From a cognitive standpoint, development and learning are not the same thing. Some types of knowledge are universally acquired in the course of normal development, while other types are learned only with the intervention of deliberate teaching (which includes teaching by any means, such as apprenticeship, formal schooling, or self-study). For example, all normal children learn to walk whether or not their caretakers make any special efforts to teach them to do so, but most do not learn to ride a bicycle or play the piano without intervention.
Infants and young children appear to be predisposed to learn rapidly and readily in some domains, including language, number, and notions of physical and biological causality. Infants who are only 3 or 4 months old, for example, have been shown to understand certain concepts about the physical world, such as the idea that inanimate objects need to be propelled in order to move (Massey and Gelman, 1988).
Young children have a natural interest in numbers and will seek out number information. Studies of surprise and searching behaviors among infants suggest that 5-month-olds will react when an item is surreptitiously added to or subtracted from the number of items they expected to see (Starkey, 1992; Wynn, 1990, 1992). By the time children are 3 or 4 years old, they have an implicit understanding of certain rudimentary principles for counting, adding, and subtracting cardinal numbers. Gelman and Gallistel (1978) studied number concepts in preschoolers by making a hand puppet count a row of objects in correct, incorrect, or unusual ways; the majority of 3- and 4-year-olds could detect important counting errors, such as violations of the principles of one-to-one correspondence (only one number tag per item and one item per tag) or cardinality (the last ordinal tag represents the value).
Thus in mathematics, the fundamentals of ordinality and cardinality appear to develop in all normal human infants without instruction. In contrast, however, such concepts as mathematical notation, algebra, and Cartesian graphing representations must be taught. Similarly, the basics of speech and language comprehension emerge naturally from millions of years of evolution, whereas mastery of the alphabetic code necessary for reading typically requires explicit instruction and long periods of practice (Geary, 1995).
Even though young children lack experience and knowledge, they have the ability to reason adeptly with what knowledge they do have. Children are curious and natural problem solvers, and will try to solve problems presented to them and persist in doing so because they want to understand (Gelman and Gallistel, 1978; Piaget, 1978). Children can also be deliberate, self-directed, and strategic about learning things they are not predisposed to attend to, but they need adult guidance to develop strategies of intentional learning. Much of what we want to assess in educational contexts is the product of such deliberate learning.