Demand Side Learning

Applied Research on Mechanisms, known to be involved in learning

The author's research on mechanism has evolved to support a new learning pedagogy, called the Lifting Pedagogy. (Prueitt, 2008) This pedagogy seems necessary if the American school and higher education systems are to overcome the failures associated with conveying the nature of mathematics and science to a majority, at least, of students entering college. The pedagogy is based on a demand side theory of learning where student engagement is enhanced when an internal experience becomes involved in an awareness of the most fundamental elements of set theory, arithmetic and algebra.

Models of Mind and Physical Phenomenon

Our modeling task has to do with the natures of the mind and physical phenomenon. These natures are only partially understood and in many instances the science has controversial elements, many related to beliefs about the spiritual natures of mankind. In order to account for controversy, we start with something that seems obvious.   We assert that mind exists because the physical universe exists.

The assertion is accompanied by a second possibility. Mind may also exist because of what are often called spiritual causes. Because this possibility is not an alternative, but is in addition to the assertion, it seems that we need not make a commitment one way or the other about spiritual causes . If the assertion is reasonable then it is clear what may be done. To create a foundation in science, for understanding the mind, one must understand a great deal about physical phenomenon. We therefore ask the question, “How does common human behavior arise, at least in part, from physical phenomenon?”

This is not an easy objective. The 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 an underlying physical dynamic and this dynamic is felt in how the image of self is expressed.

We pursue science, not superstition. This point was made by Karl Pribram, in the book he did with Merton Gill. (Pribram and Mertonm 1976) Freud had an early thesis that a scientific grounding could be given to psychology. Pribram was pointing out, in the early 1970s, that Freud abandoned this project 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 and by Pribram. (Luria, 1973)

Our examination of some common phenomenon uses the tools of higher mathematics, in ways that is consistent with the notions of David 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 Prueitt’s 1988 PhD thesis (Prueitt, 1988) and in Levine and Prueitt (Levine and Prueitt, 1988).

A gated dipole mechanism is implemented in the biology in many ways and is involved in many kinds of response behaviors. We again see that a mechanism exists not in only one system, but in many systems. The development of mechanism would seem to involve the formation of universals from particulars, a topic that involves us in foundational notions about induction both in nature separate from human mechanisms and in the human mechanisms, such as those involved in cognition and immunological response.

A second example was also developed in Prueitt’s 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.    This model of immune response gives direct insight into how well formed self-limitation is, conjectured, to hold students away from an understanding of higher mathematics.

Self efficacy and performance in mathematics class

Freshman non-mathematics majors when taking a mathematics class experience negative self-efficacy. The phenomenon of self-efficacy is viewed as a 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 (1994) has established an academic discipline focused on a particular view of human image of self.   There are a few other areas of related research, but having only specific areas of investigation related to adolescent learning behaviors.   (Pajares and Urdan, 2006) We bring new elements to this literature by appealing directly to biological mechanism as modeled by first order differential equations, stochastic field dynamics and a particular kind of finite state machine. Together these formal elements provide a means to create computer simulations of the phenomenon of self-efficacy and related phenomenon such as associative memory and anticipation. These simulations may provide guidance in national policy towards reforming mathematics and science education for teachers and liberal arts majors.

A 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. This was called ‘group think’. Again, after the failures in intelligence leading up to the Iraq War; the media termed the collective behavior as “group think”. Collective intelligence, as seen in wiki development, is also shaped by the image of self. A number of issues are revealed in knowledge management literatures, including the degree to which multi-modal viewpoints are allowed within a wiki definitional context. (Tapscott, 2006)

How are all of these issues related? A relationship between viewpoint, paradigms and orientations is seen to also involve efficacy. These other instances of self-efficacy may be used to generalize the study of student self-efficacy and hopefully show that a general systems theory approach to notions of mental coherence lends itself to formal modeling. (Pribram, 1991) The generalization supports an enrichment of Prueitt’s original model (1988) on mechanisms involved in learning.

Outcome metrics about high school students’ preparation in mathematics and science is well known. All colleges struggle with incoming freshman students whose skill level seems to almost not exist. This condition persists even in high quality universities, and where students have scored high on placement exams. These observations point to the student’s ability to study for a placement test, take the multiple-choice test, and yet not retain an understanding past the test. In under-served populations, such as those Prueitt has been working with, students will claim to have knowledge of foundational concepts when they do not.

The theory has interdisciplinary support. For example, physical field coherence is a phenomenon that manifests at several temporal time scales. Field coherence may be seen as a model of social and psychological experience and behaviors. Field coherence is seen as the support mechanism involved in cognitive processing.   Specific physical theories, related to a thermodynamic model, exists and will be reviewed and extended.   A theory of process stratification is identified in specific literatures and will be extended to demonstrate natures of emergence, of field coherence, and thus is seen to be applicable to this issue of self-efficacy. These results will be complemented by computer simulations and grounded in a specific educational theory.

Genetic algorithms, neural networks, evolutionary programming, computational linguistics are increasingly the mainstream of pure mathematics. Our research proposals are focused at linkages between discrete dynamical systems and continuous dynamical systems. The reason is discussed below, but in summary it is conjectured that deterministic models of biology are not sufficient and that discrete mathematics is needed, along with computational theory.

The insufficiency of deterministic models of human consciousness, or more generally of living systems, is controversial. We will not go into the controversy here; however, we do assume that some new principle must be examined before the nature of a living system can be fully understood. This principle may be tentatively associated with the concept of Rosen complexity. (Rosen, 1978, 1985).

The result from the combination of continuum mechanics and discrete, finite state switching networks, is a model that will take into account Rosen complexity.   Rosen complexity is defined in his work as a degeneracy in (sub)structural-functional relationship seen in the emergence of generated biological response; such as immunological response.    This response is also seen in mechanisms involved in learning. Learning emerges from the interactions between the living system and the experiences that living systems have with the environment. The mechanism involved in these interactions must be seen to arise from or be part of physical reality. (Prueitt, 1995)

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. Experience is filtered by efficacy. Students come into a classroom with their own experiences and a cognitive structure based on those experiences. These structures are valid, invalid or incomplete. The 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. This acquired viewpoint may hide a natural interest and capability.

A generalized model of emergence is developed, with specific instances of the model being applied to the mechanisms underlying selective attention, memory and anticipation. When a challenge to an acquired viewpoint is made, Rosen complexity manifests as a potential to re-enforce the old viewpoint, by discounting evidence, or a potential to develop a new viewpoint. In other words, a tipping point is achieved as a consequence of natural complexity. How might the dynamics of this model help us in the remediation process? The answer lies in the conjecture that an image of self limits many of the freshman students, and that by shifting this image and reinforcing an alternative we create a tipping point.

The new constructionist grounding

The Lifting Pedagogy is based on constructivist, participatory and Socratic principles. This pedagogy requires the students to become engaged in a learning experience that is not the same as previous experiences. The 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. The purpose of the cards is to create an externalization of an inner dynamic on the set of topics and how a student is viewing these topics. This mnemonic is coupled with a modified R. L. Moore learning strategy.

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 a negative self-efficacy may interfere with the formation of positive cognitive or emotive associations about topics in the freshman curriculum. 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 learn able.

The issue of how “new” knowledge is associated with existing knowledge is the key issue. There are mechanisms known from neuroscience to be involved in forming new associations.   Some of these mechanisms have been modeled by our published research, as well as the published research of others.   What is new is our linking neural models of associative memory to a field dynamic that represents a coherent viewpoint in such a fashion that shifts in coherence is accompanied by changes in the way in which information is processed. Acquired Learning Disability is then to be modeled using this work.

Modeling is far more complex than most psychological studies. Student engagement is essential. 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. This is because the information is not associated with a sense of self. In short, the learner must actively construct new information into his/her existing mental framework for meaningful learning to occur. In some cases, this means that a new framework has to be developed.

Acquired Learning Disability (ALD)

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 are constructing an inability to learn. Our model may shine a light on regular behaviors involved in keeping a negative efficacy stable. Maturana and Varela (1992) certainly set the stage for the philosophy about self identity - but there is some kind of "phase coherence" involved. Pribram's neurowave equation is involved also.   The literature on mechanism takes into account the neurowave equation, as a primary carrier of the cognitive content of awareness. What is needed is an integrating theory and some domain of application.

Model of self-limitation within a social framework

The model may 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 as more important than evidence that would support an alternative viewpoint. A utility function is conjectured to stabilize 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 of self-limitation is 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. A neurological field emerges in the fashion described by Pribram’s neurowave equation. Stimulus inputs are each seen as perturbations to state transitions defined by field coherence. Because of “degeneracy in the model” it is necessary to create field localization where a differential is manifest between specific experience and the coherence of the field. The physical systems supporting experience is seen to re-enforce the field or in some cases to collapse the field.

Individual collapses of a neuro-quantum field, such as discussed by Hameroff (2005),   are part of a process. This process supports learning, awareness, and the formation of the cognitive or emotive response mechanisms.   The process is part of more complex action-perception cycles. As these cycles create experience, individuals make decisions. 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 a viewpoint, are also about how to regard concepts that fit or do not fit with one’s image of self.

Self-limitation is seen as part of a reinforcement mechanism maintaining a specific view when evidence is provided discounting this view. One thinks about Thomas Kuhn's (1970) work regarding paradigm shifts,   and the works on “explanatory coherence” by Paul Thagard (1999).   David Schum’s (1994) work on evidential reasoning has also been important to our initial work.   The works of these scholars is illustrative of an extensive literature on coherence and evidence. These works provides the basis for a computational model where a competition of ideas is mediated by coherent field stability.

Imagine that one system is created in such a way that the second system’s field 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 breeding 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. There are mechanisms involved in holding a pattern of stability even in spite of the real time observed inputs.

Suppose that this second school of thought is in fact the view that a liberal understanding of mathematics and science is not accessible and not of value to average college graduates. Some scholars may conclude that this condition is un-natural in spite of our observation about many college freshman students’ viewpoint about the nature of mathematics. What the computational model suggests is that a driving force is present that strongly re-enforces the acquired learning disability.

First order differential equations, seen in even the simplest neural model, have on-center off-surround networks. We use this classic on-center off-surround system of first order differential equations. Our model of the two-system field 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)    we have a layer of input and a layer of output processing nodes with a gated di-pole serving as the mediator. So there was, in the 1989 model, a reset mechanism for failure to fulfill a utility function. This feature of our work provided an orienting mechanism when failure to match utility results in a new contextual search. Frontal lobe mechanisms complete a biologically implemented architecture whereby agility is supported. Orientation to novel stimulus over rides familiarity with past experiences.

Without the normal frontal lobe function, an autopoietic envelope might form whereby failure to fulfill the demands of a utility function, e.g., human needs, is accommodated. An "acquired inability" to make proper decisions is constructed as part of the systemic response mechanism. If this is so, students might be capable of making decisions that shift the viewpoint from first to second school.