Every year, when I give my first test in a grammar or literature class, some new student asks me whether the test will be multiple choice. Every year, I look him in the eye and say “I can assure you that you will never, in any class, under any circumstances, at any point in your education at VanDamme Academy, have a test that is multiple choice.”
The vast majority of the students’ work at VDA is written–in complete sentences, paragraphs, or essays. There is no surer way for the student to master the material, and for the teacher to determine whether he has mastered it.
For the student to write explanations, in complete sentences, about every subject, requires that he have a true understanding of the concepts at hand. But he can often do well on multiple choice, matching, or other rote exercises with no real understanding.
Children have incredible, sponge-like brains, that give them an almost unlimited capacity for memorization and pattern recognition. The teacher’s job is to ensure that this amazing talent does not become a substitute for understanding.
I have encountered this issue repeatedly in grammar class. Grammar texts typically introduce a new concept, such as the prepositional phrase, define it, provide examples, and then ask students to do a series of rote exercises in which they identify the prepositional phrases in a sentence.
Year after year, I find that students do very well recognizing prepositional phrases, such as “in the park,” “after the show,” “with my friend,” and “under the bed,” but will also occasionally underline groups of words like “is the winner” or “has the answer” because these groups of words seem to vaguely fit the pattern of a prepositional phrase.
The vast majority of the time they will properly identify the prepositional phrases, and will appear, therefore, to understand what they are doing–but the fact that they identify just one or two of these other groups of words indicates that they in fact have no understanding of the concept, and are simply pattern-seeking and performing the exercise by rote.
If, on the other hand, they are required to write, or at least to explain, that a preposition indicates the relationship between its object and some other word in the sentence, if they are required to describe the nature of that relationship, and if they already have a good, conceptual understanding of verbs and their complements, then they have a real understanding of prepositions, and will not make this error.
David Harriman tells a story about his own educational history that perfectly illustrates the difference between pattern seeking and knowledge.
When Dave was a sophomore at UC Santa Barbara, he took his first course on differential equations. It was a class with 200 students, so the teacher didn’t assign homework that was turned in and graded. Instead, he handed out long lists of practice problems, and recommended that the students select and solve enough of the problems to gain confidence in their understanding.
Dave, given his brilliant mind, intellectual ambition, and (according to him) lack of much of a social life at the time, did ALL the practice problems. He thinks he may have been the only student in the class who did. The final exam in the course was supposed to take two hours, but Dave finished in 40 minutes, and got a perfect score.
About a year later, Dave was working on a physics problem, and it involved solving a differential equation.
He remembers staring at the equation and drawing a complete blank, thinking, “What the hell do I do with this?” A year earlier, he would have been able to solve the equation without even thinking. But, of course, that was his problem: he had always solved the equations without really thinking.
Solving differential equations, according to Dave, is an art. There are quite a few techniques, and the trick is to recognize which technique will work on the particular equation of interest.
Faced with the application of differential equations to physics, Dave discovered that he had developed a subconscious, automatized ability to look at an equation and instinctively just know what technique to use. But he had never explicitly identified what he was doing, or why that was the right approach to solving this particular problem.
What he possessed was not real knowledge, but an acquired talent of pattern recognition, which–as it always does–faded when it was no longer in use.
The goal of promoting real understanding rather than memorization or pattern-seeking–is accomplished through hierarchical, integrated, purposeful lectures, and by requiring the students to write. In every subject, students are consistently required not just to provide an answer, but to explain how they arrived at the answer, to justify why it is the answer. For example:
