"Amazing new discovery: Piaget was wrong": Response.

Abstract

In the cause of clarity we first list a number of our positions that the two critics either accept or at least do not speak against (taking their silence for consent). Throughout, unless we indicate otherwise, we will confine our remarks to the principles relating to the conservation of amount of matter, mass and volume in solid bodies under transformation of shape. Owing to a number of misunders - tandings, to which we turn in the next section, Henry Markovits may be surprised at some of the points of agreement that we list. Linda Siegel much less so since she accepts the substance of our paper.Extent of Agreement1. There are grave problems about the validity of Piaget's methods in the conservation studies. We agree with Siegel that we might have emphasized more the extent of the dissatisfaction with those methods, but the issue was somewhat tangential to our purposes.2. The true laws relating to the conservation of quantities cannot be deduced logically from any humanly possible set of empirical observations that we can imagine.3. The ability to reverse the operation of transforming shape, either in perceptual imagination or in logic does not lead logically to the conclusion that any quantity is conserved under the transformation. Henry Markovits agrees, but surprisingly, in view of our citation of Piaget's own words, denies that Piaget thought such reversibility important in this connection.4. Compensation of increased length by diminished breadth does not lead logically to the conclusion that the quantities in question are conserved. 5. The matter of which properties are conserved under transformation is one of the deepest in science and in mathematics and the theoretical justification of conservation laws is highly problematic. Perhaps one has to apply for an explanation to insight -- a notion that is poorly understood.6. The relevant conservation laws are not innately given to the child or to anyone else. How otherwise explain the fact that Piaget and most of his followers were mistaken about the conservation of volume of solids under transformation of shape?7. Neither is an appreciation of those principles learned in the sense of being accepted from a teacher.8. Children progress best in such matter when they are actively engaged in the task of exploring the physical properties of bodies by manipulating them.It is also in the interest of clarity that we set the record straight about certain statements that are inputed to us.Misapprehensions1. Most important, we do not propose any of how children learn physics or principles relating to the conservation of quantities. This defuses a great part of Henry Markovits's criticism, which is aimed at an illusory alternative theory of physics learning. We do speak of a program of studies, but that is a quite different matter, and we do have a few common sense suggestions to make about some of children's sources of beliefs about the properties of physical objects. Nothing so ponderous as a theory!2. We did not say, nor do we believe, that the grasping of true conservation principles is simply an accumulation of knowledge (Markovits's words), if by that is meant either rote learning or the recording of observable facts.3. We did not say, nor do we believe, that between the child and the adult nothing of any conceptual importance occurs (Markovits). We take the learning of calculus to be an enormous endeavour that greatly alters one's ability to solve problems in physics. We appreciate that it is an enormous struggle to grasp the interrelations among mass, weight, volume, area, acceleration and the like. We believe, however, that the psychological dimensions of these developments are scarcely even glimpsed, let alone understood.4. Like Saul Kripke (1972) we believe that at least some necessary truths, certain conservation laws among them, are empirical discoveries. …