Charles R. Granger
University of Missouri-St. Louis
- Rules and Guidelines of the Game
- An Instructional Theory Hypothesis
- Cognitive Degredation
- Implications of NET
- Theoretical Postulates of NET
- Pragmatic Propositions in the Use of NET
- Education Theorists
Exploring the Naturalistic Education Theory (NET) as a strategy to engineer an appropriate sequence of topics it can be demonstrated how to produce a pedagogically sound curriculum and more efficient instruction. There has been a vast discrepancy between the demand for effective and efficient curriculum materials and the framework and guidelines to fulfill that need (McKenna, 1976; Granger, 1992). Without a major change in our fundamental approach to pedagogy we will not be able to increase the low percent science literacy rate by an order of magnitude that is needed to serve a technology-based society (Granger, 1998).
Rules and Guidelines of the Game
The mind, as well as all of the other components of the universe, must obey the rules of physics, chemistry, and physiology. This sounds obvious and simple, yet some psychologists, educators, and theologians have historically continued to offer more esoteric explanations for how the mind works, forsaking the mechanical and supporting the mystical. Assuming a mechanistic phenomenon, the recording and processing mechanisms of the mind must be based upon on-off, present-absent, high-low, flip-flop, excited-nonexcited, or similar phenomena. The “astonishing hypothesis” espoused by Francis Crick (1994) and the neuronal group selection theory developed by Gerald Edelman (1992) are two of the more progressive explanations of the mechanisms of brain functioning. Both explanations are chemically based at the neuron mass level and offer exciting understandings for shaping and directing learning environments. Although critically important for establishing the complete picture and assuring optimal efficacy, knowledge of the exact biochemical-physical mechanism is not critical to the application and manipulation of the traditional sensory input and processing procedures. However, the propositions offered in this thesis are congruent with the hypotheses of both Crick and Edelman.
If the mind is electro-physical and not parapsychological, then there must be an instructional method that would be the most effective and efficient strategy for learning. Based on other physiological phenomena derived from basic genetics, one can assume that the mechanical variation in the internalizing system allows for either no-function or function with some degree of variability in rate. As we know, there is some variability with respect to efficiency of the sensory input mechanism from person to person, but the biochemistry/biophysics for recording, retrieval, filing, and processing would be essentially the same and it would either work or not work.
Therefore, learning can be facilitated by providing stimuli that enhance the effectiveness of the input mechanisms and that are congruent with the recording, filing, retrieval, and processing mechanisms of the brain. It is generally agreed, if not always practiced, that every possible input stimulus should be utilized for instruction of every concept or informational byte and that this should be made as individualistic as possible. Tinkering with this aspect of teaching can be very creative and rewarding. The theoretical basis for the operation and effectiveness of these techniques is known well enough for proper utilization. However, no matter how well this is done, in and of itself, it will not produce the needed increase in instructional efficiency to bring the rate of learning and knowledge base to a satisfactory level (Granger, 1994).
On the other hand, the process of internalization and utilization of information is not understood and proposed theories on enhancing learning are somewhat inconsistent and incongruent, certainly not holistic. Because of this lack of solid foundation, we see the curriculum engineers fall into the same trap of doing the same thing over and over again expecting different results. Perhaps write another, a little more detailed, textbook...perhaps a purple version. Let's develop one more curriculum. Maybe we could put together a national list of concepts to be learned. Let's add more body parts to the pedagogy—hands-on, heads-on, heart-on, and feet-on experiences are the ticket. Question our questions. Wait a little longer. Let's break down the concept into smaller and smaller components. Perhaps a little more discerning evaluation instrument. History convinces us that all of this effort is doomed. How long did humanity pursue the dream of flight? How many people attempted to fly only to find themselves kissing the ground hard, crashing headlong into a wall or worse dropping like a rock off a cliff? When did flight really begin to take off? It was the discovery of the Bernoulli effect by Daniel Bernoulli (1700-1782) that led to a major principle of physics and opened the door for Wilbur and Orville Wright (1871-1948) to successfully attack human flight from a principled, scientific approach. Major advances in teaching and learning are no different. First must come the philosophical underpinning that account for our observations on cognition. Then the strategies can be developed to address the enhancement of cognition. What approach can be employed that takes into account the physics, physiology, and chemistry of the brain and is in harmony with observations of what appears to be effective instructional strategies and learning behavior?
An Instructional Theory Hypothesis
Philosophers of education have attempted to develop comprehensive theories of education that lead to pragmatic methods of efficient instruction. The first recorded, inclusive, systematic approach was espoused by John Amos Comenius in 1623. He stated that:
"We are so bold as to promise a Great Didactic...a complete treatise on how to teach all subjects to all men, and how to teach them in such a say that the result will be certain.... We shall show that all this is done a priori, that is to say, deriving from the immutable nature of things...and that a universal system is thus established which is valid for the institution of universal schools." (Comenius, 1623)
Although the underlying theme in Comenius' theory was clouded by religion, moral, and sometimes mystic perspectives, his concept, that there is a natural index of instruction derived from experiential interactions with nature, forms the foundation for many subsequent theories. The work of Comenius was never widely implemented and restricted to some individual attempts on his part to start schools based on his philosophy of education.
In the early part of the 20th century, John Dewey (1933) led the progressive education movement following Comenius' lead. Although "progressive schools" sprang up here and there in name, few were practitioners of Deweyism in the true sense. David S. Ausubel's (1968) work stressed the significance of sequence and the critical nature of the association and interrelationship of concepts. Jean Piaget (1972) proposed that the cognitive level of the concept must be appropriate for the cognitive skills of the learner and that the educational experience be made real in the sense of direct student involvement through exploration. These learning theories have common ground that form the foundation for current thinking by the constructivists.
However, something seems to be lost in the translation of the learning theories of these philosophers into the pragmatic setting of the classroom. What is missing? Perhaps what we have not been able to derive from these proposals is a straight forward mechanistic learning theory, one that makes biological and pedagogical sense, is easily interpreted, and leads to pragmatic postulates and reasonable mechanisms of implementation in the classroom. What is the unifying theory that can be used to tie these ideas together in a holistic approach to the science of education?
One of the beauties of nature is that it appears so complex but yet is governed by simple principles—a complex structure with non-random rules and basic elements. The Naturalistic Education Theory (NET) is a unified learning theory of instructional methodology and tactical education. NET originates with the melding together of the propositions of Comenius (1623), Ausubel (1968), Benjamin S. Bloom (1976), Jerome S. Bruner (1960), Robert M. Gagne and L.J. Briggs (1979), and Piaget (1972) into a neo-constructivistic approach. The mechanical classroom manifestation of Ausubel's learning theory materializes in the form of concept map-based lesson designs as presented by Joseph D. Novak and D. Bob Gowan (1984). Implementation of Piagetian learning theory into the classroom takes the form of the Robert Karplus, et. al. (1977) learning cycle.
In the NET, the philosophical bases of these strategies are amplified and extended to incorporate a learning spiral (Granger, 1987) rather than a cycle, and a historical, natural sequencing of concepts rather than a two dimensional, somewhat spontaneous knowledge Vee (Novak, Gowin & Johnanon, 1983) association of terms. NET, a historical-based natural sequencing theory (Granger, 1989), proposes that information consists of bytes which should be arranged and taught in the same order in which they were originally discovered, disregarding artificial categorization by traditional academic disciplines. This historically-based sequence sets up a learning spiral symbolizing the continuity of information bytes and their systematic linking together, web style, for a meaningful, multi-dimensional concept structure and continuous association; in other words, a four-dimensional, dynamically expanding cognitive map creating a continuous association of concepts. It is a mental construction process fueled by natural curiosity and a developmentally-based need to know. The total mental construct will continue to expand and become more complex if intellectual energy is expended to form interconnections between existing mental constructs and new experiences. This latticed association is engineered by design, not stumbled upon by pragmatic trial and error or the artificial selection process that seems to be prevalent in the pedagogy of today. The structure and function relationships of the construct flow naturally as if the discoveries were their own architects and their revelation engineered by their own processes of evolution. Together these broad principles form the NET (Granger, 1996).
If we assume the universe of knowledge is, at present, in a continuing state of expansion and development, then just as the components of the physical universe have become more complex and interrelated, but more flexible and open, so does the mind and its contents over time. In both cases, time is the fourth dimension (really should be called the first dimension, for without it there are no other dimensions) that limits the complexity of form and format of the universe and the development and incorporation of knowledge constructs in the mind.
One can not develop a holistic view of the universe by snipping out a time segment, say 10-10 seconds after the initiation of the universe, a.k.a. the "Big Bang," and studying leptons, for example. Likewise, to snip out a segment from the continuum of the development of human knowledge also produces only a stand-alone phenomenon that makes little sense in the context of the holistic understanding of the human experience and the universe in which it occurs.
This is not to say we cannot do it; we can do both. We can indirectly see traces or inferences of muons and we can indirectly identify DNA, for example, as a cloud of information floating in the mind, in its own space. Neither conceptualization is useful or explanative in its own right, even though each may exist and can be seen, albeit indirectly, that is, symbolically, because these single bytes of information will not be tied to a meaningful mental construct representing the known portion of the universe as we currently understand it.
Concepts developed about our universe that form our mental pictures can be likened to a jigsaw puzzle, where a single, isolated piece (byte) is not very useful in and of itself in solving the overall puzzle or yielding an accurate image of a concept or series of concepts that lead to an illustrative principle. Some pieces are more useful than others, depending on the quality and quantity of information riding on them and the relatedness that information has to previous experience of the puzzle solver. However, assuming uniqueness, the piece could be oriented in a multitude of positions and spatially anywhere within the framework (parameters of which we might not even know) of the picture or concept to be developed. With no external clues for orientation, random choice of position could lead to a multitude of resulting perceptions and meanings of the picture, including, perhaps, an upside-down misconception. Our idea of the concept could not only be upside-down, but backward and out of context, if we were working with a four-dimensional phenomenon.
If you are lucky to start the puzzle with a corner piece and you have gained some operational or process skills, you have limited your outcomes to only four possible positions in context of the picture, however, overall orientation could still be highly varied. If however, the corner piece fits against or was attached to an existing, correctly oriented set of pictures, then everything would work out okay and reflect the reality of the situation, at least in the context of the existing cognitive structure. The correct position in time and place for a picture would be fixed. How the original piece is laid down has a great effect on how the whole will look.
"A small error in the beginning leads to a large error in the end."
There is a reason why puzzle manufacturers have developed a continuous line of puzzles from the simplest forms to those so complex that it appears only the creator can figure out the solution. In order to capture young minds in the joys of puzzle solving the makers start with puzzles of few pieces, say three to four with easy fit connections. The pieces are large and easily handled. They have designs or pictures that are universally recognizable and the pieces fit into a frame with preformed border, usually with a continuation of the picture or design. Unless manufacturers never want to sell another puzzle, they do not give the unskilled puzzle solver a 10,000 piece puzzle printed on both sides with a vague, low resolution picture. Of course this is a simplistic analogy, but there is a useful lesson here. To gain meaningful understandings, concepts must be learned in a sequence that moves over time from simple to complex. The learning spiral as symbolic representation of the NET can be thought of as a four-dimensional puzzle. By taking the time dimension into account, the NET-based engineering of the learning experience can allow for a temporal and spatial sequence of curriculum development that incorporates the natural orientation, interrelationship, and interaction of concepts and thought and helps to build a meaningful cognitive structure in the mind of the learner.
We believe quarks preceded leptons, that in turn preceded hadrons, that preceded nuclei, etc., for systematic reasons. We also know why the discovery of the cell theory preceded the understanding of mitochondria, that preceded DNA, etc. As we as organisms move through stages of understanding based on experiences, the historical sequence of instruction follow the pattern of our developmental ability to understand, coupled with the sequence of our exposure to phenomena in a need-to-know-as-we-go hierarchy. The instructional exposures are revealed in sequence based on the chronology of the original discovery experiences. Thus our growing knowledge spiral establishes our propensity and perceptiveness to recognize and internalize the existence of the next experience in sequence. Psychogenesis recapitulates chronology. The history of intellectual development is the natural architect for individual cognitive development. Natural curiosity and the need-to-know is the engineer for designing the curriculum of life.
“For effective learning, students need an orderly and ordered set of activities that can result in the completion of a learning process.”
- John Dewey
Starting at the beginning of cognitive time (tc), the origin of the individual, where tc=0, it follows that the origin or nucleation site of the learning spiral would be an informational byte that would be described as science.
Figure 1. The Axis of Content Outlining the Cognitive Development Playing Field.
Inquiry and science are natural phenomenon, genetically based, they provide both the origin and backbone for the lattice of the learning spiral. They become the tools of acquisition.
“A new education from birth onward must be built up.”
- Maria Montessori
The highly developed natural curiosity of the human being, honed by natural selection, is the centerpiece for intellectual development and the mechanistic base for the philosophy of science. Unlike the man-made constructs of mathematics, language, theology, etc., science is a natural behavior, essential to survival and therefore the engine for other mental constructs. Science, in its broadest definition, is the essence of our cognitive structure—both knowledge and process.
“Education must be reconstructed and based on the laws of nature and not on preconceived notions and prejudices of adult society.”
The central axis or regression line of mental tendency of each individual would be defined as a line in four dimensions with (x,y,z,t) coordinates, radiating from the same origin. The perfect state of this line representing the center of mental gravity might be expressed by the two points with coordinates (0,0,0,0), (0,∞,0,∞). The coordinates of the line can be altered by the systematic addition of knowledge in the various quadrants within which the spiral lattice exists (Xn,Yn,Zn,tn).
As the knowledge base grows and the cognitive structure develops the possibility of intercommunications between concepts increases and the interface between the known (experienced) and unknown increases. The more experiences you have the more experience you are able to have.
Figure 2. The Learning Spiral Imposed on Temporal and Spatial Sequencing by the Naturalistic Education Theory.
This does not mean that everyone's learning spiral would or should look identical. In actuality, identical learning spirals would be rare, a perfect one improbable.
“The direction in which education starts a person will determine their future.”
Only in the perfect state would the resulting construct be a complete, symmetrical, radiating spiral lattice. This idealized or all-knowing structure would be unlikely to exist in the human condition given our mental limitations and or temporal restrictions. Affective factors open or close the possibilities of additions to the construct, in some instances causing deviation from the idealized coordinates to the extreme point of rendering the individual inoperative in typical environmental contexts. However, society and the educational system it produces should shoulder the responsibility for providing each individual with the most comprehensive experiences for the development of a complete, basic mental framework, particularly during the critical, early formative years.
“The solution which I am urging is to eradicate the fatal disconnection of subjects which kills the vitality of our modern curriculum. There is only one subject matter for education and that is life in all its manifestations.”
- Alfred North Whitehead
The complex structure of the cognitive spiral lattice labors under the second law of thermodynamics as do other constructs of nature. There is a natural degradation of organization and systematic processes of the cognitive structure. According to the NET, the total construct will continue to become more complex if intellectual energy is expended to form interconnections between existing mental constructs and new experiences. Use and maintenance of existing constructs are essential for concept integrity. Reversal of the learning process or rate of decay (RCD) is a function of the same parameters as construction, time (t) and space (P), thus RCD=f(t,P).
The outermost bytes of the cognitive structure are liable to erosion to the highest degree since there are fewer interconnections or stabilizing factors associated with them. Those innermost bytes which form the cognitive core of the spiral lattice are saturated with interconnecting ideas and processes and therefore the most stable.
Distorted cognitive structures that branch singularly from the idealized center of mental gravity enhance the possibility of erosion of other, not so well developed constructs in other quadrants. Spatially separated multiple lines or unconnected branches of the cognitive structure are more unstable than contiguous lattice structures that approach the idealized, complete cognitive spiral.
Concepts and processes have a half-life in which decay is a function of chronological origin and subsequent renewal or maintenance. The older the concept in the mental construct and therefore the more interconnections there are, the most stable the byte. In general, last on, first off. The decay rate of concept 1 compared to concept 2 is a function of time where tC1<tC2 and therefore RCDC1>RCDC2. The more frequent and current the reinforcement the more resistant to decay. Since time, in the case of NET, dictates position and position indicates time, RCD=f[t(P)], we can devise a mental picture for an index of cognitive decay by RCD=k1t + k2P(xn,yn,zn).
The principles of cognitive degradation do not preclude internal or point erosion of lattice components. Without energy expenditures for lattice maintenance, the lattice could become permeated with hollow sections or regress to multiple linear or branch structures and therefore are more liable to decay. This erosion could be initiated by lack of maintenance, electro-physical factors, aging, the incorporation of misconceptions, or a combination of these factors.
Misconceptions are a problem in building the lattice in that they, just as puzzle pieces, may be incorrectly placed and yet may partially fit and interconnect with some existing cognitive structures. However, they cannot make additional interconnections and form a completed harmonious cognitive element. They may even distort the whole web and influence the spatial and temporal acquisition of additional knowledge and processes. Although misconceptions are natural phenomena and are operative constructs at certain levels of human need and cognitive development, they substantially reduce the efficiency and effectiveness of the overall learning process and speed up the processes of cognitive decay.
What pragmatic meaning does NET have for the classroom teacher? How can it facilitate the construction of an effective and efficient curriculum? NET has many implications associated with its premises and they can be categorized into two sets, theoretical postulates and pragmatic propositions. The mechanisms of the operation of the brain are not fully understood. However, NET is based on several postulates that are consistent with behavioral, physiological, and psychological observations.
- The mechanisms of the brain are electro-physical/chemical.
- Mental development in human beings is predictably sequential, albeit multi-dimensional and varied in rate.
- Science, its processes and concepts, is the natural and fundamental mechanism from which knowledge and cognitive skills grow and develop.
- A byte of information has specific coordinates that define its place in time and space in the cognitive structure and this coordinate is critical to its effective and efficient translation and establishment in a mental niche.
- Sequencing of the individual learning experience parallels the cognitive, affective and psychomotor development of the evolution of human understanding over time.
- The potential for the rate and breadth of concept incorporation and process skill development increases over time with development and expansion of the learning spiral lattice of the mind.
- Meaningful interconnections that are formed through temporal and spatial relations exist among all subject matter concepts and process skills.
- Motivation and curiosity flows naturally from need and understanding.
- Mastery learning is an achievable goal as learners progress along chronologically-based concept/skill paths.
- The cognitive decay sequence is inverse to temporal acquisition and maintenance, and related to spatial position, and rate is inversely proportional to maintenance frequency and directly related to distance from the central core of the cognitive spiral lattice.
Assuming the theoretical postulates to be true, the adoption of NET would lead to a set of inescapable propositions needed to be taken into consideration by the curriculum designer and teacher when engineering an educational experience for prospective learners.
- Curriculum engineering should be founded on a discovery-based chronological sequencing and spatial continuity of concepts and process skills.
- Learning experiences for specific concepts and associated process skills should be engineered, within the boundaries of accuracy and efficacy, analogous to the original discovery process.
- Science should form the nucleus as the underlying theme for curriculum construction.
- The whole of the educational experience should be integrated, throughout the body of knowledge.
- Learning experiences should be developed, sequenced, grouped, and delivered according to the cognitive developmental stages of the learners.
- Instructional programs should be built on the existing cognitive structure of the individual, taking into account missing, incomplete, or incorrect components of the knowledge/process spiral lattice.
- Rate of exposure to concepts and process skills should coincide with the construction incorporation rate of the individual and should not exceed this pace.
- Curriculum engineering and associated activities should review and utilize prior knowledge and processes in a comprehensive and systematic manner.
- Student evaluation and progress should be charted according to the position of the learner on the cognitive learning spiral of the human experience.
- Teacher education should focus on developing expertise at various chronological stages of cognitive development, rather than separate disciplines, as circumscribed by the physiology and experiential base of the learner and in synchrony with the chronological development of the body of knowledge and the processes associated with its acquisition.
- Learning experiences should be available that are engineered coherently from birth to death.
Without a major change in our fundamental approach to pedagogy, we will not be able to increase the current seven percent science literacy rate in our population by an order of magnitude. To achieve this desired level of understanding in the general populace, we have to abandon our trial and error approach to instructional strategies in favor of a science-based learning theory that dictates a systematic approach to education.
The NET acknowledges the brain's rules for meaningful and lasting learning and demands organizing the processes of pedagogy based on those rules. The NET provides an integrated, holistic explanation of the recording, filing, retrieval and processing mechanisms of the brain in so far as they relate to pedagogy. Based on mechanistic premises, it provides a theoretical foundation on which sound instructional engineering can begin.
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