> You mentioned *****.   She is quite a brilliant scholar. I have 
> enjoyed studying Piaget under her for the past year-and-a-half. The greatest
> problem I am having with Piaget and constructivism is similar to the one I
> mentioned in my email regarding your article--the theory needs to be
> interpreted (simplified) and developed by teacher educators into forms that
> can be understood and used by teachers.

I think there is a bigger problem with that, which is one that Dr. ***** seems to recognize only when pinned into a corner, and then she forgets right away: 
The notion of which material is "developmentally appropriate" --i.e., potentially readily learnable at a given age or state of development-- cannot be dependent on what kids know and when kids know it UNDER particular teaching methods. E.g., the fact that most American third graders don't understand place value does not mean that third graders cannot learn place value, nor that even first graders cannot learn place value in a way that they can understand it. It may only mean, and in fact, usually only means, that the way they are currently taught does not give them a very good understanding of place value. You can never determine potential from simply examining any current state of affairs or from examining the results of the existing training or teaching methodology. The fact that any state of affairs exists for anything does not necessarily mean it could not have been otherwise had the prior conditions been different. Determining potentials requires a different kind of evidence. 

I also believe that the particular Piaget method of questioning kids (which in certain salient ways is unfortunately similar to how teachers question students) is not a good one because it is too superficial in a way that is extremely important, particularly for, or in, classroom practice. I believe that conclusions drawn from using that method do not necessarily show much about kids' understanding. E.g., in the study where he laid out two equal length pieces of string parallel to each other, with one of them pulled straight, and the other in a curvy pattern, and then asked kids which string is longer, kids of a certain age tended to say the straight string was longer. Piaget drew some conclusion about that with regard to kids' not understanding that matter was conserved or that length was not dependent upon formation, etc. 

But there are at least three ways to take the question, and Piaget and his proteges, in the accounts I have read, do not follow up with children's answers to see what they might have meant and why they answered the way they did. The question could perfectly well be interpreted to mean: 
(1) which string goes further (in which case the straight string, which is extended more -- the ones the kids' picked) is the proper answer.
(2) which string would take the longest to traverse if it were, say, a road? In this case, the curvy road would be the longer path to the same point as a straight road. 
(3) Which string contains the most matter (in some fairly complex sense that is actually pretty difficult to state, and which assumes they are the same diameter and that the matter is equally distributed in both of them, etc.)? Or, which string would be longer if they were laid out in the same way? This is clearly the conceptual meaning of the question Piaget had in mind, but there is no reason for a child to know that is the meaning he had in mind. It is not because children CANNOT understand that concept; it is that they have never had any reason or experience to think of it in the way Piaget was. And it is because that is not a common way of talking about length. And when length is talked about that way, it is often difficult to determine it. For example, it is pretty much impossible to even estimate the length of shoe laces you need by just looking at your shoes, so you have to look at the package which gives average lengths based on the number of pairs of holes for the laces. And it is almost impossible to estimate a circumference or irregularly shaped perimeter one is not familiar with without calculating it from an estimated diameter or radius. 

Moreover, with regard to conceptual meaning and understanding concepts, even adults live in their own heads in this way; we all do. Unless one is looking for ambiguities or has some sense there is one coming between you and another person, no one ever thinks another person means something different from how they themselves happen to be seeing it. Many people don't even recognize ambiguities AFTER they are pointed out. E.g., if we pointed out the above three meanings of the "length of the string" to *****, she would more than likely say that (1) and (2) clearly are not what is meant by the question. Well, that is not "clear". And the reason this is important is that kids ALL THE TIME are working with some sort of meaning that needs to be ferreted out of them by adults because it will either be a meaning the adult hasn't thought of or a meaning the adult has long forgotten. 

I give numerous examples of this in the papers at my web site. The fact that a kid's concept is not the same as some adult's concept during a Piaget-type questioning interview, does not necessarily mean anything about a kid's developmental state; it only has to do with their state of socialization into the world of how adults use certain concepts (and their willingness to answer the question in the way the adult wants to hear the answer if the child knows). I presume if we questioned most Americans about milking cows, or growing corn, or catching fish, or programming their VCRs, they would not know how to do many of those things; but that is not because they are not developmentally ready to do them. It is because they were never exposed to them in a way that they (could likely have) internalized. Most people have to become socialized into any new job or new office or situation because they are not likely to know how the new place works; that is a matter of proper introduction and exposure, not developmental readiness. 

Oppositely, kids can often do things that appear to demonstrate a terrific grasp of a concept that they really don't have the least clue about. When my younger child was in kindergarten or first grade, I brought home a software program for my second or third grader that had arithmetic stuff using a Pac-Man type game. They had addition, subtraction, multiplication, and division games where you tried to get to the right answers before the Pac-Men type creatures caught up with you and ate you. Well, one of the games was finding the PRIME NUMBERS, among sets of numbers that appeared on the screen. I happened to go into the room one day while Lydia, at age 5 or 6, is playing with this program, and she finishes the Prime Number game and has something like 11,000 points! The program gives the top scores, and she has all the previous top scores, and they have increased by leaps and bounds each time. I ask her to play the game in front of me, and she does; and she is whizzing through the sets finding all and only prime numbers, and hardly ever getting eaten by a Pac-Man because she gets to the numbers long before they do. I am astounded. So later when we are upstairs, I ask her what (presumably) her teacher has told her about prime numbers that has helped her learn them so well. She says the teacher did not talk about them. So I asked what it means for something to BE a prime number. She has no idea. She has just learned from trial and error playing that game, what the prime numbers are; not what their defining property is. That is often the way older students and even adults demonstrate thinking supposedly, in many cases: they give the answer the teacher wants to hear, because the student has learned that is the answer to give, without really having any understanding of it. That is explained more fully in the paper "Having Understanding, Versus Knowing Correct Explanations." 

So, it is my view that anything which simplifies the questioning process and makes it automatic is going in the WRONG direction. Part of what my papers are about is trying to get teachers to learn to really listen to kids, to learn to find out what kids really MEAN by what they say or write, to understand what possible ambiguities or alternative meanings there might be, and to think about what kids really mean and why they mean that or why they think what they are saying is true, and how to respond appropriately and reasonably. That requires a great deal of the kind of reasoning and conceptual skills teachers are not generally trained to have, and it requires perspectives and attitudes teachers are not encouraged or trained to have either. The answer is to educate and train teachers properly, not to try to figure out ways to by-pass their lack of training and understanding.