Dans les champs de l’observation le hazard ne favorise que les esprits préparés.
(In the field of observation, chance favors the prepared mind.)

—Louis Pasteur, in a lecture at the University of Lille, December 7, 1854

Why Is the Sequence Sequenced?

by Robert Shepherd

In seeming contradiction of Pasteur, John Malone published in 2002 his It Doesn’t Take a Rocket Scientist: Great Amateurs of Science, a compendium of wonderful stories of scientific discoveries made by interested amateurs. Michael Faraday, for example, was the son of an impoverished blacksmith and received very little formal education. Nonetheless, he discovered electromagnetic induction (that a changing magnetic field produces an electric field) and so became the father of the technological age. Albert Einstein and Jack Horner almost failed elementary school, but Einstein revolutionized fundamental physics, and Horner redefined our understanding of the appearance, social lives, and methods of locomotion of dinosaurs. David Levy wasn’t a professional astronomer, but he was the co-discoverer of Shoemaker-Levy 9, the comet that plowed into Jupiter in July of 1994, creating the largest explosion our solar system is likely to see (we hope) in our lifetimes.

Inspiring stories, all. However, the more one learns of these stories, the more one realizes that the leading characters were all amateurs in the root sense of the word (Latin, amo, amat) — they lacked professional credentials and training, but they made up for their deficiencies by spending years in solitary, single-minded pursuit of the objects of their affections. To a person, these great scientific amateurs were tenacious autodidacts, driven to read and learn and think about their subjects almost to the exclusion of everything else. The point is that stories of scientific discoveries by amateurs, wonderful as they are, rarely provide counterexamples to Pasteur’s general rule: Chance favors the prepared mind.

Nasa clip

Photo courtesy NASA Jet Propulsion Laboratory.

E. D. Hirsch, Jr., reminds us time and time again that “Knowledge builds on knowledge.” Newton famously remarked in a letter to fellow scientist Robert Hooke that he [Newton] was able to see far because he stood on the shoulders of giants. Those are different ways of saying the same thing that Pasteur said. In effect, every school child, at every point in that child’s school career, stands on the shoulders of his or her former self. This may seem a self-evident observation, but it’s one that has escaped the attention of those who build curricula in most American schools.

One cannot do differential equations without having learned one’s algebra. One can’t learn algebra without having learned arithmetic. The application of Hirsch’s (and Newton’s and Pasteur’s) idea is clear enough in mathematics, but it can be applied with equal, if less obvious, appropriateness in other curricular areas. One cannot understand what a Eb+7 chord is without knowing, first, what an Eb major chord is, and one can’t understand what a major chord is without understanding that the chord is built on a major scale and is built up from intervals (3 and 5) of that scale. If you want to teach students what abstract painting is all about, it’s a good idea to start by teaching them the basics elements of which compositions are made: hue, saturation, value, shape, and line. Then introduce them to representational painting. Next show them how representations can be progressively stylized, becoming less and less pictorial and more and more abstract.

Then you can talk about that crazy Russian guy Wassily Kandinsky, the founder of abstract expressionism, and how he thought that a pure element could “represent” an emotion without being a picture of anything at all: Blue is sad. Sharp corners are angry. (See Kandinsky's delightful little book Concerning the Spiritual in Art.) By building knowledge upon knowledge, you build genuine understanding. The key to a great lesson and to a great curriculum is cumulative sequencing.

In no part of the curriculum is the importance of building upon prior knowledge more completely ignored, these days, than in language arts. The Beat-era novelist, poet, and sometime producer of audio art William S. Burroughs experimented with a method of composition that involved writing something, cutting out the sentences, and then pasting them back together again randomly. Burroughs was aiming for the shock of the new — for unfamiliar juxtapositions that would stimulate thought. That might be an interesting and even valuable exercise for creative thinking — useful, say, for overcoming writer’s block — but it’s a lousy way to design a curriculum. Unfortunately, most language arts curricula in the United States today look as though they were designed using Burrough’s method. In the old days, teachers used to do separate units on expository composition, on public speaking, on writing the short story, on the grammar of sentences, on the Romantic Era in British literature, and so on—units that built knowledge upon knowledge, sequentially. These days, under the guise of “integrating the language arts,” these subjects are typically fragmented into random readings and random activities — here a lesson on puns, there a lesson on making inferences, and so on. This is no way to run a railroad or a classroom. When one has designed a course of study, one ought to look at what students are doing on a given day and ask, “Does the student have to know today, in order to do this, what he or she learned yesterday?” If the answer is no, then the course of study is badly designed. Here’s why: Knowledge builds on knowledge.

There are two ways in which new learning depends upon prior knowledge, and they are worth distinguishing:

First, studies in cognitive psychology and in child language acquisition have demonstrated conclusively that we are much more likely to retain new learning (to transfer it from short-term to long-term memory) if we have a preexisting memory framework to which the new learning can be attached. So, if you already know something about baseball, and you encounter the term infield fly rule, the new term connects to existing neural machinery that encodes your memories of what an infield is and what a fly ball is. But if baseball isn’t cricket to you, the new memory will find no place, in your brain, to call home. One might teach a student to memorize, by rote, the definition of infield fly rule, but he or she isn’t likely to transfer that learning to long-term memory unless his or her brain already contains a semantic framework for baseball. In such a case, the prior knowledge is prerequisite to retention of the new knowledge. It’s for this reason that people tend to learn new words in batches. You take a painting class at a local arts center, and in a few days’ time, without being aware of it, you have learned not only what the instructor taught, specifically, about sgraffito and pointillism, but also a great deal that you picked up incidentally — the meanings, for example, of terms like sable brush and gesso and blocking in. Furthermore, you retain this incidental learning not because you’ve worked at doing so but because the learning has taken place in the context of other learning about the same subject, and quite without your being aware of it, you’ve rehearsed the learning again and again. When you learn the new word, it is connected to a whole network of memory related to being in that art class and doing that painting and interacting with the other art students and thinking about art in general. This is the reason why kids learn new words at the astonishing rate of about ten per day up through early adulthood. Most word learning takes place in a semantic context. Only in schools, and only under the influence of crazy pedagogical theories like “integrating the language arts,” do we divorce learning from the context of other learning about the same subject and then expect it to stick.

Second, in other cases, the prior knowledge is prerequisite to understanding, at all, what is being communicated in the learning situation. If you know absolutely nothing about baseball, not even that it is a game, and you read that “The shortstop caught the infield fly,” then that sentence might as well be written in Coptic or Urdu. What educators often fail to realize is the extent to which any act of comprehension is dependent upon hundreds, even thousands, of bits of prior knowledge. To someone who has never heard of baseball at all — to a Trafalmadorian or Klingon, say — even the concept of catching has to be elucidated. Glosses on the terms shortstop and infield fly will be insufficient. Of course, the kid who has tossed a whiffle ball back and forth with Dad or Mom in the backyard needs no such instruction. He or she has had the prerequisite course.

That, in a nutshell, is why the Core Knowledge Sequence is a sequence. It was carefully prepared to present knowledge in various curricular domains in a way that builds that knowledge incrementally. Such cumulative, or incremental sequencing ensures that the student will not miss learning information that is essential to later learning. It also ensures that new material will be learned in the way that the brain is set up to learn — by adding to existing memory. For the existing memories — the prior knowledge — are like flypaper. They make the new learning stick.

Don Hirsch adds: "Sequencing avoids the evil of fragmentation, so that the kids in a class share similar background knowledge, thus improving learning and creating a sense of community as well as a learning community in the classroom."