Sunday Oct 26th, 2008
Technical grounds for web based Lifting Pedagogy
This paper develops a top level overview of the "retrieval" mechanism of a glass bead game. <*> The mechanism is discussed extensively in Prueitt's "Foundations", particularly the two appendices. <*> The core innovation is the development of a stratified inference engine having a computational form and linked to the demand side theory. Given a subset of "topics" deemed to be known, the inference engine brings forward a set of topics closely related but not deemed to be known.
First we will review the elements of the topic mapping process, and the categorization of topics into those one is comfortable with and those topics one is not comfortable with. A web based system allows a number of aids to topic mapping. One aid will be to create a means to justify the accreditation of students grades, and to link outcome metrics with national standards such as the National Council of Teachers of Mathematics K-12 focus elements.
This linkage of curricular elements to national K-12 focus elements will be used to create a new educational layer in the United States, a bridge between high school and college. <*>
Teacher education and distance learning programs will be able to use the web based system to learn about demand side theory and the related constructivist and participatory educational theories. As may be seen by the reader, if one looks at our background documents, the underlying "demand side technology" may be foundational to a new information science, a discipline that is destined to replace the existing entertainment and computer technology sectors. <*>
The topic mapping mechanism is to be used as part of the web interface supporting the SecondSchool.net Lifting Pedagogy. <*>
The data structure <*> is essentially a set of topics { ai } and relationship tokens { r }.
< an, r, am
>
such as
< slope, is related to,
graphing a line >.
For a fixed curriculum this data structure may be pre-established but modifiable. One version of a group "on line game" is to fill in a part of the largest possible knowledge ontology about the class curriculum by interacting with the software and up loading scanned images of hand written notes. [1] When the software and classroom support system is in place, students may place initials on those scanned images they individually upload. However, the professor would make the adding of new topics by one individual more difficult as a function of the number already provided, so that the class as a whole would be called on the complete the game. As the class or group completes a course of study, the "bead game" <*> would have multiple scanned images associated with topics. This architecture will evolve to support any curriculum. The model that this architecture is based on has historical roots which may itself become the basis for a glass bead game.
Hand written "topic presentations" show individual personality and creativity as well as exercises a certain individualized discipline related to working on blank paper with pencil. Thus topic mapping and the lifting strategy may be used without any web based support. The use of the web will be as an aid to creating a comprehension of the topics of the curriculum sufficient to allow the student to sit down with blank computer printer paper and pencil and write about the topics known, including notation, theory and individualized examples.
Prueitt's three and one half years of teaching experience with this pedagogy shows that much can be done without the web based system. The issues that are advanced with the web based system has to do with duplicating classroom results and creating a means to measure outcomes so that colleges will be able to adopt to demand side technology.
Rehearsing only topics well understood creates a ‘field of remembrance’ which may spontaneously arise. <*> When this arises, the student should stop what he or she is doing, if possible, and work for a few minutes on the rehearsing process. Each student's system profile knows, by various devices, which topics the student is comfortable with and which topics the student is not comfortable with. According to the theory advanced by Prueitt, as the topics known and comfortable with are rehearsed, the individual develops a sense of self that is contrary to the acquired learning disability (if this disability is in fact impacting the student's image of self). <*>
A continuous rehearsal of topics understood may be managed by various functions of the software. One of these functions is a nearest node algorithm that is used in semantic extraction software for understanding natural language text. <*>
Whereas some tutoring about topic not understood might be managed by the software, the Lifting Strategy is designed to bring questions to the mind of the student, rather than to ask the student questions. This is part of the demand side theory, as contrasted with the supply side theory.
Thus communication with someone in the class or the instructor is a means to optimize the learning experience. Supporting this communication is to be done using cell phones, mobile devices, and computers. Ideally the communication should focus on a specific topic, not a word problem, unless the word problem is seen as an exemplar of a specific topic theory. The descriptor set
P =
{ notation, theory, application }
has an order to it. The notation required to communication about that topic is needed, then the general theory, and then the exemplars.
The ideal web based system will allow a student to enter any phrase or word and either get a statement asking for clarification or a specific introductory topic. This introductory topic will lead to one or more additional topics and may in fact to linked eventually to every other topic in the set
C = { topics in the
standard curriculum in Chapter }.
This ideal web based system will also have a linkage or mapping between
C X
P = { ( c, p) | c is an element of C and p
is an element of P }.
and the National Council of Teachers of Mathematics K-12 focus elements.
So what is Inferential Coherence?
The synthesis of basic research from cognitive neuroscience and computing theory results in an alternative to the inference engines developed for the Recourse Description Framework (RDF) knowledge representation language when equipped with Ontology Inference Language (OIL). The logical inference underlying the OIL and RDF technologies is criticized based on the same arguments that are used to criticize artificial intelligence.
The use of "n"-ary knowledge ontology is developed using topological logic that Prueitt derived from a study of Soviet era applied semiotics, and is discussed and justified in "Foundations" <*> .
The above figure suggests some of the technical detail that might be incorporated in the inference engine supporting the web based aids for the Lifting Pedagogy. Each part of this "n"-ary knowledge ontology within the contours is part of a basin of attraction.
Footnotes
[1] We are talking about the hand written topic presentations (to be scanned and linked here in the near future) that Prueitt's students at three colleges (1993-94, 2007-08, 2008-09) have or are writing.
[1] We are talking about the hand written topic presentations (to be scanned and linked here in the near future) that Prueitt's students at three colleges (1993-94, 2007-08, 2008-09) have or are writing.