Piaget applied the tools of clinical psychology to childhood development to come up with a theory that learning is subordinate to neurological development. Piagetian development is primarily chronological and biological; once a child is old enough they can be taught a concept by anyone, or even pick it up out of a book. Although this development can be inexplicably delayed by nebulous cultural factors which vary from country to country, it can't be significantly influenced by active instruction, except perhaps negatively. The role of a teacher is not to get in the student's way.

A piagetian cirriculum largely seems to consist of finding what a child is ready for, and passively following along after the child's development supplying content knowledge. A piagetian cirriculum mostly seems to be concerned with what a teacher should NOT do, such as determining what subjects a teacher should not attempt to teach to a given group of students. Most criticisms of Piaget have focused on the passivity it encourages among instructors, and instead finding a useful positive role for the teacher to play, and a model that suggests how they might do a better job at teaching.

The Information Processing theorists took the opposite view from Piaget, using a computer analogy to view the mind as a symbol processing machine, with a collection of programs that operate on symbols to produce results. Instruction could take a central role in this model, helping children acquire better rules for use in symbol manipulation production systems. Piagetian stages were seen as the cumulative result of acquired content knowledge and the processing done on it, rather than biological or neurological development.

The information processing theorists did help the teaching field move beyond pure piagetian clinical sterility, but it was not a complete model of how humans work. The computer metaphor is fundamentally incomplete because computers merely run programs; they do not create them. Computers are programmed by humans, and despite the best efforts of artificial intelligence researchers no model of a self-programming computer yet exists. (Even with genetic algorithms, a human must define the goals and test criteria.) Therefore, information processing is based on comparing what computers might someday be like to what humans actually are like, which can only be done with a huge glue layer of speculation.

The conceptual change model largely focuses on the study of misconceptions. It posits that students have a network of interconnected beliefs, a "conceptual ecology" composed of accumulated content knowledge and the derived relationships between concepts, with which they explain the universe at large and the phenomena they encounter in it. Beliefs which do not explain encountered phenoma (misconceptions) may be replaced by new beliefs that more accurately model the known universe by pointing out phenomena that they mispredict (challenging the misconception).

Even then, new concepts require a mental processing to be integrated into the learner's belief system. Two such types of processing are assimilation, where the new belief is connected to existing beliefs, and accomodation, where the new belief at least partially replaces existing beliefs. These processes deal primarily with the interconnections between beliefs in the student's mind, sometimes in subtle ways. A new belief that fails to explain as many phenomena as an existing belief may have a hard time replacing it, even in the face of direct evidence that the old phenomena is inconsistent with some parts of the the exterior world.

One potentially useful approach to challenging existing misconceptions is to focus on contradictions within the student's existing conceptual structure, gaining leverage against existing beliefs to dislodge the misconception. This can help create dissatisfaction with the existing misconception, after which the new concept must simply be made intelligible to the student and seem a plausible explanation for the percieved phenomena to be at least tentatively integrated into the student's conceptual ecology. If the new concept then leads to new insights and discoveries (it is "fruitful"), the child will be internally motivated to maintain and develop it.

Vygotsky's theory of proximal development points out that the sterility of the piagetian clinical interview process leads to some gaps. In an effort to avoid the "clever hans" trap, clinical interviewers typically remain as passive as possible to avoid contaminating their research results. But the full extent of a student's abilities cannot be determined purely passively, and must be actively probed for to be accurately determined. Students have two levels of development; tasks and concepts they have mastered and can handle independently, and tasks and concepts that they can follow along with if they are led through them, and are capable of performing or understanding themselves with external assistance (like learning to ride a bike with training wheels). Only the first "mastery" level was dealt with by Piaget.

The gap between these two levels is Vygotsky's "zone of proximal development", and represents the area a student's mind is currently capable of expanding into. Vygotsky points to studies indicating that the zone of proximal development is indicative of the future mastery level detected by piagetian clinical methods. Thus a teacher can take an active, productive role helping a student progress through their zone of proximal development.

Personaly, I find Piaget's developmental stages almost completely useless since I'm studying to teach at the community college level, and even perfectly true and accurate statements about early childhood development, whether chronological or biological, are unlikely to be of much use. Piaget collected a lot of raw data and shot down much of what came before him, which is nice, but I see things like Duckworth's "The Having of Wonderful Ideas" (probably my favorite paper so far) as moving beyond Piaget (just like the other three schools of thought in this paper), rather than a close adjunct of Piaget's own theories as she herself categorizes them.

Information processing is something I have rather a lot of previous experience with as a computer scientist, and I didn't encounter too much conceptual novelty in the information processing papers. I also don't see it as a remarkably useful classroom teaching model. Students are not little computers, issues such as motivation and confidence are of primary importance to instructors in the real world.

The skill of programing a computer, which is largely a matter of breaking down your own content knowledge and problem solving skills into bite-size pieces with no unrecognized prior assumptions or undocumented interactions, is useful in teaching. (It gives you plenty of practice in explaining things.) But the application differs enormously, and studying the information processing model is unlikely to help anyone get better at explaining things clearly.

The conceptual change model is useful, but its focus on challenging misconceptions may be a bit overzealous. Misconceptions can be useful. They serve as a placeholder for more advanced ideas, allowing a conceptual framework to grow up around the misconception until the framework becomes self-supporting and the crutch of misconception can be removed. Sometimes the most effective approach is to nurture the conceptual framework around the misconception until it grows rich enough to challenge the misconception all on its own. And sometimes the best approach is to replace a misconception with a more accurate misconception.

For example, in kindergarten the earth is flat so gravity can make sense. In middle school, the earth is a sphere, a big ball of rock. In college, the earth is an oblate spheroid with a rotating core lubricated by molten rock, with the continents floating on top and subject to convection currents. Similarly, teaching students Einsteinian physics without first teaching them Newtonian physics is likely to be a frustrating experience for all concerned, even though Einstein contradicts Newton in many places.

I really like Vygotsky. Conceptual change is nice, but Vygotsky's zone of proximal development gives a general theory of learning that appeals to me. It suggests a useful model for classroom instruction that meshes with my previous teaching experience. Rather than attempting to prevent inappropriate instruction, Vygotsky provides a test for finding an appropriate and productive instructional range in which an instructor may have a positive effect.