Breadth Versus Depth: A Premature Polarity
From Common Knowledge, Volume 14, Number 4, 2001
In the education wars we encounter a lot of "premature polarities." This is a phrase I have adapted from I. A. Richards, the brilliant Cambridge theorist of an earlier generation, who spoke of "premature ultimates" — those conversation stoppers which, he said, "bring investigation to a dead end too suddenly" (Principles of Literary Criticism, 1925, chapter 6). I would define "premature polarities" in education as the habitual, almost automatic taking of sides on educational issues based on whether one considers oneself to be a liberal or a conservative in politics. Unfortunately, such ideological stand-taking not only brings investigation to an end, it tends to replace thought.
For example, in the reading wars, premature ideological polarization has caused phonics to be viewed as an agency of right-wing suppression that deprives reading of naturalness and impairs love of literature. "Whole language" on the other hand, is attacked as a left-wing abandonment of adult responsibility. Similarly, in the math wars, memorization of the multiplication table is viewed as a "conservative" principle of teaching, whereas the use of calculators is viewed as a pernicious "liberal" pedagogical policy. It is mysterious how these educational theories came to be associated so mindlessly with politics. Ideological polarities are valuable spirit-raisers in a real war. Everyone understands that "in war the first casualty is truth." But in the "phony wars" of education, sloganized polarizations are barriers to progress. And no barrier is greater than the sloganized polarity between "deep understanding" or "learning to learn" on one side versus the "rote learning of mere facts" on the other.
Concerning this controversy there exists some relevant and reliable research that has yielded a solid scientific consensus in the field of cognitive psychology. (An excellent summary of the current consensus in cognitive psychology is provided by Daniel B. Willingham in his book, Cognition, 2001, especially chapter 4-7 and 10.) Yet I do not find many references to that research-consensus in journals devoted to education. The research relevant to the premature polarization of "learning to learn" versus "piling up of mere facts" can be summarized in four principles.
- The ability to learn something new is not primarily a general, formal skill. It is chiefly a domain-specific skill. For instance, the ability to learn something new about math or music or history is highly dependent on the knowledge that one already possesses about math, or music, or history. This means that "learning to learn" always entails acquiring relevant knowledge about specific domains.
- General ability to learn is highly correlated with general knowledge. There is a stunning statistic on this point. The positive correlation of learning ability with socioeconomic status is .422, whereas the correlation of learning ability with general knowledge is nearly twice as high — .811 (D. Lubinski and L. G. Humphreys, "Incorporating General Intelligence into Epidemiology and the Social Sciences," Intelligence 24, 1997, pp. 159-202). We are so used to emphasizing the importance of socioeconomic status that this datum comes as a surprise. Yet it is just what we might have inferred from point 1 above that learning ability depends chiefly on having relevant prior knowledge.
- The optimal way to learn a subject is to learn both its general principles and an ample number of diverse examples that illustrate those principles. That's obvious in math. One needs to know what multiplication is in principle, but to gain real insight into what multiplication is one also needs to do a number of multiplication problems of different types. This finding bears directly on the depth/breadth issue in education. A broad range of examples should be studied, but studying too many is a waste of time.
- Another finding is that broad general knowledge is the best entree to deep knowledge. This is a conclusion from the field of psychology called "discourse analysis." The most effective way to introduce the meaning of a discourse is to start with a summary such as an abstract found in learned journals. After the learner gains a broad context through a sense of the whole domain, he or she can mentally fit the various parts that follow into that whole, and make sense of them. An example would be introducing first graders to a globe that shows oceans and continents before going on to teach them about specific places. What do these four principles imply for the question "What Should We Teach"?
They logically force us to abandon the sloganized polarity between "deep understanding" and "the rote learning of mere facts." One cannot gain deep understanding without having broad knowledge of a lot of facts. On the other hand, it is a waste of time to pile up more and more facts that don't really add much to one's understanding or ability to learn.
So, if we wish to educate students to become competent people and lifelong learners, these four principles give us a preliminary handle on an answer to the question "What Should We Teach?" We should teach a diversity of subjects that will lead to broad general knowledge, and we should also teach in some depth a moderate number of specific examples. From this simple inference it is clear that neither the "deep understanding" pole nor the "lots-of-facts" pole is an optimal approach. Since competence and ability to learn are correlated with broad knowledge, it is plausible to infer that we should teach a broad range of subjects, not just reading, writing, and arithmetic, but also science, history, ethics, literature, and the arts.
But within those fields what shall we teach? Our four principles have already established that it is not optimal to teach either a single thing in depth or a great many things superficially. Yet we still have the problem of choosing a moderate number of topics in the different domains. How do we choose what that moderate number of topics should be? Will any set of topics do? There is a school of thought that essentially says "yes, any set of topics will do." According to this view, studying any topic provides access to a whole domain. I have argued elsewhere that this conception is not well based in theory or in fact (The Schools We Need, 1996, pp. 127-175). It is a theory that has left us with sub-par achievement as a nation, and has perpetuated the test score gap between socioeconomic groups. My colleagues and I at the Core Knowledge Foundation have sponsored an alternative view. We hold that schools need to develop a specific sequence of topics at each grade level that will prepare the student to learn what the next grade has to offer.
This curricular structure is implied by principle 1 above, that new learning depends on relevant prior knowledge. That is an important reason why those nations that follow a common core curriculum in early grades have significantly higher achievement and greater equity than nations that do not. Students in core- curriculum nations enter each new grade ready to learn the new lessons (L. Woessmann, "Why Students in Some Countries Do Better: International Evidence on the Importance of Education Policy," Education Matters, Summer 2001, pp. 67-74).
But that still leaves unanswered the question we started with. Even if the arguments are strong in favor of a common core curriculum which covers several domains and provides a moderate number of specific topics, that still does not determine what the specific topics should be.
It is here that Core Knowledge has made a theoretical contribution. We have argued in favor of teaching topics that have the greatest potential for developing general competence and narrowing the test-score gap between groups. We made an inventory of the knowledge that is characteristically shared in American society by those at the top of the socioeconomic ladder. That turns out to be the knowledge taken for granted in American society — in college classrooms, in conversations with strangers, and in books and newspapers addressed to the general reader. Since that knowledge is taken for granted and not explained, ignorance of that assumed knowledge will seriously handicap those who lack it. We therefore argue that this "elite" knowledge ought to be the possession of every citizen in a democracy. The desire to change and improve the character of that assumed knowledge is admirable, but until we succeed in doing so, we should not withhold it and thereby handicap those who lack it because of accidents of birth.
People who have called this approach a collection of "mere facts" or called it names such as "Eurocentric" and "elitist" have not bothered to find out just what is in the Core Knowledge Sequence, or to notice how carefully selective are the topics it sets forth. Our experiences in the field suggest that these guidelines strike a reasonable balance between deep, large scale generalizations and specific factual knowledge. We know from independent evaluations that teaching the Core Knowledge topics in a coherent and cumulative way enhances student achievement and narrows the test score gap between socioeconomic groups.
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Last updated: Fri, May 23 2008
