A Research Project on Mechanisms, known to be involved in learning

 

Paul S Prueitt PhD

Monday, January 21, 2008

 

Self efficacy and performance in mathematics class

Model of self-limitation within a social framework

Models of Mind and Physical Phenomenon

So, what is publishable?

Application: New Educational Theory

The importance of teaching and working with students

Teaching and Funding

Journal quality research on neural models of behavior

Practical theory from well grounded foundations

 


 

Self efficacy and performance in mathematics class

 

The focus of my work is a theory of negative self-efficacy as experienced by freshman non-mathematics majors.  This phenomenon is seen as a more general system property of living systems and systems composed of living systems.  For example, negative self-efficacy is widely seen in adult and student populations, and even in human communities. 

 

A theory of self that accounts for all forms of self-efficacy experience has not been advanced, although the work by Albert Bandura has established an academic discipline focused on a particular view of human image of self. [1] There are a few other areas of research, but having only the specific area of investigation related to adolescent learning behaviors. [2] A review of the literature will be completed, and integrated by my research.  I will bring new elements to this literature by appealing directly to biological mechanism as modeled by first order differential equations and stochastic field dynamics.

 

The self-limiting aspect of student behavior in college classrooms is also seen in other settings involving belief systems.  For example, this behavior was seen in the U. S. intelligence communities’ reports on Pakistani progress towards testing a nuclear weapon.  The pre-test intelligence reports ignored direct evidence while holding on to accepted belief.  Collective intelligence, as seen in wiki development, is also shaped by the image of self and the degree to which multi-modal viewpoints are allowed within a wiki definitional context.  [3]

 

These other instances of self-efficacy are to be used to generalize the study of student self-efficacy and hopefully show that a general system theory approach to notions of coherence lends itself to formal modeling.  Physical field coherence is a relational phenomenon that manifests at several temporal time scales.  Specific physical theories, related to a thermodynamic model, exists and will be reviewed and extended. [4] A theory of process stratification is identified in specific literatures and will be extended to demonstrate natures of emergence, of field coherence, and thus be seen to be applicable to this issue of self-efficacy. 

 

We have reviewed the theory of constructivism as perceived in various theories of education.   From the constructivist viewpoint, the meaning of personally acquired knowledge is intimately connected with direct experience.  Students come into a classroom with their own experiences and a cognitive structure based on those experiences.  These structures are valid, invalid or incomplete.  My theory of acquired learning disability suggests that a number of invalid perceptions about mathematics have developed into a viewpoint that is part of a coherent experience of self.   This coherent experience of self becomes inferential, where new experiences are framed to support an acquired viewpoint. 

 

The pedagogy developed in my unpublished paper “Potential Sponsored Program” is based on constructivist, participatory and Socratic principles.  My students are shown that there are always three categories of topics within an enumerated curriculum.  These are “known”, “not known”, and “not known that not known” topics.  Students are given the task of knowing what the topics are in a standard curriculum, and to then categorize all of these topics into one of the first two categories.  Index cards are used, and the point is made that on the edge of the cards one may list the topics that are in the third category; thus creating a mnemonic.

 

In the constructivist viewpoint, a learner will reformulate his/her existing cognitive or emotive structures when new information or experiences are associated to knowledge already in memory.  What constructivist theory does not have, at this point, is a neurologically grounded theory of how the self-efficacy may interfere with the formation of cognitive or emotive associations.  Specifically, classroom observation demonstrates that many students have a well-formed self-image that requires re-enforcement and which denies any evidence that mathematics is learnable. 

 

There are mechanisms known from neuroscience to be involved in forming new associations.   Some of these mechanisms have been modeled by my published research, as well as the published research of others.   What is new in my proposed research is my linking neural models of associative memory to a field dynamic that represents a coherent viewpoint.  Acquired Learning Disability is then to be modeled using this work. 

 

Inferences, elaborations and relationships between old perceptions and new ideas must be personally drawn by the student in order for a new idea to become an integrated useful part of his/her memory. Memorized facts or information that has not been properly connected with the learner's prior experiences will be quickly forgotten.  In short, the learner must actively construct new information onto his/her existing mental framework for meaningful learning to occur.

 

Two ways to describe the Acquired Learning Disability (ALD) behavior are:

 

·        ALD behavior is behavior that is seeking evidence that supports the assertion that "I" cannot learn the material (curriculum context)

·        ALD often expresses as a behavior that finds that part of a set of concepts where the greatest difficult exists, rather then focusing on what is clearly understood and trying to see how to extend that understood part.  The student asserts an inability to learn. 

 

These behaviors may shine a light on regular behaviors involved in keeping an identity stable, in various cases both positive and negative.  Maturana and Varela [5] certainly sets the stage for the philosophy about self identity - but there is some kind of "phase coherence" involved.  Pribram's neurowave equation seems involved also. [6] I will review the literature on mechanism and produce a draft that would take into account the neurowave equation, as a primary carrier of the cognitive content of awareness. 

 


Model of self-limitation within a social framework

 

The model I have developed will be applied to a theory of multi-modal cognitive/emotive coherence.  The nature of cognitive/emotive coherence is seen as having multiple modes of self-image.  The modes each define very secure assertions in which evidence about one viewpoint is seen, operationally, as more important than evidence that would support an alternative viewpoint.  A utility function stabilizes a system that supports the view that mathematics cannot be learned, and discounts evidence that mathematics is both interesting and useful to the individual.

 

The modeling that I would like to do has to do with self-limitation, reflected in decision making, when there are multiple autopoietic envelops (Maturana's term) and a reinforcement mechanism such as career rewards.   The envelopes are seen each as a field having non-locality similar to a quantum potential field.  Stimulus inputs are each seen as perturbations to state transitions defined by the field coherence.  This is necessary to create field localization where a differential is manifest between specific experience and the coherence of the field.  Experience is seen to support the field or in some cases to collapse the field.

 

Individual collapses of a field, such as discussed by Hameroff, [7] are part of a process and that process supports learning, awareness, and the formation of the cognitive or emotive response mechanisms.  A decision stream is defined as a stream of individual decisions, taken one at a time.  The decisions about whether or not concepts are consistent with viewpoint are about how to regard concepts that fit or do not fit with one’s image of self.  

 

A general model of decision-making is developed when self-limitation is possible.  Self-limitation can be compared to religious fundamentalism where one sense of cognitive/emotive coherence is adopted so strongly that any other sense of cognitive/emotive coherence is strongly inhibited. The same mechanism is likely involved in supporting many positive spiritual or religious, of philosophical viewpoints, as well as professional identity.

 

The self-limitation is thus seen as a reinforcement mechanism maintaining a view when evidence is provided discounting this specific view.  Suppose that two systems of thought co-exist.  One thinks about Thomas Kuhn's work regarding paradigm shifts, [8] and the works on “explanatory coherence” by Paul Thagard. [9] David Schum’s [10] work on evidential reasoning seems also illustrative of an extensive literature on coherence and evidence. 

 

These works provides the basis for a model over a competition of ideas.  Imagine that one system is created in such a way that the second system is inhibited by the success of the first system.  This model would be similar, and also dissimilar, to the classical model of foxes and rabbits where low levels of rabbit population would inhibit the population of foxes.  As the population of foxes comes down, the natural breading characteristics of rabbits elevate the population of rabbits.  However, in this case, suppose that the second system of thought may not excite the first system even when the second school is almost extinguished. 

 

Suppose that this second school is in fact the view that a liberal understanding of mathematics and science is not accessible and not of value to average college graduates.  This condition is un-natural and is in fact the condition we see in most college freshman’s viewpoint about the nature of mathematics. 

 

First order differential equations, often seen in even the simplest neural model, have on-center off-surround network.   As an underlying architecture support to coherence fields, I use the classic on-center off-surround system of first order differential equations.  Our model of the two systems is then captured if one system achieves a critical mass and then dominates the other system as a limiting distribution (or state).   In Levine and Prueitt (1989) [11]  we have a layer of input and a layer of output processing with a gated di-pole serving as the mediator.  So there was a reset for failure to fulfill a utility function.  This feature of our work provided an orienting feature when failure to match utility results in a new contextual search.  Frontal lobe mechanisms complete a biologically implemented architecture where by agility is supported so that orientation to novel stimulus over rides familiarity with past experiences.

 

Without this frontal lobe function, an autopoietic envelope might form whereby failure to fulfill utility function (human needs) is accommodated, and an "acquired inability" to make proper decisions is constructed as part of the systemic response mechanism.  If this is so, students might actually be incapable of making decisions that shift the viewpoint from first to second school.  

 

I know of no way to introduce this complete issue, but feel that a neural model similar to the Levine Prueitt (1989) model of selective attention and orientation to novelty might help the education community examine the conjecture I have made about Acquired Learning Disability.

 


 

Models of Mind and Physical Phenomenon

 

The modeling task, that I have sought, has to do with the natures of the mind and physical phenomenon.  I start with something that seems obvious.  Mind exists because the physical universe exists.  It has always seemed to me that to create a foundation in science to an understanding about the nature of mind, one must understand a great deal about physical phenomenon. 

 

I am interested in understanding of how common human behavior arises from physical phenomenon.  This is not an easy objective and my work has not always been helped by classical theories about the nature of mind.  The philosophy of mind may be interesting to some, but less interesting than understanding mechanisms of biological processes that contribute to the induction of mental content.  The mind does have a dynamic and this dynamic is felt in how the image of self is expressed.

 

We pursue science, not superstition.  This point was made by one of my mentors, Karl Pribram, in the book he did with Merton Gill. [12]  Freud had an early thesis that a scientific grounding could be given to psychology.  Pribram was pointing out, in the early 1970s, that this early project was abandoned by Freud and that the consequent development of the disciplines of psychology missed the opportunity to reveal an understanding of mechanisms based on the cognitive neuroscience later developed by Luria [13] and by Pribram.

 

My examination of some common phenomenon uses the tools of higher mathematics, in ways that is consistent with the notions of Hilbert.  For examples, metabolic resources are used up locally during activation.  That local depletion during activation leads to a temporary depletion in metabolic reactants and, consequently, a temporary reduction in capability.  A reset mechanism is thus implemented as part of biological response mechanism.  This reset mechanism, a gated dipole, is a good example of biologically feasible mechanism involved in ordinary cognitive behavior. A first order differential equation models this behavior in my PhD thesis and in Levine and Prueitt (1988). [14]

 

We again see that a mechanism is seen not in only one system, but in many systems.  A gated dipole mechanism is implemented in the biology in many ways and is seen in many kinds of response behaviors.  For example, the depletion of oil reserves in the world wide economic system may lead to a reset where political-social alternatives that are now hidden are given a chance for life. One can conjecture that at a certain point, a critical mass is reached, and the reset mechanism takes hold and economic and political viewpoints shift.

 

A second example was also developed in my PhD thesis, involving iterated stimulus – response as seen in immunological mechanism.  This example is concerning how the self builds a sense of self and responses to stimulus that is “not-self”.  This second example is published separately in Eisenfeld and Prueitt, 1988.  [15] This model of immune response gave me the direct insight into how self-limitation is, conjectured, to hold students away from an understanding of higher mathematics. 

 

Immunological response can be seen in social and economic systems.  Accommodation is of critical importance to survival within environments where the environment behavior is larger that the subsystem’s ability to express the positive drives for reform or restructuring.  From within the “old system”, a positive drive might be regarded as a drive towards some type of undifferentiated good.  There are philosophical and even religious questions.  However, the study of mechanism in the biology and sociology can be done objectively and within the practices of scientific methodology.

 

Finally, my work, 1995 – 2003, on knowledge engineering and logic leads to an architecture that may one day be used to construct “web ontology” from the linguistic structure in text.  The primary mechanism in this architecture involves the use of measurement of data invariance and the aggregation of patterns of invariance at three organizational scales.  Associations to the biological mechanisms involved in memory, awareness and anticipation link the scales. 

 

The processes supporting induction may involve a matching between particular sensory activation and categorical abstraction encoded in the non-local but nevertheless content addressable manifold first discussed by Pribram in 1991 in “Brain and Perception”. Pribram conjectured that induction, in particular the induction of the contents of mental awareness, involves emergence and that emergence involves more that one organization level.  This conjecture leads to “stratification theory”, the “tri-level” architecture having correspondences to memory, awareness and anticipation being one instance of the stratification architectures. 

 

During the period 1996 – 1998 I developed extensive work on the use of n-ary ontological modeling formalism and a tri-level computational architecture that uses a version of the Pribram neurowave equation, Mill’s logic and some work, applied semiotics, initially developed in the former Soviet Union.  My purpose was to create a computational recognition system that had architecture consistent with a vast simplification of the human brain’s architecture. This work became coupled with what is called knowledge engineering, where an applied paradigm developed that “reifies” category specification using particular instances of data.

 

I want to understand biological function, and feel that any paradigm of computational intelligence that is agnostic to the science on biological function will not persist. Over time, and as certain computational formalism is completed, there will be supporting publications in pure mathematics. One of these areas is defined by elementary number base conversion and the relationship that these have to a theory of linguistics and translatability. [16] There will also be many applied publications that are framed by my work.  The work by Dr Peter Stephenson is one example. [17] This work uses a weak coupling of category representations into computational formalism.  Categories exist as context, substructure and compound and expresses as an n-ary with the first element being an indication of context category.


 

Application: New Educational Theory

 

I have never taken my work lightly, nor under estimated the difficulties involved in figuring out and then publishing materials leading to a scientific knowledge of human experience of knowledge.  I have published in complex systems, mathematics, and in neural models.  I have also worked and published in knowledge management, information technology architecture and algorithms. 

 

Some of my work in computing theory involves elementary number theory and formal logics.  This work is exceedingly beautiful and simple.  The simplicity manifests in a number of independent works.  I hope that this work will be gathered together into several volumes and published.  There is moreover, a professional discipline that I believe could rapidly develop based on my theory of acquired learning disabilities.  This discipline might even replace certain non-productive aspects of the mathematics education discipline. This new discipline could alter the practice in mathematics education. 

 

I believe that, due to the stage of development of my work now, mathematics education journals will publish my work in learning theory.  What is needed is a suite of testing processes, and outcome metrics. 

 

To take the next steps in developing the new discipline, I need to institute procedures that sort students into learning communities. The procedures should be instituted so that underlying process difficulties can be separately accounted for.  This work could occur within the context of single freshman mathematics programs.  However, the on-line instructional programs are more ideally suited.  Placement examinations would be considered only as part of a larger effort at understanding the specific needs of each student.  An iterated series of measurements will guide both the kind of strategy used in teaching, within each group, and the curriculum approached. 

 

Ideally this strategy will allow the formation of temporary assignments and reassignment of individual students during the semester, as well as over the course of the undergraduate liberal arts major’s study of pure and higher mathematics.  An adaptive process for dealing with ALD and other learning disabilities is entirely within reach.  The justification for new programs based on these procedures requires a scientific foundation for the understanding of self-limitation. 

 

What could be achieved is an opening of the minds of a generation of students to the natures of higher mathematics and science.  What might this be worth in terms of national identity? The answer seems to be predicated on questions about self-limitation.  Our society has accommodated an almost universal fear of arithmetic.  This fear limits all of us at a time in history where knowledge of self and or the physical world seems very important.  We all know that profound changes in cultural conditions are on the near horizon.  These changes may be made more positive than otherwise if our society alters the educational outcomes in mathematics and science. 

 

Altering, means altering.  This means that the purpose of education has to shift to express the notion of a liberal education for all. A liberal education includes arithmetic, the history of formal systems, and shared understanding about the nature of this physical universe. 

 

I have puzzled over the nature of the mathematics education community for over two decades.  This puzzle has been deeply perplexing to me, personally.  However, I understand that publishing in education journals is a key objective over the next five years.  Education, as a discipline, has not been supportive of my work or related work that might shed new light on how to address the underlying causes of the failures in American education.  However, formal models of actual biological phenomenon will publish following the traditions of biomathematics.  So I have a very clear perception of what my research and teaching objectives are. 

 

The work that is contemplated will benefit from my returning to collaboration with my PhD thesis advisor, Daniel Levine.   This joint work ties into a strong tradition.  This tradition includes biomathematics, reaction rates, switching networks and architectural constraints on computing.  I need to be close to a fine research library and be able to attend several scientific conferences each year.  During my three years of post doctorial experience at Georgetown (1990-1993) I was able to attend over 40 conferences, and many graduate seminars in a number of supporting areas, linguistics, biochemistry, physics, quantum cognitive neuroscience, neural models, and pure mathematics.

 


 

Teaching and Funding

 

For me, teaching will be of higher priority than research.  I am able to teach at the advanced undergraduate level in topology, differential equations, numerical analysis, abstract algebra, number theory, probability, etc.  Including classes taught while a graduate student, I have taught over 90 sections of mathematics, and several other classes including high school physics, graduate and undergraduate computer science and economic theory. 

 

I believe that the virtualization of a specific learning strategy will generate additional student enrollments and external (NSF) funding.  This possibility is very exciting to me, because there is a chance that the applied aspects of my work in learning theory may make a difference in over all national outcomes in mathematics and science.  The non-mathematics and non-science majors have a great deal to contribute to the very notion of freedom, if and only if they are not fearful of foundational intellectual context.

 

Within our experience of this situation many teachers of mathematics, at the high school and college level, are looking for a new methodology and a new philosophical framework.  This interest could be the foundation for a new movement in mathematics training. 

 

My conjecture has been that acquired self-limitation shapes almost all students’ learning behavior, as expressing in mathematics and science curriculum.  When the limitation is lifted, and it can be, the student begins to develop an awareness of individual self and the cultural traditions embodied in our scientific and mathematical literatures.

 

If the student has a major in liberal arts, this new awareness of cultural heritage would seem particularly beneficial to the individual and to society at large.  Something is given back to our collective understanding of deep issues affecting modern civilization.

 


 

Journal quality research on neural models of behavior

 

The theory of Acquired Learning Disability (ALD) was first proposed in 1988 as part of the unpublished part of the author's PhD thesis, "Mathematical Models of Biological Systems Exhibiting Learning" (1988).  The PhD thesis had two parts, one in the area of switching networks and models of the immune response system and the second in the area of biologically feasible models of neural cognitive behaviors.  The two parts were attempts to provide a bridge between two kinds of biological response systems, the neural system and the immune system. 

 

In the early part of the 1990s, several important journal articles were published, jointly by Levine and Prueitt and by Eisenfeld and Prueitt. The work benefited from a close friendship with cognitive neuroscientist Karl Pribram.  The immunological theory is based on a deep study of the biological literatures, and is related to Stuart Kaufman’s theory of emergent computing.  [18]

 

My doctorial work was, however, only suggestive of a larger work.  This larger body of work is now being outlined in this research plan.  

 

The research plan is complex and involves a number of disciplines; namely cognitive science, elements of biochemistry, learning theory, social theory and applied mathematical modeling.  The focus is on building a scientifically grounded theory of human learning, where learning is inhibited by self-efficacy and shifts in viewpoint occur due to some type of challenge to the coherence of self.  The theory has a formal realization that is primarily a computational and deterministic model.  It also draws on a body of primary scientific results in phenomenon like micro-catalytic environments, where the emergence of function from form may be isolated in relatively simple systems.   Emergence is seen as degenerate, in immunological theory, and non-deterministic. [19] This model necessitates the specification of an aggregation or orchestration of substructural elements into a functional whole. 

 

The use of the concepts related to the concept of non-deterministic elements in any emergence phenomenon is conjectured to necessarily involve two interacting levels of biological organization, giving rise to the appearance of locality as distinct from non-locality.  Metaphors in biochemistry and in quantum physics are useful, and instructive. 

 

A whole range of metabolic phenomenon has been studied and will be revisited in order to identify categories of mechanisms instrumental to the maintenance of self.  Self is roughly defined here as that which persists biological functions, with phenomenon like awareness and cognitive function inherited as partially consequent to these functions.  However, this is not a reductionistic view.  To understand a trans-reductionism viewpoint, Maturana’s notion of autopoiesis [20] is useful, as are some of the concepts from the complex systems literature.  To be viable, the trans-reductionism viewpoint must have grounding in formal models, including models of reaction rates and other elements of biologically feasible neural network modeling, as seen in the work by Prueitt and Levine. [21]

 

Trans-reductionism must establish strong evidence for principles related to anything not completely deterministic, and express this evidence using strict and formal deterministic models.  Thus the natures of non-deterministic phenomenon may be exposed. 

 

A role for human, or living system, choice is seen not as a primitive concept or asserted assumption, but as a necessary outgrowth of the modeling.  The mechanism supporting a resolution of indeterminacy, metaphorically seen as the collapse of the quantum wave, is precisely where the mechanism should be and that is in a theory of real world emergence.  The theory describes how localized phenomenon and non-localized phenomenon might interact at the point of emergence. 

 

Any mechanism supporting choice should also be a mechanism supporting learning, and we show that any such mechanism always requires an emergence of physical electromagnetic coherence.  This emergence may be seen as also having some type of coherence in the quantum reality (if we use this language).  Thus an application to my work is envisioned within social and economic theory, as suggested below.

 

Technical definitions of coherence, self-efficacy, learning, viewpoint, and inhibition are to be given.  In each case, the Embedding Field Theory, developed by Stephen Grossberg in the early 1970s will be used to model isolated instances of these phenomenon.  Dr Levine was one of the early MIT PhDs that extended Grossberg’s Embedding Field Theory ( EFT). [22] The richness of the work done by the Grossberg school cannot be understated.  However, the problems in modeling awareness and image of self were not well addressed, nor successfully addressed.  There is more to say about the limitations of embedding field theory, and about the program of Hilbert, concerning the capability of formalism.  This discussion should involve those concepts developed well by Robert Rosen [23], and Sir Roger Penrose. [24]

 

As Roger Penrose points out, an additional category of mechanism might be necessary to manifest the phenomenon associated with actual learning in biological systems.  Every few scholars have tried to do what it is that I wish to do, and that is to give a mathematical formalism that interfaces with singular perturbations of the measured (modeled) causative factors.  As suggested above, this work is not based on buzz words and over simplifications.  The biological interface is Rosen complex, in that the formal system and a non-formal (human or living system) interact via an action perception cycle.  The foundational work on action perception cycles starts with the research by J.J. Gibson in the late 1950s on how pigeons orient in flight. [25] I mention Gibson’s work in the context of my long personal friendship with Peter Kugler, Robert Shaw and others from the school of Gibsonian science at University of Connecticut. 

 

A relationship between difference equations and differential equations was explored in my PhD thesis.  This difference delineates a relationship between discrete and continuum mechanics.  An underlying thesis is that the manifold defined by first order differential equations is sufficient to describe bifurcations that arise in precisely those places where response degeneracy is seen, in learning theory.  However, a precise definition of the routes to emergence may not provide the means by which paths are actually chosen, in even the most insignificant of phenomenon, such as molecular state transitions involved in cell signal pathways.

 

“Switches” may be necessary [26] in order to explain actual observed phenomenon.  The introduction of “jumps” in the trajectory of a “solution” to a system of first order differential equations, at points close to mathematical degeneracy may be simulated using methods from numerical analysis. 


 

Practical theory from well grounded foundations

 

The modeling work will target behaviors exhibited by students in mathematics learning settings.  This work will not be done in a careless fashion, but rather as a serious scientific investigation of human learning dynamics.  The quality of research will be compared to Levine and Prueitt’s several referred journal articles published in early 1990s. 

 

The behaviors will be described using cognitive neuroscience language and will be linked to normal and abnormal behaviors occurring inside and outside the classroom setting.  These behaviors have a natural state, i.e. unchallenged by traditional mathematics classroom practice; and a response state, i.e., sets of behaviors that arise when the student recognizes the learning theory. 

 

A remediation strategy has been proposed and utilized in successful teaching efforts.  The remediation involves the use of novel curriculum, arithmetic in arbitrary bases, and a modification of the well known R. L. Moore teaching methodology.  The R. L. Moore methodology is essentially Socratic in nature.  It is engaging and participatory.   The modification of the method by Prueitt involves the shifting of responsibility for learning from textbooks and teachers to the student. 

 

This modified method has been used in teaching fifteen sections of mathematics, primarily but not exclusively at the pre-college algebra level. 

 

Our formal models of behavior will target the social and biological origins of acquired learning disability and responses to this specific remediation program.  These origins of causative mechanism do introduce unsettled scholarship in areas called social network theory, as mentioned above.  Academic works in these areas are funded.  I seek funding and publications in these areas that are directly related to understanding the cognitive engineering that might model student responses to remediation strategies.  There are significant areas of work to delineate acquired learning disability phenomenon from a very large group of labeled learning disabilities.  This work has both clinic and theoretical aspects.

 



[1] Bandura, A. (1994). Self-efficacy. In V. S. Ramachaudran (Ed.), Encyclopedia of human behavior (Vol. 4, pp. 71-81). New York: Academic Press. (Reprinted in H. Friedman [Ed.], Encyclopedia of mental health. San Diego: Academic Press, 1998)

[2] Pajares, Frank, Urdan, Tim (Editors) 2006.  Self-Efficacy Beliefs of Adolescents.  A volume in the Series Adolescence and Education.  Published by Information Age Publishing, Greenwich CT.

[3] Tapscott, Don; Williams, Anthony D. (2006) Wikinomics: How Mass Collaboration Changes Everything. 

[4] Kowalski, J. ; Ansari, A. ; Prueitt, P. ; Dawes, R. and Gross, G. (1988.) On Synchronization and Phase Locking in Strongly Coupled Systems of Planar Rotators. Complex Systems 2, 441-462

[5] Maturana, Humberto E; Varela, Francisco. (1992). The Tree of Knowledge: The Biological Roots of Human Understanding.

[6] Pribram, Karl (1991) Brain and Perception: Holonomy and Structure in Figural Processing. Hillsdale, NJ: Lawrence Erlbaum Associates. Appendix B

[7] Hameroff, Stuart (2005) Consciousness, Neurobiology and Quantum Mechanics: The Case for a Connection, In: The Emerging Physics of Consciousness, edited by Jack Tuszynski, Springer-Verlag, In press 2005

[8] Kuhn, Thomas, S. (1970).  The Structure of Scientific Revolutions.  University of Chicago Press

[9] Thagard, Paul. (1999) Model Based Reasoning in Scientific Discovery.  Springer

[10] Schum, David (1994). Evidential Foundations of Probabilistic Reasoning.  Wiley Series in Systems Engineering. 

[11] Levine, D. & Prueitt, P.S. (1989.) Modeling Some Effects of Frontal Lobe Damage - Novelty and Preservation, Neural Networks, 2, 103-116

[12] Pribram, Karl; Gill, Merton (1976).  Freud’s “Project” Re-assessed.  Basis Books.

[13] Luria, A. R (1973) “The Working Brain, An Introduction to Neuropsychology” Basic Books. 

[14] Levine, D. & Prueitt, P.S. (1989.) Modeling Some Effects of Frontal Lobe Damage - Novelty and Preservation, Neural Networks, 2, 103-116.

[15] Eisenfeld, J. & Prueitt, P.S. (1988.) Systemic Approach to Modeling Immune Response.  Proc. Santa Fe Institute on Theoretical Immunology. (A. Perelson, ed.) Addison-Wesley, Reading, Massachusetts.

[16] My basic research on these topics is extensively published in a non-peer review form as pages on my web sites.  One of the indices is at URL:

http://www.ontologystream.com/cA/index.htm?

[17]  Prueitt, Paul and Peter Stephenson. "Towards a Theory of Cyber Attack Mechanics." First IFIP 11.9 Digital Forensics Conference. Orlando, FL,

2005.

[18] Kauffman, Steward (2000).  “Investigations”  Oxford University Press

[19] Edelman, Gerald (1987).  “Neural Darwinism: the Theory of Neuronal Group Selection” Basic Books. 

[20] Maturana, H. and Varela, F. 1980. Autopoiesis and Cognition: The Realization of the Living. Dordecht: Reidel.

[21] Levine, D. & Prueitt, P.S. (1989.) Modeling Some Effects of Frontal Lobe Damage - Novelty and Preservation, Neural Networks, 2, 103-116.

[22] Grossberg, Stephen. (1972a). A neural theory of punishment and avoidance. II. Qualitative theory. Mathematical Biosciences, 15, pp. 39-67.

Grossberg, Stephen. (1972b). A neural theory of punishment and avoidance. II. Quantitative theory. Mathematical Biosciences, 15, pp. 253-285.

[23] Rosen, Robert.  Rosen’s work is very difficult for most people to grasp, even those trained in related areas.  So I will reference his entire life’s work and leave this issue to a more detailed discussion. URL: http://en.wikipedia.org/wiki/Robert_Rosen

[24] Penrose, Sir Roger.  Sir Roger’s 1989 book, “The Emperor’s New Mind” was written before meeting Stuart Hameroff, at a conference hosted by Pribram in 1992.  The consequence of this meeting is seen in Sir Roger’s 1993 book, “Shadows of the Mind”.  

[25] Gibson, J. J., The ecological approach to visual perception, Houghton Mifflin, Boston, 1979,

[26] Robert Shaw, quantum physics and founding member of the ecological psychology group at University of Connecticut private discussions 1998