A new way to identify if variation in children’s input could be developmentally meaningful: Using computational cognitive modeling to assess input across socio-economic status for syntactic islands

Abstract

While there are always differences in children’s input, it is unclear how often these differences impact language development – that is, are developmentally meaningful – and why they do (or do not) do so. We describe a new approach using computational cognitive modeling that links children’s input to predicted language development outcomes, and can identify if input differences are potentially developmentally meaningful. We use this approach to investigate if there is developmentally-meaningful input variation across socio-economic status (SES) with respect to the complex syntactic knowledge called syntactic islands. We focus on four island types with available data about the target linguistic behavior. Despite several measurable input differences for syntactic island input across SES, our model predicts this variation not to be developmentally meaningful: it predicts no differences in the syntactic island knowledge that can be learned from that input. We discuss implications for language development variability across SES.

1 Introduction

1.1 Identifying if input differences are developmentally meaningful

There is a lot of naturally-occurring variation in children’s input, including how long children are talked to every day, which people talk to them (e.g., adults, other children), what environments they experience language interaction in (e.g., home, daycare, school), and what people talk to them about, among many other types of variation. Importantly, not all this input variation is developmentally meaningful – that is, not all input variation impacts language development in a way that causes different trajectories (e.g., measurable delays in knowledge development) or different knowledge to develop (e.g., dialectal variation). So, while input differences may appear, the input is not different when it comes to supporting language development. However, some input variation does indeed impact language development – this variation is then developmentally meaningful.

For instance, developmentally-meaningful input deficits would lead to language development delays. As a concrete example, we have evidence that language development delays appear across socio-economic status (SES), with lower-SES children behind their higher-SES peers for different components of language development (e.g., vocabulary development: Hart & Risley, 1995; Hoff, 2003; language processing: Fernald, Marchman, & Weisleder, 2013). Importantly, variation in children’s input can often predict later language development (Hart & Risley, 1995; Huttenlocher, Vasilyeva, Cymerman, & Levine, 2002; Huttenlocher, Waterfall, Vasilyeva, Vevea, & Hedges, 2010; Rowe, 2012; Weisleder & Fernald, 2013; Hirsh-Pasek, Adamson, Bakeman, Owen, Golinkoff, Pace, Yust, & Suma, 2015; Schwab & Lew-Williams, 2016), suggesting a causal link between observed input variation and language development variation, including the observed language development delays across SES.

Still, when we identify developmental delays that may be linked to variation in children’s input, it is often unclear which of the known delays may be caused (at least in part) by which specific input differences, and why. Certainly, there are observed differences in total input quantity as well as the composition of the input across SES (though input differences also exist within SES: Blum, 2015; Sperry, D. E., Sperry, L. L., & Miller, 2018). For instance, when it comes to total input quantity at the word level, some studies have found that lower-SES children may encounter significantly fewer words of caregiver speech than their higher-SES peers (Hart & Risley, 1995; Schwab & Lew-Williams, 2016). For input composition, differences across SES have been observed at the lexical and foundational syntactic levels (Huttenlocher et al., 2010; Rowe, 2012; Rowe, Leech, & Cabrera, 2017). These differences include the relative frequency of word types, word tokens, and rare words, the diversity of syntactic constructions, and the relative frequency of decontexualized utterances like explanations (Oh, we can’t put them in the bus because the bus is full of blocks), pretend (I’ll save you from the wicked sister), and narrations (He is going to look in your nose and your throat and your ears).

Again, what is often unclear is whether a specific measurable input difference matters for developing a specific component of language. For instance, there are components that do not appear to be delayed across SES, despite the input differences (e.g., some types of complex syntactic knowledge: de Villiers, Roeper, Bland-Stewart, & Pearson, 2008; Vasilyeva, Waterfall, & Huttenlocher, 2008) – that is, some aspects of language development remain constant despite contextual variability that surfaces as measurable input differences (Hoff, 2006). Moreover, there are many components where we simply do not know if there are developmental delays across SES, despite known input variation.

From an intervention perspective, if we believe an input-based language delay is occurring, it is important to understand what aspect of the input has the disparity so that interventions can target that aspect – that is, not only is it useful to know that a developmentally-meaningful input difference exists, but it is useful to know exactly what part of the input is in fact impacting the development of specific language knowledge and why. So, being able to causally link children’s input to their developing language knowledge is valuable, because this link allows us to predict if a measurable input difference will potentially cause a difference in language development.

One way to make this causal link between children’s input and their developing knowledge, often measured via some observable behavior, is to use computational cognitive modeling (e.g., Dickson, Pearl, & Futrell, 2022; Pearl, 2021; Pearl & Sprouse, 2013, 2015, 2019, 2021; Scontras & Pearl, 2021). A computational cognitive model aimed at explaining some component of language development can concretely implement a specific learning theory that describes how the input is used by children to update their hypotheses about language over time; children’s language knowledge is then reflected in their observable language behavior. In this way, computational cognitive modeling connects theories of language development, empirical data on children’s input, and child behavioral experiments. Thus, a computational cognitive model allows us to test explicit hypotheses about the language knowledge that could be derived from the information available in children’s experience (Hoff, 2006). In other words, a computational cognitive model can test hypotheses about what particular aspects of the input may matter and why. More specifically, we can use a computational cognitive model to predict if a measurable input difference will matter for the development of a specific component of language knowledge – that is, when a difference is predicted to be developmentally meaningful, and why it is predicted to be developmentally meaningful.

This computational cognitive modeling approach complements a standard way that relies on correlation to determine if a measurable input difference is developmentally meaningful: observe some input difference, observe language development outcomes, and then see if the observed input difference is correlated with any observed outcome difference. If so, the language input difference might cause the language development outcome difference. In this case, targeting the input difference for intervention may lead to improved language development outcomes (e.g., input-based interventions allowing lower-SES students to improve their language comprehension: Huttenlocher et al., 2002). If input-based intervention is indeed effective, this is support that the language input difference caused the observed language outcome difference, and was therefore developmentally meaningful. However, why that input disparity caused the language development outcome difference is still unknown. Moreover, carefully designing, implementing, and evaluating such interventions can often be costly in terms of both time and resources. Computational cognitive modeling can offer a way to predict beforehand if an input difference is likely to cause a language development difference, and so help inform the design of intervention-based approaches that assess if an input difference is developmentally meaningful.

Importantly, because a computational cognitive model describes exactly how the input can cause the predicted knowledge to develop, the model can also determine if an observed input difference is predicted not to be developmentally meaningful – that is, the model can identify contextual variation surfacing in children’s input that is predicted not to impact language development (Hoff, 2006). In this case, we would expect an input-based intervention targeting that aspect of the input to be ineffective at improving children’s development of the language knowledge that depends on that input aspect.

1.2 Input differences for syntactic island knowledge

Here, we harness this computational cognitive modeling approach to identify if input differences across SES for certain aspects of complex syntax are predicted to impact development of that knowledge and so be developmentally meaningful. We focus on a certain type of complex syntactic knowledge called syntactic islands that concerns wh-dependencies, such as wh-questions (e.g., the acceptable Who did Lily think the pretty kitty was for? vs. the far less acceptable Who did Lily think the kitty for was pretty?). In syntactic theory (Chomsky, 1965, 1973; Ross, 1967), syntactic islands are structures that interfere with wh-dependencies, so that wh-dependencies crossing them are far less acceptable (sometimes called “ungrammatical”). Knowledge of syntactic islands thus allows speakers to judge which wh-dependencies in their language are more vs. (far) less acceptable; that is, even if speakers have never heard a particular wh-dependency before, they can use their knowledge of syntactic islands to judge how acceptable it is. This ability to judge dependency acceptability means that speakers with knowledge of syntactic islands have internalized something quite sophisticated about the syntax of wh-dependencies: not simply how to understand the wh-dependencies that occur in their language, but also (i) how acceptable different wh-dependencies are, and (ii) which ones are far less acceptable (and therefore unlikely to occur) because those wh-dependencies cross syntactic islands. From a developmental perspective, we can then investigate how children come to have this knowledge about syntactic islands, and more specifically, how children’s input influences that language development.

We first briefly review what is currently known about the development of wh-dependency knowledge, particularly with respect to syntactic islands. We then discuss syntactic island knowledge in more detail, and describe the particular syntactic islands we focus on; we selected these islands due to the available empirical data on the behavior that signals successful knowledge development (specifically, judgment data from adults and children). We then review a computational cognitive model for learning syntactic islands that specifies how the input causes the relevant knowledge to develop (Pearl & Sprouse, 2013); this model implements a specific learning theory for how children use their input to acquire knowledge of syntactic islands. The learning theory implemented in the model specifies that the relevant aspect of children’s input involves wh-dependencies, which rely on “wh-words” like what and who in English (among others). We additionally summarize prior modeling results by Pearl and Sprouse (2013) where the model learned from higher-SES child input and successfully demonstrated knowledge of four syntactic islands, as evidenced by the acceptability judgment patterns it predicted. We hypothesize that children across SES would use the same learning process to learn about syntactic islands from their input, as specified by the learning theory implemented in the computational cognitive model. With this hypothesis in hand, we then use the same computational cognitive model to investigate the impact of input variation across SES for learning about syntactic islands.

We begin by looking at the distributions of wh-dependencies in American English child-directed speech (CDS) between higher-SES and lower-SES populations. We first provide a descriptive corpus analysis comparing higher-SES to lower-SES input. We then assess total input quantity differences by deriving realistic estimates of the total quantity of wh-dependencies that higher-SES vs. lower-SES children would hear by age four; age four is when children across SES seem to demonstrate some knowledge about one of the syntactic island types we investigate (de Villiers et al., 2008). This input quantity assessment highlights what can potentially be a significant difference in total quantity of wh-dependencies that children hear across SES by age four.

With realistic estimates of the input data to higher-SES and lower-SES children, we then provide a computational cognitive modeling analysis of the input composition, using the model of Pearl and Sprouse (2013). The model predicts the syntactic island knowledge that higher-SES and lower-SES children would be able to acquire on the basis of their wh-dependency input by age four, as evidenced by the acceptability judgment patterns they would generate for a variety of wh-dependencies.

Our computational cognitive modeling analysis predicts that the lower-SES input supports the development of knowledge about the four syntactic islands we investigate by age four just as well as the higher-SES input does. This is true despite the differences in both total quantity and the distributions of wh-dependencies. Our results thus suggest that the input variation across SES is not developmentally meaningful by age four; that is, the input for learning about these four syntactic islands does not fundamentally differ across SES. This result accords with known developmental evidence for one type of syntactic island, and predicts additional developmental similarities for the other three types we investigate here.

Interestingly, our modeling analysis predicts that a syntactic building block involving complementizer that (e.g., that in Who do you think that Lily likes?) is crucial for successfully developing knowledge of two syntactic island types. This building block comes from a different wh-dependency type in higher-SES CDS vs. lower-SES CDS, which highlights that surface input composition differences may mask deeper input composition similarities. We discuss limitations of our current findings, model predictions that are testable with future work, and implications for variability in language development across SES.

2 The development of wh-dependency knowledge across SES

Currently, less is known about the development of complex syntactic knowledge across SES (especially with respect to wh-dependencies) than about the development of lexical and foundational syntactic knowledge. Still, we do know about the development of some wh-dependency knowledge and a little about the wh-dependency input.

For wh-dependency knowledge, higher-SES English-learning children at 20 months seem to represent the full structure of wh-dependencies in wh-questions (e.g., Which cat did the dog bump?) and relative clauses (e.g., Show me the dog [who the cat bumped]), rather than relying on vocabulary-based heuristics to understand these wh-dependencies (Gagliardi, Mease, & Lidz, 2016; Perkins & Lidz, 2020; Seidl, Hollich, & Jusczyk, 2003). Higher-SES children are also able to correctly repeat back well-formed wh-questions like Who can Falkor save? and generate new well-formed wh-questions by two and a half to three years old (Valian & Casey, 2003).

By age four, we see similar knowledge across SES about several aspects of wh-dependencies (see de Villiers et al., 2008 for empirical data across SES, as well as a review of prior empirical data from higher-SES children). This knowledge includes sensitivity to preferred interpretations of certain wh-dependencies – that is, which interpretations are more or less preferred because those interpretations depend on which wh-dependencies are more or less preferred.

For instance, four-year-olds (like adults) can interpret wh-dependencies like “How did the boy say he hurt himself?” with how modifying the embedded clause verb hurt; so, the wh-question can be interpreted as asking about how the boy hurt himself. Children as young as four are also sensitive to the difference between the possible interpretations of “How did the mom learn what to bake?” The preferred interpretation has how modifying the main clause verb learn (i.e., a possible answer is “from a recipe book”); the strongly dispreferred interpretation has how modifying the embedded clause verb bake (i.e., a possible answer would be “in a glass dish”).

As another example, four-year-olds across SES are sensitive to the difference between the possible interpretations of “What is Jane drawing a monkey that is drinking milk with?” The preferred interpretation has what linked to a position outside the relative clause (“What is Jane drawing [a monkey that is drinking milk] with_{__what} ?”), with a possible answer of what Jane is drawing with (e.g., “a pencil”); the strongly dispreferred interpretation has what linked to a position inside the relative clause (“What is Jane drawing [a monkey that is drinking milk with _{__what}]?”), with a possible answer of what the monkey is drinking with (e.g., “a straw”).

So, developmental outcomes by age four across SES are similar with respect to preferred and dispreferred interpretations for certain wh-dependencies; these interpretations rest on children being sensitive to how preferred (or dispreferred) the different wh-dependencies themselves are. These developmental outcome similarities suggest that input differences across SES for these types of wh-dependency knowledge should not be developmentally meaningful.

Still, we know much less about any input differences there might be for wh-dependencies, let alone how children’s input leads to the development of these types of wh-dependency knowledge despite any input variation that might be present. More generally, much remains unknown, including (i) the input variation present across SES for learning about wh-dependencies, (ii) how the input scaffolds the development of this complex syntactic knowledge, (iii) why any input variation present does not lead to different developmental outcomes for certain wh-dependency knowledge across SES by certain ages, and (iv) whether any input variation present is developmentally meaningful for other types of wh-dependency preferences that have yet to be assessed in children across SES.

3 Syntactic islands

A key component of syntactic knowledge is the ability to have long-distance dependencies, where there is a relationship between two words that are not next to each other. Long-distance dependencies, such as the wh-dependencies between the wh-word what and eat in (1), can be arbitrarily long (Chomsky, 1965, 1973; Ross, 1967). In (1), we can see that this wh-dependency can stretch across one, two, three, or four clauses. In each case, what is understood as the thing Falkor ate, despite what not being next to eat.

However, adult speakers find different wh-dependencies to be more or less acceptable (sometimes referred to as “allowed” or “grammatical” vs. “disallowed” or “ungrammatical”), with some wh-dependencies being far less acceptable than others. As mentioned previously, this marked decrease in acceptability has been attributed to specific syntactic structures, called syntactic islands, that interfere with long-distance dependencies (Chomsky, 1965, 1973; Ross, 1967). Four example syntactic islands are in (2), with * indicating very low acceptability and […] highlighting the proposed island structure that interferes with a wh-dependency in English.

During language development, children must infer and internalize the knowledge that allows the appropriate preferences for long-distance wh-dependencies. This knowledge allows them to recognize that the questions in (2) are far less acceptable, while the questions in (1) are much more so. We note that this recognition is a measurable behavior of children’s internalized knowledge – that is, distinguishing more acceptable questions like (1) from far less acceptable questions like (2) is one way to indicate knowledge of the relevant syntactic islands (whatever form that knowledge may take).

4 Assessing knowledge of syntactic islands

Previous work assessing children’s knowledge of syntactic islands has focused on which interpretations of wh-dependencies are preferred, rather than the relative acceptability of the wh-dependencies directly (Coles-White, de Villiers, & Roeper, 2004; de Villiers, Roeper, & Vainikka, 1990; de Villiers & Roeper, 1995; de Villiers & Pyers, 2002; de Villiers et al., 2008; McDaniel, Chiu, & Maxfield, 1995; Otsu, 1981; Roeper & Seymour, 1994; Vainikka & Roeper, 1995). The idea was that it is easier to ask children if they prefer a particular interpretation that relies on a certain wh-dependency (something more similar to naturalistic communication) rather than asking children directly how acceptable they find that wh-dependency (something more meta-linguistic that requires reasoning about language forms). Suppose children disprefer a certain interpretation (e.g., “What is Jane drawing a monkey that is drinking milk with?” with what interpreted as “the straw”); this (dis)preference can be interpreted as children finding the wh-dependency that the interpretation relies on (e.g., “What is Jane drawing [a monkey that is drinking milk with _{__what}]?”) less acceptable. So, this behavior can then be interpreted as children knowing about the syntactic island that interferes with that wh-dependency (e.g., a Complex NP island) – that is, when children disprefer a particular interpretation, this indirectly indicates their knowledge of a particular syntactic island: the syntactic island interfering with the wh-dependency that the dispreferred interpretation relies on.

A more direct way to assess syntactic island knowledge is with the less-natural task of directly judging how acceptable a wh-dependency is (e.g., in the previous work of Sprouse, Wagers, & Phillips, 2012). When the stimuli are carefully designed (as discussed below), relative differences in judged acceptability can be used to compare the acceptability of island-crossing wh-dependencies against the acceptability of wh-dependencies that do not cross islands, yet are similar in other important ways to the island-crossing ones. The key idea is that knowledge of the relevant syntactic island is signaled when the island-crossing wh-dependency is still judged as far less acceptable (Sprouse et al., 2012). We therefore follow Sprouse et al. (2012), and use acceptability judgment data to indicate knowledge of syntactic islands, and follow Pearl and Sprouse (2013, 2015) in using these acceptability judgment patterns as a measurable target state for development. In particular, following Pearl and Sprouse (2013), the computational cognitive model we implement will attempt to predict the appropriate acceptability judgment patterns found by Sprouse et al. (2012) that indicate knowledge of different syntactic islands.

Sprouse et al. (2012) investigated the four islands from (2). A sample stimuli set for each island type is shown in (3)-(6), where island structures are indicated with […]. These stimuli were designed using a 2x2 factorial design, involving two factors deemed important for judging acceptability: wh-dependency length (matrix vs. embedded) and absence/presence of an island structure in the utterance (non-island vs. island). Each island stimuli set therefore had four wh-dependency types: matrix+non-island, embedded+non-island, matrix+island, and embedded+island. The embedded+island stimulus in each case involved an island-crossing wh-dependency, and so was supposed to be far less acceptable than the others.

This design allows syntactic island knowledge to surface as a superadditive interaction of acceptability judgments; this superadditivity appears as non-parallel lines in an interaction plot, such as those in Figure (6), which come from the judgments of higher-SES adults tested by Sprouse et al. (2012). We briefly review the logic behind this interpretation, as described in Sprouse et al. (2012).

For example, consider the Complex NP plot in the top row, where there are four acceptability judgments, one for each of the stimuli in (3). The matrix+non-island dependency of (3a) has a certain acceptability score – this is the top-lefthand point. There is a (slight) drop in acceptability when the matrix+island dependency of (3c) is judged in comparison to (3a) – this is the lower-lefthand point. We can interpret this as the unacceptability associated with simply having an island structure in the utterance. There is also a drop in acceptability when the embedded+non-island dependency of (3b) is judged in comparison to (3a) – this is the upper-righthand point. We can interpret this as the unacceptability associated with simply having an embedded wh-dependency. If the unacceptability of the embedded+island dependency of (3d) were simply the result of those two unacceptabilities (having an island structure in the utterance and having an embedded wh-dependency), the drop in unacceptability would be additive and the lower-righthand point would be just below the upper-righthand point (and so look just like the points on the lefthand side). However, this is not what we see. Instead, the acceptability of (3d) is much lower than this. This much-lower acceptability is a superadditive effect for the embedded+island stimuli. So, the additional unacceptability of an island-crossing-dependency like (3d) – interpreted by Sprouse and colleagues (Pearl & Sprouse, 2013, 2015; Sprouse et al., 2012) as implicit knowledge of syntactic islands – appears as a superadditive interaction in these types of acceptability judgement plots. This superadditive acceptability judgment pattern appears for all four island types tested by Sprouse et al. (2012) from (2): Complex NP, Subject, Whether, and Adjunct islands.

5 Linking children’s input to syntactic island development

From a computational cognitive modeling standpoint, a modeled learner who can successfully acquire knowledge from its input of any of the four syntactic islands, as measured via acceptability judgments like those of Sprouse et al. (2012), should be able to reproduce the superadditive judgment pattern described above. So, the target behavior for successful development is generating the superadditive judgment pattern for a set of wh-dependency stimuli associated with a particular syntactic island. Pearl and Sprouse (2013) proposed a concrete learning theory – the first of its kind – to specify a precise quantitative link between children’s input and this measurable output behavior, and then implemented this learning theory in a computational cognitive model. ¹

This learning theory is based on the intuition that children will learn what they can from all the wh-dependencies available in the input, rather than ones that are identical to the wh-dependencies they need to judge the acceptability of. To do this, the learning theory proposes that children break wh-dependencies they encounter into smaller building blocks that can be used to construct any wh-dependency, and not necessarily just the wh-dependencies they have encountered before. So, these smaller building blocks comprise the internalized knowledge that corresponds to syntactic island knowledge – that is, by drawing on these learned building blocks, children can generate acceptability judgements, just as they would presumably draw on their syntactic island knowledge to generate acceptability judgments.

Pearl and Sprouse (2013) evaluated their computational cognitive model by allowing it to learn from a realistic sample of higher-SES CDS, and then seeing if it could generate the superadditive acceptability judgment patterns from Sprouse et al. (2012). They found that the modeled learner could indeed generate the appropriate patterns (see Figure 2). This finding supported the learning theory implemented in the model for explaining the development of syntactic island knowledge in higher-SES children. Additionally, the specific finding that wh-dependencies crossing Complex NP islands are far less acceptable (Figure 2, upper left) aligns with higher-SES child wh-dependency (dis)preferences at age four for wh-dependencies crossing Complex NP islands (de Villiers et al., 2008); this alignment also supports the learning theory implemented in the model. Because the model could match available data on output behavior when it learned from children’s input, we use it here as a tool for evaluating variation in children’s input.

Figure 1. Higher-SES adult acceptability judgments from Sprouse et al. (2012), showing means and standard deviations of adult judgments. These judgments are interpreted as demonstrating implicit knowledge of four syntactic islands via a superadditive interaction of acceptability judgments for the selected wh-dependencies that cross dependency length (matrix vs. embedded) with the absence/presence of an island structure (non-island structure vs. island structure) in a 2 x 2 factorial design

Figure 2. Higher-SES child judgments generated from the computational cognitive model in Pearl and Sprouse (2013). These generated judgements can be interpreted as demonstrating implicit knowledge of four syntactic islands via a superadditive interaction of acceptability judgments for the selected wh-dependencies that cross dependency length (matrix vs. embedded) with the absence/presence of an island structure (non-island structure vs. island structure) in a 2 x 2 factorial design. Log probabilities correspond to acceptability judgments, with log probabilities closer to 0 indicating higher acceptability

The model’s learning theory assumes children can characterize a wh-dependency as a syntactic path from the head of the dependency (e.g., What in (7)) through a set of phrase structures that contain the tail (e.g., _{__what} ) of the wh-dependency, as shown in (7a)-(7b). These structures correspond to phrase types that make up wh-dependencies, such as Verb Phrases (VP), Inflectional Phrases (IP), and Complementizer Phrases (CP), among others. Importantly, these are the structures that wh-dependencies would cross to create the link between the head of the dependency and the tail of the dependency. Under this view, children simply need to learn how acceptable the syntactic paths are for different wh-dependencies, which cross different phrase structures.

The learning process itself is implemented as a probabilistic learning algorithm that tracks local pieces (i.e., the building blocks) of these syntactic paths. The learning algorithm assumes the learner breaks the syntactic path into a collection of “syntactic trigrams” (groups of three units derived from the syntactic path) that can be combined to reproduce the original syntactic path, as shown in (7c). ² The modeled learner then tracks the frequencies of these syntactic trigrams in the input, encountering one data point at a time. After the learning period is complete, the modeled learner uses these learned frequencies to calculate probabilities for all syntactic trigrams potentially comprising a wh-dependency ³ and so generate the probability of any wh-dependency (as shown in (8)-(9)). More specifically, any wh-dependency’s probability is the product of the individual trigram probabilities that comprise its syntactic path, as shown in (10). Importantly, relying on the frequencies of syntactic trigrams (rather than the frequencies of entire wh-dependencies) allows the modeled learner to generate probabilities for any wh-dependency, including wh-dependencies that it has never seen before in its input. So, an unseen acceptable wh-dependency can still have a higher probability than an unseen one that is less acceptable, depending on the syntactic trigrams comprising each wh-dependency.

The probability generated by the modeled learner corresponds to how acceptable the wh-dependency is predicted to be. In this way, the modeled learner can generate judgments of wh-dependencies. If the learner can generate the same pattern of judgments that adults do, we can interpret this predicted judgment behavior as the learner internalizing some version of the knowledge adults use to make those judgments. In this case, that means the modeled learner has internalized knowledge (via the syntactic trigrams) that allows it to replicate the knowledge contained in syntactic islands. So, we can interpret this as the modeled learner having learned about those syntactic islands.

For the stimuli sets used by Sprouse and colleagues (Pearl & Sprouse, 2013, 2015; Sprouse et al., 2012), each wh-dependency stimulus can be transformed into its respective syntactic path (see Table 1). Then, the syntactic trigram probabilities learned from children’s input can be used by the modeled learner to generate predicted acceptability judgments. This is the process that allowed Pearl and Sprouse (2013) to generate the judgment patterns in Figure 2, which matched higher-SES adult judgment patterns and so were interpreted as the modeled learner successfully developing knowledge of those four syntactic islands, when given higher-SES children’s input.

Table 1. Syntactic paths for experimental stimuli that the modeled learner can generate acceptability judgments for, in a 2x2 factorial design varying dependency length (matrix vs. embedded) and absence/presence of an island structure (non-island vs. island). Island-spanning dependencies are indicated with a *

We note that the learning theory implemented in this computational cognitive model requires children to have certain (potentially sophisticated) knowledge and abilities in place. More specifically, children are assumed to be able to reliably (i) parse utterances in their input into phrase structure trees, (ii) extract the syntactic paths for the wh-dependencies, (iii) track the frequency of the syntactic trigams, and (iv) calculate the probability for the complete syntactic path of a wh-dependency, based on its syntactic trigrams. It remains for future work to determine when children are able to accomplish these prerequisite tasks, especially if there is variation with respect to when they can. However, once children can indeed do these things, children would be able to harness the input the way this computational cognitive model does.

6 Input analysis across SES through age four

Here we assess input variation across SES, focusing on the information necessary for developing knowledge of the four syntactic islands in (2). The learning theory reviewed above assumes that the relevant input aspect is the wh-dependencies and the syntactic trigrams that comprise those wh-dependencies. So, we consider information available to children across SES in both the wh-dependencies and the syntactic trigrams. Because prior child behavioral work indicates that both higher-SES and lower-SES four-year-olds disprefer wh-dependencies crossing Complex NP islands (de Villiers & Roeper, 1995; de Villiers et al., 2008; Otsu, 1981) ⁴ , we consider variation present in children’s input across SES through age four.

We begin characterizing children’s input for learning about syntactic islands by providing a descriptive analysis of the wh-dependencies and syntactic trigrams available in samples of higher-SES and lower-SES CDS. ⁵ We then estimate the total quantity of wh-dependency input available across SES through age four, finding a potentially large difference in the total quantity of wh-dependencies.

We then use the computational cognitive model from Pearl and Sprouse (2013) to predict the syntactic island knowledge children would learn by age four from their input. More specifically, the modeled learner learns from the estimated wh-dependency input that higher-SES and lower-SES children encounter by age four, in terms of both the total quantity of wh-dependencies encountered and the distributions of those wh-dependencies. The modeled learner then predicts the acceptability judgments that would be generated by higher-SES and lower-SES children for the four sets of stimuli from Sprouse et al. (2012). We see if these predicted acceptability judgments suggest any input-based differences across SES by age four, which would signal that differences in the wh-dependency input were indeed developmentally meaningful. Conversely, similarity in the predicted acceptability judgment patterns would signal that wh-dependency input differences are predicted not to be developmentally meaningful.

6.1 Input samples

Higher-SES

Our higher-SES input samples are the data used by Pearl and Sprouse (2013), and come from the structurally-annotated Brown-Adam (Brown, 1973), Brown-Eve (Brown, 1973), Valian (Valian, 1991), and Suppes (Suppes, 1974) corpora from the CHILDES Treebank (Pearl & Sprouse, 2013). These data are child interactions involving 24 children between the ages of one and a half and four, containing 101,838 utterances with 20,923 wh-dependencies.

Lower-SES

Our lower-SES input samples come from a subpart of the HSLLD corpus (Dickinson & Tabors, 2001) in CHILDES (MacWhinney, 2000), where SES was defined according to maternal education and annual income. Maternal education ranged from 6 years of schooling to some post-high school education. Annual income did not have hard lower and upper bounds; instead, 70% of the families reported an annual income of $20,000 or less, while 21% of the families reported an income of over $25,000. The annual income of the remaining 9% was unreported. In this dataset, we focused on the Elicited Report, Mealtime, and Toy Play sections, which represent more naturalistic interactions. We also drew our samples from Home Visit 1, which recorded child language interactions involving children between the ages of three and five. Our sample contained 31,875 utterances and 3,904 wh-dependencies directed at 78 children. We extracted and manually annotated all wh-dependencies with syntactic structure, following the format of the CHILDES Treebank, as described in the accompanying documentation for the CHILDES Treebank ⁶ (Pearl & Sprouse, 2013).

Limitations of corpus samples

Because we draw our samples from already existing corpora freely available through CHILDES, they do differ on other factors besides SES. Such factors include age range of the children sampled, number of children sampled, gender ratios of the children sampled, size of the samples, and myriad factors related to the child language interactions themselves, including specific topics of conversation and contexts in which the interactions occurred. Though there are overlaps for some of these factors, such as age range (three- and four-year-olds) as well as some topics and contexts of interactions (meal times and toy-playing sessions), it is certainly possible that the non-SES-based differences between these samples impact the wh-dependency distributions.

With respect to the age range differences in these samples, analyses from Pearl and Sprouse (2013) suggest that there is little difference in wh-dependency distribution when comparing higher-SES CDS between one and four years old with adult-directed speech. Because the differences between CDS and adult-directed speech are generally more pronounced than CDS at different ages, this prior analysis suggests that the age range differences in the samples here may not impact the wh-dependency distributions so much. However, a valuable avenue for future work is to collect data across SES that more explicitly controls for many other factors in order to know more clearly which factors do and do not impact the wh-dependency distribution in the input.

Wh-dependency coding

The structural annotations of the wh-dependencies in each sample indicate the syntactic structure necessary to characterize the syntactic paths of wh-dependencies. We coded the syntactic paths of the dependencies as in (7b), shown below with a different example in (11). Following Pearl and Sprouse (2013), the CP phrase structure nodes were further subcategorized by the lexical item serving as complementizer, such as CP_that , CP_whether , CP_if , and CP_null. This subcategorization allows the modeled learner to distinguish dependencies judged by higher-SES adults to be more acceptable, like (11a), from those judged to be far less acceptable, like (11b) (Cowart, 1997). With these syntactic paths characterizing wh-dependencies, we can then assess the distribution of the wh-dependencies in each input sample.

6.2 Descriptive corpus analyses

Wh-dependencies

Our corpus analyses found 12 wh-dependency types in common between the higher-SES and lower-SES child input samples (out of 26 total in the higher-SES and 16 total in the lower-SES). ⁷ So, the higher-SES input sample contained 14 wh-dependency types not in the lower-SES input sample, and the lower-SES input sample contained 4 wh-dependency types not in the higher-SES input sample, as shown in the lefthand column of Table 2.

Table 2. Wh-dependencies and syntactic trigrams unique to speech samples directed at higher-SES and lower-SES children, respectively. Unique syntactic trigrams are on the same row as the unique wh-dependencies they come from

We see first that there is a striking similarity in the two most frequent wh-dependency types across SES: the same two account for the vast majority of wh-dependency types in children’s input across SES (higher-SES: 89.5%, lower-SES: 85.8%), and these two types seem to occur in similar proportions – shown in (12). ⁸ This suggests a high-level distributional similarity in the wh-dependency input across SES, despite the individual wh-dependency differences.

When we compare the rate of wh-dependencies across SES (i.e., how often an utterance has a wh-dependency), we find another difference, with wh-dependencies occurring more frequently in higher-SES CDS (higher-SES: 20,932/101,383 = 20.5%, lower-SES: 3,904/31,875 = 12.2%; two-proportion z-test: z=33.3, p $ < $ .01). Over time (as detailed in section 6.3), this rate difference can lead to a considerable difference in the total quantity of wh-dependencies encountered.

Syntactic trigrams

For syntactic trigrams, which serve as the building blocks of wh-dependencies under the Pearl & Sprouse learning theory, our corpus analysis found 19 syntactic trigrams in common between the higher-SES and lower-SES child input samples (out of 29 total for the higher-SES and 20 total in the lower-SES). So, the higher-SES input sample contained 10 syntactic trigrams not in the lower-SES input sample, and the lower-SES input sample contained 1 syntactic trigram not in the higher-SES input sample, shown in the righthand column of Table 2. ⁹

As might be expected from the wh-dependency descriptive analysis, the most frequent syntactic trigrams are also very similar across SES; this is because these trigrams come from the most frequent wh-dependency type, start-IP-VP-end. More specifically, the two trigram types that collectively account for the majority of the trigrams in the wh-dependency input (start-IP-VP, IP-VP-end) are the same across SES and account for the vast majority of the input (higher-SES: 81.7%, lower-SES: 80.3%). Moreover, these two syntactic trigrams occur in similar proportions ¹⁰ – shown in (13). So, as with the wh-dependency types, this descriptive analysis suggests a high-level distributional similarity in the syntactic trigram input across SES, despite the individual syntactic trigram differences.

6.3 Realistic estimates of total input quantity across SES through age four

To estimate the total quantity of wh-dependency data that children from different SES backgrounds encounter through age four, we can draw on available empirical data sources to estimate both how long children have to learn (i.e., the learning period) and how much data they encounter during that learning period. More specifically, we can estimate when children would begin harnessing the wh-dependency information in their input (i.e., when the learning period for syntactic islands could plausibly start), how much time passes between that starting point and age four (i.e., the length of the learning period), and how many wh-dependencies children across SES would encounter during that learning period.

When children’s learning period plausibly starts

To begin learning about the relative acceptability of different wh-dependencies, children must be able to process the structure of wh-dependencies. Current research suggests that children begin to represent the full structure of wh-dependencies (e.g., wh-questions and relative clauses) at 20 months (Gagliardi et al., 2016; Perkins & Lidz, 2020; Seidl et al., 2003). So, we estimate 20 months as the starting point of the learning period for syntactic islands, which depend on wh-dependencies.

How much time awake during the learning period

Taking four years old as the end point of the learning period for syntactic islands, the estimated learning period is then from 20 months through the end of age four (59 months). We estimate the number of hours awake by drawing on Davis, Parker, and Montgomery (2004), who summarize the hours asleep for young children at different ages (one through four), as shown in Table 3. Based on these estimates, we can then estimate the hours awake between 20 months and 59 months, and sum those hours to estimate the total hours awake during this learning period. Our calculations in Table 3 yield about 14,174 hours awake ( $ \approx $ 850,450 minutes awake).

Table 3. Calculating the total hours (cumulative waking hrs) and minutes (cumulative waking mins) awake for children between the ages of 20 and 59 months, the estimated learning period for syntactic islands. These calculations are based on waking hours per day (waking) and total waking hours. Cumulative hours awake are shown at age one (20-23 months), two (24-35 months), three (36-47 months), and four (48-59 months).

How many wh-dependencies during the learning period

Based on the estimated minutes awake during the learning period, we can then estimate the total quantity of wh-dependencies children encounter. More specifically, we estimate this quantity by drawing on estimates of the number of utterances children from different SES backgrounds hear per minute and our own corpus samples of the rate of wh-dependencies in children’s input.

To estimate utterances per minute across SES, we draw on work by Rowe (2012) and Hoff-Ginsberg (1998). Rowe (2012) examined word tokens per minute at ages 18 months, 30 months, and 42 months across SES, finding that quantity of word tokens per minute appears to remain steady (rather than increasing). So, we assume here that the rate of utterances per minute across SES also remains the same during the learning period from 20 months to 59 months. Hoff-Ginsberg (1998) identified average rates of utterances per minute for children age 21 to 24 months from families with different SES backgrounds: (i) parents who were college-educated and worked in professional positions (which we will associate with higher-SES), and (ii) parents who were high-school educated and worked in semi-skilled, unskilled, or service positions (which we will associate with lower-SES). The higher-SES children heard 15.8 utterances per minute (standard deviation 4.2), while the lower-SES children heard 13.0 utterances per minute (standard deviation 4.2). To capture 95% of each population, we consider the range of utterance rates within two standard deviations from the average, as shown in Table 4 (higher-SES: 7.4-24.2 utterances/minute; lower-SES: 4.6-21.4 utterances/minute).

Table 4. Calculating the range of total wh-dependencies (total wh-dep) that higher-SES and lower-SES children encounter between the ages of 20 and 59 months, the estimated learning period for syntactic islands. These calculations are based on 850,450.2 waking minutes between these ages, estimated ranges of utterance rates per min (utt/min), based on average rates (average) and standard deviations (s.d.) across SES, and wh-dependencies in the input (wh-dep/utt) across SES.

Our corpus estimates of wh-dependency rate suggest that higher-SES children’s input consists of about 20.5% wh-dependencies (20,923 wh-dependencies of 101,838 utterances), while lower-SES children’s input consists of about 12.2% wh-dependencies (3,904 wh-dependencies of 31,857 utterances). Table 4 shows the resulting range of total wh-dependency quantity heard during the learning period across SES: 1,293,545-4,230,241 for higher-SES children, and 479,144-2,229,063 for lower-SES children. While there are some points where there appear to be similar total quantities of wh-dependencies in children’s input across SES (e.g., 2 standard deviations below the higher-SES average = 1,293,545 while the lower-SES average = 1,354,103), there can be a marked disparity in total quantity. On average, higher-SES children will hear about twice as many wh-dependencies as lower-SES children ( $ \frac{\mathrm{2,761,893}}{\mathrm{1,354,103}}=2.04 $ ). In the most extreme case, higher-SES children at the top of the higher-SES range (2 standard deviations above the average: 4,230,241) hear nearly 9 times as many wh-dependencies as lower-SES children at the bottom of the lower-SES range (2 standard deviations below the average: 479,144): $ \frac{\mathrm{4,230,241}}{\mathrm{479,144}}=8.8 $ .

6.4 Summary and implications of corpus analyses

Our descriptive corpus analyses highlight both high-level similarities and differences in the distributions of wh-dependency information in children’s input across SES. Children’s input is similar with respect to the most frequent wh-dependency types and syntactic trigrams, as well as how frequent they are; children’s input is different with respect to specific wh-dependency types and syntactic trigrams unique to each sample, as well as the rate of wh-dependencies in the input. Moreover, our estimate of the total quantity of wh-dependencies heard during the estimated learning period for syntactic islands (through age four) highlights how the total quantity can be quite different across SES, with higher-SES children potentially hearing nearly nine times the quantity of wh-dependencies as lower-SES children.

However, recall that for at least one syntactic island type we investigate (Complex NP islands), children across SES seem to have developed a similar (dis)preference by age four for wh-dependencies crossing that island (Otsu, 1981; de Villiers & Roeper, 1995; de Villiers et al., 2008). So, we might expect that the input differences across SES that we have found so far are not developmentally meaningful by age four for learning a dispreference for wh-dependencies crossing Complex NP islands. This is a prediction we can evaluate using the computational cognitive model from Pearl and Sprouse (2013). Note that each island type involves different syntactic structures – therefore, even if knowledge of one syntactic island type can develop from children’s input (e.g., Complex NP islands), there is no guarantee that knowledge of all these island types can develop from that same input.

Of course, as noted previously, there is suggestive evidence from prior modeling work by Pearl and Sprouse (2013) that higher-SES input can support development of all four syntactic island types. However, the input sample used in those prior analyses is not as realistic as the range we explore in our own modeling analyses here, summarized in Table 4. Thus, our analysis with a more realistic range of higher-SES input will serve as a more comprehensive comparison to our analysis with lower-SES input, and thus of input variability across SES for learning about syntactic islands.

6.5 Computational cognitive modeling analysis

We conducted the computational cognitive modeling analysis by implementing a modeled learner that uses the learning theory of Pearl and Sprouse (2013), and then allowing that modeled learner to learn from the estimated input samples described above. In particular, the modeled learner learned from the range of quantities of wh-dependencies estimated for higher-SES children by age four, with the wh-dependencies distributed as in our higher-SES corpus sample; similarly, the modeled learner learned from the range of quantities of wh-dependencies estimated for lower-SES children by age four, distributed as in our lower-SES corpus sample. For each input set, the modeled learner estimated syntactic trigram probabilities and could then generate probabilities for any desired wh-dependency, whether seen or unseen in its input.

We then demonstrate what this modeled learner would learn about the syntactic island types we investigate from its input, as measured by its predicted judgments on the wh-dependency stimuli from Sprouse et al. (2012), reviewed in (3)-(6) and characterized by the syntactic paths in Table 1. The target state for development is adult-like acceptability judgment patterns – which are superadditive, as in Figure (6). As mentioned above, previous computational cognitive modeling results from Pearl and Sprouse (2013) using higher-SES input were able to generate this superadditive judgment pattern for all four syntactic island types, as shown in Figure 2. Our current analysis will see if the higher-SES predicted judgment patterns replicate when using more realistic estimates of higher-SES input encountered by age four. We will additionally be able to predict the lower-SES judgment patterns resulting by age four, and see how those compare to the predicted higher-SES judgment patterns. In this way, we will be able to compare the input across SES by age four for learning about these four syntactic island types.

6.5.1 Analysis implementation and visualization

For each SES type (higher vs. lower), a modeled learner was run on 1000 representative input sets sampled according to the relative frequencies of the wh-dependencies in our corpus samples; each input set matched the estimated input quantity being modeled (2 standard deviations below average, 1 standard deviation below average, average, 1 standard deviation above average, 2 standard deviations above average). Averages of these 1000 runs for each SES type and estimated input quantity are plotted in Figures 3 and 4, with the log probability averages and standard deviations for each wh-dependency stimuli type available in Appendix C. Standard deviations were not plotted as they were too small to appear on the graphs.

Figure 3. Predicted four-year-old child judgments for Complex NP stimuli by a modeled learner learning from higher-SES (left) and lower-SES (right) input data ranges: 2 standard deviations below average (-2sd), 1 standard deviation below average (-1sd), average (avg), 1 standard deviation above average (+1sd), 2 standard deviations above average (+2sd). Averages are shown from 1000 modeled learner runs per input range. Both interaction plots show the superadditive pattern that appears in adult judgments of these wh-dependencies, given the factorial design crossing dependency distance (matrix vs. embedded) with the absence/presence of an island structure in the utterance (non vs. island)

Figure 4. Predicted four-year-old child judgments for Subject, Whether, and Adjunct stimuli by a modeled learner learning from higher-SES (left column) and lower-SES (right column) input data ranges – 2 standard deviations below average (-2sd), 1 standard deviation below average (-1sd), average (avg), 1 standard deviation above average (+1sd), 2 standard deviations above average (+2sd). Averages are shown from 1000 modeled learner runs per input range. All interaction plots show the superadditive pattern that appears in adult judgments of these wh-dependencies, given the factorial design crossing dependency distance (matrix vs. embedded) with the absence/presence of an island structure in the utterance (non vs. island)

6.5.2 Complex NP islands

The computational cognitive modeling analysis for Complex NP islands predicts acceptability judgment patterns for the wh-dependency stimuli from Sprouse et al. (2012), as shown in Figure 3. For higher-SES child-directed input (left side of Figure 3), we see the same superadditive judgment pattern that higher-SES adults had in Sprouse et al. (2012), and which the prior computational cognitive modeling analysis of Pearl and Sprouse (2013) found. This judgment pattern can be interpreted as demonstrating implicit knowledge of the Complex NP island. In particular, the island-crossing dependency (an embedded dependency with an island structure in it) is far less acceptable than expected if its acceptability were solely based on it being an embedded dependency with an island structure present in the utterance. Thus, these results support prior computational cognitive modeling work suggesting that higher-SES input can lead to implicit knowledge of the Complex NP island, as assessed by the superadditive judgment pattern.

We see this same judgment pattern in the predicted judgments derived from lower-SES child input (right side of Figure 3). So, these results additionally suggest that there is no predicted difference in Complex NP island knowledge by age four across SES. In particular, both higher-SES and lower-SES children should find wh-dependencies that cross Complex NP islands to be far less acceptable. These results align with prior child behavioral data from de Villiers et al. (2008) suggesting that children across SES disprefer wh-dependencies crossing Complex NP islands – that is, our computational cognitive modeling results predict that four-year-olds across SES should judge such wh-dependencies as much less acceptable, which seems to be true.

So, the computational cognitive model correctly predicts that (i) higher-SES children should disprefer wh-dependencies that cross Complex NP islands, and that (ii) lower-SES children should also disprefer these wh-dependencies. Moreover, a more precise prediction is that both higher-SES and lower-SES children should show the same, adult-like superadditive acceptability judgment pattern on this wh-dependency stimuli set by age four. Taken together, these results suggest there is no predicted developmentally-meaningful difference by age four in children’s input across SES for learning about the Complex NP island, and this prediction aligns with currently available empirical evidence. With this in mind, we now turn to the predictions for the other three island types.

6.5.3 Subject, Whether, and Adjunct islands

The computational cognitive modeling analysis for Subject, Whether, and Adjunct islands predicts acceptability judgment patterns for the wh-dependency stimuli from Sprouse et al. (2012), as shown in Figure 4. For higher-SES child-directed input (left side of Figure 4), we see the same superadditive judgment pattern that higher-SES adults had in Sprouse et al. (2012), and which the prior computational cognitive modeling analysis of Pearl and Sprouse (2013) found. This judgment pattern can be interpreted as demonstrating implicit knowledge of Subject, Whether, and Adjunct islands. In particular, the island-spanning dependencies (embedded dependencies with an island structure in them) are far less acceptable than expected if their acceptability were solely based on them being embedded dependencies with an island structure present in the utterance. Thus, these results support prior computational cognitive modeling work suggesting that higher-SES input can lead to implicit knowledge of Subject, Whether, and Adjunct islands, as assessed by the superadditive judgment pattern.

We see this same judgment pattern in the predicted judgments derived from lower-SES child input (right side of Figure 4). So, these results additionally suggest that there is no predicted difference in Subject, Whether, or Adjunct island knowledge by age four across SES. In particular, both higher-SES and lower-SES children by age four should find wh-dependencies that cross Subject, Whether, and Adjunct islands to be far less acceptable.

So, as with the Complex NP island, the computational cognitive model predicts that (i) higher-SES children should disprefer wh-dependencies that cross Subject, Adjunct, and Whether islands, and (ii) lower-SES children should also disprefer these wh-dependencies. As with the Complex NP island type, a more precise prediction is that both higher-SES and lower-SES children should show the same, adult-like superadditive acceptability judgment pattern on these wh-dependency stimuli sets by age four. Taken together, these results suggest there is also no predicted developmentally-meaningful difference in children’s input by age four across SES for learning about Subject, Whether, or Adjunct islands.

6.5.4 Summary of modeling results

As mentioned above, our computational cognitive modeling analysis predicts no difference in children’s knowledge across SES by age four about these four island types, as assessed by acceptability judgment patterns for specific sets of wh-dependencies. These predictions can be tested experimentally in future child behavioral work that gathers acceptability judgments.

If these predictions are indeed true, and there is no difference in acceptability judgments for all four of these island types by age four across SES, then those future behavioral results would additionally support our basic finding: lower-SES input is equivalent to higher-SES input when it comes to the development of this syntactic island knowledge – that is, the measurable input differences across SES are not developmentally meaningful. Importantly, because of the learning theory implemented concretely by the modeled learner, we understand why this result occurs, both in general and more specifically. In general, the observable differences in the wh-dependency distributions in children’s input across SES do not matter for the part of that input that scaffolds knowledge of these syntactic islands. More specifically, the necessary building blocks (i.e., the specific syntactic trigrams associated with each wh-dependency) appear in the appropriate relative frequencies in children’s input across SES.

7 Discussion

Our computational cognitive modeling analysis suggests that higher-SES child input is equivalent to lower-SES child input with respect to how the wh-dependency input can support the development of certain syntactic island knowledge by age four. This is true despite the small differences in wh-dependency distribution and the potentially large differences in total quantity of wh-dependency input encountered by age four. Notably, small distributional differences could have mattered, as children’s learning is often impacted by relative frequency differences of different items in their input (e.g., see Ramscar, Dye, & Klein, 2013a; Ramscar, Dye, & McCauley, 2013b). Yet, we did not find this – instead, any measurable wh-dependency input differences across SES are not predicted to be developmentally meaningful with respect to learning this syntactic island knowledge. That is, surface input differences mask deeper input similarities across SES.

One benefit of our computational cognitive modeling approach is that it implements a learning theory specifying a causal link between children’s input and their observable language behavior. In particular, it makes predictions about children’s observable behavior (here: acceptability judgments for wh-dependencies at age four) that can be evaluated against existing and future child behavioral data. Current data from de Villiers et al. (2008) align with the predictions for Complex NP islands, supporting the learning theory implemented in the computational cognitive model. We note again that, to our knowledge, this is the first learning theory of this kind for syntactic islands that is specified enough to generate precise, testable predictions from children’s input. Thus, we believe it is valuable to continue evaluating the learning theory’s predictions against empirical data, though of course future work may explore other learning theories for syntactic islands and evaluate their predictions against available empirical data.

In particular, future child behavioral work can investigate the specific predicted acceptability judgements for Complex NP islands, to further evaluate both the learning theory and the prediction that there should be no difference in this Complex NP island knowledge across SES by age four. Future child behavioral studies can also investigate the predictions for the other three island types (Subject, Whether, and Adjunct), where the computational cognitive modeling analysis also predicts no differences across SES by age four.

Below, we first discuss some interesting input differences across SES involving the complementizer that, which the learning theory implemented by the computational cognitive model identifies as important for the development of certain syntactic island knowledge. We then turn to other testable model predictions for related syntactic knowledge concerning wh-dependencies. We then consider the plausibility of the prior knowledge and abilities assumed by the learning theory implemented in the model; these prerequisites are also potential points of variation across SES that could therefore impact when children across SES could harness the information in their input in the way the learning theory proposes. We additionally discuss limitations of this computational cognitive model, and consider alternative computational modeling approaches that can be used to evaluate developmentally-meaningful input variation.

7.1 Interesting input differences involving complementizer that

There is a striking difference in the exact wh-dependency distribution across SES that is predicted by the learning theory to be crucial for learning about two of the syntactic island types, Whether and Adjunct islands. This input difference involves particular structural building blocks, which come from wh-dependencies that have the complementizer that and so are characterized by syntactic trigrams with CP _that in them.

As noted before in (11), the only distinction between certain wh-dependencies judged more acceptable and other wh-dependencies judged less acceptable by higher-SES adults is the complementizer. With respect to the wh-dependencies we have investigated here, wh-dependencies like (14a) with complementizer that are judged as more acceptable, while equivalent wh-dependencies like (14b) with complementizers like whether (Whether islands) or if (Adjunct islands) are judged as far less acceptable. Again, the only difference in the syntactic path of these wh-dependencies is CP _that for the wh-dependency in (14a) and CP _whether or CP _if for the wh-dependencies in (14b).

This instance highlights that it is important for children to encounter wh-dependencies in their input that involve complementizer that (and not whether or if), if children are to learn about Whether and Adjunct islands the way the learning theory here proposes. When children do in fact encounter wh-dependencies with complementizer that (CP _that ), the learning theory here can leverage the CP _that piece to predict that (14a) should be judged as more acceptable than (14b).

However, wh-dependencies involving CP _that are actually fairly rare in naturalistic usage. Pearl and Sprouse (2013) only found 2 of 20,923 (0.0096%) in higher-SES CDS. ¹¹ (7 of 8,508 = 0.082%) and adult-directed text (2 of 4,230 = 0.048%). Based on our estimated input ranges by age four for higher-SES children, this would correspond to about three to ten wh-dependencies with CP _that every month. ¹² In our lower-SES CDS sample, there are 2 of 3,094 (0.051%) wh-dependencies involving CP _that. Based on our estimated input ranges by age four for lower-SES children, this would correspond to about six to 29 wh-dependencies with CP _that every month. ¹³ If these corpus samples are accurate, this calculation highlights that lower-SES children could actually hear a crucial building block far more often in their input than higher-SES children do (i.e., lower-SES: 29 times vs. higher-SES: ten times per month even at the highest input estimates); this is true despite higher-SES children likely hearing more wh-dependencies overall before age four. That is, input quantity for this particular input aspect (i.e., wh-dependencies involving CP _that ) is estimated to be more for lower-SES children, rather than for higher-SES children, in contrast to total wh-dependency quantity.

Interestingly, the type of wh-dependency in children’s input that contains the crucial CP _that building block also appears to differ across SES, based on our corpus samples. In the higher-SES sample, both CP _that dependencies are of the same type: start-IP-VP-CP_that-IP-VP-end instances like (14a). However, in our lower-SES CDS sample, the CP _that building block comes from a different wh-dependency type, which happens to be a “that-trace violation” judged as much less acceptable by higher-SES adults (Cowart, 1997): start-IP-VP-CP_that-IP-end instances like (15).

That is, the key linguistic experience allowing a lower-SES child to acquire the same syntactic knowledge about Whether and Adjunct islands as a higher-SES child actually comes from data that would be unlikely to occur in a higher-SES child’s input. It is unlikely to occur because that data type is judged less acceptable by higher-SES adults, who produce the CDS. This finding underscores the power of learning theories that generate the linguistic knowledge of larger structures (such as wh-dependencies) from smaller building blocks (such as syntactic trigrams), like the learning theory here. In particular, children with different input experiences who rely on smaller building blocks may be able to find evidence for the same building blocks (e.g., syntactic trigrams involving CP _that ) in different places (e.g., different wh-dependencies involving CP _that ).

However, we note again that these findings and implications rest on the accuracy of our corpus samples. In particular, for the lower-SES CP _that wh-dependencies, it is possible that these wh-dependency instances were speech errors from the adult speakers. We feel this possibility is less likely, as the two wh-dependency instances came from two different speakers, and so are more likely to reflect naturalistic lower-SES usage. Still, future work can evaluate this prediction that these wh-dependencies would in fact be judged as acceptable by lower-SES adults.

However, suppose these wh-dependency instances in the lower-SES corpus samples were in fact speech errors and so are unlikely to occur in lower-SES children’s input in general (this would be because lower-SES adults would find them as unacceptable as higher-SES adults do). In that case, we would not expect lower-SES children in general to encounter these CP _that wh-dependencies. Because these were the only wh-dependencies in our lower-SES sample containing CP _that , we might then expect that lower-SES children do not in fact encounter any CP _that wh-dependencies. Without the crucial CP _that building block in lower-SES children’s input, the learning theory would predict that lower-SES children would not in fact judge wh-dependencies crossing Whether and Adjunct islands as any less acceptable than wh-dependencies crossing embedded clauses with complementizer that. That is, the learning theory would predict no difference in judged acceptability of the wh-dependencies in (14a) and (14b). So, lower-SES children would not learn the same syntactic knowledge as higher-SES children with respect to Whether and Adjunct islands, as reflected in judged acceptability of the relevant wh-dependencies.

In this situation, the computational cognitive modeling analysis would predict a developmentally-meaningful input difference across SES for Whether and Adjunct islands. In particular, higher-SES children’s input would be predicted to support the development of this knowledge, while lower-SES children’s input would not. More specifically, lower-SES children would be predicted to not have the adult-like superadditive judgment pattern by age four for the Whether and Adjunct wh-dependency stimuli, in contrast with higher-SES children.

To explore whether this input situation is in fact occurring, there are at least two specific things we can investigate in future work, using both corpus and behavioral techniques. First, we can analyze larger samples of lower-SES input to see if and how wh-dependencies with CP _that occur. The CHILDES database (MacWhinney, 2000) has additional data from the HSLLD corpus (Dickinson & Tabors, 2001) that we drew from for our lower-SES corpus sample here, as well as other lower-SES CDS samples in the Hall (Hall & Tirre, 1979) and the Brown-Sarah (Brown, 1973) corpora.

Second, we can use behavioral techniques to evaluate whether lower-SES adults judge as acceptable the specific wh-dependency with CP _that that we found in our lower-SES sample (i.e., the “that-trace violation”). If so, this would support the plausibility of lower-SES adults using this wh-dependency type in lower-SES children’s input, rather than it being a speech error. Lower-SES children would then be likely to encounter this wh-dependency type, and importantly, the CP _that building block it contains. If instead lower-SES adults find that CP _that wh-dependency type less acceptable (as higher-SES adults do), this would suggest that the instances in our lower-SES corpus sample were speech errors. In that case, lower-SES children would not be likely to encounter this wh-dependency type in their input in general. Information about the CP _that building block, used to learn about Whether and Adjunct islands, would need to come from some other type(s) of wh-dependency involving CP _that , if lower-SES children are to learn about these islands the way higher-SES children are proposed to do.

7.2 Other predictions

While our investigation here focused on four island types and the specific wh-dependency stimuli related to them, where empirical data were already available about their judged acceptability, the learning theory is capable of generating predictions for any wh-dependency. Recall that this is because the learning theory proposed that all wh-dependencies are composed of the same building blocks (i.e., the syntactic trigrams). So, the learning theory proposes that children are learning about those building blocks from their input, and then can use those building blocks to judge the acceptability of any wh-dependency.

There are in fact additional data available about children’s preferences and dispreferences for certain wh-dependencies across SES (e.g., from de Villiers et al., 2008). So, the learning theory itself can be evaluated by seeing how well it can capture those known preferences. For instance, de Villiers et al. (2008) found that four-year-olds across SES prefer a wh-dependency like What did he fix the table with _{__what} ? (with syntactic path start-IP-VP-PP-end) over a wh-dependency crossing a Complex NP syntactic island. This preference is easily captured by comparing the probabilities generated by the model learning from either higher-SES or lower-SES input data: the probability for the preferred wh-dependency is much higher ¹⁴ , yielding a prediction that children across SES prefer that wh-dependency, just as children across SES actually do.

Of course, there are many wh-dependencies for which we do not know children’s preferences (e.g., the that-trace violations discussed above). In these cases, the model’s predictions can be used to design future child behavioral studies that can evaluate those predictions. In addition, because the model generates more precise predictions about judged acceptability patterns (for which we do not currently have child behavioral data) rather than simple preference, future child behavioral studies can be designed to test predicted acceptability judgment patterns in children across SES.

7.3 Learning prerequisites and possible variation

It is not trivial to leverage the information from wh-dependencies that the learning theory relies on. More concretely, several foundational knowledge components and processing abilities must be “good enough” to learn the specific syntactic island knowledge investigated here the way the learning theory assumes. First, children must know about syntactic phrase structure; they must be able to use that phrase structure knowledge to extract the syntactic path of a wh-dependency in real time (including accurately identifying where the wh-word is understood). As noted in section 6.3, current research suggests children begin to represent the full structure of wh-dependencies at 20 months (Gagliardi et al., 2016; Perkins & Lidz, 2020; Seidl et al., 2003), which is why we took that age as the starting point for our modeled learners. Yet, it is possible that that there is variation across SES on when this ability is good enough, as there are known delays in language processing in lower-SES children compared to their higher-SES counterparts (Fernald et al., 2013).

Children must also know to break syntactic paths into smaller syntactic trigram building blocks that can be used to generate a probability for any wh-dependency; they must be able to identify these syntactic trigrams in real time. As with extracting the syntactic path, it is possible that a “good enough” version of this ability could be delayed in lower-SES children relative to their higher-SES counterparts because it involves language processing.

In addition, children must know to track the relative frequency of the syntactic trigrams and know to combine these syntactic trigrams to generate the probability for a new wh-dependency; they must be able to do both of these in real time. These components rely on statistical learning abilities, as they involve sensitivity to input frequencies and the ability to aggregate probabilistic information. Recent work on statistical learning abilities across SES (Eghbalzad, Deocampo, & Conway, 2016; Eghbalzad, Deocampo, & Conway, 2021) found no differences by age 8. It is therefore possible that younger children across SES also would not differ in statistical learning abilities, though of course they might.

More generally, it is possible that the components reviewed above that are related to language processing are delayed in lower-SES children, while the domain-general components related to statistical learning are not. Any delays could lead to lower-SES children being less able to harness the complex syntactic information available in their input as early as higher-SES children do. This inability to harness information would occur even if the necessary information is in fact there (as our modeling analysis predicts it to be). However, prior child behavioral work by de Villiers et al. (2008) suggests that any delays present are surmounted by the time children are four years old when it comes to learning certain preferences about Complex NP islands, as there are no delays across SES. So, those prior behavioral results suggest that the necessary prerequisites for learning about syntactic islands are good enough across SES for some amount of time before age four. This then means the computational cognitive model predictions here are likely plausible by age four.

7.4 Using computational models to evaluate input variation

The computational cognitive model we used here to evaluate input variation seemed reasonable because prior work demonstrated its ability to learn from children’s input and match available empirical data on observable behavior. Yet, this model has limitations. For instance, this model currently only learns about wh-dependencies, rather than implementing a more general-purpose syntactic learning theory. That is, it is unclear if the model can be used to learn about other syntactic phenomena involving dependencies (e.g., binding relations between pronouns like him and their antecedents like Atreyu in Jareth banished Atreyu_a after meeting him_a ). ¹⁵ If we believe children do not use a learning strategy tuned to wh-dependencies specifically, then the computational cognitive modeling analysis here may not accurately represent what children would learn from their input.

Another limitation is that the model here operates over the abstract representations of phrase structure. While it is generally uncontroversial that children have abstract representations they rely on when learning from their input, the exact form of those representations is often not agreed upon. In contrast, models that learn from less-abstract representations that are easier to agree upon, such as words, may serve as alternative input evaluation tools. Several recent computational models learn by trying to predict the next word in a sequence, and along the way, these models internalize a variety of syntactic knowledge, including knowledge about syntactic islands (e.g., Chaves, 2020; de Warstadt, Parrish, Liu, Mohananey, Peng, Wang, & Bowman, 2020; Futrell, Wilcox, Morita, Qian, Ballesteros, & Levy, 2019; Wilcox, Futrell, & Levy, 2021; Wilcox, Levy, Morita, & Futrell, 2018). To the extent we believe the computations that these models perform are equivalent to the mental computations that children perform, future work can use these models to evaluate input variation as we have done here.

More generally, future work can aim to use the modeling approach demonstrated here to evaluate input variation, relying on whatever computational cognitive model seems reasonable. However, it is indeed important that the chosen model be a plausible implementation for what children could be doing to extract information from their input and learn from that extracted information. When the particular computational cognitive model is plausible in this way, we can be more confident in using that model to evaluate whether input variation is potentially developmentally meaningful, as we have done here.

8 Conclusion

We have provided a new approach for identifying if and when variation in children’s input could be developmentally meaningful. This approach harnesses computational cognitive modeling and complements existing behavioral approaches. In particular, a computational cognitive model can be used to assess if a particular measurable difference is likely to be developmentally meaningful; the model does so by predicting what children should be able to learn from their input, because the model concretely implements a theory of learning from that input. If input variation is potentially developmentally meaningful, then the model predicts different learning outcomes; in contrast, if input variation is not developmentally meaningful, the model predicts similar learning outcomes.

One practical benefit of this approach is that it is typically less costly to implement in terms of time and resources, compared to behavioral approaches that assess developmental outcomes and then look for correlations with children’s input. However, this approach does require that reasonable samples of children’s input are available, as well as a learning theory that specifies how the input causes linguistic knowledge to develop over time. Still, with the input samples and learning theory in hand, the computational cognitive modeling approach can provide a “first pass” input variation assessment, which can predict if input differences are likely to matter. These predictions can be followed up by targeted behavioral work evaluating the predictions, and thus offer a way to guide future research relying on behavioral approaches.

To demonstrate the computational cognitive modeling approach, we applied it to input variation across SES related to the development of syntactic island knowledge. Our model predicted that there were no developmentally-meaningful input differences by age four, as equivalent outcomes were predicted to occur for all the island types we investigated, despite measurable input differences. One predicted developmental similarity about a specific island type aligns with prior child behavioral work, though more targeted behavioral work can investigate the precise outcome predictions for that island type as well as the predictions for the other island types. More generally, because the learning theory implemented in the model provides an explicit link between the input and language knowledge development, this approach can help us better understand (i) when and why observable input differences are not predicted to be developmentally meaningful, (ii) what parts of the input are predicted to be especially important, and (iii) where those important parts appear in different input samples that reflect different language input experiences.

This result broadens the body of research on language input variation across SES to include the nature of the input for more complex syntactic knowledge, such as syntactic islands. This is the first comparison across SES that uses a computational cognitive modeling approach to investigate the impact of input variation with respect to learning about syntactic island knowledge. Our results suggest that if we do see developmental differences in syntactic island knowledge across SES, it is not because of meaningful differences in the information available in the input. Instead, children’s ability to harness that information may differ. In short, the information for learning about these syntactic islands is predicted to be there for children to use, no matter their SES – a key developmental step may instead be for them to figure out how to use it.