Chapter 13
13
The Argumentative Child
The Pert age . . . is characterized by contradicting, answering back, liking to “catch people out” (especially one’s elders); and by the propounding of conundrums. Its nuisance-value is extremely high.
—Dorothy Sayers, “The Lost Tools of Learning”
Somewhere around fourth grade, the growing mind begins to switch gears. The child who enjoyed rattling off her memorized spelling rules now starts noticing all the awkward exceptions. The young historian says, “But why did Alexander the Great want to conquer the whole world?” The young scientist asks, “What keeps the earth in orbit around the sun?” The mind begins to generalize, to question, to analyze—to develop the capacity for abstract thought.
In the second stage of the trivium, the student begins to connect all the facts she has learned and to discover the relationships among them. The first grader has learned that Rome fell to the barbarians; the fifth grader asks why and discovers that high taxes, corruption, and an army made up entirely of mercenaries weakened the empire. The second grader has learned that a noun names a person, place, thing, or idea; the sixth grader discovers that gerunds, infinitives, and noun clauses can also act as nouns.
The third grader has learned how to multiply two-digit numbers together to produce an answer; the seventh grader asks, “What if I have only one two-digit number and an answer? Can I discover the missing number if I call it x ?”
Now it’s time for critical thinking.
“Critical thinking skills” has become the slogan of educators from kindergarten through high school. Critical thinking books, software, and curricula abound. Catastrophe is predicted for children who miss out on this vital training. “Are you going to wait until schools teach thinking directly?” asks the back cover of one critical-thinking tome. “That may be too late for your children.”
But what are these “critical thinking skills,” and how are they to be taught?
A quick look through education materials reveals certain phrases popping up again and again: “higher-order thinking,” “problem solving,” “metacognitive strategies.” All these boil down to one simple concept: critical thinking means that the student stops absorbing facts uncritically and starts to ask “Why?”: “Why do you multiply the tops and bottoms of fractions?” “Why did the North and South really go to war?” “Why do scientists believe that nothing can go faster than the speed of light?” “Why do words that begin with pre- all have to do with something that comes ‘before’?” “How do we know that water boils at two hundred twelve degrees Fahrenheit?”
The student who has mastered “higher-order thinking” and “problem-solving techniques” doesn’t simply memorize a formula. (”To find the area of a square, multiply the length of a side by itself.”) Instead, she memorizes the formula and then figures out why it works. (”Hmmm . . . the sides of a square are the same, so the area inside the square is always going to measure the same horizontally and vertically. That’s why I multiply the side by itself.”) Once she knows why the formula works, she can extrapolate from it to cover other situations. (”How would I find the area of a triangle? Well, this triangle is like half a square . . . so if I multiply this side by itself, I’ll get the area of a square . . . and then if I take half of that, I’ll know how much area the triangle covers. The area of a triangle is this side, times itself, times one-half.”)
Some critical-thinking advocates suggest that “thinking skills” can somehow replace the acquisition of specific knowledge. “Traditional teaching” is referred to, with scorn, as “mere fact assimilation” or “rote memorization,” an outdated mode of learning that should be replaced with classes in “learning to think.” The popular teacher’s journal Education Week defines critical thinking as “the mental process of acquiring information, then evaluating it to reach a logical conclusion or answer,” and adds, “Increasingly, educators believe that schools should focus more on critical thinking than on memorization of facts.”1
But you shouldn’t consider critical thinking and fact gathering to be mutually exclusive activities. Critical thinking can’t be taught in isolation (or “directly,” as the above quote from a critical-thinking manual suggests). You can’t teach a child to follow a recipe without actually providing butter, sugar, flour, and salt; piano skills can’t be taught without a keyboard. And your new focus on the whys and wherefores doesn’t mean that your child will no longer learn facts. A math student can’t think critically about how to find the area of a triangle unless she already knows the formula for finding the area of a square. A fifth grader can’t analyze the fall of Rome until she knows the facts about Rome’s decay.
So we won’t be simply recommending workbooks that claim to develop isolated “critical-thinking skills.” Instead, as we cover each of the subjects— math, language, science, history, art, music—we’ll offer specific instructions on how to teach your middle schooler to evaluate, to trace connections, to fit facts into a logical framework, and to analyze the arguments of others. The middle-grade student still absorbs information. But instead of passively accepting this information, she’ll be interacting with it—deciding on its value, its purpose, and its place in the scheme of knowledge.
BUILDING ON THE FOUNDATION
The poll-parrot stage has prepared the middle-grade student for the logic stage in two important ways. First, the middle-grade student should no longer be struggling with the basic skills of reading, writing, and arithmetic. A child must read fluently and well before entering the logic stage; the student who still battles her way through a sentence cannot concentrate on what that sentence means. The logic-stage student will write extensively as she evaluates, analyzes, and draws conclusions; the study of grammar and punctuation will continue through high school, but the basic mechanics of spelling, comma placement, capitalization, and sentence construction should no longer act as barriers to expression. The middle-grade child will begin to think of mathematics in terms of concepts and ideas; she can’t do this unless the basic facts of arithmetic are rock solid in her mind.
Second, the student has already been exposed to the basics of history, science, art, music, and other subjects. Now she has a framework of knowledge that will allow her to think critically.
On pages 221–225, we discussed the differences between parts-to-whole and whole-to-parts instruction. When you taught bugs in first grade, you used parts-to-whole instruction. You got out all the pictures of bugs (or used actual bugs) and described the five different types of legs and feet. Then you asked the child to tell you what she just heard, to point out the different types of legs, to write a sentence or draw a picture. In other words, you taught the bits of information—the parts—to the child and then helped her to assemble them into a whole.
The middle grader has already learned something about bugs, though. And her mind has matured and developed beyond the need for spoon-feeding. In the middle grades, you’ll move toward a whole-to-parts method of teaching—presenting the student with a piece of information or a phenomenon and asking her to analyze it. When you study biology with a fifth grader, you lay out a trayful of insects and ask: “What differences do you see between these legs and those?” “How would you describe each leg?” “What function does each have?”
In the following chapters, we’ll guide you through this type of teaching in the middle-grade curriculum.
LOGIC AND THE TRIVIUM
A classical education isn’t a matter of tacking logic and Latin onto a standard fifth-grade curriculum. Rather, logic trains the mind to approach every subject in a particular way—to look for patterns and sets of relationships in each subject area.
But formal logic is an important part of this process. The systematic study of logic provides the beginning thinker with a set of rules that will help her to decide whether or not she can trust the information she’s receiving. This logic will help her ask appropriate questions: “Does that conclusion follow the facts as I know them?” “What does this word really mean? Am I using it accurately?” “Is this speaker sticking to the point, or is he trying to distract me with irrelevant remarks?” “Why is this person trying to convince me of this fact?” “Why don’t I believe this argument—what do I have at stake?” “What other points of view on this subject exist?”
These are questions that very young minds cannot grapple with. A seven year old has difficulty in understanding that (for example) a public figure might twist the facts to suit himself, or that a particular text might not be trustworthy because of the writer’s bias, or that newspaper reports might not be accurate. But in the expanding universe of the middle-grade child, these questions will begin to make sense.
You may find yourself indebted to formal logic as well. Any parent of a fifth grader should be able to point out such logical fallacies as the argumentum ad nauseam (the incorrect belief that an assertion is likely to be accepted as true if it is repeated over and over again) and the argumentum ad populum (if everyone’s doing it, it must be okay).
LOGIC IN THE CURRICULUM
In language, the logic-stage student will begin to study syntax—the logical relationships among the parts of a sentence. She’ll learn the art of diagramming (drawing pictures of those relationships). The grammar-stage student wrote compositions that summarized information—how the Egyptians wrote, the important battles of the Civil War, the life of George Washington. Now, compositions will begin to focus on questions of motivation, of historical development, of debated fact. How did picture language such as hieroglyphics develop into written language? What were the real causes of the Civil War? Why did George Washington keep slaves? Logic-stage students will also begin to read literature more critically, looking for character and plot development.
Properly speaking, grammar-stage math is concerned with arithmetic— adding, subtracting, multiplying, and dividing actual numbers. Arithmetic isn’t theoretical. Arithmetic problems can be worked out in apples and oranges and pieces of bread. But in the second stage of the trivium, the student begins mathematics proper—the study of the many different relationships between numbers, both real and theoretical (negative numbers, for example). In other words, arithmetic is the foundation for mathematics proper.
History in the logic stage will take on a new character. The student will still be responsible for dates and places, but you’ll encourage her to dig deeper into the motivations of leaders, into the relationships between different cultures that existed at the same time, into forms of government and causes of war. Morality should become a matter of discussion as well. Was this action (this war, this threat) justified? Why?
The study of art and music at this point will become synchronized with the study of history. The student will learn about broad developments in society and culture, and will try to understand how these are reflected in the creative works of the times.
HOW TO TEACH THE LOGIC STAGE
For you, the teacher, the teaching process will change slightly. In first through fourth grades, your focus was on memorization—on the learning of rules, dates, stories, and scientific facts. You told the student what she needed to learn, either by reading to her or by giving her a little lecture, and you expected her to be able to repeat that information back to you. You used narration and notebook pages to bring this about.
Now, you won’t be feeding the child with a spoon. You’ll be asking her to dig a little deeper, to do more discovering on her own. Instead of lecturing, you’ll concentrate on carrying on a dialogue with your child, a conversation in which you guide her toward the correct conclusions, while permitting her to find her own way. You’ll allow the child to disagree with your conclusions, if she can support her points with the facts. And you’ll expect her not simply to repeat what she’s read, but to rework the material to reflect her own thoughts. Once she’s done this, she’ll have learned the material once and for all.
Here, one-to-one tutoring has an obvious advantage over the large public-school classroom. Classrooms encourage children to answer questions set to them; one-on-one instruction encourages children to formulate their own questions and then pursue the answers. Even the most dedicated teacher can’t allow a class of thirty to dialogue their way to comprehension—the noise would be overwhelming.
As the logic stage progresses, you’ll be using more and more original sources, steering away from “textbooks.” Many textbooks are boring. And most present information in a way that’s actively incompatible with the intent of the logic stage. History, for example, is often given as a series of incontrovertible facts. As Neil Postman observes, there is usually “no clue given as to who claimed these are the facts of the case . . . no sense of the frailty or ambiguity of human judgment, no hint of the possibilities of error.”2 A textbook leaves nothing for the child to investigate or question; it leaves no connections for the student to discover.
How do you guide this journey toward discovery?
Start with logic. In the next chapter, we’ll introduce you to the formal study of logic. In the chapters that follow, we’ll guide you in applying the categories and structures of logic to the various subjects.
We cover logic and mathematics first; then, since the middle-grade humanities curriculum is structured around the logic of history, we present history before continuing on to reading, writing, grammar, science, foreign languages, art, and music.
PRIORITIES
The logic-stage student is doing much more independent work than the grammar-stage student and is requiring much less one-on-one attention from you. Home-educated students typically spend an hour in self-directed work for every ten minutes of parental tutoring.
Because of this new time economy, and because the student has now mastered the most basic elements of reading, writing, and math, you’ll find that you’re able to cover more material. Language, mathematics, logic, history, and science are staples of the logic stage; art and music should be pursued, if possible.
While you won’t need to do as much one-on-one teaching with the student, maintain close supervision. Every home-schooling parent has made the mistake of handing a textbook off to a seemingly mature seventh grader only to find at Christmas that two lessons had been completed. Check assignments on a weekly basis.
By the middle grades, students will often develop a particular fondness for one subject (or a loathing for another). Because home education is flexible, you can structure your academic day to allow a child to follow an interest. If, for example, your seventh grader acquires a passion for King Arthur, let her follow the knights of the Round Table throughout literature and history for several months; don’t insist that she move to the Reformation right on schedule. At the same time, though, do insist that the student keep up in each subject area. Don’t let math slide for history, or foreign language for math. It’s too early for the child to develop a speciality; she still hasn’t been exposed to the full range of possibilities.
1“Critical Thinking,” Education Week on the Web, www.edweek.org.
2Neil Postman, The End of Education: Redefining the Value of Schools (New York: Knopf, 1995), p. 115.
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