throwing it aside for another; he focuses intently on brilliantly conceived activities that help him to systematically build a foundation of early concepts.
The Montessori curriculum for preschoolers consists primarily of hands-on manipulatives (physical materials that isolate and concretize a simple concept). Take, for example, a Montessori student's introduction to place value. One cornerstone of the Montessori classroom is the Golden Beads. This manipulative consists of individual beads, rods of ten beads, squares of a hundred beads, and cubes of a thousand beads. When a child is learning to represent quantities with numbers, he uses the Golden Beads. For example, the teacher will lay out 3 cubes, 4 squares, 7 rods, and 2 units. The child will then select the appropriate cards to represent these quantities: 3000, 400, 70, and 2. He then overlays the cards, seeing that the number representing this quantity is 3,472. This gives him a meaningful, concretized understanding of numbers and of place value.
Montessori materials, such as the Golden Beads, provide the child with an activity that intrigues him, that he can do independently, and that isolates a particular concept: in this case, the concept of numbers or place value. There is no better way for him to learn these concepts than to work with physical quantities, and see the relationship of those quantities to their abstract representation.
Unfortunately, while the Montessori curriculum is stellar for children ages three to six, it poses serious problems for older children—problems involving violations of the hierarchy of knowledge. One problem with the Montessori elementary curriculum is that its “learning by doing” approach to education, in which the students learn concepts by working directly with physical materials, is maintained even with concepts at a much higher level of abstraction. Montessori teachers bend over backward to create concrete materials that demonstrate highly abstract concepts, despite the fact that those concepts do not refer directly to perceptual level entities.
For example, in the book Montessori Today, Paula Polk Lillard describes the Montessori child's introduction to chemistry. “The basic sciences,” she says, “can be well understood if they are presented in a manner that appeals to their imagination by using clear visual symbols.”4 Children are introduced, at nine years old, to the concept of valence and the attractive power between hydrogen and oxygen in water through symbolic representation. In other words, molecules and the forces that unite them are supposed to be made interesting and intelligible by presenting the child with a physical model consisting of a large ball with two smaller balls fastened to it.
Another popular Montessori science lesson attempts to demonstrate photosynthesis. The Montessori teacher takes the highly complex process of food production in plants and tries to make it accessible to children by using drawings and diagrams. For example, in teaching the child about chloroplasts, the teacher draws a picture of a leaf covered with little green men who love the sun. With other diagrams, they learn that the roots take in water and minerals, that the stem transports them to the leaves, and that the leaves release water and oxygen.
In place of the sensorial experiences of the preschooler, Montessori says, the elementary student is given images of the abstract. Because chloroplasts cannot be directly perceived, the teacher creates an image that can be perceived: a leaf covered with green men.
Students do not understand chloroplasts after seeing this drawing. It is a mistake to think that abstract concepts can be made intelligible simply by representing them in concrete form. The preschool child learns first-level concepts from physical concretes because that is the only way to learn them. More abstract concepts cannot be learned directly from physical objects—they presuppose a chain of conceptualizations. The only way to teach an abstract concept is to present, in a logical, hierarchical order, the knowledge that is a prerequisite to grasping that concept.
How should photosynthesis be taught? It should be taught through the series of discoveries that enabled scientists to learn that plants produce their own food. Students should learn about the Greeks' theory that plants get food from the soil and how a Flemish physician later disproved this theory. They should learn about Joseph Priestly's experiments showing that plants emit something that replenishes air damaged by the burning of a candle. They should learn about a scientist in Holland who discovered that the green parts of the plants, the leaves and young stems, are the parts involved in the purification of the air, and so on. This is probably not a process that should be taught to eight-year-olds. But it is a process that is eminently understandable to older children if it is taught by this historical method.
A related error is made by Montessori in her “Great Stories”—stories told to set context and provide motivation for the later study of history, math, and science. These stories consist of sweeping views of existence, covering topics such as the nature of the universe and the origin of man. Montessori places great importance on the “Great Stories,” because she intends them to be the framework for all the learning that will take place in the classroom. The following is an excerpt from the story that begins the science curriculum:
At first there was chaos, and darkness was on the face of the deep. . . . In this measureless void of cold and darkness light was created. There appeared something like a vast fiery cloud which included all the stars that are in the sky. The whole universe was in that cloud, and among the tiniest of stars was our own world; but they were not stars then; as yet there was nothing except light and heat. So intense was the heat that all the substances we know—iron, gold, earth, rocks, water—existed as gases, as insubstantial as the air.5
Leaving aside the fact that this story is based on the metaphysical contradiction of the “Big Bang” theory—which has the universe bursting out of nothingness—such a story, even if it were true, could not properly set context or provide motivation. What does it mean for a story of the universe to serve as a framework for simpler knowledge gained in science? How is a student supposed to integrate facts he observes about the world with broad abstractions he cannot possibly comprehend? You cannot integrate knowledge with what in the student's mind must stand as a fairy tale.
Such a story can be motivating in a superficial, “Wow, cool!” way, not in a deep and meaningful way. Real motivation comes from real understanding, and a child will develop a sincere love of science only if he comes to recognize the power of his mind to make sense of the physical world.
One other important hierarchy-related mistake is fundamental to the Montessori elementary program. According to Montessori, “freedom” is essential to a proper classroom. To suggest that the teacher can consciously form the intellect of the student, she says, is as absurd as suggesting a mother can consciously form the body of a fetus. All either can do is offer optimal conditions for natural and spontaneous growth.
The freedom Montessori advocates, let me qualify, is freedom in a carefully prepared environment, stocked with materials to advance the child's education; nevertheless, it is freedom for the student to direct his own activities to a great extent. This freedom is essential to the proper education of three- to six-year-olds. Elementary students, however, are learning different kinds of concepts, more abstract ones, and have different needs.
This insistence on freedom in the classroom for elementary students is incompatible with a hierarchical curriculum. It is the teacher's responsibility to give order to the presentation of knowledge, to carefully define the steps by which a child can proceed from the concepts he has already mastered to new, more abstract knowledge. Left to guide his own learning, it is impossible for the student to discover knowledge in the proper order. He will necessarily skip important steps, delving into information he does not have the ability to grasp.
Several years ago, I visited a Montessori classroom in which the elementary students had become fascinated by the Solar System. All their activities were integrated around this theme. They drew pictures, wrote poems, and prepared reports about the planets. Displayed on the wall was a report about Saturn written by a third-grader. The report contained the following information: “Saturn is a gaseous planet made of hydrogen and helium. It also contains traces of water, methane, ammonia and has a rocky core.” I wanted desperately to pull this child aside and ask, “What is methane? What is ammonia? What does it mean for a planet to be gaseous? For that matter, what is a planet?” The teacher was obviously impressed by the sophistication of this paper, and never stopped to consider whether it represented any real understanding on the part of the child. Montessori believes that the teacher's job is to intrigue the child, to open up a new world and show him its potential. Once this door is open, she must leave the child free to explore it on his own. It is only through independent discovery, she says, that he can really learn.
On the contrary, once a child reaches material far removed from the perceptual level, he is utterly dependent on the guidance of a teacher. The teacher must take him by the hand and lead him carefully through the material, ensuring that he firmly and independently grasps each step along the way. Only then will his abstract concepts represent real understanding.
Conclusion
Because of my experiences as a teacher, in which I have come to accept the principle of hierarchy as an absolute, I now know not to measure my success by whether my students can solve differential equations, describe protein synthesis, or propose solutions to world problems. I have succeeded in educating my students if their knowledge of history, science, literature, and math is real, first-handed, grounded in reality.
I have come to see that even schools with the appearance of a rigorous academic curriculum are not giving their students a real education, but are filling their heads with floating abstractions and reducing learning to memorization. As Ayn Rand wrote in her essay “The Comprachicos”:
When applied to conceptual material, memorizing is the . . . epistemological destroyer of understanding and of the ability to think. But throughout their grade- and high-school years, memorizing becomes the students' dominant (and, in some cases, virtually exclusive) method of mental functioning. They have no other way to cope with the schools' curricula that consist predominantly of random, haphazard, disintegrated (and unintegratable) snatches of various subjects, without context, continuity, or systematic progression.6
Students who graduate from high school able to recite abstract formulations but unable to tie those abstractions to reality have not learned and cannot think. To borrow Ayn Rand's metaphor for my own purposes, their education is like the hollow tree—grand and impressive on the outside, empty and hollow at its core. This must change.
Education is a realm that nearly everyone regards as disastrous, and nearly everyone wants to improve—yet it keeps getting worse. What few realize is that fundamental improvement can come only with an improvement in basic educational philosophy. Those of us who are concerned with the proper education of children must understand and fight for the principle of hierarchy in education.
I am fighting for it with my own school as a testing and learning ground and as an example for others to emulate. I am offering parents a radical alternative to today's schools: a school whose curriculum respects the hierarchy of knowledge; a school that presents the right material in the right order, producing students who are happy, confident, knowledgeable, and able to think. Let there be more of the same.