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
Application: New Educational Theory
The
importance of teaching and working with students
Journal quality research on neural models of
behavior
Practical
theory from well grounded foundations
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.
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.
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.
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.
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.
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.
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:
[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