Placeholder Structures
Initial learning of new facts, by necessity, must be formulated in terms of the available conceptual repertoire, or they must be represented as placeholder structures, not yet interpreted in terms of available concepts.
From The Origin of Concepts, by Susan Carey:
A numerical system that encompasses fractions and decimals is incommensurate with the preschool child's hard-won numeral list representation of the positive integers . . . A physical theory in which weight is conceptualized as a continuous quantity that provides a measure of the amount of matter, and in which weight and density are differentiated, is incommensurate with the preschooler's physical theory, in which material is not differentiated from physically real, and in which the concept of heaviness conflates those of weight and density . . . children hold each as coherent, stable, symbolic structures; . . . To distinguish the two CS1–CS2 transitions [Conceptual System 1 to Conceptual System 2], I will call the successive numerical systems Numerical System 1 (NS1; numeral list representation of integers) and Numerical System 2 (NS2; rational number), and I shall call the two Physical Theories 1 and 2 (PT1 and PT2). . . .
The challenge to understanding the transition from CS1 to CS2 derives from the incommensurability of the two successive conceptual systems. In cases of incommensurability, the child cannot express the propositions of CS2 in the conceptual vocabulary of CS1. Simply telling children, "Fractions are numbers resulting from dividing one number by another" clearly does not help because children limited by NT1 [sic] do not distinguish division from subtraction and reject 2/3 as a number. Similarly, telling children "All matter takes up space and has weight" does not help because those who have only PT1 represent the world in terms of concepts that do not include matter or weight, concepts that are incommensurable with those the holder of PT2 is expressing with that sentence. . . .
How do children learn facts and causal accounts that they do not have the concepts to express? . . . . Initial learning of new facts, by necessity, must be formulated in terms of the available conceptual repertoire, or they must be represented as placeholder structures, not yet interpreted in terms of available concepts. . . .
This last sentence is a little funny: initial learning must, by necessity, be formulated this way—or not. But it is also important, I think, because—as has been discussed in this space many times—instructional acts that are thought to create placeholder structures (e.g., memorization, imitation, testimony) represent very human and very common ways of learning. The fact that placeholder structures do not represent the desired end of learning—that they are often brittle, temporary, passive—is totally beside the point. They are also, without a doubt, natural, nearly everywhere, and, in many cases, necessary. If you can't hold this latter idea in your head at the same time as the former, then you have a severely distorted view of how people learn.
