Quality Matters Standards for Online Courses --> link
  
CSM Learning Outcomes as a best practice --> link
                          Market Analysis --> link

-->   link  <--    Two New College and Student Outcome Assessements                     
-->   link  <--    STEM oriented Liberal Art General Education Learning Outcomes
-->   link  <--    Symopsis: Measurement of Deep Learning within a Two-Year Pure and Applied Mathematics Program
 
  Presentations at USG Conference in Learning and Teaching (April 4, 5, 2013) 
-->   link  <--
        New Paper on Deep Adaptive Learning (May 15th 2013)       
                                   -->  
link  <--
                   .




The Orgins of a Theory (April 2013)
-->  link  <--

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We are, perhaps, close to a tipping point, in which the


National Education Bridge;

a highly secure and stable, "walled garden",

create a transition pathway between high school and a first semester of college level study.  The proposal we make is to expend federal dollars so as to create a social media system open to all young Americans. 

If funded, each sixteen, seventeen, or eighteen American citizen would have the right
to enroll in a digital world based online tutoring system,
with little or no cost to the individual.

The architecture we have designed for the National Education Bridge depends on topic level measurement,

at three levels of assessment, of demonstrated knowledge of those topics.

The first two levels are skill, measured by ALEKS; and synthesis, as measured by a subjective assessment, about a handwritten narrative exam, by a certified professor of higher mathematics.

The capacity to evaluate is measured from assignments asking the individual to make up applied problems, for example simple but original applied problems in arithmetic set theory or theory of functions of two variables. 

This evaluative assessment measures the degree in which the individual creates a goal and then an inquiry regarding the simplest and yet foundational concepts in higher mathematics. 



New -- Fifteen page pdf:
Summary of “The National Education Bridge,

A Proposal”
--> link

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Second School in Second Life


Set of fourteen one page student essays

Mission Statement (one page pdf)  -->  link

November 2012, Proposal Summary (17 pages pdf) --> link

Two Year Plan - Draft Three  - Dec 14th 2012 -->   link


The Three Pillars
are to be treated with two assumptions:

1)    That most individuals have suffered some type of social abuse while in math class, and

2)    Most individuals are so confused as to what higher mathematics is that a sense-of-self has been created, inhibiting the individual’s capacity to learn. 

The means to overcome what has been suffered lies in the pure mathematical foundations of sets, probability, and arithmetic.  An understanding of how one's individual mind works is also involved in creating a new sense-of-self.  

The Proposal
makes the case that applied algebra and arithmetic is NOT part of the core foundational concepts of higher mathematics.  The foundational concepts of higher mathematics are “pure” in nature. The Bridge is not designed to help the store clerk make change.  It is designed to make the person whole through a knowledge of something important to our society and our history.  The Bridge is designed to help each person be liberally educated.

Our purpose is to open the door to higher mathematics by introducing the individual to the pure elements of set theory and arithmetic.  This point is one that is unexpected. 

A second unexpected point is relevant to understanding what we propose to teach, if not applied problems like finding the area of a pasture.  It is this curriculum, word problems that we will avoid entirely.  The second point is that the pure foundations of set theory introduce probability, and probability introduces statistics.  It is the pure foundations of statistics that we seek to teach.



 

 

Our Use of Systems Theory

Paul Stephen Prueitt, PhD (Pure and Applied Mathematics, 1988, UTA)

 

This Draft  February 24, 2013

This Draft: February 24, 2013

 

 

Much of the text in our Proposal is intended to explain a theory of interaction and co-evolution of systems.  General systems theory[1], neuroscience [2] [3] [4], complex systems theory[5], and formal ontology modeling theory [6] are used to create a very generic model of systems.  Genetic algorithms [7] [8] are applied computationally to digital systems so as to change the code in the digital system, in near real time.

Digital systems might be evolved, much like biological systems.  Isomorphic algorithms might form a layer of control [9].  The question now becomes, “How are these systems to be governed?”  The answer must be, “By humans expressing intention via democratic processes.”  Otherwise we are in for a stark future, one that is feared by most.  The alternative is democratic governance.  The choice is clear. 

To make correct choices, a democracy must exhibit a type of group intelligence.  It is thus important to understand what is group intelligence, and other emergent phenomenon.  An emergent system induces characteristics of individual interactions, over time.  We adapt.  But how might digital systems model emergent behavior?  What is adaptive behavior in purely digital systems?  Adaptation requires a system that is adapting and a system’s environment in which the adaptation is occurring, plus a measurement/action transaction[10] involving the computing device and natural intelligence. 

A stratified architecture was developed[11].  With this computing architecture, human communities and individuals might produce machine ontology that assists in computing services requested by the community.  We see this occurring already. 

This capability to adapt computing architecture as a function of collective human intentions, is everywhere manifesting.  A model of most of the general systems properties of the real world creates a malleable stratification of how digital systems interact.  The induction of meaning to symbol produces a community-based reification of assessed meaning[12].  The results from computations might be aggregated into a decomposition of archetypal elements into several organizational layers[13].  Within each layer the interactions are Newtonian, in the classical sense.  This is unlike natural systems that are Rosen complex [14] [15]. 

What are the expected consequences from these new architectures?  Measurement creates the possibility of a utility function governing genetic algorithms, and affecters instrument the possibility of an action into the real world, based on computed results [16].  The utility function for social networks will become less a product of random induction.  Quick and agile group intelligence will manifest[17].  Social media will make democratic forms of human governance, ubiquitous. 

So what has systems theory to do with education? [18]  Our general thesis is that an induction of specific properties from individuals and from past history has occurred, and always will occur.  This is part of the nature of evolving systems.  Digital systems are different from natural systems, in specific ways[19].  But the simulation of real worlds by digital simulation worlds is already occurring[20]. 

Social and personal reality might be better when there is an increase in the value of educational processes.  We humans largely, but not exclusively, construct our own social realities.  We do this as individuals and within social units.  Sometimes the constructions are good, and sometimes; like when we go to war, it is not good.  Constructions such as racism are often presented to the individual holding this view as justified.  Universal education is necessary if these constructions are to be properly placed into the history books. 

Properties consequent from specific negative cultural characteristics are, we conjecture, deeply ingrained in the American educational system.  This viewpoint seems clear on the surface, but is somehow discounted by social viewpoints regarding human natures.  We address this elsewhere in the National Education Bridge proposal [21].   Evolutionary forces might construct a well functioning educational system supporting the ideal of universal education for all citizens. 

We are at least partially responsible, collectively for what we have or do not have.  In spite of what appears to be best efforts, we have ourselves been the instruments through which specific structural problems are rooted in our social and personal existence.  We can change this, collectively.

What is the connection between a false sense of best effort and a decline in American educational outcomes?  Here we come up against the limits of a cultural capacity, holding onto classical theories as if these might be the only path to truth and understanding.  But the decline is not explained in classical terms.  Why should complex systems be explained by classical theory?  The decline might be explained as a type of collective induction.  Understanding what collective intelligence might become is the challenge of the next generations. 

Universal education would help.  Mass education is causing deep rifts to magnify.  Consider the possible connections between the set of all personal experiences and individual sense-of-self.   How well is this connection understood?  As the reader might easily agree, our science does not yet have a good hold on this type of question.  We are crippled in this positive effort by the power of social fundamentalisms.   Massive Open Online Tutoring Systems (MOOTS), were these to manifest in social media, will create new types of social power.  Universal education, for all, empowers all of us to exercise our God given rights to vote and participate in a democratically defined social system. 



[1] von Bertalanffy, Ludwig 968, General System Theory: Foundations, Development, Applications, New York: George Braziller, revised edition 1976: ISBN 0-8076-0453-4

[2] Pribram, K. H. (1991). Brain and Perception: Holonomy and Structure in Figural Processing. Hillsdale, NJ: Lawrence Erlbaum Associates. And

[3] Pribram, K.H. (1971). Languages of the Brain, experimental paradoxes and principles in neuropsychology. New York: Wadsworth.

[4] Edelman, G. M. (1987). Neural Darwinism. New York: Basic Books.

[5] lbus, J, A. Meystel, D. Pospelov, & T. Reader (Eds). (1995) Architectures for Semiotic Modeling and Situational Analysis in Large Complex Systems. 10th IEEE International Symposium on Intelligent Control 1995. Cynwyd, PA, USA. AdRem Inc.

[6] MacLennon, Bruce. (1994). Continuous Computation and the Emergence of the Discrete, in Pribram, K. (Ed). Origins: Brain & Self Organization . Hillsdale, NJ, ERA

[7] Holland, John (1989) "Using Classifier Systems to Study Adaptive Nonlinear Networks", in: Daniel L. Stein, editor. Lectures in the Sciences of Complexity (1989). Addison Wesley

[8] Holland, John (1995) "Can There Be A Unified Theory of Complex Adaptive Systems?", in: Harold J. Morowitz, Jerome L. Singer, editors. The Mind, The Brain, and Complex Adaptive Systems (1995). Addison-Wesley

[9] Prueitt P. (2001). Use of In-Memory Referential Information Base (I-RIB) for Data Mining. Presentation at the First Conference of the U. S. Einstein Institute,  University of Connecticut June 23, 2001.

[10] Kugler , P.N. & Turvey, M.T. (1987.) Information, natural law, and the self-assembly of rhythmic movements. Hillsdale, NJ: LEA.

[11] Prueitt, Paul Stephen (2011) Original paper published in Systems Science and Service Computing, http://www.servicetechmag.com/I57/1211-3 Published Dec 14th 2011, Service Technology Magazine.

[12] Levine D; Parks, R.; & Prueitt, P. S. (1993.) Methodological and Theoretical Issues in Neural Network Models of Frontal Cognitive Functions. International Journal of Neuroscience 72 209-233.

[13] Prueitt, Paul S. (1995a) A Theory of Process Compartments in Biological and Ecological Systems. In the Proceedings of IEEE Workshop on Architectures for Semiotic Modeling and Situation Analysis in Large Complex Systems; August 27-29,  Monterey, Ca, USA; Organizers: J. Albus, A. Meystel, D. Pospelov, T. Reader

[14] Rosen Robert (1991, Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life, Columbia University Press  Published posthumously

[15] Rosen Robert (1991, Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life, Columbia University Press

[16] Kugler, P.N., Shaw, R.E., Vincente, K.J. and Kinsella-Shaw, J. (1990). Inquiry into intentional systems I: Issues in ecological physics. Psychological Research, 52: 98- 121

[17] Prueitt, Paul Stephen (2011) Stratification Theory as Applied to Neural Architecture enabling a Brain-like function for Social Networks .  Presented to Winter Chaos Conference of the Blueberry Brain Institute, Southern Connecticut State University, March 18-20 2011

[18] Prueitt, Paul Stephen (2012) American Education Bridge, technology and pedagogy.  Accepted: The 3rd International Conference on Education, Training and Informatics: ICETI 2012 March 25th - 28th, 2012 – Orlando, Florida, USA

[19] Prueitt, Paul S. (1996b). Is Computation Something New?, published in the Proceedings of NIST Conference on Intelligent Systems: A Semiotic Perspective. Session: Memory, Complexity and Control in Biological and Artificial Systems. IEEE October 20-23.

[20] Prueitt, Paul S. (1996d). Structural Activity Relationship analysis with application to Artificial Life Systems, presented at the QAT Teleconference, New Mexico State University and the Army Research Office, December 13, 1996.

[21] Prueitt, Paul Stephen (2012) New Proposal for Educational Reform, accepted Interdisciplinary Research, Education, and Communication (IDREC 2012)  March 25-28, Orlando Florida as part of The 3rd International Multi-Conference on Complexity, Informatics and Cybernetics: IMCIC 2012


 


Short, four page pdf on Acquired Learning Disability (in math) --> link

Three Classes of Innovations
--> link

.Index to the Proposal to the American President.