How Do Children Acquire Number Concepts ECI 314 Early Childhood Mathematics

The geocentric theory became untrue when people

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Unformatted text preview: Behaviorism can explain changes in animals’ surface behaviors, and associationism can explain children’s learning of bits of knowledge (such as nonsense syllables and sums). However, the deep and general logic underly­ ing children’s construction of number concepts can be explained only by Piaget’s constructivism. It is true that human beings can be conditioned, but there is much more to human knowledge than what animals and young chil­ dren can learn. As can be seen in Figure 1.5b, the relationship between behaviorism and Piaget’s constructivism is analogous to the one between the geocentric and he­ liocentric theories of the universe. The geocentric theory existed first and was based on common sense. The heliocentric theory went beyond the primitive theory by encompassing the old one. An interesting phenomenon in a scientific revolution is that while the new theory makes the old one obsolete, the old theory remains true within a limited scope. The geocentric theory became untrue when people stopped believing that the sun went around the earth. However, from the limited perspective of earth, it is still true today that the sun rises and sets. This “truth” is reported daily in the news. It is likewise still true, from the limited perspective of surface behavior, that drill and reinforcement “work.” From a deeper and longer-range perspective, however, we no longer think that human beings acquire knowledge by internalization, reinforcement, and conditioning. Figure 1.5c shows a similar relationship between Euclidean and nonEuclidean geometry. When non-Euclidean geometry was accepted, it became un- How Do Children Acquire Number Concepts? 17 Figure 1.5. The relationships between (a) behaviorism and Piaget's constructivism, (b) the geocentric and heliocentric theories, and (c) Euclidean and non-Euclidean geometry. true that the shortest distance between two points is a straight line. Within the limited perspective of Euclidean geometry, however, it is still true that the shortest distance between two points is a straight line. Many other examples of scientific revolutions can be given to show that a more adequate, later theory goes beyond a primitive theory by encompassing it. The relationship between Newtonian physics and quantum physics is another example of a scientific revolution. All that a scientific theory does is to describe and explain phenomena, and the practical application of an explanatory theory to an applied field like medi­ cine, architecture, or education is not the business of science itself. However, a scientific theory can be enormously useful in an applied field because it enables us to change the focus of the debate from “this method of teaching versus that method of teaching” to how children acquire number concepts (or any other kind of knowledge). As stated at the beginning of this chapter, there is no disagreement in medicine about the fact that the cause of cancer has not been explained scien­ tifically. Disagreement about how to treat cancer always begins with agreement about what is known and unknown scientifically about the cause(s) of cancer. 18 TheoreticalFoundation In education, by contrast, debates about how to teach arithmetic rage on with­ out even asking how children acquire number concepts. Debates in education are often based on unproven assumptions, just as people in medicine used to argue in favor of bloodletting and the use of leeches, citrus fruit, and herbs. Once we agree, scientifically, on how children acquire number concepts, we can debate at a higher level how best to foster children’s process of learning. A growing minority of educators have recognized the superiority of Piaget’s constructivism and have drastically changed their way of teaching. Just as con­ serves cannot go back to nonconservation, and humanity cannot go back to the geocentric theory after accepting the heliocentric theory, teachers who know how children acquire number concepts cannot go back to empiricist teaching. It took 150 years for the heliocentric theory to become universally accepted (Taylor, 1949). We hope it will not take 150 years for Piaget’s constructivism to be accepted by educators....
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