A DYNAMIC PERSPECTIVE ON ACADEMIC ENGLISH L2 LEXICAL DEVELOPMENT

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A DYNAMIC PERSPECTIVE ON ACADEMIC ENGLISH L2
LEXICAL DEVELOPMENT



Tal Caspi and Wander Lowie


University of Groningen
, the Netherlands


w.m.lowie@rug.nl

t.caspi@rug.nl


Research
has

shown that transfer of passive L
2 vocabulary into production is
far from linear, and that the interactions between levels of vocabulary
knowledge depend on learning context and duration, word frequency, and
learner proficiency (Schmitt & Meara 1997; Laufer & Paribakht 1998). In
this arti
cle, we suggest that

the

L2 lexicon is a dynamic system, similar to
natural self
-
organizing systems, in which developing components interact i
n

a
complex way, and variation is inherent to development. We use a case
study of the development of four levels o
f academic English (L2) vocabulary
knowledge to illustrate the explanatory power of dynamic systems theory.


Key words: Vocabulary acquisition, dynamic systems, DST, LAVT,
Longitudinal, passive, active.


1
.


I
ntroduction



Vocabulary development has been
studied in a wide variety of context
s,
focusing

on several
knowledge
dimensions
that
rang
e

from passive to active,
from incidental to e
xplicit and from learning to acquisition
.
In this paper, we
suggest

a converging view on L2 vocabulary

development,

by ap
plying

a

Dynamic Systems Theory (DST)

perspective. DST
has been extensively
used to analyze a range of natural, social and behavioral phenomena

and
has
recently
been
appli
ed

to L2 development (Lars
en
-
Freeman, 1997;
d
e Bot
et
al
., 2007).
DST

is

essentially

a theory of change
, and

its
most important
merit for L2 development is its emphasis on the developmental process
itself, rather than on products of th
is

process at
a single
moment in time.
In
addition, DST
allows
for
the combination of
several factors affe
ct
ing

development

into
a single
model.
This paper will concentrate on

the
varied
developmental rates of lexical knowledge levels and the influence
of
word
frequency
, learner proficiency, and learning context and duration

on their
interactions
, which result

in nonlinear transfer of passive L2 vocabulary
knowledge into production (Schmitt & Meara
,

1997; Laufer
,

1998; Laufer &
Paribakht
,

1998)
.

T
o investigate L2 lexical development from a DS
T

perspective, we focus on
variation
in the development and interactio
ns
of
four
L2 lexical knowledge
levels: word recall and recognition
i
n the passive
knowledge dimension, and controlled and free production
in
the active
knowledge dimension.

We will demonstrate that the two dimensions are
strongly interrelated and that
pat
terns of
variation in their development and
interaction is

compatible with
characteristic
s

of
dynamic system
s
.

The
paper begins with an overview of DST
,

its
relevance

to
language and the value of data
variation
in
research from a
DST
perspective
.
After
rev
iew
ing

dynamic models of vocabulary knowledge

and

relating
them
to empirical findings
,
we
conclude with
a case study
which illustrates how
academic English
(L2)
vocabulary

development
can be investigated from a
dynamic
perspective
.



1.1
.
Language as a Dyn
amic
System


Dynamic systems can be identified in virtually any field that involves growth
and interaction, such as ecology, biology, psychology, social behavior and
cognition.
An example of a dynamic system is a flock of birds, in which
dynamic interactio
ns between individual birds generate
continually changing

shapes and movements.
Generally speaking, a dynamic system is a set of
changing components that influence each other. These components can be
described as dynamic subsystems nested in the greater sy
stem, and are in
turn comprised of interacting, developing components. Not only do these
components change over time, but their interaction is also dynamic and
changes
with
time. Change over time, or systemic ‘growth’, cannot be fully
predicted, but always

follows from
a previous state of the system. This
iterative growth
is
inherently nonlinear, as small changes at one stage may
lead to drastic qualitative changes in developmental pattern. The
consequence of the iterative development and the ever
-
changing
interactions
of a dynamic system’s components is that the system is ‘self
-
organizing
’.
The self
-
organization

of a dynamic system is limited by availability of
both
external
and
internal
systemic
resources. As a result
of the
limit
ations of
these

resources,

the
developmental pattern of the system alternates between
attractor and repellor

states
. Attractor states

are
configurations that the
system is inclined to remain in unless perturbed by a sufficient amount of
input; while repellors are states in which
th
e system

is seldom or never
found.

It has been convincingly argued elsewhere (for instance
by Van
Geert, 1991; Larsen
-
Freeman
,

1997; and
d
e Bot
et al
., 2007) that language
,
both
for

the individual learner and
for a
language community,

can be
regarded
as a
dynamic system. Like other dynamic system
s,

language
develop
s

nonlinear
ly

and
is
affected not only by input, but also by
interactions between
its componential
subsystems, such as specific
languages known
.

Within these languages, another level of subsystems

such
as grammar, vocabulary and phonology can be considered as nested
,
interacting subsystems
. The dynamic nature of language development is
further emphasized by the stochastic pattern of
an
initial state
that develops
iteratively
.
The r
esources for lang
uage learning
are varied
. Some
of them,
such as working memory capacity and language learning aptitude, are
inherently
limited

for a particular learner
,
while
other resources, such as
motivation, are more easily affected by the
sociolinguistic setting in w
hich
the

language
is learned
. Like all dynamic systems,
language
growth
is
restricted by the limitations on its resources
, and shows patterns of repellors
and attractors,
characterized

in L2 as

fossilization

.

L
anguage studies often concentrate
on attempt
s to l
ink growth
effects and external factors

linearly
,
thereby d
isregard
ing

data
variation both
between and within individual learners as noise or measurement error
.
However
, this variation can be “substantial, stable, and have [its] own
developmental cou
rse" (Bates
et al
., 1995: 1).
R
ecent dynamic approaches to
L1 (Ruhland
,

1998; van Dijk
,

2003) and L2
development (
cf
.

Larsen
-
Freeman, 1997;
d
e Bot
et al
., 2007)

emphasize
that
its
trajectory is far from
a
straightforward
linear
transition
from
a complete
l
ack of knowledge to full
command
. They

focus
instead
on patterns
of variation

that accompany
developmental trends
.


F
rom
this
perspective
,

variation

is inherent to
, and in fact enables,

language change

and evolution

by

altering
the
language
s

of

individuals

and
the
ir

communities

(Larsen
-
Freeman, 1997).

I
ncreased variation coincide
s

with periods of
accelerated
development

known as “de
velopmental
jumps”

(
Thelen & Smith, 1994
)
. Acquisition
has been shown to be
a series of
changes in relative frequencies of str
ategies, leading to a decrease
in
less
mature strategies
, rather than an abrupt replacement of older strategies with
new ones

(
v
an
Geert &
v
an

Dijk
, 2002). Moreover,
variation
not only
reflects change, but
can
also
be regarded as
the
condition
that enables

it
(Bertenthal, 1999)
.

A
ll levels of language development and use
,
on
every
time scale
,

are
characterized by variation
.

At the
macro level of a learner’s
lifespan,
periods
of rapid growth, like the

vocabulary
spurt”
during
the second year of a
chil
d
’s li
fe (
Ganger & Brent, 2004)
, alternate with

periods of vocabulary
attrition due to non
-
use

(Hansen, 2001)
. At the
micro
-
level of the
millisecond
,

rapid
word retrieval alternate
s

with strenuous word finding.

Here, too, a

detailed
longitudinal study of
variati
on
in lexical use can yield
valuable information about
the
mental lexicon
.



2
.

A
D
ynamic
V
iew on L2
V
ocabulary
D
evelopment


Vocabulary, the largest area of linguistic knowledge, is also
the area
most
affected by attrition
,

both
in
individual learners and
in language
communities
(Gross
,

2004).
T
raditional accounts of the mental lexicon describe it as a
static
dictionary
-
like structure

that

exists
independently of its use;

more
recent accounts address
its
complexity, comp
o
nentiality and
interconnectivity and

the dynamic nature of
lexical

processing (
Singleton,
1999;
Elman
,

1995
, 2004
;

Meara
,

2005).
However, a
s in
most
L2
studies
,
lexical studies typically
focus on
pre
-

and post
-
treatment
group
effects

rather
than on developmental processes in individuals, and

eliminate variation by
applying regression analysis to data
.

The dynamic approach perceives the mental lexicon as
comprised of

word representations which are

highly context
-
sensitive, continuously
-
varied, and
probabilistic
” (Elman
,

1995: 199). These repr
esentations are

trajectories through mental space
” (Elman
,

1995: 199)

rather than
fixed
construct
ions
.
In this episodic view
, word recognition
, recall

and production
are
graded process
es

affected

by
interactions
that determine the speed of
word retrieval
in a given context.
In other words,
a word
does not have a
fixed meaning that is stored in the lexicon, but a particular set of meanings in
a particular context at particular moment in time

(for a detailed account of
the episodic lexicon, see Goldinger, 19
98).

The state of the dynamic lexicon
,
at any given moment, is a function reflecting its prior state (Elman
,

1995:
203). Although so far DST has not been applied to empirical L2 vocabulary
data,
current lexical models using the activation metaphor are larg
ely
compatible with dynamic views

(Jacquet
&

French, 2002)
.


A simulation
of

a strongly simplified model of

the

bilingual lexicon
as an on
-
off network of
a small number of items ha
s

shown
that it exhibits
interactive relations and iterative development
cha
racteristic
of dynamic
systems (Meara
,

2005). The interacting L1 and L2 lexicons typically settle in
a steady

attractor

state
,

in
which
L1
vocabulary
i
s dominant and L2
is
dormant (Meara, 2005).
The
dominant
L1 lexicon remains relatively stable,
while the
L2
lexicon
was unstable and sensitive to perturbation.
Thus,
activati
ng

L1 lexical item
s

did not produce large or lasting effects, whereas
the
activating
even
a small number of
L2
items
sometimes generated
iterative
activation

patterns
.

These patterns wer
e
comparable
with
the
“butterfly effect” (Lorenz
,

1963 in Hilborn
,

2004)
,

a phenomena
characterizing unstable dynamic system in which, through a series of
iterations, slight changes in parameters have profound effects on the entire
system. In Meara’s model
, this
manifested in
large vocabulary gains
render
ing

the
L2 lexicon
temporarily
dominant
within the bilingual system.

W
hen activation
of the L2 items stopped
, the system returned to
the
L1
dominance
-
L2 dormancy equilibrium
.
Meara concluded that his

simula
tion
mirror
ed

the Boulogne Ferry Effect, in which dormant French vocabulary of
British
passengers on the cross
-
channel ferry
is
activated by
a
sudden
exposure to a small number of vocabulary items

(2005).

While
Meara’s
simulation
successfully model
s

the d
ynamic nature
of the lexicon,
it does
not incorporate the
ever
-
changing
,

interactive
and
hierarchical
nature
of
word
knowledge
, which can be described as a
continuum ranging from


barely knowing
[a word]
receptively to being able
to use it productively wit
h stylistic and collocational appropriateness”
(Schmitt

& Meara
, 1997).
Similarly
, most vocabulary studies focus on
single
words rather than
on
the overall state of the mental lexicon

(Read
,

2000).
In
a
ddition,
it has been recommended that
cross
-
sectional,

group
-
trend findings
be supplemented with case studies
of
vocabulary
development
(Schmitt
&
Meara
,

1997; Singleton
,

1999
).

The current study
,

therefore
,

is a

longitudinal
study of the
development and interactions of
two

levels
of lexical knowledge

in two

dimensions within an individual learner
:

free
vs.
controlled production

in the
active knowledge dimension
;

and
recall
vs.
recognition

in the passive
knowledge dimension
. Free production is spontaneous usage

of target words

in writing

(Laufer & Nation, 199
9
)
. Using initial letter of target words as
cues,

controlled production is elicited by a context

from which
the target
word is missing

(a gap fill task)

(Laufer & Nation, 1995)
,

recall
by supplying
the word’s
meaning

through a
dictionary definition

(Laufer

et al
.
, 2004)
, and
recognition
by supplying the meaning
as one option out of four (Laufer
et
al
., 2004)

(see also section 3.3).

XXX


2.1
.
Empirical
F
indings
: the
L2
L
exicon as
a
D
ynamic
S
ystem


So far, DST
had not been

explicitly applied to
empirical
lex
ical data
, and

v
ocabulary

studies generally refer to the lexicon
as a collection of
stored
lexical items, sometimes in connection with activation models. Yet the
results of several studies suggest that L2 lexical development
is compatible
with the characte
ristics of a dynamic system.

While in L1 the
re is no large

difference between passive and active
vocabulary

knowledge dimensions
,
in
L2
they
develop in
markedly
different
rates
. These rates are manifested in the
number

of vocabulary items that can
be retri
eved or used in each knowledge dimension, and
vary across learner

proficiencies, learning contexts and durations, and
word
frequencies
.
For
instance, it was shown that
at least
two
years’ immersion
in
a
L2
environment
was
necessary
for
passive knowledge
to

trans
fer

into
production
, and even then,
an

i
ncrease in passive vocabulary knowledge
d
oes

not
necessarily
manifest in free production
, and

depend
s

on
the
learning

context (EFL
or

ESL)
, learner proficiency (
manifested in
passive vocabulary
size), and word
frequency (Laufer, 1998; Laufer & Paribakht, 1998).


In other words, although
relationships between passive
vocabulary
knowledge
and controlled
or free
production
1

were
predictable
,

correlations
between
these
knowledge levels

were
neither

uniform
n
or stabl
e
, and
differ
ed

as a function of

word
frequency

and

learner proficiency (which
affects
passive vocabulary
size
)

(Laufer & Paribakht
,

1998).
Laufer &
Paribakht (1998) show that w
hile more

frequent
words
were

found to be

likelier to
transfer

into

production
in general
, controlled
production

d
id

not
develop at the same rate as passive vocabulary in any
learning
context or
duration
. Consequently,
they

s
uggested
that
some
passive
vocabulary
items
might
never
transfer into
production
.
When passive vocabulary know
ledge
was categorized in accordance with learners’ proficiency levels, free
production

was shown to progress only when
a
threshold between
intermediate and advanced proficiency was crossed
2
. In an ESL context,
there was
a significant correlation between pa
ssive vocabulary knowledge
and free production across learners, regardless of proficiency. However, this
correlation was not found within each proficiency level separately. This
indicated that passive vocabulary knowledge, controlled production and free
pr
oduction develop at different rates in different proficiency levels, or
stages
of
learning.
F
ree production, in particular, was found
develop more
slow
ly

and
unpredictably than

passive vocabulary knowledge
3
.

Laufer & Paribakht also found that
word frequen
cy
influenced
the
correlation between passive knowledge and controlled production
. However,

the strongest influence was attributed to the length of stay in an ESL learning
environment
. A
t least two years were needed
before
the correlation between



1

As generated by Lexical Frequency Profiles
(Laufer & Nation, 1995) of the
participants’ written assignments, and the controlled and passive versions of the
Levels Test (Laufer & Nation, 1995; 1999
)
.

2

F
or example, a 0.7 ratio means that when 4,00 words are known passively, 2,800
are known actively,

resulting in a 1,200 word difference. When the passive
vocabulary reaches the level of 5,000, the active becomes 3,500, yielding a 1,500
word difference, and when it reaches 6,000, the active arrives at 4,200, which is a
1,800 difference

(Laufer & Paribak
ht, 1998).

3

A

large amount
of vocabulary
might need to be learned passively in order to
before
transferring into free active level
(L
aufer
&

P
aribakht,

1998).

controlle
d active and passive vocabulary

was affected
, but no significant
effect
was found
on free active vocabulary. The
y explained the

latter finding
by a plateau reached by free active vocabulary. Yet the
y could not specify
the

cause and nature of this plateau,

nor
could they
determine whether “the
different developmental rates (of the types of vocabulary knowledge) reflect
the nature of lexical learning or rather are “a consequence of the learning
context” (Laufer & Paribakht
,

1998: 387).

Similarly,
in
a
study

of vocabular
y gains over a year

of L2
immersion
, Schmitt & Meara (1997)
found that while there was an overall

increase

in vocabulary size
,
which

did not manifest in
certain w
ord
frequenc
ies
. Moreover,
in
certain
learners
,

rather than the group as a whole,
a decrease
over time
in certain word frequencies
was even noted
.

As mentioned earlier, dynamic system
s are characterized by

changing
interactions

between
their

components over time.

These changes
in
turn affect the degree to which input from the environmen
t influences the
system
.

The findings of the aforementioned empirical studies, such as the
changing interactions between passive and productive lexical knowledge
levels over time and across learning contexts, can be seen as compatible with
DST.


Following
these findings, the current study
investigate
s

the
L2
lexicon

from
a dynamic perspective
,
by
focusing on
the
development and
interactions
of

passive and productive
lexical
knowledge levels.
Th
is study is

described
in the

following

section.


3
.

The
C
ase

S
tu
dy

T
o test
the
applicability
of DST
for

lexical development, we
investigated
development and
interactions
of
four
vocabulary knowledge
levels: word
recognition
vs. word
recall in the passive knowledge dimension
;

and
controlled
vs.
free production in the ac
tive knowledge dimension.
We
targeted

academic
ESL
vocabulary,
as included
in
the University
Word List
(UWL
)

(
Xue & Nation
,

1984)
and
the
Academic Word List (
AWL
)

(
Coxhead
,

2000). The limited
scope

of this vocabulary enable
d us to

assess
a
percentage of kn
own

vocabulary
at each knowledge level,
while the fact that
it is distributed across frequency levels allowed us to control for the
frequency effects found by the empirical studies mentioned
in the previous
section

(Schmitt & Meara, 1997; Laufer, 1998; Lau
fer & Paribakht, 1998).
The decision to test words from both lists was derived from the need to
create a large item database that would enable repeated test administration
while avoiding practice effects. Both lists were shown to contain words
shown to be
indispensable for successful completion of academic studies in
English. The UWL was
shown to successfully discriminate between
proficiency levels (Laufer & Nation
,

1999), while familiarity with the AWL,
in combination with the most
-
frequent 2,000 English w
ords that constitute
79.9% of written English
, was found to be essential for
critical for

academic
success (Beglar

& Hunt
,

1999).


The UWL contains 808 words common in academic texts, divided
into 11 frequency levels, and excludes the most frequent 2,000
words listed
in the General service List (West, 1953).
T
he AWL includes 570 word
families in ten frequency bands, which are characterized by high degrees of
frequency and coverage in texts across academic topics and disciplines. Like
the UWL, it excludes t
he most frequent 2,000 words of the General Service
List (West, 1953).



3.
1
.
Participants,
M
aterials
and
P
rocedures


Since this was a longitudinal study of development, we focused on one case
study. The study participant was a 28 year old female native sp
eaker of
Mandarin enrolled in an English
-
speaking Master’s program. Prior to her
academic studies, the participant successfully completed a standardized
English examination (TOEFL or IELTS), and was employed as trainer for
English teachers at a university
in China.

Data were collected during the first semester of the participant’s
studies, when it was expected that her academic English vocabulary would
undergo change due to language contact in the academic environment.

During
3.5

months,

the participant c
ompleted 12 different versions
of a
test
assessing passive and controlled production academic English
vocabulary knowledge
(see section

3.
2
)
, and wrote 23 assignments which
were used to asses
s

her free
production of academic English vocabulary
.
The
partici
pant completed a test

every
seven to ten days, and
wrote two
assignments a week.

The
se
assignments
were home compositions on
assigned topic
s

that constituted a part of
her
coursework, and were
therefore
no
t restricted in

time
,

amount of their revision,
or
accessibility to resources
such as dictionaries.

Samples
of approximately 350 words were extracted

at

random from
different parts of the
these assignments, in accordance with the view that 300
word essays are needed in order to obtain stable voca
bulary siz
e estimates
(Laufer &

Nation, 1995) and the fact that lexical ratio and density measures
are highly dependent on text size.

The participant’s
free production of academic
English
vocabulary
was
operation
a
li
z
ed
as the ratio of academic word types to
the
tot
al
number
of
word types, to correct for multiple uses and overgeneralization of
academic vocabulary

items
.
Controlled production, word recall and
recognition were tested by a test
designed for

longitudinal assessment of
academic word knowledge on the basis

of words sampled from the UWL
and AWL. This test is presented in the following section.


3.2
.
The Longitudinal Academic Vocabulary Test (LAVT)


To

assess

the
development of
controlled production, recall and active
recognition of
academic E
nglish

vocabula
ry
,
we
devised
a
test
ing method
which from now onwards is

refer
red to

as the
Longitudinal Academic
Vocabulary Test (LAVT) (see appendix I).
The LAVT design incorporates
adaptations of two testing methods: the productive version of the Levels Test
(PVLT) (L
aufer & Nation
,

1995) and two parts of the monolingual version
of the Computer Adaptive Test of Size and Strength

(
CATSS) test (Laufer
et
al
.
, 2004): active recognition and active recall.

The LAVT consists of controlled production, paired in the study
wit
h free production of academic English vocabulary manifested in written
assignments, active recall and active recognition.
The term “active” refers
here not to production, but to the fact that the target word itself is elicited
rather than its meaning, in a
ccordance with the knowledge continuum
specified by Laufer
et al
.,

(2004). This continuum consists of

four
consecutive levels of word

knowledge.

The lowest level of knowledge in this
continuum is

passive
word
recognition
.

P
assive” in this case refers to
k
nowledge of word meaning
, and “active” to knowledge of the word itself,
rather than to usage.

Passive recognition was operationalized by Laufer
et al
.

as
the ability to identify
the words definition

out of
four possible options
(2004).

The second word know
ledge level is
active recognition
, which is
operationalized as the ability to recognize the target word our of four options
when presented with the word definition

(Laufer
et al
, 2004
)
. The third level
is

passive recall
, which was
operationalized

as
the ab
ility to recall
a
meaning
of a word
when being presented with
the word itself. Finally, the highest
level of word knowledge, according to this continuum, is
active recall
, which
is the

ability to recall a word when being presented with its meaning

and the
initial letter of the word serving as a cue that prevents the recall of a
synonym (Laufer
et al
.,

2004).

Within
this continuum, we focus on active word recall and
recognition, in which the word itself rather than its meaning is elicited.
We
excluded passi
ve recall and recognition from our study,
because
we found
that
definition
s

are often elicited partial, ambiguous, or context dependent
meanings, and that the learner population that we focus on, namely
nonnative users of academic
English
at an intermediat
e to high proficiency
level, showed a near
-
complete acquisition of the target vocabulary at this
level, leaving little room for development.

A key consideration in designing the LAVT was preventing practice
effects between different test versions as well a
s test parts
.

S
ince it is a test
aimed at repeated administration, obviously if the same words were tested,
any development seen would reflect the effect of the test itself rather than
represent academic vocabulary knowledge.
We therefore compiled

a
databa
se of
test
items
based on words that are randomly extracted all UWL
and AWL sublists by spaced sampling, a procedure in which items at preset
intervals, starting from randomly determined points, are picked. No
distinction was made between based and derived

forms From this database,
we randomly generate
each
test
version. Th
is
procedure
in turn
generates
a
need to ensure equivalent forms reliability
.
A

significant correlation (p<0.01)
between two
LAVT
versions
completed by Dutch
-
speaking first year
English s
tudents (n=32)

at the same time proved that the method of
randomly generating LAVT versions from an item database indeed results in
equivalent test versions (see
Table
1.
).


Table
1.

Results from a cross
-
sectional stu
dy of
LAVT

equivalent forms
reliability

Test part

Pearson’s
r

coefficient

Number of participants

Controlled
p
roduction

0,775

27

Active recall

0,844

32

Active recognition

0,733

31


3.3
.
Hypotheses


We expected to see an increase in recognition, recall,

and controlled
production of academic vocabulary and a relative stability in the amount of
academic vocabulary produced in free production, in accordance with
previous findings (Laufer
,

1998; Laufer & Paribakht
,

1998).
T
he dynamic
approach to learning in
general and language development in particular
anticipates variation in interactions between knowledge levels

and a
consequent variation in development, due to the limited resources of the
developing system
. Therefore
, we expected that

levels

within
each
d
imension

of knowledge
, passive

and productive
,

would exhibit a
competitive relationship in which increase in one level would entail a
decrease in the other. Als
o in accordance with the characteristics of dynamic
system development, we anticipated that thes
e levels of knowledge that
showed an increase would also show a higher degree of developmental
variation
. This variation will be

manifested in fluctuation above and below
the linear trend, in relation to levels which decreased or remained in a stable
degre
e of consolidation.



3.4
Analysis and
R
esults


Two
-
tailed Person’s
r
correlations were calculated between all four
vocabulary knowledge levels. It was found
that neither
active recall and
active recognition
, nor controlled and free production,

correlate
d

significantly
with each other
.
However, controlled production correlated
significantly with active recall (0.644;
p

< 0.05), and active recognition and
free production showed a near
-
significant negative correlation (
-
.0.588
;
p

<
0.05
)
.

Following this step
, the development of

the paired
knowledge levels
within the passive and productive dimensions
was plotted
separately
.

L
inear
regressions added to the data showed that while one level increased, the
other decreased. This was more apparent in the productive
dimension, where
free production decreased as the amount known academic vocabulary in
controlled production increased, than in the passive knowledge dimension,
where active recognition decreased only slightly as active recall increased

(see
Figure
1

and
Figure
2
)
.
When we inspected the variation around the
trend, it became
evident that
it was larger in the knowledge levels which
increased
-

controlled production and active recall


rather than in the levels
which decreased


free production and active recognition.


0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0
5
10
15
20
25
Measurements
Ratio of known vocabulary
Free
Production
Controlled
Production
Linear
(Controlled
Production)
Linear (Free
Production)

Figure
1
.

Raw data and developmental trends of free and controlled
production of academic English vocabulary. Due to the smaller number of
co
ntrolled production results (since 12 tests and 23 written assignments were
completed by the participant during the study period), the CP results were
connected by a moving average of two data points)


0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1
3
5
7
9
11
13
Measurements
Ratio of known vocabulary
Active
recall
Active
recogniton
Linear
(Active
recall)
Linear
(Active
recogniton)

Figure
2
.

Raw data and deve
lopmental trends of active recall and
recognition of academic English vocabulary
.


A correlation was calculated between
the data
residuals
, the values
from which the growth over time, manifested in the trend,
h
as been
subtracted. This correlation yielded a

representation of interaction
s

between
the knowledge levels within the passive and productive dimension which
was not obscured by the developmental trend, or growth over time. These
correlations were not statistically significant, probably due to the smal
l size
of the data set

and due to the variability of the correlation over time
.
However, from a dynamic perspective, we were still interested in seeing if
and how the interaction between knowledge levels within each dimension
varies. For this purpose, we e
mployed a moving window technique

which
enables track
ing

fluctuations in correlations over time. It uses “windows” of
a fixed number of measurement points (five in this case), which partially
overlap with the preceding windows and includ
es

the measurement
occasions depicted in the preceding minus the first and plus the next.

The
movement of the window enables the representation of

changes in
correlation
s

as a developmental trajectory.

Applying this technique showed fluctuations between positive and
negativ
e correlations in both pairs of vocabulary knowledge. These
fluctuations were more pronounced in the interaction between the productive
knowledge levels, as can be seen in the number of transitions from positive
to negative correlations and in the “heights
” and “depths” of the
developmental trajectories’ “peaks” and “valleys”

(see figure
s 3

and
4
)
.


-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0
2
4
6
8
10
12
14
16
18
20
Measurements
Pearson's correlation coefficient

Figure
3
.
Moving window (five measurement points) of

correlation between

controlled and free production of academic English vocabula
ry
.

-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0
2
4
6
8
10
12
Measurements
Pearsons' correlation coefficient

Figure
4
.

Moving window (five measurement points) of
correlation between
active recall and active recognition of academic English vocabulary
.



4
.
Discussion


The development of lexical knowledge levels was shown to be consis
tent
with DST.
First, in both the passive and productive knowledge dimensions,
while
one level

of knowledge showed a developmental increase,
the
others
decrease
d
.
This discrepancy was more apparent in the productive knowledge
dimension, while in the passiv
e vocabulary knowledge, the regression or
linear trend of active recognition was characterized by a very small slope
angle. Considering that passive
vocabulary
knowledge has been shown to
consolidate earlier and to higher degree than production (for examp
le Laufer
& Paribakht
,

1998), this might indicate that
it

is a more stabilized subsystem
of L2 lexical knowledge
. Such a system would exhibit
less competition
and
more stable interaction
between its component
s
. In contrast, the interaction
between the prod
uctive knowledge levels is more competitive and
varied
, a
finding which may be explained by the fact that productive knowledge is
a
less
stable
subsystem
of the L2 lexical knowledge system, since it is
acquired later and at a slower pace, and therefore
exh
ibits a more obvious
competitive interaction.


Although in
both the passive and
the active
knowledge dimensions,
th
e
knowledge levels that
increase
d

also
showed more
variation in
cross
sectional studies (cf
.

Laufer & Paribakht
,

1998) controlled and free
pr
oduction did not develop simultaneously, and controlled production
showed a large degree of fluctuation.
The increase in controlled production
,
which

was larger than the increase in active recall (again evident in the slope
of the linear trend),
was accomp
anied by a higher degree of variation around
the linear trend. This is in line with the “growth accompanying variation”
characteristic of dynamic systems, again suggesting that each knowledge
level within the two knowledge dimensions of passive and product
ive
knowledge acts as a componential subsystem of a dynamic system. This
finding resonates with studies of first and second language from a dynamic
perspective, which found that acquisition data showed a generally increasing
bandwidth in addition to a gene
ral increase i
n its level (
v
an Geert &
v
an Dijk
2002; Verspoor
, Lowie & van Dijk, 2008
).

Finally, the
interactions between active recall and recognition and
controlled and free production fluctuated from a negative to a positive
correlation, suggesting sh
ifts from a competitive to supportive interaction.
This finding reinforces the precursor model of language acquisition, which
views language components as competing for the limited resources of the
developing language system (Robinson & Mervis
,

1998). The
fact that more
variation, evident in a larger number of changes from positive to negative
correlation values,
emerged

in the correlation between the productive
knowledge levels again reinforces the claim that developing, and especially
growing, components
are characterized by a higher degree of variation and
competition. Since the productive knowledge dimension is consolidated later
and to a lesser degree than passive vocabulary knowledge, we suggest that it
can be viewed as a less stable system, which is m
ore sensitive to
perturbation.





5
.
Conclusion


Dynamic systems are characterized by nonlinear, unpredictable and iterative
development that tends towards attractor states
. A dynamic

system

typically
has limited internal resources

and
shows
cha
nging int
eractions between its

components
, which

alternate between competition and mutual support,
which are impacted by, and in turn impact, the influence of external input on
the system.
In
our

study

of the development of academic English lexicon in a
nonnative s
peaker immersed in an academic setting
, we asked whether the
development of
passive and active lexical knowledge
is compatible with
dynamic systems theory and characteristics.
We focused on longitudinal
assessment of

two pairs of passive and active knowled
ge dimensions:
word
recognition
vs. word

r
ecall;

and controlled
vs.
free production
, respectively
.
We hypothesized that while certain knowledge levels increased, namely the
passive levels and controlled production, free production would remain at a
plateau

or decrease. We based
our
hypothesis both on previous empirical
findings
(Schmitt & Meara, 1997; Laufer, 1998; Laufer & Paribakht, 1998)
and on
D
ynamic
S
ystems
T
heory, which
considers

limited
systemic
resources
as a
determin
ing

factor affecting
of interac
tions between
system

components.
M
ore stable systems, such as passive knowledge
, exhibit

more
supportive
componential
interaction
s

or a mild competition,
than
th
ose found
in
less stable system
s



such as
active
vocabulary
knowledge
. The
y

also
show more flu
ctuation in interaction
s between components of less stable
system
. We also expected to see more variation
in

knowledge levels that
increased, in accordance with the view that variation is inherent to, and in
fact enables, growth
in a dynamic system
(Thelen

& Smith, 1994;
Van Geert
&
Van Dijk
, 2002).



The findings of this study were compatible with our hypotheses. Passive
academic vocabulary knowledge of the participant increased

or declined
only slightly
,

while

there was a decline in
free
production
.

I
ncreasing
variables of
vocabulary knowledge showed greater fluctuation and
variability. The interaction
s

between
levels of
lexical knowledge, expressed
in
a

moving window of correlation between
data residuals
, also showed a
pattern of increased fluctuatio
n and variability.
These findings suggest that
the
L2 lexicon is a dynamic system, comprised of interacting, developing
subsystems, and can have theoretical and pedagogical implications. Bearing
in mind that the case study presented in this paper was fairl
y short and that
replication in other learners over longer durations is necessary, we would
nevertheless like to suggest that the dynamic perspective can explain and
supplement cross sectional findings on the nonlinear nature of lexical
knowledge level dev
elopment and interaction. It also highlights the
discrepancy between learners


passive and productive lexical knowledge
levels and the need to take the nonlinear and
stochastic
nature of L2
vocabulary learning into account. Often the expectation is that le
arners’
passive vocabulary knowledge, manifested prior to their academic studies in
testing, would be immediately transferred into production
. However,

as the
current study hopefully showed, when language in general and lexicon in
particular are viewed and

investigated from a dynamic perspective, the
unpredictable, nonlinear nature of their development can be anticipated and
to a certain degree explained
.

Obviously, this is only a short case study,
which can only serve to illuminate certain characteristics
of L2 lexicon. If
we want to determine the compatibility of dynamic systems theory to the
mental lexicon, this study should be expanded, while still focusing on
individual learners and variation as complementary to group effects and
general trends. We ther
efore would like to suggest the explanatory power of
dynamic systems theory with regard to language development in gener
al and
L2 lexicon in particular and its potential contribution to research and
contribution. We

hope that this study will be followed by

further
investigations of the mental lexicon from a dynamic perspective, in learners
of varied proficiency and language backgrounds, in
varied

durations
and
learning contexts, and with a focus on additional

aspects of
L2
lexic
al
knowledge.


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Appendix I: Examples of LAVT items


1)

Controlled production:


This debate is becomin
g too a_________
-

let's have some hard facts!; Truth
and beauty are a________ concepts.



2) Active recall:


T
o act or work together for a particular purpose, or help someone willingly
when help is requested c________



3) Activ
e recognition



To communicate with or react to

a) interfere; b) interlock; c) interact; d) intervene


To take part in or become involved in an activity

a) sustain; b) capture; c) participate; d) emphasize