Ambiguity, Cognition, Learning, Teaching, and Design

Workshop and special panel session held at the International Conference of the Association for Educational Communications and Technology, Anaheim, California, October 22-25, 2003, and organized by the Learning Development Institute

 

"What is not surrounded by uncertainty cannot be the truth."

        Richard Feynman, cited by Timothy Ferris in M. Feynman (2005), Perfectly reasonable deviations from the beaten track: The letters of Richard P. Feynman. New York: Basic Books.

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RATIONALE AND DESCRIPTION OF THE EVENT

The above event brought together a group of people, representing different disciplines and connected in different ways to the practice and theory of cognition, learning, teaching and design, around the issue of ambiguity. The concept of ambiguity occurs relatively infrequently in the literature on learning and teaching. A Web search intersecting “learning” and “ambiguity” reveals a certain dominance of the concern with ambiguity in the literature on learning algorithms. As regards human learning, the concept of ambiguity gets mentioned in connection with learning styles (some learners get turned off when confronted with too much ambiguity). “Tolerance of ambiguity” is a concept employed by theoreticians who deal with the learning of foreign and second languages. The concept also occurs in some of the literature on problem-based learning. It may also be linked to issues of a more philosophical nature, such as the question, “Can we really understand the world?” There are instances in which our ordinary (Aristotelian) logic is an insufficient basis for the advancement of understanding. Some of the literature on transdisciplinarity deals with this issue and proposes (e.g. Nicolescu, 2002) a logic based on the “included middle” (as opposed to the excluded middle in Aristotelian logic). Another connection here is with what physicists have known – and had difficulty to come to grips with – since early in the last century – that at the level of description of nature that is incommensurate with the levels for which common language was developed there is complementarity of knowledge in the sense that, in order to know with precision one thing, like the speed of a particle, it becomes fundamentally impossible to know a complementary aspect, such as the position of that same particle at the same time. Yet another area of ambiguity occurs when people’s emotions lead them in a different direction than their cognition. This issue is well known to researchers who look into human behavior regarding the prevention of HIV/AIDS or smoking.

These are but a few areas where one can see that a discussion around the theme of ambiguity in learning and instruction could be highly relevant. The idea for the workshop wasn thus to look at ambiguity in the first place as a fact of life, rather than as something that should be avoided in the instructional context. If in real life we have to deal with ambiguity in its many guises all the time, then the question is, "What should one do in the learning environment to optimally prepare people for life in an ambiguous world?"

REFERENCE

Nicolescu, B. (2002). Manifesto of transdisciplinarity. New York: SUNY Press.

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PARTICIPANTS

The following persons contributed to the workshop in Anaheim (the names of those who were unable to be physically present but who contributed with a paper are preceded by an asterisk):

Muriel Visser, who researches adolescent health related behavior, particularly in response (or lack thereof) to the threat of HIV and AIDS;

* John Shotter, who is probably best known for his contributions to our thinking about learning as a social and dialogic phenomenon;

Yusra Laila Visser, whose research focuses on problem-oriented learning;

Gil Suzawa, whose work and research focuses on the teaching of economics with ambiguity in mind;

Ron Burnett, who is too broadly defined to be captured in one short phrase, but who was expected to contribute (and indeed he did) from the perspective of his experience as an administrator of a significant institution that introduces young and not so young people to the world of art and design, his experience as an educator, and his scholarship in the communications field;

* Gordon Rowland, known for his contributions to thinking about learning and design from a system theoretical perspective as well as his research into the factors that make learning powerful.

Jan Visser, who expected his contribution to have something to do with his current interest in questions about the development of “mind” (as opposed, or rather in addition to specific competencies) and with his background as a theoretical physicist and someone who is conversant with the fascinating history of science since its known early beginnings in Mesopotamia as well as by his work in an international development context.

In addition, two discussants, Brent Wilson of the University of Colorado and Kyle Peck of the Pennsylvania State University, contributed to the dialogue during the conference session by providing their reflections on the various written contributions by the above authors.

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AECT PROGRAM DETAILS OF SPECIAL PANEL SESSION

Title: Tolerance of Ambiguity
Description: The concept of ambiguity occurs relatively infrequently in the literature on learning and teaching. A Web search reveals a certain dominance of the concern with ambiguity in the literature on learning algorithms. As regards human learning, the concept of ambiguity gets mentioned in connection with learning styles; the learning of foreign and second languages; and problem-based learning. It may also be linked to epistemological questions regarding how we know the world and advance our understanding of it. Physicists have long known that at a level of description of nature incommensurate with the levels for which common language evolved, there is complementarity of knowledge in the sense that, in order to know with precision one determining aspect of a phenomenon, it becomes fundamentally impossible to determine a complementary aspect of it. Yet another area of ambiguity occurs when people’s emotions lead them in a different direction than their cognition. This issue is well known to researchers of human behavior regarding the prevention of HIV/AIDS or smoking. All these examples suggest that ambiguity is a fact of life to be lived with rather than to be avoided. The question then is, "What should one do in the learning environment to optimally prepare people for life in an ambiguous world?"
Length: 2 Hours
Time: 1:15 pm-3:15 pm
Date: 10/23/03
Location: Hyatt Regency-Terrace A&B
Session Type: Concurrent
Facilitator and Key Presenter: Dr. Jan Visser, President, Learning Development Institute

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CONTRIBUTIONS

The following papers were contributed by the participants in this exercise. They are presented, following the alphabetical listing of the author names below, in the chronological order in which they were received.

Ron Burnett - Ambiguity/Language/Learning (text - received October 21, 2003 - as well as PowerPoint presentation)
Gordon Rowland - A little ambiguity can go a long way (received July 21, 2003)
John Shotter - The necessity for ambiguity if we are to achieve specificity in communication (received October 19, 2003)
Gil Suzawa - Ambiguity and teaching economics (received October 16, 2003)
Jan Visser - Science and ambiguity: Have we thrown the key away? (received October 19, 2003)
Muriel Visser - "Inverted commas": A critical reflection on ambiguity in the context of HIV/AIDS (received October 20, 2003)
Yusra Laila Visser - Ambiguity in learning: Issues and implications for instructional design (received October 22, 2003)

A Little Ambiguity Can Go a Long Way

Gordon Rowland
Ithaca College and Learning Development Institute

There are at least two ways the term ambiguity can be defined and used, and these point toward different views of the processes of learning, teaching, and helping with organizational change. I refer to these as allopoietic and homeopoietic, elsewhere (Rowland, 2003), and I will return to those terms after briefly exploring the views. The major point I will attempt to make is that a modest level of ambiguity can have very positive effects.

According to the Oxford English Dictionary (Compact OED, 1991), ambiguity can mean "wavering of opinion, hesitation, doubt, uncertainty, as to one's course" or it can mean "capable of being understood in two or more ways, double or dubious signification." Similarly, ambiguous can mean "doubtful, questionable, indistinct, obscure, not clearly defined" or it can mean "admitting more than one interpretation or explanation; of double meaning or of several possible meanings; equivocal; of doubtful position or classification, as partaking of two characters or being on the boundary line between."

The definitions relating to wavering and uncertainty point toward an attitude of avoidance. As a learner, one wants clear presentation of facts and answers to questions, and, as a worker, one wants clear management direction. Consequently, the teacher or manager is seen as the source of expertise, and perhaps vision, and is responsible for controlling processes that lead to defined outcomes.

In contrast, the definitions relating to multiple interpretations and boundary spanning point toward an attitude of acceptance. A learner would understand that concepts and language are human constructions and would look for guidance from someone with more experience, as opposed to "truthful" answers from an expert source. A worker would look for performance support (and/or removal of obstacles) in achieving mutually agreed upon goals, as opposed to orders. Both would expect to have input into decisions and a certain degree of self-direction, so, the teacher and manager would take the role of respectful facilitator.

The distinction between definitions, and thus selection of approach, may stem from one's view as to the nature of human individuals and organizations. They can be seen as simple deterministic systems, for which a limited number of cause-effect relationships can be identified and translated into predictions and prescriptions for achieving desired outcomes. Or they can be seen as complex adaptive systems that self-organize through complex and dynamic interrelationships and are characterized by nonlinear processes and unpredictable outcomes. Further, the latter view may be amended to see humans and organizations as complex creative systems that evolve with human intention, as opposed to only adaptation to changing circumstances in their environment.

Support for a complexity (complex adaptive or complex creative) rather than simplicity (simple deterministic) perspective is growing through a confluence of a number of sources: new sciences and their application to living systems (e.g., Gell-Mann, 1994; Strogatz, 2003; Capra, 2002; Morowitz, 2002); behavior of experts in solving problems (e.g., Akin, 1994; Rowland, 1994); powerful/meaningful learning experiences (Perry, 2002 Rowland & DiVasto, 2001; Rowland, Hetherington, & Raasch, 2002; Visser & Visser, 2000,); learning theories (e.g., Wilson, 1996); as well as everyday social interactions (Stacey, 2001). However, approaches to learning, teaching, and organizational change based on a complexity view are just now appearing in the literature and are largely speculative (e.g., Shaw, 2002; Rowland, 2003)

These approaches can be characterized as either allopoietic-making for others-or homeopoietic-making with others (Rowland, 2003). The allopoietic approach is quite familiar to all of us who have been "schooled" or who have worked in a traditional management hierarchy. In the context of teaching and learning, it refers to the design and delivery of instruction, literally meaning the furnishing of knowledge. On the other hand, the homeopoietic approach calls for mutually constructing knowledge (and organizations) through the intentional complex responsive processes of relating (see Stacey, 2001). This involves what has variously been called living in the midst of change, in the creative tension of apparent opposites, with the paradox of being simultaneously in and out of control, in far from equilibrium states, at the edge of chaos, in flow or liminal states, in a space for novelty, or in a network characterized by certain levels and types of connectivity-not too much or too little (e.g., Barabási, 2002; Rowland & Wilson, 1994; Stacey, 1996; Streatfield, 2001; Strogatz, 2003) This special condition contains the simultaneous potential for continuity (identity) and transformation (Stacey, 2001), and, when a system is in it, outcomes can be dramatically affected by minor perturbations (e.g., Waldrop, 1992). It is where new order (knowledge, organizational capability) emerges (Morowitz, 2002), and it is thus an important point of leverage for evolutionary guidance (Banathy, 2000). However, given that situations are unique and outcomes are unpredictable, the homeopoietic approach involves sensitivity to local conditions and modest, indirect attempts to influence them, as opposed to general control and direction from a centralized source.

The implications for learning, teaching, and assisting with organizational change are numerous. Here I'll list some responses to Jan Visser's initial question to us: "What should one do in the learning environment to prepare people for life in an ambiguous world?" Taking a complexity perspective, one could:

A little ambiguity (not a lot) can go a long way (have a non-proportional outcome) in a positive direction (more probable through conscious intention), so we should look at it positively.

I hope these thoughts are useful to the group. I look forward to reading other contributions here on-line and regret being unable to attend the event.

References
Akin, O. (1994). Creativity in design. Performance Improvement Quarterly, 7(3), 9-21.

Banathy, B. H. (2000). Guided evolution of society. NY: Kluwer Academic.

Barabási, A. (2002). Linked: The new science of networks. Cambridge, MA: Perseus Publishing.

Capra, F. (2002). The hidden connections: Integrating the biological, cognitive, and social dimensions of life into a science of sustainability. NY: Doubleday.

Compact Oxford English Dictionary (2nd Ed.) (1991). Oxford: Clarendon Press.

Gell-Mann, M. (1994). The quark and the jaguar: Adventures in the simple and the complex. NY: W. H. Freeman and Company.

Morowitz, H. J. (2002). The emergence of everything. Oxford: Oxford University Press.

Nelson, H. G., & Stolterman, E. (2003). The design way: Intentional change in an unpredictable world. Englewood Cliffs, NJ: Educational Technology Publications.

Perry, D. L. (2002). Profound learning: Stories from museums. Educational Technology, 42(2), 21-25.

Rowland, G., & DiVasto, T. (2001). Instructional design and powerful learning. Performance Improvement Quarterly, 14(2), 7-36.

Rowland, G., Hetherington, J., & Raasch, J. (2002). The individualized nature of powerful learning experience. Educational Technology, 42(2), 26-30.

Rowland, G. (2003). Designing with: A homeopoietic ethic for organizational change. Draft of invited paper for special issue of Systems Research and Behavioral Science.

Rowland, G. (1992). What do instructional designers actually do? An initial investigation of expert practice. Performance Improvement Quarterly, 5(2), 65-86.

Rowland, G., & Wilson, G. F. (1994). Liminal states in designing. Performance Improvement Quarterly, 7(3), 30-45.

Shaw, P. (2002). Changing conversations in organizations: A complexity approach to change. London: Routledge.

Stacey, R. D. (1996). Complexity and creativity in organizations. San Francisco: Berrett-Koehler.

Stacey, R. D. (2001). Complex responsive processes in organizations: Learning and knowledge creation. London: Routledge.

Streatfield, P. J. (2001). The paradox of control in organizations. London: Routledge.

Strogatz, S. (2003). Sync: The emerging science of spontaneous order. NY: Hyperion.

Visser, J., & Visser, Y. (2000). The learning stories project. Retrieved May 22, 2003, from the World Wide Web: http://learndev.org/LearningStories.html

Waldrop, M. M. (1992). Complexity: The emerging science at the edge of order and chaos. NY: Touchstone.

Weick, K. E., & Sutcliffe, K. M. (2001). Managing the unexpected: Assuring high performance in an age of complexity. San Francisco: Jossey-Bass.

Wilson, B. G. (Ed.) (1996). Constructivist learning environments: Case studies in instructional design. Englewood Cliffs, NJ: Educational Technology Publications.

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Ambiguity and Teaching Economics

Gilbert S. Suzawa
University of Rhode Island

Abstract

This paper provides a discussion of the "full and proper sense" of the philosophical concept of ambiguity (uncertainty). It also provides a discussion of how the concept can help mold the practice of teaching college-level economics in an effective manner with some examples taken from the author's own teaching practices. Since the inquiry utilizes references from many disciplines and is quite holistic in nature, one could say that it is consistent with the mode of transdisciplinary thought as expounded by Basarab Nicolescu (2001).

Introduction

I once presented a paper entitled "Teaching Introductory Economics with Some Ambiguity" (2000) at a conference on teaching economics. One question raised in response to the title of the paper was: "Do we need more ambiguity in the way we teach economics?" Because the focus of my paper was on statistical assessment of the efficacy of what I was doing in my college-level course, my response to the question was to tersely say that the term "ambiguity" served as a "code word" for more of a constructivist's approach utilized in my course design and teaching conduct. In retrospect, I realized that there did not yet exist a strong association in most economists' mind between the word "ambiguity," in its lexical meaning of "uncertainty," and the nexus of teaching and learning based on a constructivist theory of knowledge. Thus some clarification of the "full and proper" sense of the concept of ambiguity and an elaboration of how it can influence our teaching practices were warranted.

1. The Different Senses of Ambiguity

Do I believe that we need more ambiguity in the way we teach economics? The answer is yes and no. It clearly depends on the sense in which the term is being used. In general, instructors of economics make extensive use of the blackboard and verbal explanations. This has been dubbed "chalk and talk." (Becker and Watts, 1996) Ambiguity can occur in the language that we use to teach. In semantics, ambiguity refers to a word, phrase, or sentence having more than one literal meaning. Consider the statement: "I'll give you a ring tomorrow." The sentence has more than one literal (lexical) meaning because a particular word in the sentence (i.e. a component) has more than one meaning. The word "ring" could refer to an engagement ring or to a call on the telephone. In this case, semantic over-determination prevails if only one meaning is intended. Some process of "disambiguation" would have to be undertaken to delineate the intended message. (Bach, 1994) In many cases, the context in which the statement is made would serve that purpose. If not, there are some formal techniques for disambiguation that can be applied. Over-determination is not intentional [except in cases were "strategic ambiguity" is being purposefully adhered to, see for example, D'Amato (1996)] and needs to be corrected. You might say that I made this kind of mistake in my use of the term "ambiguity" in the title of my conference paper with the assumption that the reader would interpret it as I did. I would say that we need less of this kind of semantic ambiguity in our teaching of economics.

Getting rid of unintentional ambiguities, however, is not an easy task. The process of expanding economic knowledge makes extensive use of metaphors. (Henderson, 1998) When metaphors are "alive," they surprise readers and listeners and are clearly understood in a non-literal manner. After awhile however, what was once a metaphoric use of a word becomes a literal use. Examples of "dead" metaphors abound in the discipline of economics, e.g. liquidity, elasticity, and depression. In this historical context, the problem of disambiguation is especially acute in introductory economics courses, as students may be more accustomed to a metaphor's original literal meaning and must now be somewhat indoctrinated to the word's technical meaning in economics. Dead metaphors certainty do not help students understand (learn) economic concepts and, pedagogically speaking, new (live) metaphors are generally required for this purpose. In a sense, metaphors are both a boon and a bane to professional economists. I would say that they are "delightful" when you are doing path-breaking research developing new concepts, but a "pain in the neck" (metaphor intended) when, as an educator, you have to help students understand existing economic concepts which are essentially enshrined in textbooks in the form of outdated metaphors.

Another kind of semantic ambiguity, which I believe we should have less of in the teaching of economics, is structural or logical, ambiguity. This sense of ambiguity relates to the manner in which language and mathematics can be (foundations) and are (applications) used in reasoning processes. Here we are dealing with the "chalk" aspect of teaching as well as the "talk" aspect. In language, a sentence or phrase can have more than one meaning not because any words in the expression has more than one meaning, but because of the structure, or arrangement, of words in the sentence (syntax) is ambiguous. A good example of this is the sentence: "Everybody loves somebody." There are at least two distinct propositions embodied in this sentence. One proposition is that each member of the group loves another member of the group. (The mapping is within the set.) The alternative proposition is that all members of the group love a particular member of another group. (The mapping is between sets.) Thus, when it comes to the matter of determining the truth or falsity of the sentence, which of the propositions are we supposed to evaluate? Is it the first or the second?

One can see that the above mentioned meaning of ambiguity implies "vagueness" in both symbolic and linguistic (logical) reasoning and is not generally considered desirable in teaching economics. [For a more comprehensive discussion regarding ambiguity and vagueness refer to Keefe and Smith (1996). Also, interested individuals may want to read Empson's (1947) exposition on (seven) types of ambiguities in literature.] Of course there are some exceptions to the rule here. From a pedagogical perspective, we may find it useful to employ examples of "bad" logic to teach "good" logic. In these instances, we are utilizing the concept of "fallacies" in our teaching. The teaching task here is to use someone else's fallacy as an example of what not to do, but not to unintentionally create an example of fallacy on your own. (This normative statement is biased towards the principle that you "ought" not to purposely distort the purity, or accuracy, of the information being transmitted to the pupils.)

2. Greek Philosophy and the Foundations of Western Logic

So far I have said "no" to the sense of ambiguity as semantic ambiguity, i.e. multiple meaning of words, phrases or sentences. When I say, "with some ambiguity," what sense of ambiguity do I want to infuse the teaching of economics with? The lexical meaning that I have in mind is "uncertainty." For the "full and proper sense" of this meaning of ambiguity, we need to explore the roots of our Western way of thinking--Greek philosophical thought. Greek philosophers grappled with three fundamental concepts of epistemology (and ontology): presupposition (necessity), ambiguity (possibility) and negation (impossibility). In one line of Greek philosophical inquiry (Protagorean doctrine, or commonly referred to as "sophistry"), the three epistemological concepts where considered to be completely autonomous, i.e. not reducible to any of the other two concepts. However, starting with Aristotle, presupposition and negation gained supremacy in Western logic and this perspective on logic has prevailed for over two millenia. Some very thought-provoking reinterpretation of Plato's dialogue entitled Theaetetus is shedding new insight on the Protagorean doctrine and how it relates to human knowledge. I am particularly influenced by Rosemary Desjardins' The Rational Enterprise: Logos in Plato's Theaetetus. In a chapter specifically entitled, "Ambiguity," she states:

The ostensible subject of the Theaetetus is introduced by what
must surely be one of the most lightheartedly ironic of all Plato's
understatements: "I am puzzled about one small matter…this is
what I am perplexed about and cannot fully grasp by my own efforts:
what knowledge is." To all appearances, the question is never answered.
In reality, so this study will argue, we are provided with a carefully
worked-out answer---an answer recognized as explicit, however,
only if the dialogue is taken self-referentially. [p. 15]

According to Desjardins, "…the cross-examination of Socates' dream points to the sense in which knowledge must be recognized, and actually achieved, as not only many but also 'one': an emergent whole born in generative interaction between its constituent elements." [p.163] In this "full and proper sense" of the word, ambiguity can be expressed as the paradoxical notion of unity and multiplicity, or nothing and something, and it is the self-referencing foundation of our knowledge.

Another interpretation of Plato's Theaetetus is provided by Ronald M. Polansky 1992). He claims that: " For Plato the Theaetetus is quite complete. It considers every promising account of knowledge, of ignorance, and of account, and even the most extreme options." [p.244] He further states that: "The commentary often resorted to deliberate ambiguity or different perspectives of the different interlocutors to explain how there might be several layers of meaning. Not only does this add to the comprehensiveness of the dialogue's treatment of its themes, but it also reconciles many disagreements of commentators." [p. 245]

Furthermore, if we utilize the refractive relationship (i.e. the subject-predicate perspective) between existence (being) and cognition (mind or consciousness), we find that we can relate "ambiguity" to "possibility" in their respective "full and proper" senses. Similar to Plato's examination of the multiple layers of knowledge in search of the ultimate foundation of knowledge (episteme), the late Italian philosopher by the name of Nicola Abbagnano searched for the proper sense of the word "possibility" as an essential foundation for his own "radical" existential philosophy. According to the American translator, Nino Langiulli (1992), Abbagnano's positive definition of possibility is "…that which can exist or [and] not exist and [which] obtain only as such." Another, somewhat negative, formulation of the third sense of possibility might be this: A possibility is neither that which is necessary nor that which is impossible." [p. 127] Thus, it would appear that Abbagnano affirmed the autonomy of possibility in the ontological sense. Possibility in this "proper sense" could be interpreted as the paradoxical "being and not being " or "becoming," i.e. "some degree of being and not being. This suggests the idea of a spectrum notion of existence. In metaphorical terms, everything is neither "black" nor "white," but a shade of "gray." Returning to epistemological terms, cognition would not be complete (i.e., as comprehensive or "full" as it possibly could be) unless it entails "black," "white" and all the shades of "gray" as well. Thus, restricting cognition to either black or white would constitute "incomplete" cognition as opposed to "complete' or "full" cognition.

According to physicist Basarab Nicolescu (2001), the logical system that has served as the foundation of virtually every scientific discipline's structure of inquiry up to now has been the logic of the "excluded middle." The proper ambiguity (possibility) concepts are essentially "ignored" in the axiomatic system that generates all of the logical structures that are used by the various scientific disciplines, including economics. The three postulates (axioms) of the prevailing logic are (1) The axiom of identity, i. e. A is A. (2) The axiom of non-contradiction, i.e. A is not non-A. and (3) The axiom of the excluded middle, i.e. There does not exists a term T such that T is both A and non-A or is not both A and non-A. With the third postulate of this prevailing axiomatic approach to scientific inquiry, there is no way of over-riding the mutually exclusive nature (either/or) of reasoning cognitively in any scientific discipline using this logical system. The alternative is to change postulate (3) to (3') The axiom of the included middle, i.e. There does exist a term T, etc. etc.

There is an old adage: "If it works, why fix it?" If the Old Logic has been so useful in assisting the various disciplinary sciences in increasing knowledge, why change the rules of inquiry at this juncture? But that's just it, the Old Logic is impeding progress in the scientific discipline of physics and a few other disciplines. Theoretical physicists are not making much progress in developing new knowledge of the physical universe beyond the level of what can be called quantum mechanics. In their concerted attempts to resolve the discontinuities that they have encountered in their endeavors to expand the knowledge of their field of inquiry, they (or at least some of them) have reached the point of seriously challenging the basic postulates of their science. Thus, the perception of the problem-solving utility of altering the third postulate of the Old Logic has gained momentum in theoretical physics. And some physicists have also become advocates for the "unification of (human) knowledge" under the rubric of the New Logic, i.e. the logical system with the "included middle." An example of this is the "transdisciplinary" category proposed by physicist Basarab Nicolescu (2001) that serves as an umbrella concept for an extensive range of holistic research endeavors. A couple of competing notions are "consilience" proposed by entomologist Edward O. Wilson (1998) and "beyond social constructivism" ("knowing of the third kind") as outlined by sociologist John Shotter (1999). For the purpose of this essay, I have chosen the phrase "transdisciplinary inquiry" to signify this "quest" for the generation of new knowledge.

3. Perspective of Complexity Theory

As an interesting historical example of how advancement in the knowledge of any one discipline occurs with some conceptual transfers from other disciplines is the case of the development of the concept (theory) of complexity. In the early 1960s, as a result of working on the problem of statistical estimation design with respect to time-series data on cotton prices the mathematician Benoit Mandelbrot (1963) introduced an interesting new idea, which is now commonly accepted under the rubric of complexity theory. Mandelbrot confronted a paradox in his research. The nature of the paradox is as follows: The science of statistical analysis conforms to the logic of the "excluded middle." Very briefly, this congruence between the science of statistical estimation and Old Logic is based on the theory of temporal convergence to some limit mean value (normal probability distribution). On this concept of limit mean value rested the truth or falsity of the underlying proposition. In other words, it may not be feasible to determine the truth or falsity of a proposition immediately (via deductive reasoning), but in the long-run one can infer (inductive reasoning) the proposition's truth or falsity. But this was all contingent on convergence to the limit mean value. What if convergence does not occur in the long run? Which is what was apparently the case in Mandelbrot's statistical analysis problem. Then one confronts a paradox or ambiguity (lack of certainty).

Mandelbrot's suggestion as to how this ambiguity could possibly be resolved is where the "transdisciplinary power" of the complexity idea lies. His reference to the possibility of deriving a second order set of laws via more powerful empirical techniques is the precursor of the notion of another physical "reality" for which these new laws would apply. Another way of putting the matter is that Mandelbrot was proposing a "radical" idea in applied empirical analysis, one that conflicted with the dominant classical logical system (Old Logic). One can also say that as a human being, Mandelbrot manifested a remarkably "positive attitude" towards ambiguity (uncertainty). By "embracing ambiguity," he has contributed to the restoring the appropriate role of ambiguity (along with presupposition and negation) in a New Logic. And this New Logic is beginning to have a pervasive impact on many scientific disciplines. [For this subsection, I have relied heavily on an essay by biologist G. Stent (1978).]

4. Disciplinary Convergence (The Unity of Knowledge Thesis)

The proliferation of notions like "transdisciplinary," "consilience" and "knowing of the third kind" is an indication that an amazing degree of disciplinary convergence is occurring in terms of the progress of human knowledge. Many intractable problems in various disciplines appear to be on the verge of yielding to the onslaught of an amalgamation of new, powerful ideas from across various disciplines, an example of which is the complexity concept (theory) discussed previously. This has engendered hope of the eventual unification of all human knowledge, which is now divided among many disciplinary domains. You can imagine this as a quest for the Grand Unification Theory of the Universe, where the comprehensive theory would be able to explain both the physical universe and the human mind. This is not as ephemeral an idea as one might think. For example, cognitive scientist George Lakoff and philosopher Mark Johnson (1999) have recently published a volume entitled, Philosophy in the Flesh, in which they propose and discuss the implications of the concept called the "embodied mind." Their work is an attempt to resolve the mind/body dichotomy that has long plagued philosophers and scientists. The central thesis of their inquiry is quite interesting. Basically, they argue that the refractive relationship that we discussed earlier with respect to Greek philosophical domains of ontology and epistemology is not as such, but is rather the complementary of body and mind. That is to say, they are proposing a theory of the unity of mind and body.

It is not my purpose in this essay to try and cover all the salient aspects of this "convergence of the disciplines" phenomena. However, germane to us in this essay is the feedback loop from new theories of the human mind to new psychological and cognitive science theories of knowledge creation (building) and learning. And from there to how these new theories of learning and knowledge creation can be applied in the practice of learning and teaching. The constructivist approach to learning and teaching is a vital part of this loop as far as I am concerned. Furthermore, it is my contention that the constructivist approach owes a lot to the re-integration of the Pre-Socratic concept of ambiguity into the analytical and affective thought processes of Western thinking.

5. Pedagogical Paradigms

Joseph Novak (1998) points out that every educational act consists of five elements: (1) learner, (2) teacher, (3) knowledge, (4) context, and (5) evaluation. We can construct concepts and theories for each one of these elements and for various sets of these elements. We also have the tendency to favor the application of certain concepts and theories over others, and are therefore categorized on the basis of schools of thought or pedagogical approaches relative to the five elements mentioned above. The distinction between a "constructivist" and a "connectionist" is such a categorical differentiation.

There is a propensity in our (ways of) thinking to treat the categories of constructivist and connectionist as mutually exclusive in nature, i.e. either one or the other. This can be attributed to the Old Logic that underlies most of our cognitive processes regarding the transmission, or exchange, of knowledge. In reality, "we are neither" and "we are both." How can this be (true)? The answer is ambiguity. We can conceive of ourselves as being a "spectrum" of the two categories. At any given moment in time I am more of a constructivist than a connectionist (or vice versa), and this degree will more likely change with the passage of time. However, many people are inclined to think of the categories as you are either a constructivist or a connectionist but not both. As the disciplines switch over from the Old Logic to the New Logic, this mode of thinking will become less and less prevalent. Thus, I use the phrase "with some ambiguity" as indicative of the spectrum property of ambiguity. No doubt, however, there are many people who would construe my usage of the phrase as an example of "vagueness being compounded by imprecision." In other words, the phrase represents an excellent example of "fallacy" in my reasoning (based on the Old Logic).

It is apparent to me that incorporating ambiguity into human thought processes implies that the human mind should have the widest possible perspective, or scope regarding the creation of knowledge and values (reasoning and judgements). This unrestricted mind, for example, can utilize dialogic thinking (Wells, 1997) as well as analytical thinking to create knowledge within the structure of the New Logic. From this new logical perspective, one mode of thinking does not have more legitimacy over any other mode. Again, we must not think in terms of "all or nothing." A mix of analytic and dialogic thinking may constitute an appropriate way to create and re-create (constructivist's view) economic knowledge. A concrete example of this in the field of teaching economics would be the design and implementation of a course entitled "Economics through Literature." Complemented with the "Mathematics for Economist" course, a student can then have access to economic knowledge via both analytic and dialogic reasoning and not be confined to either one or the other.

6. A Constructivist Theory of Knowledge (Transmission)

As I understand it, on the question of how new knowledge (invention) is constructed, there are no significant departures between the constructivist and connectionist theories. Innovative knowledge is created as a human response to some kind of complex challenge (problem) via some kind of creative and critical thinking (cognitive) process. The significant differences are in conjunction with the question of how this new knowledge can then be transferred from one person's mind to another person's mind, i.e. in explaining how the "inventor" goes about teaching someone else and how that someone else learns about the new idea (knowledge). The connectionist view is that the new knowledge then becomes meaningless information (data) that can be transmitted to another person's mind that would then process the data in some cognitive fashion to give it meaning.

The constuctivist's view on the other hand is that the new knowledge created in one person's mind must be reconstructed in some manner by another person's mind and the degree of reconstruction would most likely vary among different minds. An illustrative metaphor here is the "expert" and the "novice." Again, if we apply ambiguity, we can draw the perspective that in many practical instances, the learner is neither an expert nor a novice, but in a sense both. Thus there will be some variability in the degree of reconstruction relative to the learner's position on the scale between "expert" and "novice." We can use the concept of understanding to relate to this degree of reconstruction. Clearly, in this sense of understanding, the constructivist's statement, "teaching for understanding" (Mintzes, et al., 1998), requires some knowledge of where each student (learner) is on the "degree of reconstruction" scale and also knowledge regarding ways of advancing that learner to higher and higher levels.

An interesting question is: What would constitute understanding under the connectionist's conceptual framework? I will introduce two illustrative metaphors in order to try and answer this question. A well-known metaphor is that the teacher is the "transmitter" and the student is the "receiver." This comes from first generation information theory. Another metaphor that we could evoke relates to first generation sound reproduction technology. Knowledge can be conceived of as having a property of fidelity to it. The fidelity of sound (knowledge) reproduction would depend on the quality of the record (teacher) and the quality of the phonograph (student). The popular metaphor, of course, is the signal transmission metaphor. Under this metaphor, the quality of transmission is considered to be critical. Thus, in terms of this metaphor, understanding is related to the quality of transmission.

Under the second metaphor, the quality of both the recording and the quality of the playback device would determine the "fidelity of the sound." And understanding would relate to the "fidelity of knowledge reproduction" In both cases, understanding would be treated like a mutually exclusive concept. For example, as a teacher you are a bad transmitter of knowledge and therefore your students do not understand. We can evoke the memorable one-liner from the movie Cool Hand Luke: "What we have here is a failure to communicate." There is a difference in nuance, however, between our two metaphors. Under the first metaphor, the teacher is held responsible for the failure. Under the second metaphor, there is leeway for both the teacher and students to share the burden of blame. Consequently, a situation of blame shifting (strategic game) could ensue as a consequence of imposing an external assessment framework on education if one adheres to the latter metaphor.

Since (disciplinary) knowledge is the content of what is, for the most part, taught and learned at colleges and universities, how one conceives of knowledge building and exchange will have a significant impact on one's conception of the context of college-level teaching and learning. The connectionist theory of knowledge exchange conveys the impressions (1) that learning is "passive" while teaching is "active" and (2) that the educational act is a unilateral type of exercise, i.e. the teacher does not have to learn and the students do not have to teach. On the other hand, the constructivist theory of knowledge exchange conveys the impression (1) that both teaching and learning are active endeavors and (2) that the teacher learns as well as teach and the students teach as well as learn. Based on these impressionistic differences, the constructivist approach is distinguished as the "active learning" model (implying that both teacher and students are active learners and the connectionist approach as the "passive learning" model. Even from the constructivist's perspective, I would say that the theory of learning is currently a very "under-nourished" domain of educational inquiry relative to the theory of teaching.

7. Teaching Introductory Economics with Some Ambiguity

In a published paper, Allison King (1993) introduced the two catchy phrases: "sage on the stage" and "guide on the side." These phrases have now become living metaphors for the passive learning and the active learning models respectively. The metaphors have served a useful purpose in terms of galvanizing some change in teaching practices. However, in terms of our "deep" notion of ambiguity, the metaphors are too restrictive. The restrictive features of the metaphors are the spatial references to "stage" and "side." These terms anchor the passive learning and active learning distinctions to a strictly "either/or" pattern of thinking. In other words, How can a professor be up front on the 8stage and be at each student's side (in the audience) at the same time? Impossible is it? The only apparent way to reconcile this spatial constraint is to have a small group production (actor among the audience). It follows then that an active learning course design must pertain to small size classes and a passive learning course design must pertain to large size classes. This seems to be a popular precept among educational administrators.

Personally, I believe that active learning on the part of both instructor and students is possible (and does in fact exist in varying degrees) in a large size class environment as well. This belief, however, is not consistent with the mutually exclusive nature (Old Logic) of the above mentioned metaphors. You can consider this to be the "complex" pedagogical paradox that I have been working on for more than a decade. My current course syllabus indicates that I teach introductory economics (Principles of Economics) with some emphasis on critical and creative thinking. As far as the course context is concerned, I place more emphasis on skills like being able: to solve open-ended and closed-ended problems, to juxtapose ideas from across different disciplines and to clear written exposition; and tend to minimize skills like being able: to take accurate class notes, to memorize the definitions in the textbook and to learn by doing well-structured exercises. But how do you do you effectively accomplish this in the context of very large size classes that many of us must teach due to budgetary constraints at public universities?

In my role as an instructor of introductory economics, I learn in several sorts of ways. I try to learn as much as I can about the students' level of expertise in the economics domain in order to help them out in terms of increasing their individual levels of understanding. (I've noticed a great deal of heterogeneity on the "entry" level economics courses and this makes it quite difficult to foster a "master" and "apprentice" kind of relationship because many students are at the "novice" end of the spectrum.) I'm also humble enough to recognize that I am a "dummy" in some domains, like computer programming for example, such that I could learn from a student who may be more proficient in that domain then I am. (This has the potential for blossoming into a student-faculty collaborative research endeavor or even into a student-tutoring-other-students-because-the-teacher-is-a-"dummy" kind of tutorial endeavor.) My wife and I have raised three daughters and in the process of doing so, I have been able to transfer some learning from that domain (parenting) to my professional teaching domain, e.g. some added insight regarding what young adults conceive as being vital to their existence. This is quite different from the relevancy notion that most of us have as instructors of economics. Knowing what is vital to a student helps me to craft a learning environment, which assists the students to determine for themselves, their relationship is to the "real world." Thus, I think of "vitality" and "relevancy" as complementary notions when it comes to the meaning of learning

From the students' perspective, my course requirements include homework assignments where students must grapple with open-ended analytical problems as well as closed-ended problems and must express written opinions regarding current human affairs (open-ended essay questions) utilizing economic concepts and models. I do not have any extensive evidence, but I strongly suspect that during the week that students have to solve the problems and respond to the essay questions presented in the their homework assignment, they participate in some kind of student-to-student "teaching" outside of the classroom. In this context, student diversity is a "plus" when it comes to solving the open-ended type of problems and responding to the open-ended questions that I intellectually challenged them with. Just as an aside here, I recently had the opportunity to read the brief volume by Richard J. Light (2001) and was delighted to come across a sub-section entitled "Powerful Homework Assignments" (pp. 50-54). According to Light, a question that was asked of graduating seniors in their study was: "Which courses had the biggest impact on your learning, why was this impact so big, and exactly how were these courses structured." In his words: "The results were eye-opening. … The design of homework really matters. … Specifically, those student who study outside of class in small study groups of four to six, even just once a week, benefit enormously."

So back to the issue of whether or not my introductory economics course is one based on the "active learning" model or the "passive learning" model? As you can see, it has many features that would qualify as an "active learning" type of course, with the exception that it is taught in the context of a large size class. Based on the mutually exclusive categorical distinction previously mentioned, my course is not an "active learning" course, it just can't be so. I think that it is really time for us to change some of our popular teaching metaphors.

8. Ambiguity and Creative Ideas in the Classroom

I believe that I have recently "discovered" an innovative teaching device (technique) for fostering "active learning" in a large size class setting. Basically it entails the juxtaposition of two other apparently effective techniques used in teaching: (1) "thinking aloud" (Bloom and Broder, 1950) and the "one-minute paragraph" (Cross and Angelo, 1993). In my view, a beneficial aspect of the "thinking aloud" technique is that it permits the exchange of ideas and strategies as a person is in the process of trying to solve a difficult problem. Thus, the problem can be attacked dialogically (group interaction). In my opinion, a crucial advantage of the "one-minute paragraph" lies with efficiency as a way to collect vital information in a short period of time from a large number of people. A disadvantage of "thinking aloud" in a large size class environment is the high level of "noise" attributable to that particular mode of communication (difficulty of discerning meaningful patterns). (Perhaps you can remember the admonition of one of your elementary school teachers when she said, "Let's not all speak at once." when pupils were asked to express their thoughts on something?) In a small size class setting, the written mode ("poetic") of communication is redundant as long as the level of "noise" is not too high. In addition, you would lose some degree of spontaneity when you resort to written communication.

On the basis of the above cognitive assessment of the two popular devices, suppose we juxtapose the two known devices and invent the "thinking poetically" device specifically geared for use in the large size class. There is a long-standing adage, "Necessity is the mother of invention." On the basis of my own teaching experience, there is "some validity" (New Logic) to that statement. If we expand from our teaching of economics domain to the wider professional domain, I believe that most economists would agree with me that we utilize both the "thinking aloud" and "thinking poetically" techniques in our research endeavors. (Have you e-mailed your "thoughts" on some "complex problem" to a group of colleagues recently?) Thus, it is only in the narrower context of teaching economics that "thinking poetically" can be construed as an innovation in our profession. The inspiration for a teaching innovation could have been a realization that a research technique could possibly be adapted to serve as a teaching technique (i.e. transfer of ideas). But that was not the case in this instance. Nevertheless, I believe that as we keep on embracing ambiguity, we will tend to blend our theoretical and applied knowledge with our teaching practices.

9. The Teaching Device I Call "A Hill Climbing Exercise"

The reference " A Hill Climbing Exercise" is inspired by a comment made by Nobel Laureate economist, Kenneth J. Arrow, in an interview published in The Region (1995). One question he is asked: "For the past decade you have been involved with the Santa Fe Institute, where there have been collaborative efforts between economists and physical scientists. Do you feel that theses interactions have proven to be fruitful?" In response, Arrow says: "I think one of the things we learned from the physicists and also the theoretical biologists is the idea that when you're dealing with very complex systems you're going to get a large variety of behavior which can be interpreted as hill climbing, but hill climbing with a lot of modifications, hill climbing with big jumps occasionally. This is an elaboration of the idea of the learning model." [Italics mine] While Arrow used "hill climbing" as a metaphor for learning, I have literally devised an intellectual "hill climbing" exercise to help my students develop critical and creative problem-solving skills in order to prepare for the uncertain "real world" that they must confront when they graduate from college.

About two weeks before we cover the topic of profit maximization in reference to the economic model of business enterprise, I have student do the hill climbing exercise. Students are presented with the task (goal) of climbing to the top of a hill at night with nothing to assist them except for a lantern. They are allowed five-minutes to write out how they would go about solving the problem. I do not place any constraints regarding what "strategy" they devise to solve the problem. From an incentive perspective, I have done two versions. One with no external incentive other than each student's propensity to solve intellectual problems (puzzles) and another where I offer to provide a reward to any student who devises a strategy that will enable him or her to get to the top of the hill first (competition). The submitted results were then screened and within a week's time returned to all students in the form of some of their suggestions organized on the basis of categories of "methods and strategies". [An example of this kind of summary is provided in the Appendix to this paper.]

Subsequently, I (the teacher) made no judgement statements regarding what is "the right or recommended way" to solve the problem, but rather repeated the question about how they would go about solving the problem after they have had the access to suggests made by some of their fellow classmates. The second time around, the question was rhetorical rather than a written exercise. Again, I made no statement regarding the "right way" to solve the problem. In other words, they were left to reflect on the problem and to ultimately make their (learner's) own critical judgements regarding the matter of how "successful" they were in solving the "hill climbing" problem. Did the students pursue the problem further? I don't really know for sure if they did or did not. I presume that some did and some didn't (varying degrees) depending on how "vital" they thought the problem was, i.e. how important it was for each of them in terms of "self-realization." From my teaching perspective, the goal of the classroom exercise was not to devise a solution, but rather to get the students to think critically and creatively about an unstructured problem using all available resources, including the knowledge possessed by their classmates

As it turns out, when it came time to help students understand the profit-maximization principle discussed in the textbook, I could resort to the hill climbing exercise, at least some aspect of it, as a way of demonstrating the problem-solving capabilities of marginal analysis. I pointed out that solving the hill climbing exercise during the daytime is quite different than solving the problem during the night (assuming no full moon). During the daytime, the problem is "simple." With visibility, you can generate an overabundance in information by which you can solve the problem. However at night with only a lantern, you have limited visibility, or just information about the local terrain, the problem is more "complex." Thus, is seems rational that one would want to devise some kind of effective method of achieving the goal of getting to the "top of the hill." I then demonstrate that the condition: Marginal Revenue - Marginal Cost = Marginal Profit is analogous to the slope (gradient) of a hill (total profit curve). If we follow the rule of always moving "up hill" until the slope becomes "flat," we will have achieved the goal of getting to the top of the hill. This would be a very "cost effective" method of solving the complex problem because to the limited amount of information that would be required to solve the problem. Thus, there was an important "content" lesson in the hill climbing exercise, although it was not specifically designed to serve such a purpose.

Returning to Allison King's (1993) metaphors regarding "active" and "passive" learning, one can readily see that in the teaching context of my hill climbing exercise, I was in effect a "guide," but I was not necessarily at each student's "side" spatially speaking. Perhaps, one can more accurately say that I was a "guide along for the ride" (i.e., on the road of each student's life). I prefer the word "ride" in the sense of "ride a vehicle" because it has a "dynamic" connotation. Whereas, the word "side," in its "spatial" sense, is "static" in orientation.

Conclusion

In concluding this paper on ambiguity and teaching economics, I would like to refer readers to an article entitled, "How Students Learn," written by Ellen J. Langer (1987). Langer is a social psychologist who has developed a theory of learning based on what she calls the concepts of "mindlessness" and "mindfulness." Her approach to learning is clearly an alternative way to conceptually distinguishing between "passive" and "active" learning than the way that distinction has been presented in this paper. And as such, her article warrants some attention on the part of readers who have found the present paper interesting and of some value in course design. In fact, she uses statements very similar to those that I have used. For example, she says, "Built into a notion of a theory, model, or hypothesis is some uncertainty." [Italics mine]. Although she employs the term "uncertainty," I believe that what she has in mind is the sense of "some ambiguity" that I have been expounding on in this paper.

I was so taken in by the story that Langer presents at the end of her article. As my parting words, allow me to just repeat that story:

There is an illustrative story about a woman who was seen preparing dinner. She had a roast beef and she took off a large slice of it before cooking it. When asked why she did this she said, "Well that's what my mother always did." So, the observer sought out her mother and asked, "Why do you cut off a large slice of roast bee before you cook it?" Her mother said, "Because that's what my mother always did." The observer finally found the original woman's grandmother and asked, "Why do you always slice a large piece of roast beef off before you cook it?" She replied, "That's the only way it will fit in the pot." The point of this story is that when we originally learn something there may be a reason for it that makes sense in that context at that time. What we want to do is to give our students information so that as the context changes, that information will still be of use to them. Otherwise we're all wasting a great deal of roast beef.

References

Arrow, K. J. (1995). Interview published in The Region, 9.

Bach, K. (1994). Conversational impliciture. Mind & Language, 9, 124-162.

Becker, W. E. and Watts, M. (1996). Chalk and talk: A national survey on teaching undergraduate economics. American Economic Review, Papers and Proceedings, 86, 448-53.

Bloom, B. S. and Broder, L. J. (1950). Problem solving processes of college students. Chicago: University of Chicago Press.

Cross, K. P., & Angelo, T. A. (1993). Classroom assessment techniques: A handbook for college faculty, 2nd edition. San Francisco: Jossey-Bass.

D'Amato, A. (1996). Purposeful Ambiguity as International Legal Strategy: The Two China Problem. I. J. Makarczyk (ed.) The theory of international law at the threshold of the 21st century: Essays in honor of Krzysztof Skubiszewski, pp. 109-121.

Desjardins, R. (1990). The rational enterprise: Logos in Plato's Theaetetus. Albany, NY: State University of New York Press.

Empson, W. (1947). 7 Types of Ambiguity. New York: New Directions.

Henderson, W. (1998). Metaphors. In J. Davis, W. Hands, & U. Mki (Eds), Handbook of Economic Methodology. London: Edward Elgar Publishing.

Keefe, R., & Smith, P. (1996). Vagueness: A reader. Boston: The MIT Press.

King, A. (1993). From sage on the stage to guide on the side. College Teaching, 41, 30-35.

Lakoff, G., & Johnson, M. (1999). Philosophy of the flesh: The embodied mind and its challenge to western thought. New York: Basic Books.

Langer, Ellen J. (1987). How students learn. On Teaching and Learning, 2, 5-9.

Languilli, N. (1992). Possibility, necessity, and existence. Philadelphia: Temple University Press.

Light, R. J. (2001). Making the most of college: Students speak their minds. Cambridge, MA: Harvard University Press.

Mandelbrot, Benoit (1963). New methods in statistical economics. Journal of Political Economy 71, 421-440.

Mintzes, J. J., Wandersee, J. H., & Novak, J. D. (Eds.) (1998). Teaching science for understanding: A human constructivist view. San Diego, CA: Academic Press.

Nicolescu, Basarab (2001). Manifesto of Transdciplinarity, Suny Series in Western Esoteric Traditions. State University of New York Press.

Novak, J. D. (1998). Learning, creating, and using knowledge. Mahwah, NJ: Lawrence Erlbaum Associates.

Polansky, R. M. (1992). Philosophy and knowledge: A commentary on Plato's Theaetetus. London: Associated University Presses.

Shotter, J. (1999). At the boundaries of being: Re-figuring intellectual life. Plenary address (first draft) given at Social Construction and Relational Practices Conference held at University of New Hampshire, September 16-19, 1999.

Stent, G. S. (1978). The end of arts and sciences. In Paradoxes of Progress. San Francisco: W. H. Freeman and Company, pp.35-59.

Suzawa, G. S. (2000). Teaching introductory economics with some ambiguity. Paper presented at the 11th Annual Conference on Teaching Economics held at Robert Morris College, February 17-19, 2000. Published in Papers and Proceedings, pp. 233-245.

Wells, G. (1997). Dialogic inquiry in education: Building on the legacy of Vygotsky. Based on invited presentation at the Annual Conference of the National Council of Teachers of English, (Detroit, MI), November 1997.

Wilson, E. O. (1998). Consilience: The Unity of Knowledge. New York: Alfred A. Knopf.

APPENDIX

"HILL CLIMBING" EXERCISE: FIND YOUR WAY TO THE TOP OF A HILL AT NIGHT WHEN IT IS PITCH BLACK AND YOU HAVE ONLY A LANTERN TO HELP YOU ACHIEVE THAT GOAL
(Administered during spring, 2001 semester. Selected responses from a sample size of seventy-five.)

THE HIT OR MISS METHOD

I would have to just pick one direction to travel in and hope that it is the right way. If I heard some cheering because they found the hill, I would run as fast as I could to try to beat them to the top. C. B.

I can't think of any logical way to find the hill so I guess I would just walk in a circle just expanding the radius, which would cover the most ground. Then when the ground started to slope upward, that would be where the hill is. One other way would be to pick one direction and hope for the best. E. H.

THE GRADIENT (SLOPE) METHOD

First hold the lantern as high in the air as possible. Then, look at the grade and varying inclinations of the earth. Follow the area of highest inclination. If that is the wrong path, hold up the lantern again and follow the shadows. Usually most people have common sense and direction in order to make it to the top. Know where you are while walking, if you are moving down, turn around and start moving up. Follow your senses. M. L.

If its pitch black outside and all I have is a lantern for short-rage sight, at least I can see the area around me. I can use the knowledge of the slope of the hill immediately around me to guess where the hill rises and falls. As long as I only walk on ground that is sloping upward, I must be getting higher up on the hill. Also, I can see light from others' lanterns, and use that knowledge to determine if I am on the common/right track. M. K.

Using the lantern, search the area for where the ground rises. Follow the rise until you reach the point where it cannot rise anymore, it only leads downhill in each direction. That is the top of the hill. M. R.

Walk up hill using lantern, always walk towards the highest part of the ground that you can see with the lantern. Eventually, you will get to the top of the hill. Of course, you may not know what direction to start in. K. B.

SOME SEARCH STRATEGIES

I would use the lantern as a focal point. I would place it in the center of the field and walk the largest circle around it. If I didn't find the hill right away, I would move it and start again, repeating the large arcs until I felt an incline, thereby locating the hill. I would then walk a straight line back to the lantern, retrieve it, walk back to the hill and climb to the top. E. C.

If the hill could be in any direction from me, I would walk straight a certain distance, then walk around in a circle, staying the same distance from where I started. If I did not find it, I would walk out farther, and then walk another circle. I would repeat this until found the hill. I would form a bull's eye with this walking pattern. J. G.

Depending on the size of the field, I would walk in a grid formation so that I have covered the entire field by foot. I would soon see an incline some where within my journey and then run up the hill. B. W. Ex.

MAGNIFICATION OF TOOL STRATEGY

Climb a tree and use the lantern to see where the mountain is, then when you find it, head that way. L. T.

I would walk in the direction where the land has an upward slope at all times and hope for the best. I could also make a bigger, better lantern by making a fire, allowing me to be able to see further. J. G.

Personally, I would set the grass on fire so I could see everything. But this method would probably burn me alive and create other problems. So I guess I would start walking until I started going up. And if there were other people out there then I would watch them. If I saw someone at a higher elevation than me, I would run towards them (they are obviously on the hill) and push them out of the way (not really, that would be mean). A. W.

Set fire to all the bushes around you. This causes the whole area to light up. Follow the uphill slants to the top of the hill. Still carry the lantern around for extra shadows. Watch out for the snakes! They don't like fire and will probably be scared, slithering around. G. T.

INVENT A TOOL STRATEGY

I would yell at the top of my lungs and listen for where my echo returns from. Wherever I heard my voice in reply would be the direction that I would head in. A. B.

"LET THE OTHERS DO THE WORK" STRATEGY

If there were many other people looking for the hill with lanterns-I would wait until I saw one getting up an incline and then start up the incline in his/her direction. Either that or I would start looking for it myself. I would use the lantern to see as far as I could in each direction until I spotted it. E. R.

I would drop my lantern and let the light from everyone else's torches show the path, since I won't have a lantern I'll be able to run much faster. Although I won't be able to get too far ahead of the pack, I should get there first. A. C

SMART-ALEX'S STRATEGY

I would take a helicopter to the top of the hill. NO NAME

I would switch everybody's batteries with inferior Radio Shack ones before the competition, that way they would all die halfway up the mountain [I hope that this refers to batteries and not the other students] while I use Duracell batteries all the way up. B. F.

I would wait until daytime and then climb up. That way I could see a little better. S. J.

MULTI-STRATEGY PROGRAM

To find the hill I would walk around until I was increasing in elevation. I could also wait until the moon came out and use this light to guide me. I could also look for an increase in height of trees which might indicate that they were growing on the side of a hill. If I was to scream and there was an echo, I could listen to where the sound was bouncing off of, this would indicate the face of a hill, or cliff, or wall. B. W.

If I was in the middle of a countryside and it was pitch black an I had a lantern & 2 hours to get to the top of a hill that was 2,250 ft. high, the first thing would be to locate which direction the hill was. You could do this in a couple (of) ways. First, shine the light. If you couldn't tell by this, you could try screaming. You could tell where the hill was by how your voice echoes. Of if it had been raining the day before, or on a day like today where there was snow, but now it has melted, the base of the hill would be soggy or soggier than the rest of the ground. After you have located the hill, just use the light to guide you to the top so you don't trip. All you have to do to get to the to is keep walking up! C. G.

COOPERATIVE OR TEAMWORK STRATEGY

I will find someone to work with. We will have 2 lanterns which, together, will produce a larger spectrum of light so we could see better and farther. With our efforts joined, we could climb to the top of the hill safely and quickly. K. S.

I would think that it would be most effective to set up an organized group of people to attempt this and share any potential prize. People could set up a chain of flashlights with the next person being just beyond the reach of the person behind. This would be safer than going alone, as it leaves the hill illuminated all the way up. This would, however, have some people walking further up than others. If the line of people is assembled and does not yet reach the top, then the person farthest back would walk to the front to extend the chain up. This could be done until the top is reached. E. W.

I would suggest that each member of the group form teams and head out in a different direction to find the beginning of the slope of the hill. Once we see a difference in the elevation of the lantern, then get everyone to go in that direction. Since the lanterns are not that bright, you would need to form relays of teams to ascend the hill. D. B.

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Science and Ambiguity
Have we thrown the key away?
 
Jan Visser
Learning Development Institute
 

A mathematician is bound to be horrified by my mathematical comments,
since he has not always been trained to avoid indulging in thoughts and
doubts of the kind I develop. He has learned to regard them as something
contemptible and, to use an analogy from psycho-analysis (this paragraph is
reminiscent of Freud), he has acquired a revulsion from them as infantile.
That is to say, I trot out all the problems that a child learning
arithmetic, etc., finds difficult, the problems that education represses
without solving, I say to those repressed doubts: you are quite correct, go
on asking, demand clarification...

Wittgenstein, Philosophical Grammer, no.25, pp.381-.382 [1]

This brief essay is inspired by the words of a five years old child. In response to a remark by her mother that she was smart, she reflected: "My mind is full of brains." Actually, she had just entered kindergarten, where each child was told to be starting off with five stars for good conduct. Asked how she would retain her five-star status, she said: "You sit crisscross apple sauce. You put your hands in your lap. You zip your mouth, you throw the key away, and you don't ask any questions."

An interesting detail is that the kindergarten in question is part of a university research school. Future researchers are initiated in the practice of exploring human learning in children who have already been conditioned to keep their mouth shut and not to ask any questions. Such researchers may themselves be the product of similar conditioning processes. In fact, we are all the products of processes that have shaped our minds during a life's history that we may have difficulty tracing back to our early childhood years. Whatever we do to develop the capacity of our brains to help us know the world and contribute to knowing it better, it will be both inspired and hampered by how the cell circuitry of our brains has been configured and reconfigured over time to reflect the ever-changing totality of our life experience. In other words, we see the world through the eyes of who we are with a level of openness that should probably be seen to reflect the degree to which we perceive of ourselves as not merely being but also becoming.

I write these words as I currently live again in Africa, reliving memories of some twenty years spent during earlier periods of my life in this very continent. Yet, I'm not an African. I grew up in Europe. My childhood years coincided with one of the major crimes in human history: the industrialization of the killing of humans by humans during the second World War. Enough for a child to reflect on - in a child's way - and to come to the conclusion that there is more beauty in the physical world than there is in humanity. I became a physicist with a strong inclination to stay as far away from the dealings of humans as I could. Of course, I was wrong and would soon discover that beauty is a human experience, that physics is a human invention, and that doing physics is the business of a subset of humanity. There was no world of physics separate from the world of physicists. To heighten the level of my confusion, I also had to realize that some of the scientists I most admired for their extraordinary achievements had made their contributions - on either side of the divide of the same war time period that served as the setting for my childhood years - to projects that deliberately enhanced the destructive capacity of humankind. Having the privilege of hindsight, I could look upon those physicists as models for what I wanted to achieve as a scientist while at the same time questioning the wisdom of their decisions regarding what to work for. Would I have done the same had I been in their position and work, for instance, towards the building of a nuclear bomb? I certainly don't exclude the possibility. I fully understand the excitement that comes from facing the most fundamental questions regarding what we don't know. Being allowed to play with such fire, even with the prospect that it might destroy us, could well have enticed me to do exactly as they did. My appreciation of ambiguity was born.

Everyone has his or her stories of discovering ambiguity. I certainly could tell quite a few more. The ones that I lived through can be divided into two categories, those that represent ambiguity caused by holding simultaneously different worldviews that cannot be reconciled with each other, and those that can be characterized by my choosing to follow a particular course of action that would be at odds with what would logically follow from everything else I had done before. I don't think my case is unique. In fact, I believe that most people come to grips - to a greater or lesser extent - with ambiguity in their lives. My contention here is that a healthy dose of ambiguity is good for us at the level of personal development and that it is essential for the advancement of humanity. Hence, ambiguity should be embraced, rather than banned.

In what follows I explore this issue through a reflection on what it means to know and how we advance knowledge. Having no access at the place where I write to a library of any significant extent and only limited access to the Internet, I base myself on memory, arguing, as I did above, from personal experience as well as from my observation of other people's experience.

Some twenty years ago, I was training secondary school physics teachers in Africa. A European, who has grown up with scientific explanations of natural phenomena since early childhood, feels comfortable in a world that can be interpreted in terms of the familiar scientific principles. Trying to familiarize members of an entirely different culture, where people grow up with a dissimilar set of stories that make them feel at home in their particular environment, poses a problem. One of those stories is that lightning is a bird that lays eggs. The alternative explanation of lightning as an electrical phenomenon will, of course, be duly accepted by intelligent students. However, it won't easily replace the story of the bird, which is well embedded within the local culture. For that to happen, a major shift of not just one, but of an interconnected whole of beliefs would have to take place. So, the story of the bird, and the story of lightning as an electrical phenomenon, will co-exist. The realization that such would be the case led me to two considerations, the first one that science is a story, a beautiful story with a powerful logic that opens exciting vistas of wholeness and beauty, the second one that other stories have an equal right to exist and can be similarly mesmerizing. I adapted my teaching accordingly, devising simple experiments that allowed students to discover for themselves the principles of storytelling that are typical for the scientific worldview while leaving it to them to choose, in any particular circumstance, to look at the world from whichever perspective they would find most appealing, avoiding to declare one perspective right and the other one wrong.

Did I mislead my students while suggesting to them that science is one of various possible stories? Did I do a disservice to the pupils that my students would later on be teaching themselves, whom they might offer to live with a similar set of incompatible choices, thus nurturing in them an appreciation of ambiguity, leaving the world unexplained to them in terms of merely one monolithic vision? I don't think so. And I don't think either that it would have been necessary to go to Africa to discover the things I mentioned above. As we live in a world in which diverse cultures must be allowed to co-exist, diversity being such an essential condition for humankind's development, we must accept that there will also be cultural ambiguity (Ngoenha, 1995) and prepare ourselves for the challenge to live with it.

Science, of course, is not a Western invention. The first recorded history of the development of scientific thought dates back to the early civilization of Mesopotamia, thousands of years ago. The development of mathematical thinking owes much to the Islamic world. Nonetheless, scientific development over the past couple of centuries has been a mainstay of Western culture. Particularly during the last century many scientific developments have become dependent on large scale funding, thus linking them to interests of the economically dominant part of the world, i.e. mostly Western nations. This has unfortunately created the impression among some that the mindset that is associated with science is somehow a feature of Western culture, that culture being seen as one that is based on the pursuit of utilitarian goals that are devoid of higher values, particularly lacking a sense of consciousness that can possibly be best described as religious (I am referring here to religion in the true sense of the Latin verb reliare, i.e. as the expression of a feeling of belonging and thus representing an elevated level of consciousness about one's responsibilities vis-à-vis humanity and the world at large).

The dictum that knowledge and values should not be mixed in science is a relatively recent invention. It dates back to the hardly constructive clash in the 19th century between representatives of institutionalized religion and advocates of a rationalistic scientific worldview, particularly centered around questions regarding the origin of life and the universe. The stories of science and religion are incompatible concerning these issues. Even though they use some of the same words, they are different in terms of the overall language, or shall we say the images, they use. What one story is able to account for, the other one isn't. The fact that this is so, calls attention to a notion of inevitability of ambiguity as we interact with the world around us at different levels (not to be seen as hierarchically arranged), using different languages to reflect on and within such interactions and to engage in mental operations to structure them. As an example, I can, at one moment, be thrilled by the beauty of the universe as expressed in the mathematical equations that describe how it all seems to hang together. At another moment, a poem might make me aware of the awful reality of us, a species that has evolved to the level of becoming conscious of itself, to hang out in that same vastness that will eventually, as Eliot (1925) suggests, end in a whimper. At yet another moment I may find consolation in a religious notion that connects me up with all other members of my species - past, present and future - who find themselves equally challenged by the search for meaning while trying to locate themselves within that seeming emptiness.

In a discussion of the science of the end of the universe, Dyson (1979) refers to how frequently the process of constructing new knowledge is hampered by our hesitance to ask questions to which the answer can only be given in uncertain terms. However, says Dyson: "If our analysis of the long-range future leads us to raise questions related to the ultimate meaning and purpose of life, then let us examine these questions boldly and without embarrassment. If our answers to these questions are naive and preliminary, so much the better for the continued vitality of our science" (p. 447). Expressing himself in this way, Dyson mixes knowledge and values. He does so consciously, though, picking up the thread of a tradition of thinking and expressing oneself about the universe in ways that were still common among scientists in the eighteenth century, but that have since fallen into disrepute. It is high time that we come to our senses and rekindle the faculty to live, think and feel in accordance with our ability to interact with the world around us at multiple levels, employing different languages, at times rigorously separating one from the other for analytical purposes while at other times allowing ourselves, as does Dyson, to mix them up in order to get a more complete understanding, even though such understanding may seem fuzzy from a logical analytical point of view.

Some of the major implications of my above considerations for what we should do in terms of designing planned procedures and environments for the facilitation of human learning in the context of education and training are explained below. The five areas specified below are not separate. They interact and reinforce each other mutually.

1) We should cautiously reconsider the wisdom of our field to design instruction including no more than the absolutely necessary for the attainment of a particular learning objective. Perhaps what I am trying to assert here could be better formulated by saying that we should, when thinking about what learning objectives should be satisfied through our instructional procedures, take a more complete look at the human beings whose learning needs we serve, rather than being driven solely by the desire to install specific competencies. We should then not be afraid to attend not only to those learning needs that can be easily expressed in neatly formulated objectives, but include in our considerations also those areas for which we can only hesitatingly find inadequate (from an instructional design perspective) formulations. Necessarily, the ensuing instructional practice may equally reflect our hesitations but, if I may echo Dyson's (1979) words quoted earlier, let us do so boldly and without embarrassment, keeping our eye focused on the continued vitality of our field in a world whose problems are different from those when the foundations of that field were laid. The issue of taking a broader look at human beings, beyond the realm of their spectrum of competencies and their usefulness for well defined areas of activity, can also be expressed as a need to find a more adequate balance between the development of competencies and the development of mind (Visser, 2002).

2) Broad frameworks for value-based contemplation of human behavior have over the past half century gradually disappeared or diminished in importance, at least in Western society and those societies influenced by it. However, having such ethical and aesthetical frameworks present again will be beneficial to broadening the interest of learning to beyond the scope of the immediate. Let me immediately clarify that I would not like such frameworks to come back in the form in which they often used to function, as sets of rules to keep human behavior within rather strict bounds of the acceptable, but as contexts for reflection and dialogue regarding what should guide our behavior as the parameters of that discussion change all the time. That will in turn provide a basis for the development of thought that brings what may seem exciting from the perspective of knowledge development in a particular discipline within the purview of more comprehensive considerations. Such considerations may lead to conclude that what is good and beautiful from one point of view does not necessarily have the same qualities from another standpoint. A developing human being will be well served by a proper dose of such ambiguity, particularly as wise decisions regarding what to promote in the development of human ingenuity will increasingly call for the capacity to evaluate that question taking ethical and aesthetical issues into account.

3) The issue of appreciation of ambiguity also seems closely related to our ability to problematize our environment, i.e. to interpret the world around us in terms of challenges for which answers still have to be found. Most of the established educational practice deals with questions as opportunities for practice in areas in which the answers are already known. Those questions are typically not the ones one meets in real life. Important contributions to increasing the depth of learning to the extent that ambiguity becomes visible can be derived from bringing to within the horizon of the learner questions that have not yet been solved, thus diminishing the expectation that such questions need necessarily lead to clear-cut answers before the bell rings and the lesson is over. While this is particularly important and relevant at the level of higher education, one can't be too young to be introduced to the practice. In fact, newly born children are probably the organisms best dispositioned to engage in this behavior (see e.g. Gopnik, Meltzoff, & Kuhl, 1999). Unfortunately, the established schooling culture does not only often fail to encourage its further development, it is likely to discourage it.

4) The need to move beyond the perspective provided by well-delineated disciplines, which are kept strictly separate from each other in the majority of organized learning contexts, stands out in the perspective of providing learners with the opportunity to explore their world at multiple levels, allowing them thereby to develop different linguistic tools to describe their diverse, and often ambiguous, experience. Those same diverse linguistic tools are required for their ability to enter into dialogue with others about such experience. Stressing the importance of transdisciplinarity should not be interpreted as diminished attention to developing disciplinary attitudes and skills. Such attitudes and skills have proven very useful to the advancement of science and are expected to retain that status. Rather, the value of disciplinary approaches should be enhanced by placing them within the framework of wider interests that transcend those of single disciplines and call for collaboration across disciplines.

5) I should like to conclude my essay by calling attention to the urgency of (re )introducing in the educational practice a focus on the development of wisdom. As can be seen from what follows, such a focus encompasses and brings together much of what I said in the four points above. The essence of wisdom is not in what we know, but in what we do with what we know and our capacity to reflect on its meaning and use. Wisdom is what we need to be able to live with the ambiguity in our own and other people's lives, relating to the eternal gap between what we seem to know and how we act. It thus provides the lifelong impulse to make us better. Wisdom goes beyond possessing a profound well-organized base of knowledge. It assumes the recognition that such knowledge is contextualized, grounded in the practice of our lives, and the acceptance that all knowledge is transitory. Therefore, a learning environment that nurtures wisdom, will be

Notes

[1] I thank John Shotter (see his own contribution elsewhere in this collection of essays) for bringing the quote from Wittgenstein's (1974) Philosophical Grammer at the top of this essay to my attention in response to his reading my paper.

References

Dyson, F. (1979). Time without end: Physics and biology in an open universe. Reviews of Modern Physics, 51(3), 445-461 [Online]. Available http://www.aleph.se/Trans/Global/Omega/dyson.txt [2003, October 13].

Basarab, N. (Ed.) (2000). Niveaux de réalité (Levels of reality). Bulletin Interactif du Centre International de Recherches et Études Transdisciplinaires No. 15, Mai 2000. Paris, France: CIRET [Online]. Available http://perso.club-internet.fr/nicol/ciret/bulletin/b15/b15.htm [2003, October 19]. (Two contributions in this source, one by Peter Brook on "Does nothing come from nothing" and one by Basarab Nicolecu on "Transdisciplinarity and complexity: Levels of reality as source of indeterminacy," are written in English.)

Eliot, T. S. (1925). "The Hollow Men." In Selected Poems. London, UK: Faber and Faber (published 1954).

Gopnik, A., Meltzoff, A. N. & Kuhl, P. K. (1999). The scientist in the crib: Minds, brains, and how children learn. New York, NY: William Morrow and Company, Inc.

Morin, E. (2002). Ce que nous savions déjà (What we already knew). In B. Nicolescu & J. Visser (Eds.), L'apprentissage dans le creuset - Learning in the crucible. Bulletin Interactif du Centre International de Recherches et Études Transdisciplinaires No. 16, Février 2002. Paris, France: CIRET [Online]. Available http://perso.club-internet.fr/nicol/ciret/bulletin/b16/b16c22.htm [2003, October 19].

Ngoenha, S. E. (1995). Mukhatchanadas. Lisbon, Portugal: Editorial Escritor, Lda.

Visser, J. (2002, November). The idea of mind. In: J. Visser (chair), Mind over competency. Paper presented at the International Conference of the Association for Educational Communications and Technology, Dallas, TX, November 12-16, 2002 [Online]. Available http://www.learndev.org/ppt/MOC-AECT2002-PPT.pdf.

Wittgenstein, L. (1974). Philosophical Grammar, ed. Rush Rees, transl. by A. Kenny. Oxford, UK: Blackwell.

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The Necessity For Ambiguity If We Are To Achieve
Specificity In Communication
John Shotter
Department of Communication, University of New Hampshire

 

Now what I contend for, and accumulate examples to show, is that 'tendencies' are not only descriptions from without, but that they are among the objects of the stream, which is thus aware of them from within, and must be described as in very large measure constituted of feelings of tendency, often so vague that we are unable to name them at all. It is, in short, the re-instatement of the vague to its proper place in our mental life which I am so anxious to press on the attention. (William James, 1890, p.254)

What is most difficult here is to put all this indefiniteness, correctly and unfalsified, into words. (Wittgenstein, 1953, p.227)

Mere description is so difficult because one believes that one needs to fill out the facts in order to understand them. It is as if one saw a screen with scattered colour-patches, and said: the way they are here, they are unintelligible; they only make sense when one completes them into a shape. - Whereas I want to say: Here is the whole. (If you complete it, you falsify it). (Wittgenstein, 1980a, I, no.257)

In his celebrated The Stream of Thought chapter in his Principles of Psychology published in 1890, William James commented on the ease with which, in trying to think about the nature of thought, a confusion can arise "between the thoughts themselves, taken as subjective facts, and the things of which they are aware" (p.233). And he continues by suggesting that: "It is natural to make this confusion, but easy to avoid it when once put on one's guard. The things are discrete and discontinuous; they do pass before us in a train or chain, making often explosive appearances and rending each other in twain. But their comings and goings and contrasts no more break the flow of the thought that thinks them than they break the time and the space in which they lie... The transition between the thought of one object and the thought of another is no more a break in the thought than the joint in a bamboo is a break in the wood. It is a part of the consciousness as much as the joint is a part of the wood" (p.233).

In other words, what I think James is bringing to our attention here, is the crucial fact that in all living movements, living activities (expressions), there is always a kind of developmental continuity involved in their unfolding, such that earlier phases of the activity are indicative of at least the style, the physiognomy, i.e., the unique living identity, of what is to come later. There is a characteristic 'shape' to their unfolding in time. Thus, just as acorns only grow into oak trees and not rose bushes, and eggs only produce chickens and not rabbits, so all living activities, it seems, give rise to what we might call identity preserving changes or deformations - their possible ends are already 'there' in their beginnings. In other words, our spontaneous, expressive-responsive bodily activities, our words in our uttering of them, 'point beyond' themselves. In being responsive to their surrounding circumstances, they not only have an indicative or mimetic relation to them, even if their surroundings are invisible to those who merely witness them, but in so doing, they have an internal, rather than an external relation to them - rather than simply an 'add-on' extra, they are 'participant parts' in a larger whole. Hence the possibility of their gestural nature, and the fact that others can, so to speak, 'follow' us, and link their actions in an intelligible manner in with our's. For others also live out their lives from within the same surroundings as we ourselves, and can be, or are, oriented toward and sensitive to their features in the same way as ourselves also. Indeed, a part of what it is for us to be a member of a linguistic community, is our being able to use (express) a word with the background anticipation of the others around us will respond to our use of it in an expected manner. If they don't, then we wonder if in fact they are 'one of us'.

Because I will be referring to this feature of our living activities later, I will call it the intrinsic identity preserving nature of our living activities. It is this feature of our living activities that allows, in our meetings with other members of our community, both us and them to entertain expectations as to how we will each respond to each other's activities. As Garfinkel (1967) puts it: "The member of the society uses background expectancies as a scheme of interpretation. With their use actual appearances are for him recognizable and intelligible as the appearances-of-familiar-events. Demonstrably he is responsive to this background, while at the same time he is at a loss to tell us specifically of what the expectancies consist. When we ask him about them he has little or nothing to say" (pp.36-37) [1].

This characteristic of our living activities is very easily ignored. Indeed, I cannot agree with James when he says that it is easy to avoid the confusion between the things, which "are discrete and discontinuous," and flow of thought in which the transitions are "no more a break in the thought than the joint in a bamboo is a break in the wood." We have the utmost difficulty in thinking and talking about unbroken, continuously unfolding, temporal processes, which, in their very incompleteness, are always open to further articulation and specification. All the traditions of philosophy within which we have been schooled are inimical to the mode of thought James requires of us. They orient us instead, toward quantitative modes of thought in which the world is thought as made up of discrete, countable elements of reality.

Thus, if I had to choose just two founding statements of our current, official, empirically based, quantitative ways of knowing, I would choose the following: The first would be Socrates's claim, in book ten of The Republic (Plato, 1987), that in the face of the ease with which we can be deceived or misled by appearances, "measuring, counting, and weighing have happily been discovered to help us out of these difficulties, and to ensure that we should not be guided by apparent differences of size, quantity and heaviness, but by calculations of number, measurement, and weight... and these calculations are performed by the element of reason in the mind" (Plato, 1987, p.432). The other would be Descartes's (1968) foundational resolve, "to speak only of what would happen in a new world, if God were to create, somewhere in imaginary space, enough matter to compose it, and if he were to agitate diversely and confusedly the different parts of this matter, so that he created a chaos as disordered as the poets could ever imagine, and afterwards did no more than to lend his usual preserving action to nature, and to let her act according to his established laws" (Descartes, 1968, p.62). For such claims as these express the essential features of the world picture that has informed our more self-conscious thought, talk, and action for many centuries here in the West.

It is a picture of reality as made up of separate, self-contained, localized parts or elements (i.e., atoms or particles), that are connected to other such element only through various 'dynamical' effects (movements considered as changes of configuration), occurring in both space and time, thought of as 'containers' for such effects, which in the first instance are thought of as God's responsibility. It is this picture which has unconsciously informed almost all our academic and intellectual enterprises until very recently. But clearly and crucially, what is missing from such a picture, is life, the activities of living, embodied beings, and the fact that for us here on earth, life does not come from a mysterious god on high, but only from other life, in an unbroken chain of creativity that occurs whenever two or more living forms meet, and actively 'rub up against' each other, so to speak.

This brings me to what I think is a second crucial fact about the nature of our living activities - besides the fact of their intrinsic identity preserving nature - what I also think is crucial and arises out of the special nature of living beings, is that many things of importance to them occur only in meetings between them of one kind or another. Something very special occurs when two or more living beings meet and begin to respond to each other (more happens than them merely having an impact on one another). There is in such meetings the creation of qualitatively new, quite novel and distinct forms of life, with their own surrounding 'realities', which are more than merely averaged or mixed versions of those already existing.

The very special nature of the activities and the 'realities' occurring in such meetings, arises out of the fact that it is next to impossible not to be responsive both to the others and to the othernesses around us. As a result of our spontaneously responding to each other, instead of one person first acting individually and independently of an other, and then the second replying, by acting individually and independently of the first, all those involved act jointly, as a collective-we. And they do this bodily, in a 'living' way, spontaneously and simultaneously, without having first 'to work out' how to respond to each other. This means that when someone acts, their activity cannot be accounted as wholly their own activity - for a person's acts are partly 'shaped' by the acts of the others around them - this is where all the strangeness of the dialogical begins. Our actions within a collective-we are neither yours nor mine; they are truly 'ours'.

Bakhtin (1981, 1984, 1986) has explored the character of the dynamic realities occurring in our meetings in terms of their dialogical characteristics, while I have explored them elsewhere in terms of the concept of joint action (Shotter, 1980, 1984, 1993a, 1993b), but I now think that the richer concept is Merleau-Ponty's (1968) concept of the chaismic, for what marks them out as special is their (almost inexpressible) inextricable, reciprocal intertwining with their surroundings - and, their reversibility, i.e., the fact that our surroundings issue 'callings' to us as much as we act upon them. One of Merleau-Ponty's (1962) attempts to express the dynamic intertwining that occurs as we move around in the world is as follows: "My experience at [different moments] is bound up with itself in such a way that I do not get different perspective views linked to each other through the conception of an invariant. The perceiving body does not successively occupy different points of view beneath the gaze of some unlocated consciousness which is thinking about them... We can no more construct perception of the thing and of the world from discrete aspects, than we can make up the binocular vision of an object from two monocular images. My experiences of the world are integrated into one single world as the double images merge into the one thing, when my finger stops pressing upon my eyeball" (p.329). In other words, the chiasmic 'mixing' or 'blending' that is occurring here is of a very special kind, it is creative of relational dimensions - the perception of "depth" made available to us in our binocular vision being one such dimension - in which "seeing connections" (Wittgenstein, 1953, no.122) becomes possible for us.

Elsewhere (Shotter, 2003), I have argued more fully for the complexity of the dynamic realities that emerge in our meetings with each other. But let me here just list what seem to me to be their partially-this-partially-that features: In being only partially determined and still open to yet further specification, activities in this sphere lack complete specificity. What is produced in such dialogically - or chiasmatically - structured exchanges is a very complex mixture of not wholly reconcilable influences - as Bakhtin (1981) remarks, both 'centripetal' tendencies inward toward order and unity at the center, as well as 'centrifugal' ones outward toward diversity and difference on the borders or margins, are at work within them. Indeed, they are a complex mixture of many different kinds of influences. This makes it very difficult for us to characterize their nature unambiguously: they have neither a fully orderly nor a fully disorderly structure, neither a completely stable nor an easily changed organization, neither a fully subjective nor fully objective character; nor need they be wholly made up of living processes, dead entities may come to play a participatory role within them as well. They are also non-locatable - they are 'spread out' among all the entities participating in them. They are neither 'inside' people, but nor are they 'outside' them; they are located in that space where inside and outside are one. Nor is there a separate before and after (Bergson), neither an agent nor an effect, but only a meaningful whole which cannot divide itself into separable parts.

Indeed, it is precisely their lack of any pre-determined order, and thus their openness to being specified or determined by those involved in them, in practice - while usually remaining quite unaware of their having done so - that is their central defining feature. Hence the impossibility of any outsiders imposing on them a single, logical or systematic order of connectedness that can capture the character of their dynamic, multi-dimensional openness to further growth and development experienced by those involved as participants within them.

It is at this point that I can begin to make contact with my title: For if the 'realities' within which we must act in our meetings with others do in fact have the partially-this-partially-that character I have outlined above, then our basic systems or schemes of thought and talk must, of necessity, be in and of themselves ambiguous, if we are to apply them in our daily lives to the quite unique and specific circumstances in which we find ourselves. For if human interaction takes place in and deals with a pluralistic, only fragmentarily known, and only partially shared social world, then vagueness, ambiguity, and incompleteness - but hence also versatility, flexibility, and negotiability - must for that very reason be an inherent and essential characteristics of our ordinary ways of making sense to each other (Rommetveit, 1985). All the 'real' states of affairs between us are enigmatic, and remain so, until they are linguistically expressed in an agreed form, so that all involved in them come to respond to their features and characteristics in the same way. Indeed, it is at this point that Wittgenstein's (1953) famous maxim - "For a large class of cases - though not for all - in which we employ the word 'meaning' it can be defined thus: the meaning of a word is its use in the language" (no.43) - becomes relevant. In other words, ambiguities of word meaning (mostly) disappear as the specific use of a word becomes clear in the circumstances of its use.

If we take a purely scientific view of how the terms in a language should be defined, this lack of clearly defined prior meanings for our words may seem to be a serious defect of our language. Surely, if there is no clear correspondence between our symbols and what they represent (or picture), we don't know what we are talking about! However, if we turn from the referential-representational view of word meaning, toward the relational-responsive view, then we can see that the words we use have an open political and ethical function: a person's utterance 'points' toward the next possible steps those around him or her might take. Taking into account these ethical and micro-political features of our ordinary everyday relations with those around us, then we can see at least one reason why the insistence on a prior set of fixed meanings for all our words would be disastrous: speakers would be foreclosing on the freedom of action of those around them. The openness of the realities shared amongst those within meetings, to being specified or determined further, only by those involved in them, in practice, would be curtailed.

Garfinkel (1967) demonstrated the radical (and perhaps, surprising) consequences of what happens if we try to demand the specificity of 'scientific' definitions of word meaning in our ordinary everyday meetings. Below, after having instructed his students to demand of their friends (or spouses) rigorous specificity in their word usage, are a couple of episodes depicting the results:

CASE 1 (p.42)

The subject was telling the experimenter, a member of the subject's car pool, about having had a flat tire while going to work previous day.

(S) I had a flat tire.
(E) What do you mean, you had a flat tire?

She appeared momentarily stunned. Then she answered in a hostile way: "What do you mean, 'What do you mean?' A flat is a flat tire. That is what I meant. Nothing special. What a crazy question!"

CASE 3 (p.43)

"On Friday night my husband and I were watching television. My husband remarked that he was tired. I asked, 'How are you tired? Physically, mentally, or just bored?'"

(S ) I don't know, I guess physically, mainly.
(E) You mean that your muscles ache or your bones?
(S) I guess so. Don't be so technical.
( After more watching )
(S ) All these old movies have the same kind of old iron bedstead in them.
(E) What do you mean? Do you mean all old movies, or some of them, or just the ones you have seen?
(S) What's the matter with you? You know what I mean.
(E) I wish you would be more specific.
(S) You know what I mean! Drop dead!

CASE 6 (p.44)

The victim waved his hand cheerily.
(S) How are you?
(E) How am I in regard to what? My health, my finances, my school work, my peace of mind, my. ..?
(S) ( Red in the face and suddenly out of control. ) Look! I was just trying to be polite. Frankly, I don't give a damn how you are.

About these and other similar results, when people try to impose an already established scheme of pre-defined terms on the others around them, Garfinkel (1967) comments: "For the purposes of conducting their everyday affairs persons refuse to permit each other to understand 'what they are really talking about' in this way. The anticipation that people will understand, the occasionality of expressions, the specific vagueness of references, the retrospective-prospective sense of a present occurrence, waiting for something later in order to see what was meant before, are sanctioned properties of common discourse. They furnish a background of seen but unnoticed features of common discourse whereby actual utterances are recognized as events of common, reasonable, understandable, plain talk" (p.40).

I began my account here with William James's (1890) comment, that it is "the re-instatement of the vague to its proper place in our mental life which I am so anxious to press." To agree with James and to urge the adoption of his suggestion is, perhaps, to court total obloquy in our still avowedly scientific times. Nevertheless, that is what I have done above. If, as is clearly the case, we have not yet managed to substitute a clear order for the vagueness and mystery, uncertainty and conflict apparent in our current forms of everyday social life; if our experts in social engineering have not yet managed to replace the arenas of moral, legal, political, economic, and academic conflict in our society with various scientifically designed 'procedures of behavioral management', then I take it such vagueness and mystery still remains. We live with them continually in the living of our daily lives. If vagueness and mystery are really there in the actual structure of our social lives together, then if we are to construct a realistic account of our actual social being, they cannot be ignored; account has to be taken of them too.

Notes

[1] Wittgenstein (1980b) too notes the importance of our immersion in a background of spontaneous, expressive responsive activity: "Perhaps what is inexpressible (what I find mysterious and am not able to express) is the background against which whatever I could express has its meaning" ( p.16).

References

Bakhtin, M.M. (1981) The Dialogical Imagination. Edited by M. Holquist, trans. by C. Emerson and M. Holquist. Austin, TX: University of Texas Press.

Bakhtin, M.M. (1984) Problems of Dostoevsky's Poetics. Edited and trans. by Caryl Emerson. Minneapolis: University of Minnesota Press.

Bakhtin, M.M. (1986) Speech Genres and Other Late Essays. Trans. by Vern W. McGee. Austin, TX: University of Texas Press.

Descartes, R. (1968) Discourse on Method and Other Writings. Trans. with introduction by F.E. Sutcliffe. Harmondsworth: Penguin Books.

Garfinkel, H. (1967) Studies in Ethnomethodology. Englewood-Cliffs, NJ: Prentice-Hall

James, W. (1890) Principles of Psychology, vols. 1 & 2. London: Macmillan.

Merleau-Ponty, M. (1962) Phenomenology of Perception (trans. C. Smith). London: Routledge and Kegan Paul.

Merleau-Ponty, M. (1968) The Visible and the Invisible, Edited by Claude Lefort, translated by Alphonso Lingis. Evanston, Il: Northwestern University Press.

Rommetveit, R. (1985) Language acquisition as increasing linguistic structuring of experience and symbolic behaviour control. J. V. Wetsch (Ed.) Culture, Communication and Cognition: Vygotskian Perspectives. London: Cambridge University Press.

Shotter, J. (1980) Action, joint action, and intentionality. M. Brenner (Ed.) The Structure of Action . Oxford: Blackwell, pp.28-65..

Shotter, J. (1984) Social Accountability and Selfhood. Oxford: Blackwell.

Shotter, J. (1993) Cultural Politics of Everyday Life: Social Constructionism, Rhetoric, and Knowing of the Third Kind. Milton Keynes, UK: Open University Press.

Shotter, J. (1993) Conversational Realities: Constructing Life through Language. London: Sage.

Shotter, J. (2003) Real presences: meaning as living movement in a participatory world. Theory & Psychology 13(4), pp.435-468.

Wittgenstein, L. (1953) Philosophical Investigations, translated by G.E.M. Anscombe. Oxford: Blackwell.

Wittgenstein, L. (1980a) Remarks on the Philosophy of Psychology, vols. 1 and 2. Oxford: Blackwell.

Wittgenstein, L. (1980a) Culture and Value, introduction by G. Von Wright, and translated by P. Winch. Oxford: Blackwell.

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"Inverted Commas": A Critical Reflection on Ambiguity in the Context of HIV/AIDS

Muriel Visser
Florida State University and the Learning Development Institute

Turning Reality on its Head

When I was little, and whenever we crossed the border between two countries, I fantasized about being the queen of no-man's land. In part my fascination for this thin strip of land was fuelled by the realization that its surface area as a whole could be quite substantial. But, most of all I was intrigued by the challenge of establishing a functional kingdom within the limitations of the strange shape of my country. The realization that so much of what I normally took for granted would need to change was almost overwhelming and kept me occupied for many of the long, dust covered hours, that we spent traveling on the road.

For many years this childhood fantasy lay forgotten under the weight of my more recent memories. But it resurfaced just recently - bringing back the same mesmerizing feelings of bewilderment, anxiety and challenge - when I was listening to people verbalizing their feelings and perceptions about HIV/AIDS.

The people in question are teachers in Mozambique, who on a day-to-day basis are confronted with the machinations of a disease which turns reality on its head, requiring them to constantly examine and re-examine their assumptions about who they are as individuals, and about how the world works. These teachers - no doubt much as everyone else in that part of the world - have been confronted with increasingly complex levels of ambiguity because of the overwhelmingly pervasive nature of this disease, affecting not only individuals but also the very fabric and future of society in social, economic, cultural and even political ways.

In this kind of context describing the impact of HIV in terms of numbers has become woefully inadequate - not only because we have long relegated such numbers to the domain of facts that we cannot change - but also because such numbers create a fundamental abstraction from the highly individualistic and particularistic processes of reflection and interaction that can be crucial to learning to live and manage ambiguity. During my work with these teachers I found myself - the researcher, the one who normally asks the questions - confronted with a waterfall of questions, of interrogations, of unfinished sentences which together form the reality of what teachers are up against, until I reached the conclusion that the reality of HIV/AIDS can probably better be described as an intricate spider web of questions and interrogations. Such a process of questioning, of comparing and contrasting different elements of our understanding of the world, carries with it, in itself, enormous potential for collective self-realization but also for confusion, for a sense of endless atrophy, and for despair.

From the privileged position of an observer, of a part-time participant on the surface of these people's life, I came to the conclusion - much as Gordon Rowland (2003) notes in his contribution to this dialogue - that inconsistency/ambiguity can be simultaneously a powerful agent of change and an overwhelming inertia-provoking force. This paper therefore constitutes an effort to illustrate ambiguity from the practical perspective of individuals and groups of people attempting to manage inconsistencies. For the purpose of this analysis I interpreted the term "inconsistencies" in a very loose sense as referring to things that do not add up, or in the words of one of the teachers whom I worked with as: "those things that we place between inverted commas because they puzzle us, because they puzzle others, and lead us to questioning the truth and untruth of our lives".

Behind the Looking Glass

To get behind the looking glass of teachers' understanding of how this disease is impacting on schools and communities a variety of techniques were used, including individual essays, individual interviews and facilitated or observed group discussions. From these reflections it appears that there are essentially three spheres at which the confrontation with HIV/AIDS manifests itself as ambiguous and inconsistent, namely: a) within the individual itself; b) at the collective level of people who share a similar culture or at least the same physical space; and c) and at a macro-collective level, in other words between cultures and societies. Each of these was expressed by these teachers in some way as the examples below will illustrate.

At a very individual level there is evidence of an introspective, almost "atrophy reducing" effort - which is, because of the very nature of HIV/AIDS, on occasion reminiscent of extreme forms of chaos management (an oxymoron if ever there was one!). In the words of the teacher who was quoted earlier, it is the process of "placing oneself between inverted commas", which leads one to realize that the building blocks that should add up to what we are as individuals have been so fundamentally disturbed that we can only stand back and scratch our head in bewilderment as we contemplate the landscape around us with the nebulous look of a young child who opens its eyes under water for the first time.

At one level such bewilderment can be illustrated with interrogations that relate the fundamental questions of contradictions between what I know and what I do and what that says about the kind of person I am. This was very aptly expressed by one teacher when he explained: "I, for one, I carry a condom in my back pocket all the time [pats his back pocket] but then I may not use it. I have it with me, it is there. And then later I wonder: 'why did I do that, why did I not use it?'"

To a degree this interrogation is closely related to another question that appears often in the reflections of these teachers, namely the contradiction between what I know and what I know. This looks paradoxical, but the meaning of this statement is clearly expressed in the writing of one of the female teachers: "I know that condoms will protect me against HIV but I know that there may be condoms that are already infected with diseases such as HIV, and that if I fill a condom with water and a little salt and hang it in the sun for a few days, the tiny microbes that spread the disease will be visible to the naked eye… In some cases AIDS appears because people violate customs so then really there is nothing we can do to protect ourselves… So depending on what I am thinking I may decide to use a condom or not".

This statement illustrates the almost eerily peaceful co-existence of multiple knowledge domains within the same individual. In this particular case such knowledge domains appear to consist of that which the teacher learnt through formal HIV training, from discussions within the community, and probably also through socialization and acculturation into the society where she lives (see also M. Visser, 2002 and M. Visser & J. Visser, 2003, for further examples of learning in communities in Mozambique). In a similar statement comes the poignant reflection of a teacher who spent many months living in the same house with a female colleague who was slowly dying from AIDS: "I knew she was sick, and I knew that I could not catch the disease just from living with her. I wanted to help her because I could see her suffering was terrible, but she would ask me to help her bath because the itch from the disease was unbearable and I would find many excuses not to help her, I was too scared that her misfortune would pass on to me. I kept thinking that when she would die I would be happy. Then she died and since then I worry every time I cough, every time I have a small problem with my skin, and I wait for my turn to die". At a very fundamental level one finds here a conflict between beliefs about the world (i.e. people should do good to one another) and the reality of a disease that disturbs all such assumptions.

Being confronted with differing domains of knowledge does not in itself have to be a problem. But the problem arises when different domains of knowledge are so incompatible as to lead to incoherence in actions, or to inertia, or to a such a high degree of atrophy that it becomes impossible for the individual to make sense of the different things s/he is confronted with. From a more positive angle the question then becomes, at what point does a process of realization or awareness of different knowledge domains become evident to the individual? And what is necessary for such contradictions between different knowledge domains to be converted into a quest for understanding that could spur individuals to change their behavior?

At a second level, namely that of collectivities, the inconsistencies or ambiguities that result from the pervasive presence of HIV appear to be born in a very fundamental sense - as John Shotter (2003) points out in his paper on ambiguity - from the contrast, and sometimes even conflict, between the meaning that individuals give to concepts, words and symbols (based on how these have grown and evolved from within them) and the interpretations and understanding that others have of these same concepts, words and symbols. Dealing with and managing ambiguity is in this respect an on-going process of building bridges. Some of these bridges may take on solid and durable forms, while others will be no more than perilous ropes linking one side of a precipice to the other, constantly vulnerable to the onslaught of change and to the wear and tear of life's experiences. It is relatively easy to imagine that in some contexts and for some people the building of such bridges may be challenging and stimulating, while in other realities it can be akin to the tired back-breaking toil of those who know that their day's labor will never provide for even their most modest needs, let alone for any simple wishes. Dervin's sense making methodology (1999, 2001) goes some way to explaining such building of bridges. A striking example of how bridge building can go wrong is contained in an elaborate explanation of where the fault for HIV/ADS lies by a male teacher in a rural community: "My way of seeing this is that really it is us men who are at fault here. When we marry we say 'until death us do part' but it has a meaning to women only, not to men. It is the women who sacrifice themselves, they stay with their husband when he becomes sick, they want to support him, they continue sleeping with him, they will have babies, literally until death parts them from their husband, and often they are the first to die. We men, on the other hand, we send our women away, as soon as they get sick they go back to where they came from, or they are left to die alone. We have no shame, no shame at all." A slightly different perspective was offered by the teacher quoted at the beginning of the article who, referring to his time as a student a few years earlier said: "I was having a very difficult time, I had no money at all, and I was not eating. I have always been thin, but I became even thinner, and then I realized that people were avoiding me, they were not looking me in the eye. My girlfriend left me. It was only when a friend asked me whether I was sick that I realized that I myself had been placed between inverted commas."

And finally at a macro collective perspective there are the fundamental inconsistencies that are somehow a reflection of how groups of people - through their unceasing interaction, through the togetherness that grows from having even the vaguest of common goals, and through their common history - build some form of commonality, be it a society, a nation, a revolution, a vision or whatever label we may place on it at a given time. There are moments in history when every attempt at addressing inconsistencies leads to more war and chaos (we have only to look at the Middle East to have a constant reminder of this). And then there are those equally amazing moments where, in spite of the ambiguity within and between individuals and collectivities, precisely those divisions that may have been born out of frustration and anger become rivers of inspiration and beauty. Those who have experienced the process of post-independence nation building in former colonies, or who have ever been in the middle of a major natural disaster may recall to the bone the intensity and energy of such processes. At such times bridges are built not only horizontally but also vertically, as well as diagonally and in any direction possible, and for a time each successive bridge appears to be stronger than the last.

For many teachers ambiguity manifests itself also at this level. Ambiguity is expressed in part by an absence of any form of dialogue with those who from the outside in some way influenced the happenings within a community. "We have questions but we never get answers, only that we will die," says one teacher referring to the HIV/AIDS awareness campaign, and he continues: "we will die not knowing." Or in the words of another teacher: "All we ever hear is that AIDS is a death sentence, a person who has this disease ceases to exist, such a person has one foot in his grave and is no longer part of our community. Yet in other countries there are people who have AIDS who carry on living for many years." There is the perception of a fundamental injustice: "It is my conviction that in South Africa the Mozambican mineworkers get infected with a very special strand of HIV, or maybe they get an injection there that speeds up the progress of the disease. I know that AIDS is a disease from which you die a slow and difficult death but you only have to look around you here to see how, when the sick mineworkers come back, they die within days, not weeks, and not months, but sometimes within 48 hours they are gone."

Beyond the looking glass …

These three different spheres of inconsistencies, of ambiguity, co-exist, interact and blend into a spectrum, into a multiplicity of forces of various strengths that attract and repel one another, co-exist and destroy and are in a constant process of transformation. In the case of these teachers, I would argue that their analysis, their questions, are a recognition of the fact that they do not have all the answers, that this recognition is one step in the direction of a greater level of understanding as well as a step in the direction of a more active involvement with their environment, with this issue, and with their own behavior.

In this sense it can be argued that ambiguity is good, that it is worthwhile, that it provokes internal debate, that questions (of a more or less tentative nature) are formulated, and that this may stimulate learning and ultimately a process of growth and greater understanding. However, the same process of questioning, of confronting ambiguity, may be a dead end street since many of these teachers are painfully formulating their questions in a resource-poor environment (they have nowhere to go to seek for answers to their questions) where the HIV awareness campaign focuses mainly on spoon feeding little bits of information and promotes a sense of fatalism, and where there is not necessarily a tolerance of the process of questioning that they embark upon. For many the questions remain in their head and can not, given the constraints of their environment, be consistently addressed.

Complex situations demand complex solutions, or maybe not so. But perhaps if we placed inverted commas around much more than just the behavior of individuals, we would find a way of contributing to addressing the inconsistencies that these teachers face. HIV/AIDS is a complex disease, a complex phenomenon, simplifying the answers to the multitude of questions that teachers, and other people in communities such as these in Mozambique face, may not be the answer.

Perhaps it is necessary to acknowledge the complexity rather than to reduce it, and therefore to favor complex interpretations rather than simple ones. Perhaps it is necessary to consider ambiguity not from an individual perspective but from a social and communal perspective, in an approach akin to that suggested by Kincaid et al. (2003) in their model of social change. Perhaps it is necessary to focus not only on the negative, but also on the positive, and on that which is so strange that we do not really know how to classify it. Perhaps it is necessary to focus not only on anxiety, as Gordon Rowland points out, but also on fatalism and on conformism. Perhaps it is necessary to allow people to fully explore the existence of multiple realities, and to reach their own conclusions, rather than the conclusions that are offered to them by others. And, perhaps we need to place inverted commas in a lot more places to allow ourselves to be guided by processes of questioning rather than by answers.

References

Dervin, B. (1999, May). Sense-Making's theory of dialogue: A brief introduction. Paper presented at the annual meeting of the International Communication Association, San Francisco, California, May 27, 1999.

Dervin, B. (2001). Sense-making methodology: communicating communicatively with campaign audiences. In: R.E. Rice & C. K. Atkin (Eds). Public Communication Campaigns (3rd Ed). Thousand Oaks, CA: Sage.

Figueroa, M. E., Kincaid, L. D., Rani, M., Lewis, G. (2002). Communication for social change : An integrated model for measuring the process and its outcomes. Report produced for the Rockefeller Foundation.

Rowland, G. (2003, October). A little ambiguity can go a long way. Conference paper in J. Visser (Chair), Ambiguity, cognition, learning, teaching and design. International Conference of the Association for Educational Communications and Technology (AECT), Anaheim, CA, October 22-26, 2003.

Shotter, J. (2003, October). The necessity for ambiguity if we are to achieve communication. Conference paper in J. Visser (Chair), Ambiguity, cognition, learning, teaching and design. International Conference of the Association for Educational Communications and Technology (AECT), Anaheim, CA, October 22-26, 2003.

Visser, M (2002, November). Where teachers fear to tread - communicating about HIV/AIDS in Mozambique. Paper Published in the Proceedings of the 2002 Conference of the Association for Educational Communications and Technology (AECT), Dallas, TX, November 12-16, 2002.

Visser, M., & Visser, J. (2003, October). We closed our books and put them away: Learning stories from Mozambique - a critical reflection on communicating about the reality and future of learning. International Conference of the Association for Educational Communications and Technology (AECT), Anaheim, CA, October 22-26, 2003.

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Click here for Ron Burnett's PowerPoint presentation on Ambiguity/Language/Learning 

Ambiguity/Language/Learning

Ron Burnett
Emily Carr Institute of Art + Design

One of the fundamental assumptions about learning and education in general is that "schooling transmits knowledge or that education reproduces culture." (Grunet, Bitter Milk: Women and Teaching Amherst, Mass: University of Massachusetts Press, 1988 .)

In the spirit of ambiguity as both a mode of thinking and a particular form of practice, it would be useful to comment on a number of issues raised by the above quote:

1. The underlying concepts governing notions of knowledge transmission are literal and metaphorical. From the literal perspective, transmission is about the movement of information from a source to a subject. It is the generally superficial idea that the lines of communication or interaction between expression, meaning and speech are direct and reproduced by listeners and learners. Transmission is very much about directness, which is why it is actively used in communications contexts like broadcasting. The difficulty is that the models of interaction proposed by transmission do not take account of the fluidity of human learning and the very unpredictable nature of relationships between teachers and their students. Another issue is that information is not just a defined body of data waiting to be used in the communication of ideas and concepts. Information is a rather more complex body of discourses and modes of thinking, than an articulated and defined as well as solid set of facts awaiting even more complex processes of communication.

2. At a metaphorical level, transmission is often confused with communications. The latter is a far more multifaceted activity requiring more than a listener to explain processes of interaction. Gil Suzawa, one of the contributors to the debate about ambiguity (see the learndev.org site) suggests that 'reconstruction' is as important in the learning process as listening. Reconstruction, from the point of view of the learner is as much about imagination and creativity as it is about 'reproduction.' When I speak to large audiences, I am fond of reminding them that listening is also about daydreaming and that often there are clashes between what is being said and the meandering of the mind as we think about not only what is being discussed, but also our next appointment. This reconstructive process engages learners in a constant struggle with information, listening, thinking, daydreaming and understanding. Occasionally, these efforts lead to learning. Metaphorically then, transmission tends not only to simplify complex processes, but to make it appear as if the many different degrees of attention, awareness and interaction can be reduced to an almost formulaic linear approach.

Grunet's (4) second assertion is that our society thinks about education as a way of ensuring the reproduction of knowledge from one generation to the next. Reproduction, is of course, a very loaded term. It is not only derived from biological processes but also carries the weight of canonized and pre-determined forms of knowledge that educational institutions feel are essential to the survival and well-being of students. This 'reproductive' concern also refers to the need or desire on the part of different generations to create and recreate the world in their own image. Yet, even with designer babies on the horizon, there is an anarchic quality to the ways in which genetics, family history and environment thwart the simple connection between intention and outcome. Most teaching and learning contexts are about interpersonal relationships, even in those instances when classrooms are large and teachers are distant from their interlocutors. Interpersonal relationships are inherently, I would argue, ambiguous not because that is necessarily the desire of participants, but because communications processes are about striving to understand the many inherent distortions and weaknesses of all forms of human discourse and language.

I would suggest that most forms of learning are steeped in creative processes of mixing and matching and by creative, I mean that the imagination plays a far more important role than is often accounted for or accepted by educators. The extreme example is the student who resists everything from classroom format to the genuine efforts on the part of teachers to shape information into a form that a diverse group of learners can understand. Notwithstanding the many distortions that imaginative reconstruction can introduce into every communicative effort, it is, I think essential to incorporate these many levels into our understanding of the learning process.

This means that the design of courses cannot conflate intention with outcome, which is a genuinely difficult challenge given the effort that is put into the creation, development and maintenance of course formats and goals. In his piece, Suzawa talks about 'poetic thinking' an approach which I endorse. I would extend what he says to include the possibility for poetic speech, for the fragment and for the ungrammatical.

Let me explain what I mean here. For me, poetic speech is not 'speaking poetically.' Rather, it is a state of mind that permits and encourages everyday speech to be framed by concerns that go beyond the literal, the direct and the explicit. This can only be accomplished through enriched metaphors of engagement that seek out not necessarily what is contiguous with our thinking, but contradictory if not oppositional. Clearly, this is not an easy task. Some years ago when I was teaching a course on film and video at McGill University in Montreal, I asked the students to prepare a video in which McGill would be located in the middle of a lake without any bridges connecting it to land. The students protested. "Not possible," said one of them, a young man with a poorly developed beard and intense eyes. Subsequently, it was this student who came up with the best video. He simply developed an editing rhythm where the cutting moved so swiftly that many of the buildings at McGill seemed to be floating on a large lake. Further analysis of the video showed that he had actually built a series of models and that by moving between the models and real buildings, he created the sensation as he put it, of buildings on water. He described his solution as the 'Star Trek' answer. He had figured out that the Star Trek environment was entirely constructed out of models that were carefully edited and used to create the illusion of being in a spaceship. Now, this may seem an obvious solution, but he was the only student among thirty who actually came up with it, although there were some other very successful videotapes. My point is that he moved to a more poetic level of thinking that freed his imagination to seek answers that were not immediately apparent to anyone else. This freedom always operates under many constraints, but without it any possibility of creative engagement is profoundly hindered. And, if that level of engagement is not achieved, it is difficult to talk to the students about the quite lovely and yet essential ambiguity of using models to create worlds and environments that seem real but are, from every vantage point, illusory.

In many curricula, facts are more important than illusions, and yet, ironically, most of the creative work that we engage with during our lives, in nearly every form of artistic expression, is based on the manipulation of materials within a world steeped in fantasy and imaginative reconstruction. Often, fragments, pieces of events, stories that unfold in unanticipated directions and so on, characterize these worlds. There is a constant collision among expectations about truth, expression, medium and experience. These collisions create zones of possible learning. I stress 'possible' because for me learning is not so much defined by what is put into the design of information, as by what is taken from the collision between the desires of the teacher and the needs of the student. This collision creates a middle ground between intention and outcome that is far more ephemeral than concrete, hence the disjuncture, the almost poetic fragmentation that characterizes how we attribute what we have learned to what has been presented to us.

The irony is that learning is very much about the ownership of ideas, the sense that learners have that an idea or a fact are important if they somehow relate to their personal needs. In the same way, teachers come to 'own' the central ideas of their disciplines, if not the disciplines themselves. This is the site of another collision amplified in the digital era by the increasingly important role of auto-didacticism, which allows learners to seek out many different venues from which they can gather and transform information into knowledge. I would argue that this plethora of possibilities leads to new forms of interaction based less on what teachers know than on how they communicate what they know. The same thing applies to learners.

Yet, if I am correct and communications processes are now essential and centre stage, then as a consequence of the very nature of the communication process, ambiguity is built into every aspect of what happens between teachers and learners. Communications in this instance refers to the use of language and other forms of expression in the classroom and by learners. Discursive variety, the use of different media and the manipulation of materials, are all parts of a greater whole, in which meaning and message are never simply the product of intention, nor do participants in the process simply take up what is presented to them. In some respects, this seems like it is common sense. Yet, educational institutions spend a great deal of money in creating and testing whether what they have invested in actually produces the outcomes they desire. Governments look to graduate outcomes (employment, in particular) as a distinctive measure of whether input and cost match.

So, the tasks of arguing for the importance of ambiguity as process, as experience and as outcome are indeed great challenges. Yet, just as I cannot conceive of a world without art, imagination, creativity and fantasy, I cannot think of a learning space without all of these ambiguous and contradictory elements as inherent parts of what we describe as education.

References

Barthes, Roland. The Pleasure of the Text, Trans. Richard Miller. New York: Hill and Wang, 1975.

Becker, Carol. Zones of Contention: Essays on Art, Institutions, Gender and Anxiety. Albany: State University of New York Press, 1996.

Burnett, Ron. Cultures of Vision: Images, Media and the Imaginary. Bloomington, Indiana: Indiana University Press, 1995.

Dewey, John. Art as Experience. New York: Capricorn Books, 1934.

Elkins, James. The Domain of Images. Ithaca: Cornell University Press, 1999.

Fish, Stanley. Is There a Text In This Class? Cambridge, Mass: Harvard University Press, 1980.

Empson, William. Seven Types of Ambiguity. London: Chatto and Windus, 1930.

Rorty, Richard. Philosophy and the Mirror of Nature. N.J.: Princeton University Press, 1982.

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Ambiguity in Learning: Issues and Implications for Instructional Design

Yusra Laila Visser
Learning Development Institute
Florida Atlantic University

 

Introduction

The purpose of this paper is to explore the role of ambiguity in learning from the perspective of instructional design. To this end, this concept paper is structured around the following five elements:

  1. The recognition of ambiguity as an essential attribute of life, and thus the recognition of tolerance for ambiguity as an essential dimension of human development at the individual and social level.
  2. The assertion that the extent to which ambiguity is tolerated in a learning environment is contingent on the culture of learning that embraces the learning environment.
  3. The assertion that learning environments can be designed systematically to provide learners with opportunities to embrace - and develop a tolerance for - ambiguity.
  4. The notion that classical instructional design methods and theories are oriented toward the removal of ambiguity from learning and assessment, but that contemporary instructional design models are more effectively integrating ambiguity in learning and instruction.
  5. The position that there is a need for further development of instructional design models and theories, to better integrate ambiguity into learning and instruction.

Each of these elements is addressed in more detail in this concept paper. Recommendations for integrating ambiguity exposure and tolerance into policy, research, and practice in instructional design conclude the paper.

Ambiguity as an Attribute that Characterizes Existence

The concept of ambiguity has a variety of different connotations, ranging from ambiguity in the sense of a double-entendre in linguistics, to ambiguity in the context of lack of clarity (vagueness), and to ambiguity in situations where multiple - seemingly contradictory - states or conditions can co-exist (Simpson and Weiner 1999). Budner (1962) identifies three main types of ambiguous situations: new situations (where there are insufficient or non-existent cues), complex situations, (where there are too many cues) and contradictory situations (where contradictory structures are suggested by the cues). In addition, as noted by Owen and Sweeney (2000), Norton (1975) categorized the literature in psychology and found evidence for eight distinct definitional categories for ambiguity: 1) multiple meanings, 2) vagueness, incompleteness, or fragmented, 3) a probability, 4) unstructured, 5) lack of information, 6) uncertainty, 7) inconsistencies & contradictions, and 8) unclear.

Immediately evident, then, is the notion that ambiguity may be of both a relative and an absolute nature. In the relative sense, the extent of ambiguity may be dependent on the availability of knowledge to overcome the ambiguity. In the absolute sense, the degree of ambiguity may be characterized by the existence of dual-state conditions (such as the notion that light is both a wave and a particle). The distinction between absolute and relative ambiguity is important for individuals engaged in supporting human performance and development. Where ambiguity is the result of a lack of knowledge, there is a need for assisting learners in developing the strategies for gathering and analyzing additional sources of information, while ensuring that the existence of the ambiguity does not hamper the effort in attaining such information. In the case where ambiguity is of an absolute nature, there is above all a need for ensuring that the learner is able to reconcile the existence of the ambiguous state, and that the learner can develop the strategies for further exploring the reality within the contradictory or ambiguous state.

Ambiguity is a characteristic of day-to-day life, and educators therefore must account for ambiguity in mediating and assessing the learning process. As the state of human knowledge advances, and the speed of change increases, it might be argued that individuals are increasingly confronted with the ambiguity prevalent in nature and existence. While tolerance for ambiguity has always been an important aspect of functioning in the world, it might be argued that the changing conditions and realities of life make it even more important that we learn how to deal with ambiguity in modern society. Havighurst (in Cohen, 1972) notes:

The modern world needs people with a complex identity who are intellectually autonomous and prepared to cope with uncertainty; who are able to tolerate ambiguity and not be driven by fear into a rigid, single-solution approach to problems, who are rational, foresightful and who look for facts; who can draw inferences and can control their behavior in the light of foreseen consequences, who are altruistic and enjoy doing for others, and who understand social forces and trends.

Although ambiguity pervades our existence, it is important to note that the extent and significance of ambiguity varies on the basis of the conditions that characterize each individual's existence. This makes the need for developing a tolerance for ambiguity a more significant issue in some settings than others. In considering, for example, the training of basic researchers in Physics - a discipline where ambiguity pervades the scientist's interaction with the world - the need for ensuring a highly developed comfort with ambiguity is of great significance to ensuring that the scientist can effectively engage in the advancement of understanding of the discipline. Other disciplines, such as engineering, embody a lesser extent of ambiguity, thereby making it less critical that the engineer have highly developed skills in relation to interacting with ambiguity.

Ambiguity Exposure and Tolerance as a Dimension of the Learning Culture

Educational environments (at both the micro and the macro level) are largely structured around a common conception of the meaning and purpose of learning (embedded within the culture of education for that community). Consider, for instance, a school classroom in which students all sit facing the front of the classroom, where the instructor teachers from a podium, and where the instruction is oriented toward the transmission of knowledge. And, consider further that this classroom environment is replicated by 10 fold in the same building, and by 100 fold in the school district. Such an environment is reflective of a culture of education where learning is looked at as a primarily individual process, where the instructor is conceived of as the center of the instructional process, and where learning is believed to transpire through the transmission of knowledge from one party to another. Since learning involves an interaction with ambiguity (either resulting from a lack of knowledge in the subject area, or from an existence of a pluralistic reality), the conceptions of the role of ambiguity by a given culture of education has great significance to the manner in which ambiguity is interacted with by students, teachers, and society at large.

Ambiguity characterizes conditions that that individual interacts with - knowledge, nature, and so on. Simultaneously, however, ambiguity may characterize the internal cognitive or affective state of the individual. Given this ubiquitous presence of ambiguity within existence, it is important to consider that aspect of human nature that relates to the interaction with ambiguity. In this context, intolerance of ambiguity has been identified as "a cognitive style characterized by an inability to accept without discomfort situations or stimuli that allow alternative interpretations, and a preference for situations or stimuli that appear black and white to those that consist of shades of grey." Conversely, tolerance for ambiguity tends is associated with the ability to "perceive and interpret an ambiguous situation more adequately, in a realistic way, without denying or distorting parts of its complexity" (Stoyvecha, 2003, p. 1). Such a disposition enables people "to elaborate more adaptive and better co-ordinated behaviour (…) [and] withstand the discomfort of the ambiguous situation long enough as to accommodate and generate more appropriate and flexible responses to it (Stoyvecha, 2003, p.1).

The extent to which an educational setting supports the development of a tolerance for ambiguity is closely linked to the culture of education that the instruction is vested in. Therefore, tackling the issue of ambiguity in learning requires analysis and action at the systemic level in education. Stoycheva (2003) notes: "[E]ducation is seen as a context for socialisation in tolerance - intolerance of ambiguity. Through education young people acquire knowledge, and this knowledge impacts their images of the world, of the human being and of life in general. (…) [B]oys and girls learn those formal and informal rules and norms that help us cope with uncertainty and ambiguity in social interactions" (p.1).

In research conducted by the Bulgarian Academy of Sciences (Stoyvecha, 2003), it was found that both teachers and students valued ambiguity tolerant behavior to a greater extent than ambiguity-intolerant behavior. However, it was also found that students perceived their teachers as valuing ambiguity-tolerant behavior significantly less than the students themselves. As Stoyvecha (1998) notes; "there is a strong discrepancy between teachers' self-reported encouragement for ambiguity tolerant - intolerant behaviours and the way their reward strategies are perceived by students." While there are a number of factors that might explain this discrepancy, it points to the fact that the culture of education - as experienced by the students - is not supportive of demonstrating behavior consistent with a tolerance for ambiguity. Given the relative power positions of students and teachers in the formal educational contexts, it could be conjectured that this perception by students will extend itself into the manner in which the students interact with ambiguity in the classroom environment.

The relationship between the culture of schooling and the culture of a society is dialogical in nature, where each party in the relationship exerts influence over the other. Given the increasing prevalence of ambiguity in society, as well as the need for developing ambiguity-tolerance in individuals, there is thus a need to ensure that the culture of schooling mirrors the culture of the society in terms of ambiguity.

Dimensions of Learning and Instruction Where Ambiguity Becomes Particularly Relevant

There are a number of dimensions of learning and performance where it seems to be especially important to ensure that learners develop skills to overcome the resolvable ambiguities, and that they learn to reconcile the apparently irresolvable ambiguities. Hence, while some might argue that tolerance for ambiguity is requisite for all aspects of functioning, I propose that there are areas where constructive interaction with ambiguity is more critical than other areas. Some of these areas where ambiguity tolerance is especially significant are outlined below.

The Scientific Disposition and Ambiguity

Interaction with the world through a scientific frame of mind requires, among other things, a deep-seated comfort with - and appreciation for - the ambiguities within nature. Thomas (1974) makes the following observation in terms of the role of ambiguity in scientific research and advancement:

This is the element that distinguishes applied science from basic. Surprise is what makes the difference. When you are organized to apply knowledge, set up targets, produce a usable product, you require a high degree of certainty from the outset. All the facts on which you base protocols must be reasonably hard facts with unambiguous meaning. The challenge is to plan the work and organize the workers so that it will come out precisely as predicted. For this, you need centralized authority, elaborately detailed time schedules, and some sort of reward system based on speed and perfection. But most of all you need the intelligible basic facts to begin with, and these must come from basic research. There is no other source. In basic research, everything is just the opposite. What you need at the outset is a high degree of uncertainty; otherwise it isn't likely to be an important problem. You start with an incomplete roster of facts, characterized by their ambiguity; often the problem consists of discovering the connections between unrelated pieces of information. You must plan experiments on the basis of probability, even bare possibility, rather than certainty.

The scientific disposition is critical to the ability to interact with an increasingly complex and contradictory world. In matters of daily living, such a disposition is essential for negotiating the apparent contradictions at all level of experience. In the scientific disciplines, such a disposition is critical to advancing the knowledge of the world. To the extent that learning environments are designed to respond to the need for supporting the scientific disposition, then, the development of an affinity for ambiguity within the individual is essential.

Ill-structured Problem Solving and Ambiguity

Like ambiguity, problems pervade all aspects of life. Furthermore, much like ambiguity, problems are defined at least on part on the basis of the relative perception of the individual: A problem is not said to exist unless the individual perceives it to be there. Interestingly, problem solving is critical to resolving those types of ambiguities that emerge as a result of a lack of knowledge or as a result of a gap between an acceptable goal state and the actual state.

While classical educational theory and practice has provided a solid strategy for teaching learners to apply pre-determined rules and procedures to solving defined problems, there is a growing area of debate in regard to the appropriate strategies and mechanisms for solving complex and ill-structured problems. It is clear, however, that ambiguity is an attribute of the problem state when ill-structured and complex problems are being tackled. In the case of ill-structured problems, the very lacks of convergence in strategies and solutions to the problem forces the learner to have to accept a fair degree of ambiguity in the problem solving process and in accepting one of numerous potentially valid solutions to the problem. In the case of complex problems, the presence of incomplete knowledge and inadequately developed solution strategies makes it necessary for learners to interact with ambiguity, and to regulate their problem solving disposition such that the ambiguity does not hamper the problem solving efforts. Jonassen (2001), in his efforts toward conceptualizing a meta-theory of problem solving, identifies two types of problems where interaction with ambiguity is especially requisite: diagnosis-solution problems and situated case problems. Jonassen (2001) defines a diagnosis-solution problem as one that begins with a fault state and that is tackled through the process of hypothesis-generating, data collection, and hypothesis-testing. According to Jonassen (2001) "[f]requently, there are multiple solutions and solution paths, so the [problem solver] must justify a particular solution. It is this ambiguity in solution paths that distinguishes diagnosis-solution problems from trouble shooting" (p.13). Situated case problems, on the other hand, are situational problems in which "it is not always clear what the problem is" (Jonassen, p.14). This lack of a-priori clarity on the problem creates ambiguity in the problem space, thereby adding to the ill-structured nature of the problem (Jonassen, 2001). Because defining the problem space is more ambiguous, these problems are more ill-structured. The effective problem solver will tackle this challenge by articulating "the nature of the problem and the different perspectives that impact the problem before suggesting solutions" (p.14).

While there are few valid areas of instruction where problem solving is not required for transferring skills or knowledge to a real-world environment, the importance of constructive interaction with ambiguity becomes especially critical to effective training and development in the cases where ill-structured and complex problem solving is required. A variety of instructional strategies have been adopted for developing advanced problem solving skills of this nature, such as problem-based learning and case-based learning.

Adaptive Expertise, Domain Expertise, and Ambiguity

The last thirty years have brought about much progress in the way of our understanding of the psychology of expertise and superior performance. Findings about the mechanisms mediating the development of expertise are being used increasingly in educational settings to assist learners in advancing along the novice-to-expert continuum. Indeed, there is an increasing demand for advancing performance goals in education beyond the levels of simple competence, and for assisting learners in developing the schema and disposition that foster the development of expertise.

An ability to interact effectively with - and resolve - ambiguity is critical to demonstrating domain expertise as well as adaptive expertise. Domain expertise (i.e. expertise constrained to a clearly defined domain-area) is demonstrated typically in an ability to generate many different interpretations, where no one interpretation is accepted. Furthermore, domain expertise is also linked with an ability to defer the making of inferences (e.g. in chess and medicine), where the expert has acquired methods for operating within a highly ambiguous context by encoding only the information that is presented without interfering interpretations and inferences (Ericsson & Kintsch, 1995; Ericsson, Patel, & Kintsch, 2000).

Adaptive expertise is contrasted with routine expertise (relatively static expertise in a specific area of performance), and involves a substantively different way of interacting with the world than routine expertise. Bransford (2001) describes it as follows:

Compared to routine experts, adaptive experts are more likely to relish challenges that require them to "stretch" their knowledge and abilities. They tolerate ambiguity, at least for a while, and they think of themselves as people who know a lot, yet still know little compared to all that is knowable. They are particularly aware of the "assumptive nature of knowing" (e.g., how their current beliefs and knowledge affect their "fish is fish" constructions), and they are able to "let go" of these assumptions without feeling overly threatened. (p. 2)

Bransford notes the significance of adaptive expertise to education, stating that "the ability to change and continually innovate is where the concept of equipping students to be adaptive experts comes into play" (p. 1).

Creativity and Ambiguity

While psychology has provided us much in the way of understanding expertise, the notion of "creativity" remains relatively complex and ill-understood. One proposed definition is 'the achievement of something remarkable and new, something which transforms and changes a field of endeavor in a significant way. . . the kinds of things that people do that change the world' (Feldman, Cziksentmihalyi & Gardner, 1994, p. 1). Another definition proposes to classify creativity as 'exceptional human capacity for thought and creation' (Rhyammer & Brolin, 1999, p. 261).

In spite of a lack of completeness in the scientific understanding of creativity, there is little question that effective interaction with ambiguity is essential to creativity. That this should be the case is obvious when one considers that the creativity differs from other forms of performance by being characterized as generating something new. In cases where performance is based on replication of previously accomplished feats, the path to performance is known, and ambiguities could be removed without necessarily impacting the quality of the performance. In the case of creativity, however, the process results in the creation of something that has not been previously constructed. Ambiguity - whether absolute or relative - will therefore be a major attribute of the experience. Stoyvecha (2003) refers to research conducted by Urban (1991) and notes that "[t]olerance of ambiguity integrates risk taking, non-conformism, openness for experiences and humour in a dialectical balance between resistance and adaptation that characterise creativity" (p.5). According to research, tolerance for ambiguity is a necessary condition for creativity since it mediates the ability to defer judgment (Sternberg & Lubart, 1995; Torrance & Safter, 1999), enables effective creative decision making (Stoyvecha & Lubart, 2001), and sustains creative motivation (Stoycheva, 2000; Stoyvecha & Lubart, 2001).

There appears to be some disagreement as to the extent to which instructional designers and educators can actually address creativity as an outcome. To some, creativity is seen as something that is intrinsic to the learner, or that comes about through the learner's interaction with elements other than the school environment. Nonetheless, Sternberg & Lubart (1991) developed an investment theory of creativity, which asserts that it is possible to foster creativity in children by assisting them in learning to use a variety of different tools. The development of a tolerance for ambiguity is one of the essential aspects of this theory.

Instructional Design Models and Ambiguity

Classical Instructional Design

From my perspective, classical instructional design (i.e. instructional design housed solely in the framework of the behavioral-cognitive theoretical perspective) is not conducive to exposing learners to ambiguity. However, as instructional designers develop broader views of learning, instructional design approaches are effectively incorporating ambiguity.

The origins of instructional design lay in behavioral-cognitive theory, where learning is defined in terms of somewhat stable changes in observable behavior. From this perspective, learning can be evidenced and measured in controlled conditions that do not necessarily account for (or attempt to replicate) the complexities of real-world environments. The behavioral-cognitive view also considers learning primarily from the perspective of the individual, therefore giving little attention to interaction and dialogical processes in the learning process. In addition, the behavioral-cognitive view does not give much attention to learning as an outcome in its own right. In considering the classical definition of learning, therefore, there is little need or justification for giving serious attention to ambiguity. This is not to argue that the behavioral-cognitive perspective is incorrect, but rather that the behavioral-cognitive definition of learning constrains itself to objectively-measurable behavioral evidence and that this constraint makes ambiguity a largely irrelevant phenomenon.

In addition to the foundation on behavioral-cognitive theory, the roots of the field of instructional design are closely linked to the advent of reductionism, objectivity, and systems thinking in the hard sciences. From the classical perspective of instructional design, one might say that the overall objective of the design of instruction is to simplify and compartmentalize complex tasks such that learners can receive clear instruction that allows them to assemble the cognitive and behavioral building blocks for demonstrating a predetermined desired level of performance. Such an approach to instruction has been found to be efficient and effective in the context of a variety of learning outcomes, particularly in terms of lower order thinking skills. Classical instructional design has also been effective in teaching to higher order thinking skills such as problem solving and analysis, as long as the desired level of performance is one that allows learners to apply pre-determined rules and procedures.

Interestingly, the classical instructional design perspective espouses the role of the instructional designer as one of removing the ambiguity from the learning process and the learning material. Bannan-Ritland (2003) notes:

The process of instructional design can be described as giving structure to ambiguity, therefore designers must have a high tolerance for ambiguity and complexity (Seels & Glasgow, 1998). In attacking complex and ambiguous instructional situations, design practitioners need an arsenal of strategies and approaches to support their efforts. Knowledge of perceptual and cognitive theory is viewed as one of the key factors in finding effective instructional solutions and promoting good design (Winn, 1997; Reigeluth, 1997).

Merrill (in Draper, 1997) explains the classical perspective as follows:

In my mechanistic way I believe that higher order skills are knowable and teachable.(…) [O]nce a relationship has been discovered or even in the hypothesis stage representing this relationship in terms of knowledge objects makes the hypothesis or proposition clear so it is possible to determine when the a discovery has been made. In a like manner specifying the operation of an invention in terms of conditions and consequences makes its specification less ambiguous and thus easier to determine when the invention has accomplished the desired goal. I suspect that this formulation makes some of you uncomfortable.

Contemporary Instructional Design

Increasingly, instructional designers and learning specialists are accepting a broader definition of learning (cf. Visser, Rowland & Visser, 2002). Such broader conceptions of learning view context and environment as critical aspects of learning (Visser, J. 2002), recognize the role of communication and exchange in the learning process, and give due attention to cognitive flexibility (Spiro, 1999) as a desired outcome and characteristic of learning. A broader view of learning also challenges the traditional stranglehold of educators and instructional designers on learning and instruction. The notion of ambiguity becomes of particular significance in light of the evolution of our field, as ambiguity is a critical attribute in advancing the state of knowledge and understanding in disciplines such as physics, biology, communication, computer science, history, and economics.

As the field of instructional design continues to develop, methods and theories instructional design are being adjusted to reflect a closer match between expanded conceptions of learning and the accompanying models of instruction. This is evidenced in approaches such as generative learning (Volkl & Ritchie, 1999), problem-based learning (Torp & Sage, 2002), case-based (Schank, 1998) and, to some extent, elaboration theory (English & Reigeluth, 1996). Such approaches to instruction allow learners to develop skills and experience by interacting with complex, ambiguous environments, and to negotiate this ambiguity as they engage in the learning process. The nature of structure in the process varies between instructional strategies. Elaboration theory provides structure through the sequencing of the elaborations in the complexity of the learning environment. Problem-based learning provides structure through the facilitator's modeling of hypothesis-driven reasoning to negotiate ambiguities. Case-based reasoning provides structure through the focus of the case and through the nature of the outcome product specified for the case.

Some might argue that there is a fundamental dissonance between the notion of instructional design and the construct of ambiguity. This position could foreseeable be based on two arguments. The arguments are identified and responded to below.

1. Ambiguity is unpredictable, and can therefore not be designed or pre-meditated.

While day-to-day ambiguity is unpredictable in nature, educators can prepare learners for ambiguity in transfer (i.e. real-world) contexts by planning instruction such that learners are confronted with - and encouraged to develop a comfort with - ambiguity. In other words, while real-world ambiguity is not predictable, instructional designers can design learning environment that contain ambiguity as a characteristic. Not only is this form of design possible, but it is likely desirable. One of the functions of education is to provide an environment for people to test out strategies for interacting with the world, and to be able to do so in an environment that provides some guidance and does not have in irreversible consequences. Furthermore, through careful selection of an appropriate sequence and desirable ambiguity-fostering attributes of the learning environment, it is possible to ensure that learners receive a broad array of experiences with ambiguity. These learning environments can thus be designed to integrate ambiguity to a level that is appropriate on the basis of the learner attributes and the desired performance levels.

2. Authentic ambiguity does not operate within a structure - the individual may impose the structure to contain or manage the ambiguity. Since instruction requires structure, it cannot be designed to address ambiguity.

Once more, the distinction between the real-world and the "classroom-world" is an important one. It is my opinion that this distinction can be valuable to the learner and to the society to which the learner will contribute. While Constructivist-oriented researchers and theorists would likely espouse the need for creating learning conditions of maximal complexity - and therefore with the least structure - it appears that this may not be wholly desirable. If the intent is to replicate real-world circumstances without the guidance and structure inherent in designed instruction, it would appear to me that the value of formalized instruction is altogether brought into question. If, instead, structure and sequence is added to learning environments in a manner consistent with the needs and goals determined in the instructional analysis, ambiguity can be integrated within an instructional environment that otherwise remains efficient and goal-oriented.

Enhancing Instructional Design Through Attention to Ambiguity Exposure and Tolerance

My assessment of the current tendencies in instructional design causes me to conclude that the instructional design community is cognizant of the need for addressing ambiguity as a facet of learning, and as a condition of real-world transfer contexts. Furthermore, there is evidence that models of instructional design are being developed (such as problem-based learning, case-based reasoning, and generative learning) that tackle the issue of ambiguity, while doing so within conditions typically found in classroom environments. The need to further integrate ambiguity into learning processes and assessment is requisite for effective preparation of learners in numerous contexts. Accomplishing this goal requires additional reflection on instructional design models and theories, adjusting the training of instructional designers, and expanding the research agenda within the instructional design community. It would, therefore, be beneficial for the instructional design community to explore the following considerations:

  1. Determining effective practices for embedding ambiguity in a planned manner into instruction, through modifications to existing instructional design models or through the development of novel instructional design models.
  2. Ensuring that individuals joining the instructional design profession develop the skills and habits of mind requisite for dealing with the ambiguities that characterize learning. Bannan-Ritland (2001) notes: "Typically, designers are called upon to analyze unfamiliar settings and contexts as well as to synthesize and develop content that is outside of their expertise. (… ) Each instructional design situation presents unique challenges that force a designer to rely on questioning and creative responses to deal with ambiguity and situational constraints. In addition, instructional design teams are often comprised of individuals with various backgrounds and expertise (…) In dealing with a development team and subject matter experts, designers must posses the ability to handle diverse viewpoints within a group setting, while also focusing on accomplishing the project at hand."
  3. Conducting research on the nature of ambiguity in real-world contexts, and determining the most efficacious methods for integrating such ambiguity into planned learning contexts.
  4. Determining the effectiveness of various modalities of ambiguity integration. For example, comparing approaches that are characterized by little ambiguity, to those that are characterized by extremely pervasive ambiguity, to those where ambiguity is gradually integrated into instruction.
  5. Determining whether there is such a thing as a "way of thinking" that can be taught in regard to interacting with ambiguity. It was, for example, somewhat surprising for researchers to find that metacognitive skills cannot be effectively taught out of the context of a substantive learning situation (Garner, 1990). Similarly, it has been found that problem solving skills cannot be taught or applied at a general level - domain specificity is essential (Jonassen, 2001). This would lead to reason that tolerance for ambiguity, like metacognition and problem solving, is domain specific and/or idiosyncratic in nature.
  6. Addressing the issue of ambiguity systematically in the analysis phase of the instructional design process, such that actual and desired performance in relation to ambiguity can be determined a-priori and addressed through instruction.
  7. Analyzing skills and knowledge for outcomes where ambiguity is a pervasive aspect of the transfer environment, and ensuring that assessment of learning and evaluation of instruction is based on effectiveness in interacting with ambiguity.
  8. Considering alternate modalities for instructional design in situations where desired outcomes relate to the development of such factors as complex problem solving, development of a scientific mindset, creativity, and demonstrating domain expertise or adaptive expertise.
  9. Determining the relationship between learner motivation and ambiguity. There is conflicting data on the effect of highly structured and highly unstructured instruction on learner motivation and confidence. Likewise, it is likely that current research will provide and incomplete and contradictory picture of the effect of ambiguity on learner motivation. Conducting additional research (employing alternate research methodologies) appears highly desirable to determining the nature of the relationship between ambiguity and the affective domain.
 
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TECHTRENDS ARTICLE

Following the workshop and open discussion session at the AECT Convention in Anaheim, CA, a short invited article with the title Ambiguity, Cognition, Learning, Teaching, and Design was prepared by Jan Visser and Yusra Laila Visser for publication in TechTrends. The linked PDF file contains the text as submitted for publication. For reference purposes the forthcoming issue of TechTrends should be consulted.

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