Abstract

America’s future depends on an educational renewal.

In the past week, several scholars have been talking about the conjecture that very slow and ineffective instruction in arithmetic and algebra in K-12 leads to reduced confidence. Specifically a type of learned helplessness [1] [2] is conjectured to be caused by the educational process itself.

This specific outcome of the educational process is contrasted with the profound successes of mass education programs.

The material in the standard curriculum is justified based on basic needs to understand financial transactions and simple calculations.

However this standardized curriculum does not introduce the learner to the philosophical and cultural aspects related to the evolution of mathematics as a cultural artifact. A foundation is not established that allows the learner to see real and critical issues related to human communication and the representation of knowledge in formal and linguistic forms. We are, then, less that we could be.

Our society seeks a deeper understanding of human communication including the communication that should come very clearly from the natural scientists to average citizens.

The specific nature of the current standardization has been driven by professional mathematics education organizations and text book companies; neither group having become known for a deep understanding of the natures of mathematics, human thought, or the impact of such standardization on a dynamic living social system.

There are then two opportunities. The first is to develop a refinement of the curriculum for college that assumes that students have in fact developed an acquired learning disability towards the specific materials in the high school curriculum. The value of the standard high school curriculum will be considerably supplemented in scope and characteristic.

Fixed negative social attitudes can be, and have been, easily observed. But to dwell on this is to dwell on a problem that might be by-passed.

Opening access to this new refined curriculum requires only that we, as a nation, become aware that our negative social attitudes are an understandable reaction to poor experiences in most individual cases. This will require Presidential leadership and a long-term commitment by leading academics.

What then is this new curriculum? This question will be taken up over the next year in discussions with leading scholars. A process will be put into place that creates a rich and satisfying university liberal arts mathematics curriculum that is not merely a repeat of the high school curriculum.

The second opportunity is to free adult learners from a fear of what they regard as “math”, but is in fact a confused set of social belief constructions related to a cultural mythology about what is taught in K-12 and in freshman mathematics.

Are the word problems, the arithmetic and the algebra in the high school curriculums a proper basis for understanding the truth about nature? They are not. Nature is both more complex and less abstract than what is conveyed in K-12 mathematics education. This fact is beyond question, given the modern scholarship in cognitive science and in supporting natural sciences. But this fact of science is not reflected in our educational pedagogy or the curricular context taught to all students. As almost all American adults have be so educated, the self limiting problem related to acquired learning disabilities is present in most adults.

So this second opportunity will be addressed also. In addressing the “knowledge” needs of adults in our American society, we will be instrumental in opening access to new forms of manufacturing, new types of jobs, and new way of communicating with each other.

One might predict that an economic reward system will evolve naturally as these new forms of economic and social activities ignite.

The curriculum

Prueitt has worked on a remediation curriculum that re-teaches arithmetic, set theory and introduces foundational concepts found in topology. Some additional curricular elements are being sought as part of discussions with computer scientists and mathematicians. Elements typically found in what is called “discrete mathematics” will be included in the refined curriculum.

The remediation material is directed are enlightening each student about the mistakes that have been learned regarding how one learns the standardized curriculums. As a consequence the remediation leads to mastery of all of the curricular elements found in most freshman mathematics course work. Approximately 2/3 of the effort is made in remediation and in mastering the standardized curriculums as found in the best liberal arts courses. The remaining effort is made in developing an appreciation of mathematical reasoning related to the development of abstract construction such as the counting numbers, Peano axioms, set theory, discrete mathematics and elements of topology.

The focus of the refined curriculum is to bring the student to appreciate the foundations of computer science, information theory, and general systems theory. This material will be more broadly covered in a Junior level elective on general systems theory with applications to social science, biology, and psychology.

Distance learning and certification

Prueitt, and industry innovators, have developed computer-based technology that facilities a virtual classroom. The technology uses a multiple user domain with animated avatars, video streaming when needed, and voice to text plus text to voice automations. The available system has evolved from work conducted at DARPA in the mid 1990s, is written in C and Python and has an open source code base. It runs on all operating systems. There is very little cost related to using this system.

A voice to text technology is used so that text can be parsed to produce an anticipatory mechanism that assists in automating the order of delivery of remediation materials. Text to voice, only on the Macintosh, is used to make the interactions easier for learners. Animated avatars are used to allow student behavioral moods to express, both in the context of peer interactions as well as in the context of anticipatory predictions related to puzzlement, surprise, non-attentiveness, etc. All communications within the distance learning environment are encoded into log files that are made available to all participants as if this were an open e-forum. Our distance learning environment is a type of Safe Net, and is being made available at low or no cost by the not for profit BCNGroup Foundation.

The distance-learning environment as of June 2004

The distance learning instructional methodology is called the “Nodal Forest Teaching/Learning Strategy”. This methodology has been used in university classrooms for over a decade. In 1998, it was the basis for an experimental distance-learning environment for the State Department. The methodology requires that each student develop and maintain a list of topics within the target of study and to be aware of the changing status of each of the listed topics in regard to knowledge and comfort with that topic. The awareness, by the student, of specific learning related to specific topics provides a type of reinforcement feedback that is not obtained in most classroom settings.

Various behavioral outcomes have been seen. Levine, Benzon and Prueitt are developing a theory regarding the cognitive neuroscience associated with these outcomes.