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Wednesday, August 11, 2004





Statement of Purpose


Communicated to the Search Committee before the Interview



Dr. Paul Stephen Prueitt




This Statement of Purpose is intended to communicate both short-term and long-term goals, all focused squarely on a critical need for liberal educational renewal in mathematics and computer science.  These goals are fully expressed in my development of a knowledge based software system supporting on-line learning experiences, and in my development of the outlines of a new liberal arts curriculum.  The nature of the curriculum elevates expectations made on students by altering the context so that this curriculum is seen as relevant to a liberal understanding of the nature of abstract thought.  We do this by opening access to the history, philosophy and foundations of mathematics, seen not as rarified intellectual context, known only to the elite and esoteric; but as a substantive foundation to modern civic life. 


I have developed professional associations with diverse groups who have systems ready as infrastructure for a National Project designed to establish the knowledge sciences as an academic discipline [1].  The system software has been collectively referred to as the “Safe Net” because of a mandatory deep TCP/IP packet inspection and because all social discourse within the Safe Net is to be considered public and thus subject to centralized harvesting and representation as an evolving concept map.  The concept map is used like a poll to measure the interest of consumers.   


My life’s work has been focused on understanding the nature of human intelligence, as expressed through the complex constructions of the human behavioral/cognitive system.  Between 1980 and 1994, I taught over 70 university courses in mathematics, physics, computer science, and economics.  Between 1994 and 2004, I worked in the information technology sector and developed key technologies related to the thematic analysis of conceptual structure in text databases, and related to government collaborative environments.


The many seminars and conferences I have attended, the many discussions I have engaged in, and the many scholarly papers I have read have all been about understanding why our society has NOT achieved the type of universal education that one might otherwise, naively, expect.  Why is information often extremely difficult to acquire?  What is human knowledge?  How is social knowledge related to science, and to a moral society?   What are the political and cultural issues related to the use of computers as a mean to increase the quality of human communication? 


My pre-doctoral academic career was longer than most, almost seventeen years.   I had to work through a number of problems.  Some of the problems were related to financial aid and a personal background that included already, before college, an independent study of many advanced topics, nuclear physics, particle physics, philosophy, and the social sciences.  As I began to matriculate as a graduate student, first at Southern Methodist University and then at University of North Texas, I begin to see into the depths of mathematics, and to develop a deep love for pure abstraction.  But I was also deeply puzzled as to why a majority of freshman students in liberal arts mathematics classes were not prepared and did not want to learn anything about mathematics.  In Sept of 1985, in spite of being all but dissertation in pure mathematics, I decided to work on a College Teaching of Mathematics PhD in the College of Education at University of North Texas.  This program was designed to be finished within one year, given the coursework I had already completed.  This year of graduate study in the College of Education lead to the development of a theory of acquired learning disability as an explanation as to the behavior of freshman liberal arts majors.  The course work also introduced me to the issues related to university governance and accreditation. 


I submitted several PhD proposals to a senior faculty committee in the College.  The committee felt that a criticism was being made that might impact the integrity of the educational system.  Looking back after sixteen post doctorial years, it is easy for me to see that the social situation was in fact complex and that general systems properties were involved in the committee’s non-interest in my work.  The issues were simply much larger than anyone was aware of.  It was not time to address such issues.


My decision to move from North Texas to University of Texas at Arlington was the right one, because this move allowed me to work under Professors Daniel Levine and Jerry Eisenfeld.  Two years after the move, I was awarded a PhD in Pure and Applied Mathematics on “Mathematical Models of Biological Intelligence”.  This work set the stage for a short period of teaching at Hampton University, and for my appointment as an Assistant Research Professor at Georgetown University.  From the appointment at the Neural Network Research Facility at Georgetown University, I was introduced to many of the leading thinkers in the connectionist paradigm and to key individuals within government agencies.  I refined my understanding of medical informatics, biochemistry and neuroscience.  I meet and was influenced by many of the leading scholars.  I developed an appreciation about the policy issues related to university governance.  I came to understand the degree to which business processes define what scholars of educational theory should define, but do not.   I meet leading innovators in areas like knowledge representation and machine based ontology.  I saw first hand that these innovators could not find support within any academic department, nor from any government agency like National Science Foundation, DARPA or NIST. 


I found I was not alone, and that others had similar experiences. 


My career has included teaching in universities, community colleges and high school, basic research in cognitive systems and intelligence technologies, software design and development, and public policy.  A broad perspective on my inquiry into why students do not want to learn abstract thought is fortressed by an advanced mastery of algorithms and computer technology related to knowledge management and collaborative systems.  For example, I did design and prototype distance learning systems for the State Department and various collaborative systems for automated image and text understanding. 


I have seen first hand the impact of profound ignorance about the nature of information technology, and the role that information technology is, and is not, playing in our global society.  While it is clear to everyone that, in a moral society, all citizens need a proper understanding of the abstractions central to both mathematics and computer science, it is also clear that our citizens do not have this understanding.  Why?  What could possibility explain why our society has such a strong defensive emotion about higher learning, and about mathematics and computer science.  Could it be the curriculum and the attitude that the professional educators have about mathematics? 


Why has it been so difficult to alter the curriculum, or to acknowledge the role that teachers and professors have in creating mathematics phobia?   If one recognizes this problem, what can be done to address it?


In preparing an on-line remediation curriculum, I adopted a private learning environment where I work with a small number of students.  This private learning environment is based on work started at DARPA in the late 1980s.  In this environment, I demonstrate patience with individual students, and make myself available in this on-line environment and via the telephone.  This work is now ready to be standardized as a curriculum available in textbook and on-line formats.  They system and the curriculum was experimental but I have several students that are wanting to redevelop the system from the ground up


A successful remediation course will demonstrate active learning over topics from set theory, the nature of abstraction and counting, history of economic applications of accounting, discrete mathematics, and elements of formal algebraic theory.  We may undertake the teaching of some elements of the Python language within a Linux environment.  We anticipate a revolution in software design based on a maturing knowledge of behavioral patterns and iconic programming languages where how the behavioral pattern is encoded in digital processors has been optimized and made, freely, available under the GNU license.  The outcome metric will reflect a measurement of enrollment rates in the standard courses, and a measurement of increased success in passing courses that are core to a liberal education.


The remediation’s proposed curricular materials are not a repeat to materials that students have rejected learning already many times.  It is new and exciting material.  They have not been challenged with this material, and have not failed to learn it already.  The material is a fresh start, and can lead into areas of personal interests and to a sense of personal accomplishment.  Learning experiences, of this type, will better prepare students for life-long learning experiences.  Both in class and on-line programs provide exceptional service to the community by addressing a recognized need in a complete fashion. 


On my long term interest in educational re-newal in mathematics and computer science


My work on a new curriculum moves a considerable distance toward bringing a deeper appreciation to each student of the role that mathematics, computer science, and science more generally, will have in that person’s future.  We do not start with the notion that college students are a blank slate.  We assume that many students will have suffered experiences that have been accommodated into a comfortable acceptance that formal or abstraction thought is not for them.  We claim that in most cases, the desire to learn can be invigorated by a presentation of new materials in a rich learning environment reinforced by peer and teacher expectations. 


An opening of access to a deeper knowledge of the foundation of computing and technology is possible. 


Perhaps 35% of all college students will have such great trouble with the mathematics requirements as to significantly impact their entire college career.  Because of the fear that many students have about standard mathematics curriculums, students want to move away from mathematics.  Students want to get requirements in mathematics and computer science “out of the way”.  The remediation program reaches out and works on deeply entrenched past re-enforcement by poor learning environments.  Opening of access to minority communities is a key political objective.  Opening access into the higher knowledge that comes from science is a key objective. 


Specific remediation exercises have been shown successful in classes taught at Hampton University (1989-1991), at Saint Pauls College (1994-1995) and at community colleges.  The preliminary work on curriculum and methodology was developed during a teaching experience that included over 50 freshman mathematics classes.  More than half of these classes used innovative writing across the disciplines methodology and instructional design based on the notion that learning was inhibited by previous experiences in high school mathematics classes. 


A collection of over 200 student essays, collected at Hampton University and Saint Pauls College, demonstrate that fear and distrust about mathematics class hides a natural interest.  I point to these student essays as evidence that my innovative instructional methodology opens access to the student.  These essays demonstrate that a mentoring relationship developed between the instructor and the student.  I have claimed that this mentoring relationship is an outcome of a reasonable pedagogy that can be taught to other instructors, and so is not dependant on my direct involvement in a class.  The development of a mentoring relationship is dependant on a standard set of procedural rules that can be grounded in current empirical evidence from cognitive science and educational theory. 


A foundational theory in cognitive science and immunology suggests that the introduction of novelty in curriculum will not trigger habitual negative reactions to the abstractions, in arithmetic, found in the standard college freshman mathematics classes and in computer science classes.  The foundational theory, using theoretical immunology and cognitive neuroscience, describes how a long repetition of poor introductions to arithmetic and algebra in middle school and high school will always lead to an inhibition of interest in abstract, i.e., formal, thought.  Given that this foundation is correct, the implications are that even as adults this acquired learning disability can be remediated and lost interest regained.  After remediation, learning occurs and a new foundational experience about the nature of design principles and abstract thought can be acquired, even as young adults. 


This foundational experience will allow the student to more fully participate in distance learning and in knowledge production and sharing technology.  With the fear of computer technology removed, the student is prepared for knowledge-based life long learning experiences and the productive use of knowledge management resources. 


We should be clear here.  The implications, given the correctness of my assumptions, is that learning modules can be developed which fundamentally alter the learning experience of college students in mathematics, computer science, and applications of information technology.  The pedagogy is informed by cognitive and behavioral science. 


The provision of these modules allow students to better compete in areas where increasing technical sophistication is demanded. 


The modules lead to an understanding of the foundations to a science of knowledge systems, and make a large part of the complexity of the modern social system understandable to the liberally educated citizen. 


[1] A RoadMap was developed to reflect this community agreement: http://www.bcngroup.org/area1/2005beads/GIF/RoadMap.htm