Garlikov.com contains Richard Garlikov's writings on philosophy and logic
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garlikov
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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.
