Reid, D. (1996). Enactivism as a methodology. In L. Puig & A Gutiérrez,(Eds.), Proceedings of the Twentieth Annual Conference of the International Group for the Psychology of Mathematics Education, (Vol. 4, pp. 203-210). Valencia, Spain.
ENACTIVISM
AS A METHODOLOGY
David A. Reid
Abstract As
research is learning, theories for learning and research methodologies in
mathematics education overlap. For
the Enactivist Research Group, enactivism is both the theoretical framework
and the methodology for our research. Key ideas such as autopoesis, structure
determinism, structural coupling, and coemergence are used to make sense of
the learning of all participants in research, researchers included. This paper describes these key ideas and enactivist research
methodology in mathematics education.
Introduction
In
his plenary paper at PME-18 John Mason (1994) reminded us of the
interconnection between the theories for learning we employ as psychologists
of mathematics education, and the methodologies we employ as researchers.
It is obvious that this must be the case when we consider that our
research is a particular instance of human learning, and ought to be
understood in the same conceptual frame as that which we use to understand
human learning of mathematics. In
the following I describe how the theories of Maturana, Varela, Lakoff, and
Johnson (among others) have informed and defined the research methodology of
the Enactivist Research Group, as a model for enactivist research in
mathematics education.
Enactivism, and Experientialism and Embodied Cognition.
While
there have been some recent expositions on enactivist theory at PME (Edwards
& Núñez, 1995) and in journals (Davis, 1995) a brief review is in order.
Such a review of an entire theoretical perspective is in many ways a futile
endeavor, but I hope here to touch on those points which are important to the
following discussion of methodology, and to make some connections and
contrasts with radical and social constructivisms.
Many of the ideas of enactivism can be found in the works of
Merleau-Ponty (1962), Wittgenstein (1958), and Bateson (1987), but the first
presentation of these ideas as a general theory for cognition comes in the
works of Maturana and Varela (Maturana, 1987; Maturana & Varela, 1992;
Varela, Thompson & Rosch, 1991). They
describe and name the key concepts of autopoesis,
structure determinism, structural
coupling, and coemergence.
These ideas complement the experientialism of Lakoff and Johnson to
produce a theory for cognition as "the enactment of a world and a mind on
the basis of a history of the variety of actions that a being in the world
performs" (Varela, Thompson & Rosch, 1991, p. 9).
The idea of autopoesis will seem familiar to constructivists,
especially of the more radical variety. Autopoesis
refers to that property of complex dynamic systems of spontaneous
self-organization. The components
of autopoetic systems "must be dynamically related in a network of
ongoing interactions" (Maturana & Varela, 1992, pp. 43-44). That
is, the components interact in ways which are continually changing, but which
at the same time allow for the continuation of interactions so that the system
continues to exist. In addition,
the interactions of the components of an autopoetic system are responsible for
the production of the components themselves.
Autopoetic entities come into existence as a result of their own
properties, and also maintain their existence by modifying their own
properties.
The
problem is how to handle the problem of structural change and to show how an
organism, which exists in a medium and which operates adequately to its need,
can undergo a continuous structural change such that it goes on acting
adequately in its medium, even though the medium is changing.
Many names could be given to this; it could be called learning. (Maturana, 1987, pp. 74-75)
Learning
then, for enactivists, is precisely this continual change which allows the
learner to continue to function as an individual in a medium.
Some social constructivists will be pleased to know that any
sufficiently complex dynamic system can be described as autopoetic, and an
enactivist description of an individual's learning could be applied just a
well to a community as a whole.
Another idea which will be familiar to constructivists is that of structure determinism. What an autopoetic entity does is determined by its own structure, not by an external stimulus, which might trigger some action the structure was determined to do. There is an important distinction to be made, however, with some constructivist perspectives. It is not a matter of an individual having a cognitive structure, which determines how the individual can think, or of there being conceptual structures which determine what new concepts can develop. The organism as a whole is its continually changing structure which determines its own actions on itself and its world. This holistic vision of the cognitive entity is central
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to the
idea of embodied cognition, described by Lakoff (1987), Johnson (1987), and
Edwards & Núñez (1995).
It is possible, in fact probable according to empirical observation and
complexity theory (Kauffman, 1993, 1995), that autopoetic entities organize
themselves into networks of inter-action.
When entities are in such a state, we say they are structurally
coupled.
If I have a living system ... then this living system is in a medium
with which it interacts. Its
dynamics of state result in interactions with the medium, and the dynamics of
state within the medium result in interactions with the living system. What
happens in interaction? Since
this is a structure determined system ... the medium triggers a change of
state in the system, and the system triggers a change of state in the medium. What change of state? One
of those which is permitted by the structure of the system.
(Maturana, 1978, p. 75)
Each
acts according to its structures, but those structures are such that actions
become coordinated. From an evolutionary point of view this can be explained
by claiming that organisms which structurally couple are more likely to
survive, so such structures become the most common.
Complexity theorists would argue that such structures are inevitable at
certain levels of complexity. In
any case, structural coupling is a integral part of learning, that is the
self-modification of autopoetic entities.
Structural coupling tends to be self-reinforcing, either because of the
structures on the entities involved, or because they form part of an
autopoetic entity whose autopoesis requires maintaining structural coupling
among its parts. A favorite
example is the herd of antelope, which leaves a single member behind when it
moves from hilltop to hilltop, to act as a sentry for the herd as a whole.
This particular interaction between that antelope and the herd
threatens that individual, but for the herd as a whole it is a form of
structural coupling which allows the continuing existence of the herd as an
autopoetic entity.
Enactivist Methodology
Enactivism, as a methodology, a theory for learning about learning, addresses several levels of the activity of research. The level most familiar to most of us will be the interrelationship between researcher and data, in which we find ourselves learning new things within a context which is partially of our own creation. Enactivism can also be used to talk about the interrelationships in the research community, in which we as autopoetic researchers engage with other researchers in ways which preserve the structural coupling between us. A third level is that of coemergent autopoetic
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ideas
which live in the medium of our minds, and of which we are emergent phenomena
(as the herd is of the antelope).
A stereotypical image of research is the "experiment" in
which we create a controlled situation, set events in motion, and impartially
observe the results. This stereotype has already been extensively critiqued in
the philosophy of science, so I will restrict myself to describing the
enactivist alternative. In all
research we establish a relationship, a structural coupling, with the milieu
which is to be our topic of study. We
interact with the people, objects, chemicals, and ideas we find there.
By so doing we modify the milieu for each of its inhabitants, and the
autopoetic entities in the milieu adapt in ways determined by their structures
but triggered by our presence. At
the same time we engage in the process we are there for, adapting in response
to the triggers offered by the milieu. Note
that an important part of our structures are our theories, beliefs, and
biases. The changes which can be triggered in us, that is, what we
can learn about the research context, are determined by our theories, beliefs
and biases. What we learn is determined by what we know.
When I refer to the people, objects, chemicals, and ideas in a research
situation, I refer to what is usually considered to be the source of
"data" which is then interpreted.
And there is "data" in enactivist research.
The data generated in my research include field notes, video tapes,
audio tapes, participants' writings, transcripts, notes based on viewing video
tapes, mathematical activity traces which summarize the actions in a video
taped session, research reports, conference presentations, and notes from
discussions with other researchers. These
artifacts can be lumped together as "data", but at the same time all
of them record acts of interpretation, or a researcher learning in coemergence
with a research situation. It can
be said that there is no data, only interpretations and interpretations of
interpretations. This is an
important point to keep in mind, although I will be using "data" and
"interpretation" interchangeably in the following, mostly to improve
readability.
As a community, researchers in a field form the context in which their research occurs. I have to learn in ways which allow me to remain in interrelation with the participants and other aspects of my own research, and simultaneously in ways which allow me to remain a member of this research community. This establishes constraints. There are constraints offered by research data and constraints offered by the research community. I cannot know that the students I have worked with learn mathematics by a undertaking a series of gymnastic maneuvers and remain in interrelation with those students, or my video tapes of them. The "data" forbids some hypotheses. At the same time I cannot attribute their learning to messages beamed into their minds from outer space, even thought the data offers nothing to disprove this possibility, because such a hypothesis would sever my structural coupling with
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my
research community.
The analysis of data in enactivist research can also be seen as a
process of co-evolution of ideas. Theory
and data coemerge in the medium of the researcher. The necessity of theory to
account for data results in a dialogue between theory and data, with each one
affecting the other. As
enactivist researchers we attempt to make use of this interaction to transform
the analysis of data into a continual process of change and encourage this
process as the mechanism of our own continuing learning.
An Example of Enactivist Research
Over
the past three years the Enactivist Research Group has been engaged in
exploring enactivism both as a theory for learning and as a research
methodology (Kieren, Gordon Calvert, Reid & Simmt, 1995; Gordon Calvert,
Kieren, Reid & Simmt, 1995; Reid 1995).
In doing so we have explored two key features of enactivist research,
the importance of working from and with multiple perspectives, and the
creation of models and theories which are good-enough for,
not definitively of.
Multiple perspectives can refer to many aspects of enactivist research.
The most obvious is the participation of a number of researchers, each
with her or his own agenda, theories, and background.
Enactivist research differs from collaborative research in that there
is no common goal or question in which we are all interested (beyond the
general nature of cognition). Particular
research interests of the group include deductive reasoning, conversation,
recursive models of understanding, and mathematical beliefs.
At the same time we work with a common collection of data, about which
we each reach conclusions related to our own interests and theories.
These conclusions need not be parts of a single consistent whole.
In fact, particular interpretations might be quite different. While
some interpretations are not accepted by every member of the group, all
interpretations must be explicable. That
is it must be possible to explain the conceptual structure in which the
interpretation holds, even to others who may not see the world thorough that
conceptual structure. I use the
phrase "multiple consensual contradictory perspectives," where
"consensus" is used to mean the explanation of interpretations in
way which make sense to others, to capture the important features of
perspectives in enactivist research.
There are other ways in which multiple perspectives emerge. One is through multiple revisitations of data which brings a researcher to a situation with new theories and aims which represent the current structure of an ever changing being. Another is through the examination of a wide range of data. The aim here is not to come to some sort of "average" interpretation that somehow captures the common
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essence
of disparate situations, but rather to see the sense in the range of
occurrences, and the sphere of possibilities involved.
A third source of perspectives is the act of communicating our research
to others. By so doing we invite
audiences and readers to engage with us in enactivist research producing their
own interpretations of our ideas and data.
The selection of this wide range of data is not always a matter of
planning. Part of working with the Enactivist Research Group is continually
encountering new situations which occasion reflection and interpretation.
For each of us the data we see is in some ways "found" and
made sense of. This aspect of
enactivist research has been called "bricological" (Reid, 1995).
Bricological research combines the flexibility and creativity of bricolage,
with an underlying logic of inquiry.
Bricolage, as it is used in conceptualizing bricological research,
favors the production of complex structures, theories, models, etc.
appropriate to research on complex systems such as human learners and
societies. It can be contrasted
with a technological attitude that favors production of lots of results
through straightforward, "clean" techniques.
The logic of the bricological methodology comes from the questions
chosen for research, and the theories and models with which the research
begins. These questions, models,
and theories reflect expectations of what might be seen.
These expectations correspond to the plastic structure that determines
the actions of an individual in a context.
Just as an individual's structure changes in changing the context, so
our expectations change even as we observe, interview, and analyze according
to our expectations.
It is important to note that the theories and models of enactivist
research are not models of.
That is to say they do not purport to be representations of an existing
reality. Rather they are theories
for; they have a purpose, clarifying
our understanding of the learning of mathematics for example, and it is their
usefulness in terms of that purpose which determines their value.
The recursive dynamical models for understanding, developed by Kieren
and Pirie (Kieren, Pirie & Reid, 1994) and the language for discussing
reasoning developed by Reid (1995) are two examples of theories for.
Conclusion
As researchers we search for understanding of the learning of mathematics, making use of psychological perspectives, theories for learning, to make sense of what we see. I have given an example here of how one such perspective acts also to make sense of what we do. Enactivism, based on an equation of knowing, being and doing, provides a context in which it is easy to see research about learning as a form of learning. It is not special in this regard, but I hope that by presenting enactivism
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as
a methodology I have presented it as a theory for learning better than I might
have, and that by describing that methodology through a theory for learning I
have been able to communicate the spirit of the research that is done by the
Enactivist Research Group.
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