INTRODUCTION
This paper sets out to show how facilitation between different clause structures operates over time in syntax acquisition. The phenomenon of facilitation within given structures has been widely documented, yet inter-structure facilitation has not, to the best of our knowledge, been reliably reported so far. Our findings are based on the naturalistic production corpora of six toddlers learning Hebrew as their first language. We use regression analysis, a method that has not, as far as we are aware, been used to study this phenomenon.
Like many researchers who espouse an empiricist–emergentist perspective to language development, we interpret our results using an exemplar-based language learning approach. The main tenet of exemplar-learning models is that learning need not involve extraction of rules which refer to categories that are more abstract than the items of knowledge themselves (for clear definitions of such theories, see Hahn & Chater, Reference Hahn and Chater1998). This approach sees generalization-like behaviour as the result of similar exemplars being stored close to each other, thus creating dense clumps of exemplars, whereas items which are less similar to others inhabit more sparsely connected parts of the network. Knowledge remains associated with specific items rather than with categories which are abstracted from them, and resides mostly in the connections between different exemplars. These connections get strengthened with recurring co-activation or weakened otherwise. Such models were originally suggested for category learning in general (e.g. Medin & Schaffer, Reference Medin and Schaffer1978; Nosofsky, Reference Nosofsky1988). In relation to language, this view is now held by many researchers studying morphology and phonology (e.g. Miller, Reference Miller1994; Bybee, Reference Bybee2001) as well as syntax (e.g. Tomasello, Reference Tomasello1992; Reference Tomasello2000; Ninio, Reference Ninio1999a; Reference Ninio1999b). In the context of the early stage in syntax development which is the focus of this paper, the exemplars of interest to us are verbs, along with information about the arguments each takes.
facilitation is a process whereby previously known ‘old’ exemplars, by having already been learned, facilitate or make the learning of new exemplars easier. Facilitation operates between similar items: unfamiliar exemplars are processed like familiar exemplars that are similar though not identical to them, by way of analogy. When a new item is met, the child searches for a similar known item, and this becomes easier as the stock of learned items grows. As more exemplars from the same category are learned, the basis for their similarity becomes clearer as in the comparison process the weights assigned to their features are adjusted and refined. Consequently comparing new exemplars to old ones, learning and assimilating them into the existing knowledge structure becomes progressively easier.
Facilitation has been shown to occur both in non-linguistic learning (Homa & Chambliss, Reference Homa and Chambliss1975) and in language acquisition, specifically in syntax learning (Abbot-Smith & Behrens, Reference Abbot-Smith and Behrens2006; Keren-Portnoy, Reference Keren-Portnoy2006; Kiekhoefer, Reference Kiekhoefer2002; Ninio, Reference Ninio1999a; Vihman, Reference Vihman1999). Most of the work on facilitation in syntax has focused on facilitation between different verbs within a syntactic structure. Abbot-Smith & Behrens (Reference Abbot-Smith and Behrens2006) were the first to look for facilitation between different syntactic structures and have shown that the acquisition of later acquired structures may be supported (or at times hindered) by previously acquired ones. They focus on the role of semantics and lexical overlap as determinants of facilitation. Our research complements theirs and shows, using a different methodology, facilitation operating between early and later acquired structures. When discussing facilitation between different structures, the carriers of knowledge are again the same specific exemplars, the verbs. What we would like to show is that the effect of previously learned verbs in previously learned structures extends not only to other verbs sharing a similar structure, but also to other structures. Facilitation within a structure is usually demonstrated by showing a gradually diminishing time lag between consecutively learned items (e.g. verbs) as learning progresses. Although the first items are learned slowly and effortfully, learning new items becomes gradually easier, and new items start to be learned at a faster pace. Old items are said to facilitate the learning of subsequent items. When measuring the cumulative number of items learned per period of time, the growing pace of learning is evidenced in an accelerating learning curve.
Keren-Portnoy (Reference Keren-Portnoy2006) suggested that practice which takes place during the early stages of learning a structure can explain (at least in part) the phenomenon of facilitation. During this practice phase the child develops the skill that is involved in producing certain kinds of combinations, simply by using them over and over again and comparing her output to the input she hears. Word-order problems – determining the location of the different arguments relative to the verb – are also worked out through ‘learning-by-using’, and errors can be shown to diminish as learning progresses (Keren-Portnoy, Reference Keren-Portnoy2002). It is natural to assume that these details, once they have been mastered for one or more structures, should help to smooth and accelerate further learning. In this scenario, early learning in one structure makes later learning in a different structure easier. We therefore see it as facilitation between structures. We do not know which dimensions of similarity among structures or utterances are most relevant and beneficial for such facilitation. It may seem that having learned to use a specific verb in one structure may be beneficial for learning to use that very same verb in another structure, or that structures which contain certain argument types (such as subject or direct object) would be especially beneficial for learning further structures which contain the same argument types. Thus learning verb–direct object (VO) structures or subject–verb (SV) structures, or both, should catalyze the learning of subject–verb–object (SVO) structures. Similarly, it may be that learning is facilitated by semantic similarity, so that items tend to be learned which are semantically similar to those learned before them. There is, however, evidence that none of these three kinds of similarity (verb identity, overlap in argument structure and semantic similarity) operates in syntax acquisition in a simple and predictable manner. Regarding specific verb identity, Ninio (Reference Ninio2003) has shown that the acquisition of later learned structures does not necessarily begin with verbs already learned in previous structures. In the English corpus she looked at, 40 percent of the earliest verbs produced in SVO have not been previously produced in either VO or SV. She argues that facilitation is not, in general, carried by specific verbs, and that it is not the case that, once an argument is combined with a given verb, the child will learn to produce new structures by gradually combining more arguments with that same verb. As for the possibility that specific argument types are the vessels of facilitation – this may usually be the case, but Keren-Portnoy (in preparation) reports a counter-example. She shows that cases can be found in which mastering the word order for a multi-argument structure (e.g. SVO) did not induce the correct word order for its component structures (e.g. VO), and errors in the latter continued after having ceased to occur in the multi-argument structure. Regarding semantic similarity, Ninio (Reference Ninio2005a; Reference Ninio2005b) found no evidence that semantic similarity plays a role in mediating syntactic learning. In the current paper we have restricted ourselves to measuring facilitation between the nth and the (n+1)th acquired structure, and no attempt will be made to identify the agents of facilitation.
There are two potential objections to our interpretation of an increase in the ease of use as evidence for facilitation driven by previous learning. The more extreme objection, first suggested to us by Izchak Schlesinger and previously tackled by Ninio (Reference Ninio1999a), questions whether the development involved is at all linguistic. The other possible counter-claim accepts that we are indeed dealing with language learning, but questions the usefulness of conceptualizing the learning process as one of learning new structures.
The first objection may be phrased thus: children's cognitive and memory faculties mature, becoming faster and more efficient over time, and learning anything new becomes easier. Hence, how justified is the claim that facilitation is due to what has already been learned, rather than to simple biologically driven maturation? We contend that maturation, i.e. the improvement of the brain, the hardware, which permits faster reception, retention and processing of information, is not the whole story, and that actual early syntactic knowledge supports and scaffolds later knowledge. Murphy, McKone & Slee (Reference Murphy, McKone and Slee2003) show that implicit memory (as evidenced in priming effects) develops with age in domains in which the knowledge base develops. They thus demonstrate that automaticity and processing speed are not simply a result of maturation, but of development in the structure of the database, not through learning new items, but primarily through the creation of new connections between items. If knowledge progresses by strengthening some connections and weakening others, then the two accounts for the improvement in processing, that of the improvement of hardware and that of the increasing density of the database, can be seen as two facets of the same process. In such a system, previous syntactic knowledge shapes the brain, enabling it to work faster and more efficiently. However, hardware improvement resulting from changes in the database will be much more local than improvement which results from biologically determined brain growth.
The second objection may be that what facilitation data actually show is that combining words becomes gradually easier, due not particularly to learning new structures but rather to learning to produce multiword utterances. In essence, the claim is that specific syntactic structures do not play an essential role in syntax learning.
Both of these claims, that of general maturation and that of general word-combining knowledge, can only explain across-the-board changes. The timing of mastery of different structures will therefore be investigated: if different structures used at the same time seem to point to different levels of maturation or knowledge (some being mastered well while others are not), then neither of these two general accounts can fully explain the data. If found, such patchy knowledge would point to structures (as exemplified in specific verbs) being the likely unit of knowledge which is acquired.
The main variables and hypotheses of our study will now be presented, followed by the methods and a description of the data. Since the statistical methods used in this study are not customary in this type of research, a fairly detailed description is provided before presenting the regression results. Following these results, evidence is presented that the learning of previous structures, rather than more general mechanisms, is the factor responsible for the facilitated acquisition of later learned structures. We conclude with a brief discussion of the implications of our findings.
PARAMETERS AND HYPOTHESES
We now come to the type of evidence for facilitation that will be adduced from naturalistic production data. If later learned structures actually build on knowledge that has been acquired for previously acquired structures, they should exhibit fewer signs of struggle and fewer traces of search for solutions than earlier ones. We focus on two properties in the acquisition of new structures: (1) the number of errors made in the learning process, and (2) the trajectory of learning – the rate at which verbs join the structure.
(1) Word-order errors. Keren-Portnoy (Reference Keren-Portnoy2006) has shown that word-order errors in the earliest clauses constructed in a structure can be taken as signs of trial and error in the early stages of learning a new structure (cf. Braine's Reference Braine1976 ‘groping patterns’). Such errors seem to be the result of a search for the correct location of different arguments, for the solution to the puzzle of how those arguments ‘go together’ with the verb. If later learned structures are indeed learned more easily on the basis of what is already known, and if they involve less of a need for problem solving, we would expect children to produce fewer word-order errors among the earliest clauses constructed in those structures.
(2) The learning trajectory. It has been shown that the great majority of structures exhibit a learning curve characterized by a slow start and a gradual acceleration (Ninio, Reference Ninio1999a; Reference Ninio2005a; Reference Ninio2005b; Vihman, Reference Vihman1999; Kiekhoefer, Reference Kiekhoefer2002; Keren-Portnoy, Reference Keren-Portnoy2006). If later structures are indeed easier to learn due to some previous experience, they should exhibit learning trajectories in which the initial overcoming of hurdles followed by a ‘take-off’ is less pronounced as more structures are mastered. Later structures will therefore be expected to be learned more evenly, that is, to have a less-accelerating learning curve. At the extreme one may get a linear, non-accelerating curve, as reported by Abbot-Smith & Behrens (Reference Abbot-Smith and Behrens2006).Footnote 1
The degree of acceleration and the tendency to make word-order errors (see above) are both taken to signify the degree of difficulty. We therefore expect them to show a positive correlation, supporting the notion that they are both affected by a common underlying variable, difficulty.
We summarize the predictions to be tested in the following hypotheses:
Hypothesis 1: Errors and degree of acceleration as measures of difficulty: the smaller the proportion of errors among a structure's earliest clauses, the less accelerating its learning curve.
Hypothesis 2 (facilitation I): the later a structure is acquired, the smaller the proportion of errors among its earliest clauses.
Hypothesis 3 (facilitation II): the later a structure is acquired, the lower the acceleration of its learning curve.
To challenge the suggestion that facilitation, if found, is the result of the state of the entire mental, syntactic or cognitive system of the child and to underline the benefit of describing syntactic knowledge as being channelled through structure learning, we will investigate whether, during the very same period in a given corpus, late structures may be at their slow stage of learning while earlier ones are already in their accelerating period. Note that a similar argument has been made by Ninio (Reference Ninio1999a).
THE METHODS AND THE DATA
Participants and corpora
Our basic dataset consists of the production corpora of six children acquiring Hebrew as their first language. One child received some English input as well, but all his documented productions are in Hebrew. Data collection started before any word combinations were produced and continued for eight to thirteen months. The children were audio-recorded in naturalistic interaction with a parent. Five children were audio-recorded weekly for about half an hour. One girl was recorded for twenty minutes twice a week. The average age at the first session was 1 ; 5.29 and at the last session 2 ; 4.1 (see Table 1 for a general description of the corpora). Three of the corpora (those of Naomi, Ofer and Shuli) are much richer than the other three in terms of the number of recordings made and, as a result, in the number of clauses available for analysis. The observers transcribed the recordings in standard Hebrew orthography, often noting (in very broad phonetic transcription) the phonetic realization of the verbs. The recordings were supplemented by parents' written reports of some utterances heard outside the recording sessions; these were excluded for one child due to too great a divergence between the verbs reported by the parents and those recorded by the observer. In addition, a couple of observers documented additional utterances heard outside the recording session, usually after the audiotape had been turned off.
Primary data
For a detailed description of the data and the forms which were analyzed, see Keren-Portnoy (Reference Keren-Portnoy2002; Reference Keren-Portnoy2006). The development of each individual structure in each corpus was followed. All clauses containing a verb with some or all of its arguments were used in the analysis. Utterances containing hesitation or pauses are considered unitary utterances, unless another speaker's turn intervenes. Each clause was analyzed separately, regardless of whether it contained a finite or a non-finite verb. However, if one clause served as an argument of another, only the main clause was analyzed. Thus the following were regarded as separate clauses: coordinated clauses, relative clauses, adverbial clauses (when not serving as obligatory adverbial arguments). Only utterances which were uninterrupted, intelligible, comprehensible and spontaneous were used in the analysis
The arguments examined were:
Subject (S)
Direct object (O) (including sentential complements)
Indirect object (I) (including all datives and obliques)
Obligatory adjuncts (A) (This category included mostly adjuncts indicating goal, source, location and, in rare cases, time or manner.)
The fifteen structures that were investigated were SV, VO, VI, VA, SVO, SVI, SVA, VOI, VOA, VIA, SVOI, SVOA, SVIA, VOIA, SVOIA. Table 2 lists, for each of these structures, an example of a clause constructed by one of the children. For most of our statistics each structure in each corpus provides a datapoint. Had all six children produced all the potential structures, there would have been ninety datapoints. In actual fact for the analyses, which necessitate constructing learning curves (see below), only forty structures can be used; in those that involve error statistics, even fewer. This is due to the fact that only three children had twelve or more structures represented in their corpora, and not in all cases were there enough valid points in a structure for it to be used in our statistical analysis. As for error analysis – only four children had any errors recorded, and only their corpora could therefore be used for this purpose. Each clause was coded as belonging to a single structure. Consequently, clauses of the form SVO, for example, were not coded as instances of SV or VO as well.
Examples of clauses constructed in each of the structuresFootnote a
a: Source: Table 2 in Keren-Portnoy (Reference Keren-Portnoy2006). The orthography is conventional and does not attempt to be a faithful phonetic description of the children's pronunciation. Inflected verb forms merely approximate a possible target form.
Variables associated with the structures
Word-order errors
Each clause is coded as having a canonical or a non-canonical word order.Footnote 2 Word order is considered canonical if the subject precedes the verb and the other arguments follow the verb, with the internal order among them immaterial. Immediate repetition of a word does not affect canonicity, but repetition of an argument or of the verb in two or more different locations in the clause is considered non-canonical. Although word order in Modern Hebrew is basically SVO (Ben-Horin, Reference Ben-Horin and Cole1976; Berman, Reference Berman1990; Reference Berman and Levy1994; Dromi & Berman, Reference Dromi and Berman1986; Glinert, Reference Glinert1989; Ravid, Reference Ravid1995; Ziv, Reference Ziv and Cole1976; Reference Ziv1995), it may be altered due to pragmatic considerations (topicalization, focalization and presentation), causing, for example, the verb to precede the subject (Giora, Reference Giora, Blum Kolka, Tobin and Nir1981; Givón, Reference Givón and Cole1976; Glinert, Reference Glinert1989; Ravid, Reference Ravid1995). We assume (as do, for instance, Lieven, Behrens, Speares & Tomasello, Reference Lieven, Behrens, Speares and Tomasello2003) that such pragmatically driven variation in word order is not mastered at the early stage on which we are focusing, and clauses with non-canonical word order in the corpora, at least in the early stages, are authentic errors. Keren-Portnoy (Reference Keren-Portnoy2002) documented a decline in the proportion of non-canonical word-order errors as learning progresses. Such a decline would only be expected if, indeed, most cases of early non-canonical word order were a result of lack of knowledge, rather than a result of more sophisticated knowledge. Consequently all non-canonical clauses were coded as cases of word-order errors. Presentational clauses which have a VS word order even in very early child productions (as evidenced in our data), and which contain a specific set of verbs (e.g. nafal ‘fell’) were excluded from analyses concerning word-order errors.Footnote 3 A more detailed description of the coding schema and problems in coding can be seen in Keren-Portnoy (Reference Keren-Portnoy2002; Reference Keren-Portnoy2006).
Age of acquisition
The age of acquisition (AoA below) of each verb in a given structure is the age at which the first clause was produced by the child using that verb in the given structure. The age of acquisition of a structure is the age at which the first clause was produced in the structure. This differs from the definition of age of acquisition used in Keren-Portnoy (Reference Keren-Portnoy2006), where the age of acquisition was defined as the age at which the first clause with a canonical word order was produced. This criterion was changed in order not to create a dependency between the rate of learning and number of errors in a structure (see also discussion of the results for Hypothesis 1). AoA as defined here marks the beginning of the acquisition process. This by no means implies that learning is complete and acquisition has ended by the production of a single clause.
Secondary data
In the primary data described above, each case is a clause produced by a child. Based on this primary database, we created a secondary database, whose cases are the forty structures in the six corpora for which a learning curve was constructed (see Figure 1 and Figure 2 for examples in two structures), plotting the cumulative number of verbs acquired by the child in that structure as a function of the age of acquisition. Regressions using primary data are referred to as primary regressions. Regressions using secondary data, i.e. in which the data are values obtained from entire structures, are referred to as secondary regressions (all secondary regressions reported in this paper, i.e. the regressions reported in Table 3, Table 4 and Table 6 are weighted regressions, see below for definition. The primary regressions reported in Table 5 are unweighted). To estimate a structure's degree of acceleration using a regression at least four points, four different dates in which new verbs were learned in that structure, are needed. The estimate of the degree of acceleration, the quadratic coefficient of the regression fitted to the learning curve, labelled B2, is also interpreted as a measure of the difficulty of acquisition of a structure. This is explained below. Table A1 in Appendix A presents the secondary data in full.
Learning curves for the structure SV in all of the corpora.
Learning curves for the structure VOI. (NOTE: The VOI structure was not found in three of the corpora.)
Proportion of errors and accelerationFootnote a
a: df-weighted OLS. Variables omitted from table: Child corpus dummies. Reported values are the regression coefficients of the relevant variables; t-values in parentheses; ** significant at 0·05.
Structure's acquisition age and proportion of errors (df weighted)Footnote a
a: df-weighted OLS. Variables omitted from table: Child corpus dummies. Reported values are the regression coefficients of the relevant variables; t-values in parentheses; ** significant at 0·05, *** at 0·01.
Time of acquisition of new verbs and acceleration (primary data)Footnote a
a: Generalized Least Squares regression. Reported values are the regression coefficients of the relevant variables; t-values in parentheses; * significant at 0·10; ** at 0·05, *** at 0·01, # at 0·001; na not applicable. D-W the Durbin-Watson statistic, measures serial correlation, all of which, except Tal's are above du, i.e. no indication of serial correlation. Tal's lies between dU and dL, not ruling out serial correlation.
STATISTICAL METHODS
The acceleration estimates
The estimates of the quadratic coefficients of the primary regressions described above (‘Secondary data’) (see Table A1 in Appendix A) were obtained from the regressed learning curves of each of the structures produced by each child. These regression equations have the following form:
where y is the cumulative number of verbs produced in the structure, T the number of weeks that have elapsed from the start of the structure's acquisition (see the definition of T below) and ε is a random disturbance or error. The estimator of b 2 is the measure of acceleration, which, we claim, indicates the difficulty of acquiring a given structure. When used as a variable in a secondary regression, the estimator of b 2 is denoted B2. The other parameters are of no interest and not determinate since they depend on the exact definition of time: if, instead of T as defined below, calendrical time were used, b 1 and b 0 would adjust, but b 2 would remain unchanged. For a description of the mathematical structure of a typical secondary regression, see below.
A basic problem arises with respect to the B2 variable: different B2s are based on samples of very different sizes. Only a small selection of each child's utterances was sampled for this study, and data collection was terminated at a stage that left some structures, especially those that appear late in our corpora, poorly represented. The significance and reliability of the statistical generalizations that we make is lower for these structures than for earlier ones. Thus SV and VO often produce significant B2s, while estimators of later structures are often not statistically significant. Observe that sample size, though affecting significance, should not affect a learning curve's rate of acceleration, neither from a mathematical point of view nor from an empirical one. In fact, a previous study concerned with the acceleration of VO learning curves used only the earliest six verbs from each corpus, and its results still show quite strong acceleration (Ninio, Reference Ninio2005a).
As a result of the differing sample sizes, the samples from which we obtained our estimates are of unequal variance. The technical term for this phenomenon is heteroscedasticity. Heteroscedasticity leads to inefficient estimates in those regressions in which B2 is a predicted variable (Greene, Reference Greene2000: 499ff.). Weighted regressions, a tool used in other disciplines which face similar problems, e.g. econometrics or meteorology, are therefore used in all secondary regressions.
The statistical model for the secondary regressions
The following is a typical secondary regression:
where B2 is the estimator of b 2 from regression (1), and z any other variable that may be included in the regression, such as Structure-AoA, the age (in weeks) in which the structure was first used in the corpus. Child is a so-called dummy variable explained below. Thus the betas indicate the contribution of the predictor variables to the degree of acceleration, represented by B2.
The use of weighted regressions
The regression model assumes that all observations are drawn from the same distribution, and in particular, that if there are errors in the points for which the regression is computed, all these errors belong to the same distribution and the variance of all the errors at each point is equal. This, as mentioned above, does not hold for the secondary equations, if only because the estimated B2s were obtained from samples of highly varied sizes.Footnote 4 Although ordinary least squares (OLS) regressions run on such data are unbiased, they are inefficient, that is, their variance is larger than the data would permit, and the estimates of the standard errors are likely to be erroneous (Greene, Reference Greene2000: 503). To equalize the variances and obtain efficient estimators we use weighted regression. The value of the degrees of freedom was used as the weight in secondary regressions reported below. This is based on the assumption that all these estimators belong to the same distribution, whose variance depends on the inverse of the degrees of freedom of the relevant estimator (Greene, Reference Greene2000: 514f.). To equalize the variance we therefore have to multiply by the degrees of freedom, that is, where B2 is involved, by n – 3, where n is the number of dates in which new verbs were learned in the structure (the number of datapoints in the learning curve), and three are the degrees of freedom used by Regression (1). An alternative method, weighting by the precision of the estimates, which is the inverse of the variance, precision=1/(SE)2, seems to us less reliable, due to the poor accuracy of the estimated standard error (SE) for the regressions with few points. Furthermore, with a small numbers of observations per structure, any form of weighting may in some instances produce a worse outcome than OLS, as an anonymous reviewer commented. We have therefore run all three types of regression, weighted by df and precision as well as unweighted OLS, but only the df-weighted ones are reported in this paper. Full results can be obtained from the authors.
The child-corpus dummy variables
An additional problem in the data is that the structures were not sampled independently, and structures originating in the same corpus may be more similar to each other than to those sampled from other corpora. In all the secondary regressions reported in the text, dummy variables which stand for the corpus in which the structures originated are therefore used. A dummy variable is a device that is often used when groups of datapoints have different sources, thus accounting for the lack of independence in sampling within each group. In our case the corpus variable Child, where Child=Bareket, Lior, …, Tal represents the idiosyncratic vertical shift of the regression curve of each child. Thus, if one child progresses more slowly and acquires syntax at an older age, her coefficient would be positive, while the vertical shift for a child with a faster learning rate would be negative.
The variables used in the regressions
Variables used in several regressions are listed below. Variables used in a single regression are explained where the relevant regression is introduced.
Time related variables:
• Structure-AoA: The age, in weeks, at which the first verb has been used in a given structure. This variable is a measure of the length of time that the structure has been in use in a child's corpus.
• T:T=Verb-AoA–Structure-AoA, where Verb-AoA is the age, in weeks, in which a given verb has joined a structure. Thus T is the time in weeks between the acquisition of a given verb in a structure and the acquisition of the very first verb in that same structure in a given child's corpus. For the first verb in any structure T=0.
• T 2:T squared. The coefficient of T 2 in the learning curve, b 2, is the measure of acceleration of the learning curve, which is shown below to be a measure of the difficulty of acquiring a structure.
Other variables:
• Error proportion: The proportion of non-canonical clauses out of the first twenty clauses in a structure. For structures in which there were fewer than twenty, the proportion of non-canonical clauses out of all clauses. Two corpora in which no errors were recorded as well as all structures with fewer than four clauses were excluded from the analyses concerned with errors. This is one of the variables which we take to indicate degree of difficulty of acquisition.
• Cumulative frequency: Cumulative frequency of different verbs used in a given structure at a given point of time. The learning curves are based on the primary data and plot Cumulative Frequency as a function of T.
• B2: The estimator of the rate of acceleration of the learning curve of each structure, which we take as an indicator of its difficulty of acquisition. B2 is the estimator of b 2, the coefficient of the quadratic term T 2, in the primary regressions of type (1).
• Child: Child-corpus dummies. See above.
• Structure-rank: The rank order of acquisition of a structure in a child's corpus, an alternative measure for the length of time that the structure has been in use in a child's corpus.
REGRESSION RESULTS AND DISCUSSION
We begin with a short description of the acceleration data, and then move on to report the results of the regression analyses.
Table A1 in Appendix A presents the estimates of the B2s, the acceleration parameters of the learning curves. Only forty structures contain enough datapoints for regression analysis. Of these, thirty-one or 78% have a positive B2, and nine, 23%, are non-accelerating.Footnote 5 Structures containing an Adjunct (of which VA, SVA, VOA and SVOA appear in the table) have a much lower proportion of significantly accelerating structures (42%) than the other structures (93%). The reason for this is still unclear, and merits further investigation. The significance of B2 declines as the number of verbs per structure declines: 81% of the B2 values for structures with an average of over twenty-nine verbs per structure are significant, compared to only 51% of structures with fewer verbs. Three corpora have only three estimated learning curves each, all accelerating and all but two significantly so. Naomi's corpus includes eleven curves, eight of which are significantly accelerating, and three of which are not significantly non-accelerating. Shuli's nine include eight accelerating curves of which five are significantly accelerating, and a single significantly non-accelerating one. The outlier is Ofer, of whose eleven curves six are accelerating and five non-accelerating, three of each significantly so; even VO, an early structure with many verbs, is significantly non-accelerating in Ofer's case.
Hypothesis 1 – Errors and acceleration
Our first task is to establish that the acceleration of regression (1), measured by B2, is indeed positively correlated with the proportion of errors among the earliest clauses in the structure, thus justifying the use of these two variables as measures of the degree of difficulty encountered in the acquisition of a structure. B2 was regressed on Error proportion as the independent variable. Note that these two variables are not only conceptually independent of each other, but that each of them originates from a different set of clauses or datapoints: the learning curve, whose acceleration is given by B2, is based on the first use of each new verb in the given structure over the whole recording period; the proportion of errors is computed for the first twenty clauses in each structure, where any verb may appear more than once (see details in previous section). Thus the number of errors cannot affect the shape of the learning curve and Error proportion and B2 are statistically independent.
Table 3 presents the results of the regression. The proportion of errors is a significant explanatory variable of B2.Footnote 6 This supports the assumption that both are affected by the same latent variable, the degree of difficulty of acquiring a structure. We thus have statistical support for the claim that acceleration, like errors, is a symptom of friction, or difficulties at the start of the acquisition of a new syntactic structure, and that the rate of acceleration can serve as a measure of the degree of difficulty.
Hypothesis 2—The evolution of errors (Facilitation I)
Hypothesis 2 refers to the evolution of errors over time. The dependent variable in Table 4 is Error proportion, the proportion of errors in the first clauses produced in each structure. The independent variables are, alternatively, Structure-AoA or Structure-rank. The results are striking: the age or order at which a structure is learned are highly significant and negative explanatory variables.Footnote 7 In other words, the later a structure enters the child's vocabulary, the lower the probability of word-order errors among its earliest clauses. This decline in errors is all the more impressive as it is detected despite a probable overestimation of the errors in later structures – see above in ‘Variables associated with the structures’, subsection ‘Word-order errors’.
Hypothesis 3—The evolution of acceleration (Facilitation II)
According to Hypothesis 3, acceleration should decline over time. We test this hypothesis using two complementary tests. The first test was run on the primary data, for all structures in each corpus and also for all structures in all corpora combined together. For this purpose we add to T 2 an interaction variable, used only in the regressions reported in Table 5:
• Structure-rank*T 2: the interaction term between T 2 and Structure-rank. This term assigns weight to the quadratic variable, T 2, in proportion to the order of entry of the structure to a corpus. It measures the change in acceleration of a learning curve in relation to the order in which a structure is learned: the greater the (absolute) value of the coefficient of this interaction variable, the greater is the change in slope as acquisition rank increases. When acceleration declines over time, it is negative.
The regressions of Table 5 were run on the primary data, using all the datapoints which form the learning curves (i.e. all the dates at which new verbs joined a structure), with Cumulative frequency as the dependent variable (altogether 565 datapoints were available from all six corpora).Footnote 8 We initially focus on the coefficient of T 2. It is positive everywhere, signifying that the learning curves are accelerating, thus supporting the general finding that facilitation (of later verbs by earlier ones) occurs within structures. The interaction term Structure-rank*T 2 is significantly negative in the regression which combines data from all children (column (7)) and is negative in most regressions describing individual children's data, including all three large corpora, and positive in only two regressions, both for small corpora (containing three structures each). We thus obtain support for the hypothesis that acceleration declines the later a structure is learned. Since the interaction terms in the more reliable regressions, those based on the three larger samples, are negative (significantly so in two of the three), we consider this a strong support for the hypothesis of facilitation across structures (the third, based on Ofer's corpus, is negative, but not significantly so. However, Ofer is an outlier in other respects too).
The behaviour of B2, the measure of acceleration, as an indicator of the degree of difficulty of learning as acquisition progresses is of special interest. Therefore a second test, which complements the first, was run on secondary data, using B2 as the predicted variable (see Table 6). The independent variables are two alternative measures of the time of entry of each structure: Structure-AoA and Structure-rank. The coefficients of both variables are negative and in the case of Structure-AoA, the coefficient is also marginally significant (p=0·062). Again, the hypothesis of acquisition becoming easier gains support as acceleration declines over time.
Order or normalized age at structure's acquisition and acceleration: secondary dataFootnote a
a: df-Weighted OLS. Reported values are the regression coefficients of the relevant variables; t-values in parentheses; * significant at 0·10.
FURTHER RESULTS: THE FACILITATOR – MATURATION, SYNTACTIC KNOWLEDGE OR KNOWLEDGE OF STRUCTURES?
The evidence presented below shows that most new structures, at least during the period of early acquisition, begin with a slow phase, and the rate of acceleration of a structure's learning curve depends, at least partly, on previous experience with the specific structure in question. In other words, general maturation or general state of knowledge alone cannot explain the pattern of our results.
New structures enter with a slow start
As mentioned above (in ‘Regression results and discussion’), in 31 (78%) out of the 40 structures in the corpora for which regressions could be run, the learning curve accelerates (see Table A1 in Appendix A). This tendency continues with later learned structures. Each child's structures were divided into two groups: those learned first and those learned last (in case of an uneven number of structures, the middle structure was not counted). Table 7 tabulates the number of accelerating structures among the earliest and the later learned in each corpus. In all the corpora the number of accelerating structures is very similar among the early and late structures. For two children the number is higher by one for the early structures, and for two children the number is higher by one for the later structures. Altogether there are 12 accelerating curves out of the 17 early structures, and 12 out of the 17 late structures. The tendency for newly learned structures to accelerate does not diminish as learning progresses, although, as shown in the results for Hypothesis 3, the rate of acceleration does decline.
Acceleration among early and late structures
The rate of learning is a function of the stage of acquisition of a structure
In order to bring all structures onto a comparable scale only structures in which twenty or more verbs have been acquired were used for the following demonstration. As three of the children did not have a sufficient number of verbs in any of their structures, data from only three corpora – Naomi's, Shuli's and Ofer's – were used. For each structure, two subperiods were defined, the first during which the first ten verbs were acquired and the second during which the second ten were acquired. The first period in an accelerating learning curve is characterized by a gentle incline, while the second is faster and steeper (see Table 8 and Figure 3).
Schematized learning curves for structures with at least twenty verbs.
Time from first to twentieth verb in each structure in Naomi, Ofer and Shuli's corporaFootnote a
a: When there is a lag between the week in which the 10th and the 11th verb were learned, the time it took to learn twenty verbs is longer than the sum of the times it took the first and the second ten verbs.
The majority of structures in Naomi's corpus, all the structures in Shuli's and half of those in Ofer's took longer to acquire their first ten verbs than their second ten verbs (see the second and third columns from the right in Table 8).Footnote 9 Importantly, the rate of entry of verbs into newly acquired structures is slower than the rate of accretion of verbs in previously acquired structures during the same time period. This can be seen most clearly in Figure 3, which omits all non-accelerating learning curves.
What Figure 3 shows is that at the very same time that the earlier learned structures are accelerating, new structures are entering at a much slower pace. In Naomi's corpus, during the very same period that one structure is undergoing the slow learning phase, others are already at the fast stage: the slow stage for SV and VO ends at 103 or 104 weeks, at which point the acquisition of new verbs in these structures speeds up, while SVI, a little later at 108 weeks, begins its slow period; it takes 5 and 7 weeks to learn the second ten verbs in SV and VO respectively, and more than twice the time, 17 weeks, for the first ten verbs in the new structure SVI. Figure 3 underscores this finding: the slopes of the second halves of the SV and VO curves are considerably steeper than that of the first part of the SVI curve. The same applies to Ofer's two structures: the SVO structure starts its slow phase almost at the same time as the earlier SV structure starts its second, quicker stage (both around age 105 or 106 weeks). In Shuli's corpus the learning curves of the different structures are much closer together, yet here, too, one can see the same phenomenon: curves beginning at different times show very similar slopes.Footnote 10
In summary, for accelerating structures in all three corpora, one can find later structures which undergo their slow stage while earlier structures have already begun to accelerate. These data suggest that the rate of learning new verbs in a structure is a function of the stage of acquisition of that particular structure rather than of the stage of syntactic development in general or the cognitive system (or the brain) in general. Even for structures whose acquisition starts late, when the child is already capable of fast learning, new structures present new hurdles which must be overcome.
CONCLUSIONS AND GENERAL DISCUSSION
Our main finding in this paper is that facilitation in language acquisition is not limited to intra-structure learning but that powerful inter-structure facilitation can also be documented. We find support for facilitation in the decline of symptoms of difficulty in the learning of new structures as the process of language acquisition progresses. The first symptom is the gradual reduction in word-order errors in early stages of acquisition of new structures as more structures are learned. This is an especially robust finding: non-canonical clauses are still produced in later learned structures, but they are not necessarily the result of a lack of word-order knowledge. Rather, some of them may be the result of pragmatic considerations which the child may have mastered by later stages of acquisition. Yet in spite of these new word-order options available to the children, we still see a fall in non-canonical word order. This makes the decline even more impressive: it is clear that children base their knowledge of word order in later acquired structures on what they have previously learned through the use of earlier structures.
Our second line of evidence relies on the shape of the learning curves. We find that learning curves become significantly less accelerating over the acquisition process. The change from the slow pace of verb acquisition at first to a more rapid rate later is much more pronounced in the first learned structures.
Furthermore, the two phenomena are related. The rate of acceleration of a structure's learning curve is correlated with the number of errors at the onset of learning a structure. This lends support to the claim that the rate of acceleration, like the proportion of errors, indicates the degree of difficulty at the onset of acquisition of a structure.
Yet the signs of difficulty do not disappear altogether, even for the latest structures. Even later learned structures tend to start their acquisition with accelerating rather than straight learning curves, indicating that each new structure presents new challenges before learning can take off at a more rapid rate. In addition, it has been shown that when, within any corpus, the period of rapid learning for an early acquired structure coincides with the slow period of later structures, the former exhibits a faster rate of growth than the latter.
This finding allows us to respond to the two potential objections to the interpretation of the facilitation phenomenon mentioned in the ‘Introduction’. The first suggested that facilitation may be due to general maturation rather than to the accrual of specific linguistic knowledge. The second was that although combining words becomes gradually easier, this has nothing to do with learning new structures but rather with having learned to produce multiword utterances, or, in other words, that structures do not play an essential role in syntax learning.
We claim that maturation is not the whole story, and that actual early knowledge supports and scaffolds later knowledge. The evidence shows that a new hurdle is encountered and some new learning must take place when a new structure is met, regardless of what has already been achieved in others. New structures ‘take off’ more slowly than older structures which are their coevals, showing that the actual structure is a factor affecting the ease of learning, over and above the possible contributions of age or general syntactic or cognitive advance at the time at which it is learned. Time, the proxy for general development, cannot be the only explanatory element, and variables related to the time or order of entry of specific structures were also significant explanatory factors. These data justify the analysis of learning as a process which to some extent occurs within structures, in addition to showing the propagation of knowledge from previous structures to new ones.
These results are in accordance with a general developmental picture in which newly acquired items are integrated into networks of previously learned information, rather than remaining isolated (see also Ninio, Reference Ninio2003). Things that are similar are stored together and are connected or associated with each other, thus forming a system. That does not mean that there is a preordained or pre-planned system into which items must fit, but rather that analogy is a very strong method of organization. Facilitation between early and late structures fits well into this view of a system that is constantly evolving.
APPENDIX A: B2 BY CORPUS AND STRUCTURE
Age at acquisition, quadratic coefficients and number of verbs learned in each of the structures
Legend: * significant at 0·10; ** at 0·05, *** at 0·01, # at 0·001.
