FRACTAL MODEL OF LANGUAGE ACQUISITION
Vera Lúcia Menezes de Oliveira e Paiva
Nothing that was will be
Again the way that it once was
Everything passes, will always pass away
Life comes in waves like the sea
In an infinite going and coming
Everything we see is not
As we saw it a second ago
Everything in the world changes all the time (...)
Like a wave on the sea
1. The problem
Acquisition models,[1] in my opinion and that of many other authors (McLaughlin, 1987; Ellis, 1990; Brown 1993a e 1993b), fail to consider all the processes involved in the acquisition of a language, much less a foreign language (FL). I see these models as fragmented views of parts of a single system. Although it is possible to theorize about the existence of some generalizations in acquisition, everyone has their own individual characteristics, making it impossible to describe all the possibilities of this phenomenon. There are differences in biology, intelligence, aptitude, attitude, age, cognitive styles, motivation, personality and affective factors, besides the differences in the contexts in which the learning processes occur: the quantity/quality of input available, social distance, type and intensity of feedback, culture, stereotypes, among others. (see Ellis, 1990; Brown, 1993a and 1993b; Ehrman, 1996).
The combination of these factors, nevertheless, is not determinant in the sense that a set X, in the proportion Y of variables, would make learning either effective or ineffective. The human being is unpredictable, and different changes and adjustments can occur in similar situations.
Many authors have alluded to the to the complexity of the phenomenon of this type of learning. Nunan (2001:91) refers to the complexity of acquisition of a second language saying:
“Current
SLA research orientations can be captured by a single word: complexity.
Researchers have begun to realise that there are social and interpersonal as
well as psychological dimensions to acquisition, that input and output are both
important, that form and meaning are ultimately inseparable and that
acquisition is an organic rather than a linear process.”
Almeida Filho, after mentioning some aspects of this complexity, asserts that the “foreign language is, on the other hand, also a complex concept that instructors must consider and reflect upon in the act of exercising their profession.” However, Larsen-Freeman (1997) was the first to approach this complexity with reference to complex systems or chaos theory.
“Chaos Theory
states that small changes can result in large differences and that there is an
underlying order in all that surrounds us.”[3]
The theory “. . . attempts to explain the fact that complex and unpredictable
results can and will occur in systems that are sensitive to their initial
conditions.”[4] This
non-linear way of thinking, contrary to Cartesian logic, ignores determinist
hypotheses and abandons the concept of science as something necessarily
systematic, objective and generalizable. The concept of context becomes
essential for us to understand the diversified nature of phenomena. According
to the new way of seeing phenomena, systems are complex, non-linear, dynamic,
chaotic, unpredictable, sensitive to initial conditions, open, subject to
attractors[5],
and adaptive, in that they are characterized by the ability to
self-organize.
Larsen-Freeman presents varied evidence to
prove that there are similarities between the science of chaos/complexity and
the acquisition of a second language: the dynamism of the learning process, its
complexity, its non-linearity, its being subject to attractors, and the self-organization of the
inter-language[6], that is in
a process of continual restructuring, and can be explained by its reactivity to
feedback. In defense of her hypothesis, the author limits herself to the
discussion of five examples: the mechanisms of acquisition, the definition of
learning, the stability and instability of thein interlanguage, differentiated
degrees of successindividual differences, and the effect of
instruction.
To discuss the first example, Larsen-Freman (1997:152-154) unites Piaget (constructivism) with Chomsky (innateness), stating that “both individual creativity and social interaction combine to influence the shape of the developing grammar.” (p.154)
Vygotsky, well before the appearance of the complex systems theory, in the 1920s, had similar insight on verbal thought as a complex system. On concluding his chapter on Thought and Word, he said that verbal thought appeared as a complex, dynamic entity, and the relation of though and word within it as a movement through a series of planes. (Vygotsky,1962: 152).
Motivated by complexity theory, I intend to pursue this line of reflection, in the attempt to re-examine, by theoretical means, some hunches that I have long felt, and about which I have searched in vain for theoretical support.
The increase in qualitative research on acquisition seems to be evidence that learning is not a phenomenon that can be explained by laws of cause and effect. According to Erickson (1996:104),
“positivist
research on teaching presumes that history repeats itself; that what can be
learned from past events can generalize to future events – in the same setting
and in different settings. Interpretive researchers are more cautious in their
assumptions. They see, as do experienced teachers, that yesterday’s reading
group was not quite the same as today’s, and that this moment in the reading
group is not the same as the next moment.”[7]
For complexity science, nature is a complex system and within it there is a combination of other systems, equally complex. It seems promising to me, therefore, to think of language learning as one of those dynamic and complex sub-systems, and in that way to try to explain L2 as much as EFL without ignoring the specific qualities of either one.
There is enough evidence to argue that language learning certainly seems to be an adaptive complex system due to its inherent ability to adapt to the different conditions imposed upon it by the environment. To transform from a speaker of one’s native language into a speaker of a second or foreign language is a process as complex as changing from total order to chaos, meaning, without predictability.
2.
Acquisition
Theories
Acquisition
Some theories
have envisioned the acquisition process as a linear process with a machine’s
mechanicist
level of predictability. We can see this, in a succinct formbriefly, as it
appears in various theories:
·
the behaviorist model sees acquisition as the creation of automatic
habits acquired through imitation by repetition (drills)
·
Krashen’s (1985) input hypothesis argues for the importance of
comprehensible input adding one level of difficulty (i+1) in order for acquisition to occur.
·
Hatch (1978) emphasizes the importance of interaction, especially for
the acquisition of vocabulary: the learner interacts with more proficient
speakers, negotiating meaning and acquiring the language.
·
Swain (cited in Markee, 2000:8), argues that “learners must also
produce comprehensible output to change the interlanguage from semantic to
syntactic analysis of the input.”
·
Schumann sees L2 acquisition as a process of acculturation, that is, a
successful adaptation to the social group without the interference of affective
factors (e.g. culture shock) catalyzes the acquisition of the spoken language
of that group. In Schumann’s point of view, the more learners become insiders
in relation to the culture of the other (acculturation) the more they learn the
language. (Ellis, 1985 e 1997).
Many other
hypotheses could be cited, all of them indicating one of the sub-systems or
parts of the learning process, which make up the complex system that is the
acquisition of another language. I think of all these theories, including the
behaviorist, as efforts at explaining parts of a whole. Thus, it is not
necessary to discard them, but instead to unite them in a way that provides a
complete view of the process.
3. Learning as a Complex
System
Language
learning, like any other type of learning, is not a linear process, and
therefore cannot be as predictable as many models of acquisition have
hypothesized it to be. Minimal differences in starting conditions can produce
very different results. In complex systems, as Lewin states (1992:11),
In nonlinear systems small inputs can lead
to dramatically large consequences. This is often characterized as the
so-called butterfly effect: a butterfly flaps its wings over the Amazon rain
forest, and sets in motion events that lead to a storm over Chicago. The next
time the butterfly flaps its wings, however, nothing of meteorological
consequence happens.
Chris Langton, in support of Lewin (1992:12), explains how dynamic non-linear systems function in the following way:
“In one case you may have a few things interacting, producing tremendously divergent behavior. That’s what you’ll call deterministic chaos. It looks random, but it’s not, because it’s the result of equations you can specify, often quite simple equations. In another case interactions in a dynamical system give you an emergent global order, with a whole set of fascinating properties.”
Never can we state,
with any certainty, that what will happen is a learning process, since what
works for one student is unproductive with another. As creativity is one of the
characteristics of complex systems, the context of learning contains an
unpredictable set of dynamic behaviors. Norman, quoted by Lewin (1994:71),
calls this “creativity inherent in complex systems” at “the limit of chaosedge of chaos.”
The notion of the limit
of chaosedge
of chaos has a commonality with the concept of the zone of proximal
development (ZPD) of Vygotsky (1984), which in turn is similar to Krashen’s
(1985) input+1 concept.
Vygotsky, who revealed the historical determination of the conscience and human intellect, also believed the process of language learning to be non-linear. According to him,
“child development is a complex dialectical process characterized by periodicity, unevenness in the development of different functions, metamorphosis or qualitative transformation of one form into another, intertwining of external and internal factors, and adaptive process which overcome impediments that the child encounters. (1978:73).
To Vygotsky, learning occurs in the zone of proximal development, as he defines it:
“the distance between the actual development level as determined by independent problem solving and the level of potential development as determined through problem solving under adult guidance or in collaboration with more capable peers.” (p.86).
Krashen
(1985:2) suggests that we learn a language by receiving “comprehensible input.”
According to him, “we move from i,
our current level, to i + 1,
the next level along the
natural order, by understanding input containing i
+ 1 advoga que aprendemos uma língua através da
recepção de “input compreensível”.
Segundo ele, “nos movemos de i,
nosso nível atual, para i+l,
nosso próximo nível ao longo da ordem natural, ao entender o input que
contém i+l”. [[original quote]]
He continues,
“We are able to understand language containing unacquired grammar with the help of context, which includes extra-linguistic information, our knowledge of the world, and previously acquired linguistic competence”.
It can be observed then, that both authors refer to the emergence of
learning at a point similar to the “limit of chaosedge of chaos,” a
point sensitive to variations in the parts of the system: the learner who is enabled by
input+1 (Krashen) or by interaction with more competent speakers (Vygotsky ).
Figueiredo (2001:63) points out the differences between the constructs of both authors: Vygotsky and Krashen. He states:
Some of those who study the processes of L2 learning, for example,
Richard-Amato (1988) and Schinke-Llano (1993) directly or indirectly associate
the notion of ZPD with Krashen’s i+1
(1982, 1985),[8] with the
understanding that what Krashen (1982, 1985) is calling i conforms to what Vygotsky
(1998) calls the real development level of the child, and the i+ 1 would be the zone of proximal
development. However, Dunn and Lantolf (1998) and Thorne (2000) argue that the
similarities between the two constructs are superficial, and the differences
profound, insomuch as, to Krashen (1985), acquisition occurs to the extent that
the individual is exposed to comprehensible input, questions of interaction and
output[9],
being in a distant second place.[10]
In contrast, Vygotsky (1998), sees interaction, dialogue, as the key to cognitive
development.
For our purposes, however, the relevant point is that both recognize the existence of the origin of learning, even if Krashen’s viewpoint is centered on the question of input and Vygotsky’s on interaction.
I
propose then, that the model of language acquisition should be considered as a
set of connections within a dynamic system that moves in the direction of the “limit
of chaosedge
of chaos” transition point, (Lewin, 1994:71), meaning, a zone of creativity with the maximum
potential for learning.
The dynamic of these connections is such that the system functions as an indivisible whole, in which each part is only productive when in constant interaction with the others and not as an independent entity. As with fractal geometry, in a kaleidoscope, for example, there are infinite possibilities of combinations of these parts making up the fractals of the acquisition process. Tiny alterations can cause significant changes, with the effect of a snowball bringing about an avalanche.
4.
Attractors and the ability to adapt
Fractal structures work as “chaotic attractors,” that is, routes that a dynamic system runs.
Many dynamic systems have three types of attractors: an immovable point, periodic attractors and chaotic attractors (Lewin,1994: 65). In L2 learning, my hypothesis is that the immovable point (or equilibrium) is the knowledge already acquired, through which all the language learning paths have to pass, connecting the new knowledge with that already acquired. Cognition is the periodic attractor, and the other attractors would be chaotic or “strange attractors”[11], various factors that affect learning (interaction, input, materials, etc.) These attractors are in constant change. As Lewin (1994:93) says, “They will change, dynamical possibilities will change, as the environment changes”.
Accepting this model does not imply rejecting the previous models, but instead connecting them, as each one can explain a fraction of what happens in the complex phenomenon of language learning.
Let us
consider an analogy. In order to walk, you must have your heart and lungs in
“x” state of functioning. Walking will increase your oxygen intake and speed up
your metabolism. My Your heart will also benefit from walking.
All the parts are connected and it’s this connection that keeps the organism
alive.
A similar process occurs in language learning. The connection of sub-systems ─ biological, cognitive, and affective processes; motivation; historical and social context; processes of affiliation[12]; input processing; creation of automatic habits, and interaction ─ which could create periods of stability, alternating with peaks of change. The turbulence caused by alterations in one of the modules ripple out into other elements of the whole. As complex systems are adaptive, after these chaotic times order is reestablished, but never the same as before. On the other hand, at other times, no effects are perceived, proving the unpredictability of complex systems.
As in a narrative (as it is defined by Todorov,[13] 1979:138), in learning we also have a stable situation that any type of force can disturb, the result of which is an unstable state. When an opposing force is applied, equilibrium is reestablished; the second equilibrium being similar to the first, but never identical.
The possibilities for imbalance of this stable order, in the context of learning, are innumerable. One of the simplest examples would be to read a text and come upon an unknown word, generating an imbalance in the processing of meaning. Several alternatives of opposing forces could occur ─ consulting a dictionary, inferring the meaning from context, consulting another person ─ until an equilibrium is reestablished, which, nevertheless, is never the same as the first, because a connection was made and more information was added to the learning process .
Thus, we see that language acquisition should not be envisioned as a final product, but as a continuing and unending process in which we have a recurrent dynamic, of one pattern inside another. Moreover, we should keep in mind that the object in language learning, that is, the language itself, in not a static product, but also a dynamic, complex system, undergoing constant change.
In the same way that a net is only a net because of its various interconnections that continue repeating the same pattern; language learning, as I see it, functions like a fractal: cognitive operations catalyzed by interconnections among the multiple parts of its system repeat themselves over and over, constructing a network of knowledge/use of the language in a continuum.
According to Gleick (1987: 109), the fractal approach “embraces the whole structure in terms of the branching that produces it, branching that behaves consistently from large scales to small”. Thus, as a whirlpool is formed by a continuum of similar forms in connection, language learning is the result of a continuum of similar processes, as I demonstrate below.
Learning of an L2 is a process that undergoes many mediations, occurs in varied contexts and does not work in the same way with all individuals. Just as each human being is unique, the semiotic processes and connections made will also be unique.
The
representation of what language learning is lies in the symbolic field, that
is, it depends on cultural decisions, decisions both arbitrary and
conventional. If we examine the history of language teaching, we can see that
these representations have undergone changes and have influenced the methods
and approaches to teaching: to know a language is to understand its grammar
(syntax) and be able to translate it (grammar-translation method); to know a
language is to have an oral command of it as close as possible to the native
speaker (direct and audio-visual methods); to know a language is to be able to
use it to communicate in a comprehensible way (meaning/communicative (?)
method
approach);
to know a foreign language is to allow interior disarrangements /upsets(?)
that change the constituency of subjectivity (discourse discoursive method),
according to Neves (2002), citing Nelman (1992) and Coracini (1998).
5. The Model
I introduce below an illustrative representation of the model I propose, the fractal model, a complex dynamic system, composed of sub-systems equally complex and dynamic. The illustration is only one of the possibilities for combination of the fractals. Since the system is dynamic, other unpredictable combinations will certainly occur. In this graphic example, interaction, for example, is directly connected to the input and automatism. Other configurations would be possible. Interaction could, for example, be connected to context (e.g. interaction is face to face or mediated by a computer), or even to several other factors at the same time.
Fractal Model of Language Acquisition
Figure
1
Each subsystem is
further subdivided into several other fractals, representing variables that can
affect the whole system unpredictably, because the smaller fractals are not impervious
to changes, but are, in fact, links in the same net of connections. Each
fractal of each subsystem further divides into other fractals.
The other
components of the subsystem I call Bio-Cognitive
are: first language, age,
sex/identity, personality, cognitive styles and senses, learning strategies. In
the Input fractal, I include the
following types of input: formal, non-verbal, communicative, artificial,
authentic, sporadic, continuous, oral, written, varied. In the Interaction fractal, I list the
following possibilities: real, simulated, virtual, negotiated, in group, in
pairs, teacher-centered, with other learners, with native or more competent
speakers. The Social-Historical Context
fractal brings together aspects such as the classroom, the natural environment,
stimulus, feedback, culture, the group, the speakers, opportunity, time and
space. In Automatism there are the
sounds, intonation, structures, lexicon, chunks, placement, genders, standard
textual formats, standard discourse patterns, and international rules. In Affiliation I include identity,
prejudice, fascination, integration, stereotypes, nearness, the political
context, status and feelings of belonging or not belonging. Finally, the
fractal Affective consists of:
anxiety, attitude, beliefs, self-esteem, affective filter and types of
motivation such as: integrative, instrumental, political and affective.
For the sake of representation, I place in
the same fractal biological and cognitive components. However, each of these
aspects corresponds to a specific fractal that, in turn, also subdivides into
other fractals. The factor “learning strategies,” for example, is subdivided
also into other fractals, such as cognitive and metacognitive. In the cognitive
fractal, we also have other subdivisions, such as, memorization, translation,
inference, etc., which themselves further subdivide. In the metacognitive
fractal there is planning, monitoring, and evaluation of one’s own learning.
In the interconection among fractals, there can be many
possibilities for organization. For a learner, “interaction” for example, could
be, among other movements, connected to the anxiety generated by the belief
that learners themselves could hold that they have no aptitude for language
learning. As a consequence, the learner might undergo more obstacles to
interact in the foreign language. Another movement could create another kind of
fractal shape, in which interaction could be connected to the social context
(face to face interaction or interaction mediated by the computer). The possibilities are infinite, because the
factors that influence language learning are also infinite.
A graphic representation of the fractal
model in movement can be accessed at this address http://www.veramenezes.com/fractal1.html. Another image of the
model at the address http://www.veramenezes.com/fractal2.html shows representations of possible
subdivisions of the subsystems, whose parts, or fractals, are also in
interaction, with one of the infinite possibilities of dynamic combinations
among the fractals of the complex system of acquisition.
The model proposed here applies equally to L2 as to foreign language acquisition (FL). What distinguishes L2 acquisition from FL would be the set of variables of the context, or more specifically, if the language is learned and used in a country where it is spoken, or whether it is learned in a country which primarily uses a different language than that being learned.
Depending on the connections among the various subsystems, success in the process of acquisition could vary as much in FL contexts as in L2. That is, we can see FL learning situations experiencing great success, and L2 situations much less successful, depending on the set of connections that are created, or that fail to be created.
6.
Teaching Methods
Teaching methods have varied according to the dominant linguistic theory and, consequently, the theory of language learning has also undergone changes. Nevertheless, learners continue to learn and to use their L2, or FL, despite the methodology to which they have been subjected. The methodological changes have not been the only factors responsible for catalyzing the processes of learning: there have been other factors, among them, autonomy of the learner.
The learner is the main part of the process and should be seen as the agent of his/her own learning and not a moldable object on which the method or professor imposes a form.
By ignoring the role of the learner, several teaching methods and acquisition models have created hypotheses and linear explanations without taking into account that a human being is always the mediating sign of his/her own learning and different effects could arise in reaction to the same set of variables. Neither can we ignore “that the organism shows tendencies toward certain forms of organization before learning something that can be considered new to it. These tendencies correspond to an intrinsic dynamic of the system.[14]” (Pellegrini, 2000:33).
Paraphrasing
Pellegrini description of learning motor skills, I would say that, in language
learning, new communicative patterns (understood as syntactic, textual, international
interactional
and discourse discoursive patterns) emerge and are
established with practice (through
exposure to the language and its use), changing the state of the system.
This new communicative pattern, once acquired, with practice is incorporated as
an attractor, changing the layout of all the attractors, as new patterns
accumulate throughout the cycle.
7.
Conclusion
Throughout
my career, I have found plenty of proof that learning is a complex system. One
example is the ability to adaptcapacity for adaptation,
a characteristic of dynamic systems. In the data of my research on learning
strategies (Paiva, 1994), I confirmed that my consultants informants tried
to adapt to the context of FL learning, searching for ways to increase their
opportunities to use English. Some said that they held conversations with
themselves in front of the mirror; others tried to give the English names for everything
they saw out the bus window on their way to work. They watched lots of English
language films, listened to music, exchanged letters with speakers of the FL,
and more than anything else, read a lot.
Another
example of adaptation is the use of strategic competencycompetence[15]
(Canale e Swain, 1980), or compensation strategies (Oxford, 1989), which help
learners to overcome limitations in their knowledge. That is, to leap the gaps
in their knowledge of the language, learners take up one of these types of
strategies and thus succeed in restoring equilibrium in their interaction with
the text or another speaker.
Knowing a language is not only a question of accumulating information about linguistic structures and vocabulary, but also the ability to create new phrases based on the connections and management of oral and written interactions.
As Packard states, quoted in Gleick (1987;251), “In the development of one person’s mind from childhood, information is clearly not just accumulated but also generated – created from connections that were not there before.” This creativity, which had already caught the notice of Chomsky (1957), seems to explain the ability of learners to produce phrases they have never heard before.
I believe that complex systems theory can explain such phenomena in the following ways:
· A learner remains in equilibrium, for a certain amount of time and suddenly a fast change occurs, showing an advance in acquisition. That is, in learning we have periods of stability followed by “explosions” and change;
· The same teaching and learning strategies do not have the same effects for all learners;
· Connections are necessary for the system to function, be they cognitive or social;
· Order of linguistic difficulty in an FL teaching program is not a dominant factor for FL acquisition, because one of the characteristics of a complex system is self-reorganization, that is, order exists within the disorder.
· Small stimuli can have unpredictable consequences, dramatically negative or positive. Thus, in formal contexts, the teacher can not only activate learning mechanisms, but also construct insurmountable barriers.
Seeing language acquisition through the prism of complex systems leads me to conclude that teachers should let the creativity of the students blossom as in the Chinese saying “let a hundred flowers bloom,” instead of imposing their own way of learning, or their beliefs about acquiring a language.
It is also the role of the teacher to encourage constant contact of the student with as many forms of input as possible and to promote interactions among various speakers (learners, competent speakers and native speakers). Language learning, also a social process, depends on these connections among speakers.
In the contexts of formal learning, the function of the professor would be to encourage opportunities to use the language and give each learner the freedom to use the strategies that work best for them, so that they can learn through their own learning style. By using the language in formal or natural contexts, the complex system of acquisition follows its own path, and the learner goes on building knowledge and acquiring the language.
In this
way, our role is to “disturb” a zone of stability and provoke the chaos that
results in a zone of creativity (limit of chaosedge of chaos or
ZPD) where small changes can occur, creating significant effects on learning
processes.
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