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I have a feeling that I am missing something in the discussion of IQ versus Cognitive Development. Here is the way I currently understand the situation. The developers of IQ instruments make a major effort to "norm" the results in a manner that makes it difficult for one's IQ to increase. This is done by designing the norming process so that at each age range level the mean IQ will be 100 and the SD will be 15 (or 16, or etc., depending on the people developing the instrument. Thus, for an person's IQ to increase over time, this person must gain faster in intelligence (gain more in intelligence) that others of the same age range and IQ.? This does not mean that intelligence does not increase as a person's brain grows to maturity and as a person gains in informal and formal education and experience. It is quite clear that intelligence increases. I, personally, subscribe to the Gf and Gc idea of intelligence. In this nature/nurture theory, nurture plays a significant role. The IQ measurements norming process evens this out. But, that does not prohibit a person from increasing or decreasing in IQ—it is only the mean and standard deviation for an age range group that does not change. The stage theory and measurements of a person's stage of development is not normed. It is my understanding that cognitive development as measured by such stage theories is affected by both nature and nurture, and that through appropriate nurture a person's upward movement through the various stage levels can be increased. Similarly, the development is slowed by a poor environment. I assume that most readers of the Piaget list are far more knowledgeable about the above ideas than I am. Thus, I hope that if my understanding is incorrect, some of you will help me to better understand the situation. Finally, here is a question for the group. Once a week I have lunch with a bunch of retired professors from the College of Education where I used to work. I have raised the IQ versus Cognitive Development question with them. One of these people suggested that if we did a factor analysis on a pooled collection of the?types of results one gets from IQ test questions and the types of results one gets from cognitive development types of problems/questions, that we would find that we do not get a separation into two distinct factors. Rather, we will find that there is only one major factor being measured. That brings me back to the question I raised a couple of weeks ago. I am still trying to understand some clear distinctions between IQ and cognitive development. Moreover, I am specifically trying to understand these differences in terms of mathematics education. Is there anything that a math teacher can do that will result in: 1. The teacher's students gaining in their math IQ? (For example, this might be in the area that Howard Gardner identifies as logical/mathematical intelligence in his 8-component theory of Multiple Intelligences.) 2. The Teacher's students gaining in their stage theory-based level of math cognitive development. (I have read some of Michael Common's work that asserts that movement up through the stages is discipline independent. If that is correct, they the idea of nurture moving a person up in stage level more rapidly in one discipline area than another makes no sense.)?Help!!!