The Nature of Interaction:
Applying the Nonlinear Foundation of Educational Decision Making

Table of Contents


Ultimately, our decisions are driven by problems and the quality of the questions that emerge in tackling them. Educators in particular face persistent problems that are still in debate. How should teachers teach and be supported for that teaching? How should students learn? In the exponentially changing nature of the world in the 21st century, what should students learn? These basic questions drive educational practice. But what steers the driving of educational practice, the decisions about that practice? The answers for centuries and recent decades have been a combination of philosophy, art and science. The increasing pressure for hard answers to tough questions and a growing cultural perception that science has been the most effective in answering tough questions has led legislatures and both national and state to mandate that decisions can only be driven by scientifically proven results. Today's educational paradigm then requires that educational systems and their decisions be driven by scientific data. That raises a host of questions that too often are not addressed about the ability that science provides to predict and thereby control different kinds of systems. What do decision makers of all kinds need to understand about how good science is at predictive science? What are the boundaries, the limitations of the philosophy of scientific and mathematical thinking? If science faces limitations from minor to severe in applying its results to educational practice, how might those limitations be addressed? Do those limits have application beyond the field of education? If limits exist, what can fill those voids? How should the science of science be applied to educational science in making predictions and prescriptions?

This thought develops, describes, compares and considers the implications of an alternative paradigm for educational inquiry and provides answers to these questions. It observes that the intuitions and metaphors that have been developed and encouraged in the field of education have been built around models from the field of science and real world experience that are chosen and studied in depth because they are predictable. This is hardly unique to the field of education. People surround themselves with the most predictable systems because such predictability brings order, power and agency or control to human experience. Exploring less predictable or totally unpredictable systems appears to have little useful leverage. Instruction in science and mathematics spends an inordinate amount of time communicating information about predictable systems because such knowledge is so usable, and is challenged in communicating the significant amount of knowledge that is already known and understood. As a consequence from our real world experience and what instruction is remembered, perceptions are consequently heavily skewed against understanding that which cannot be predicted. Why bother? Models that appear to be extendable to more complex settings are not examined with the same rigor.

Piaget noted that to get accommodation or change in understanding it was necessary to learn that assimilation of new data created conflicts with prior understanding. Though demonstrations from a wide range of fields from physics onward to the field of education will be provided, it is important even in this introduction to begin to crack the facade of current understanding. First observe a basic pendulum. If you have watched the first few seconds, you can succesfully predict what you will see at any point throughout the timeline.


Knowledge of the predictable features of this system has a wide range of applications.

http://www.youtube.com/watch?v=iqpV1236_Q0 (The big predictable event does not happen until the last 10 seconds.)

http://www.youtube.com/watch?v=Ysnwvv6fods (Adjusting the time of a grandfather clock is easy and a practical application of pendulum knowledge.)

However, adding one variable, a seemingly simple change to the pendulum, a second limb with a 360 degree hinge or joint, changes the results radically. Though one can predict the range of the action within which the pendulum can move based on the length of the joints, it is impossible to predict where the point of the pendulum will be at any point in the timeline.


A more patient and thorough analysis of those studying such phenomena across all fields of study will follow in the chapters ahead. It is not so much that the world is not as it seems. Rather, it is critically important to build our decision making apparatus on seeing the world as it is.


This study's proposed alternative paradigm coalesces around an examination of the power and limits of science, which at its most basic is a study of the nature of interaction. It focuses on the more recent scientific concepts of nonlinear dynamics and its understanding of chaotic and self-organizing systems, concepts that throws new light on the foundational understandings of interaction, determinism and indeterminism and cause and effect. Further, this study develops a shell or model for comparing these paradigms. To aid discussion of this proposed conceptual shift of a world-view, models of the dominant and other alternative paradigms are proposed. It also develops a taxonomy of interaction that provides a common basis of communication across the conflicting paradigms.

This work, then, is critical analysis of the debate over the alternative paradigms, the multi-layered models of world views that form a network of ideas from philosophy to classroom practice for curriculum and instruction. It recognizes from Kuhn's ideas about scientific revolution that changing paradigms is a long process that requires some deep understanding of the conflicts within a prior model. It fixes the root problem of the current dominant and alternative models in curriculum and instruction on difficulties in understanding and dealing with interaction and complexity. It describes discoveries in understanding interaction and complexity that were made possible in part by computer technology. These conceptual advances, chaos theory and the study of chaotic dynamics, in turn has lead to computer technology driving new developments across a wide range of sciences. It finds a compelling match between these new concepts for interaction and complexity and the interaction and complexity of curriculum and instruction. The study suggests new areas of research for educational experimentalists, yet suggests reasons to re-think and reject the application of strict experimental programs of research that seek long term prediction and control and quantitative confirmation and/or falsification. It finds that an understanding of the nature of interaction results in a revitalization of elements of prior reconceptualist programs of inquiry. It does not invalidate educational science, but puts it on a much shorter leash, integrated with a renewed understanding of the value of holism and self-organization of constructivist thinking.

The original title of this book was A Chaotic Paradigm: An Alternative World View of the Foundations for Educational Inquiry. It was first completed in 1989 and the application concepts of chapter five were later transformed into a continually expanding and changing series of digital books available on the Web. Its more recent title, The Nature of Interaction: Applying the Nonlinear Foundation of Educational Decision Making, more closely hits on the central factor of its thinking. This digital online book of four chapters addresses some of the most fundamental issues that guide decision making. The response to application and the initial questions raised above continue in a web site of a series of online books that might be viewed in any order, and whose chapters have a suggested order but also stand on their own for many contexts, DigiAcademy.

This Web page provides a table of contents for the Nature of Interaction. Each Chapter will contains its own Table of Contents and links to the other chapters. Single spaced, all the related files of the first four chapters and bibliography add up to approximately 111 pages of print.

Table of Contents

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The initial work, A Chaotic Paradigm: An Alternative World View of the Foundations for Educational Inquiry, was initially completed as a doctoral dissertation in 1989 at the University of Wisconsin - Madison. (c) Copyright by Robert Stuart Houghton,1989. All Rights Reserved.

Version 1.09 Updated September 23, 2013