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:
- immerse learners in activity
in authentic context
- start from concrete (and thus
complex) experience rather than the abstract constructs of a
domain; move to the abstract through iterative cycles, diminishing
scaffolding over time
- resist simplification
- help to hold anxiety (a role
for teachers and managers)
- teach systems thinking, e.g.,
complexity, nonlinearity, unpredictability (e.g., how long-term
outcomes in a complex system cannot be accurately predicted,
how ambiguity can lead to new knowledge)
- encourage mindfulness (see Weick
& Sutcliffe, 2001) and reflection in and on experience
- work toward alignment of cognition
and emotion-a whole systems approach (e.g., bodymind as one)
- treat learning outcomes as designs
and thus as "expected unexpected" (see Nelson &
Stoltermann, 2003)
- help learners and workers examine
ambiguity as a source for understanding the richness of a unique
situation
- use ambiguity as a basis for
local, indirect action
- treat ambiguity as a sign that
the situation may be shifted dramatically by small actions and,
therefore, one needs to respect this sensitivity and exercise
great care (for example, a teacher should recognize that ambiguity
is where a breakthrough or breakdown is possible, and thus where
careful guidance is necessary)
- distinguish utter confusion
from useful creative tension (which implies competencies that
are not regularly found in lists put out by professional societies)
- encourage AND in addition to
OR thinking
- see ambiguity as an opportunity
for expansion of the zone of proximal development
- see ambiguity as an opportunity
for new order
- promote sustainability and authenticity
of process as more important than efficiency of process and effectiveness
of product.
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.
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
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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.
- 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
- one in which the capacity to
raise and formulate questions is more important than having the
answers;
- one that focuses on problems,
including those that are complex and can only hesitatingly be
formulated as they relate to the fragile nature of human existence,
which increasingly requires the emergence among members of the
human species of a level consciousness that reflects the inter-solidarity
of human beings at a planetary level (Morin, 2003);
- an environment that thrives
on collaboration, rather than competition, as it recognizes that
knowledge is being continually constructed and that its builders
are human beings who reach their most magnificent results when
they build their knowledge together;
- one that inspires and nurtures
creativity in the search of new ways of knowing, not limiting
who lives in that environment to merely copying the research
practices of the past, providing encouragement to master such
practices in order to build on them so as to make the next step;
- an environment also that foments
dialogue between as well as over and above the disciplines about
the underlying assumptions of existing knowledge, the historical
context in which it took shape, the contextual factors, and etical
and aesthetical frames of reference that condition it;
- an environment, finally, that
reestablishes the essential link with the messy reality of life
as it is lived, at different levels, in the daily practice of
humans who build their knowledge as they go along.
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].
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