Motivating the math study.

To date, reading achievement has been the primary focus of research into the role that differences in AAE and SCE grammar play in educational outcomes. Child language and literacy researchers have paid considerable attention to the general relationship between measures of children’s AAE use and other language and literacy measures (e.g., [11–17]). Many studies have shown a negative relationship between the two (e.g., [11, 14–16, 18, 19]), with a smaller number suggesting a positive relationship (e.g., [12, 20]). These mixed results help underscore the need to carefully examine the effect of specific divergences in grammar on specific educational tasks. There is no reason ahead of detailed investigation to expect all dialectal differences to have the same effect in all situations.

Collectively these studies suggest that at least some differences between home and school dialects, often referred to as dialect mismatches [3, 18], may negatively affect children’s academic achievement, and in the case of AAE, contribute to the disparity in reading performance between African American children and their White peers. For example, Terry and colleagues [14, 16] have shown that, generally speaking, non-mainstream dialect use is negatively predictive of early school-age children’s reading ability. A number of causal explanations have been suggested for this relationship. On one account, the need to separately store structures from both their home and school dialects leaves AAE speaking children with fewer cognitive resources available for understanding important aspects of classroom instruction, resulting in reading and other academic difficulties [3, 21]. Viewed this way, the principal issue is the cost, in cognitive terms, that children pay for switching between two dialects, a cost presumably paid even when the children have reasonable control over both language varieties. Although recent work on Korean/English bilinguals suggests highly proficient adult code-switchers incur little or no cost for language shifts [22], the case may very well be different for children. As an alternative to any price paid for code-switching, other researchers have proposed that it is AAE speaking children’s lack of familiarity with and control over mainstream structures and grammatical rules themselves that is the root of the problem. This lack of familiarity and control turning dialect mismatches into stumbling blocks to the acquisition and development of literacy skills [3, 14–16, 20, 23]. Of course, these two accounts are not mutually exclusive. Both may play a role, and individual children may face different challenges.

Washington, et al. (2013) [17] summarize the results of investigations into how speaking AAE at home affects children’s learning to read with the following observation: although from preschool through 5th grade AAE speaking students are more likely to struggle as readers than are their mainstream dialect speaking peers, not all children who speak higher levels of AAE are at-risk for experiencing reading failure. Who is, who is not, and why are questions still in need of answers, answers Washington and colleagues argue will only be found when we have a fuller account of the neurocognitive mechanisms underlying reading performance. They suggest computational modeling as one means to that end. Brown and colleagues (2015) [24] are among those who have used this technique to argue that children who use more AAE may, in general, be at greater risk for reading difficulties because differences in pronunciation make the task of learning to decode written-letter to-sound correspondences more complex than it is for speakers of more mainstream varieties of English [24].

The two experiments described herein are intended to move the current conversation beyond reading in that they point towards non-reading-specific mechanisms by which dialect mismatches may affect educational achievement. Labov and Baker (2010) [2] have argued that stumbling over verbal–s and possessive–s when asked to read aloud offers the clearest indication that an AAE speaking child is suffering from dialectal interference in reading. By investigating the role that verbal–s has on AAE speaking 2nd graders’ ability to answer orally presented math questions, the math experiment detailed in the current paper, side steps any difficulties children may have with written-letter to sound correspondences or any other reading-specific processes, thus leaving its results to implicate different, and likely more general, language processing mechanisms. Similarly, the auditory ERP experiment is designed not to shed light on neurocognitive mechanisms particular to reading, but on those engaged in verbally presented tasks, some of which are likely involved in the reading process as well. Together, the results of these experiments provide evidence that verbal–s can negatively affect AAE speaking 2nd graders classroom and test performance independent of reading.

Do differences in SAE and AAE grammar, in fact, affect children’s performance in class and on the tests that do so much to define their status in school? Framed this way–in terms of grammars–the question pushes researchers to be clear in their distinguishing of one grammar from another, a task that is not without its challenges. Two are particularly relevant to the current discussion. First, weather talking about morphology, syntax, phonology, or prosody, closely related dialects like AAE and SCE have far more in common than they do separating them, making it at times difficult to tell which dialect a speaker is using when. Second, individual dialects exhibit variability such that a speaker may use a feature unique to a particular dialect in one context and not in another without ever having left the dialect in question. Consider the AAE sentence She making coffee, translated into SCE as She is making coffee. Since Labov (1969) [4], the most widely accepted analysis of such sentences has been that they arise through a process of deletion. In line with Labov’s generalization that where mainstream varieties of English contract, AAE deletes, it is argued that She is making coffee becomes She making coffee in AAE through roughly the same process of phonological reduction that SCE speakers use to turn She is making coffee into She’s making coffee. The key point is that the sentence She is making coffee, is a part of both dialects. Although subject to different rules in the two different grammars, the copula is is a part of the morphological inventory of both AAE and SCE, and so the AAE speaking child who says She is making coffee is still operating within AAE grammar. Labov paints a very different picture for verbal–s. In contrast to the copula is, he argues that verbal–s is not a part of AAE. Green (2011) [25] draws the same conclusion for child AAE specifically. On this kind of account, the AAE speaking child who says Mary makes coffee is not speaking AAE. That child has either shifted from AAE grammar, where the sentence would be rendered Mary make coffee, into a more mainstream variety or at the very least mixed elements of two different systems. The distinction leads to a prediction: we expect different effects to stem from AAE speaking children’s encounters with morphology that is used variably in their home dialect than we do with morphology that is not a part of it.

This prediction is borne out in J. M. Terry et al. (2010, 2015) [9, 10], which present evidence that some, but not all, morphosyntactic differences between AAE and SCE can suppress 2nd grade AAE speaking children’s scores on the Woodcock-Johnson-R (WJ-R) Test of Applied Mathematics [26]. Examining the test scores of 75 students, this work employed a Bayesian Markov Chain Monte Carlo Method (MCMC) to estimate the effect of morphological mismatches between AAE and SCE in the WJ-R test questions, the presence of verbal–s being one. Consistent with the prediction above and Labov and Baker’s findings in the reading domain, possessive–s and verbal–s, the two features tested that are also argued to be absent from AAE grammar, were found to be the most important features in lowering overall scores. Both split the students into three groups: those highly affected, those moderately affected, and those who showed little effect of the features in question. For verbal–s, the MCMC model predicted that in the highly affected group (roughly 15% of the students), the average student would answer 9% more questions correctly if the effect of this feature were removed, suggesting an educationally significant impact, and leading directly to our predictions for the current math study: in a linguistically controlled test of addition and subtraction word problems, AAE speaking 2nd graders will perform better on questions that do not contain verbal–s than those that do.

Motivating the auditory ERP study.

The aforementioned work on AAE makes psychological claims based on indirect and naturalistic evidence. In it, the effect verbal–s has on AAE speaking children is inferred from their responses to full sentences in which the morpheme is found, sentences spoken during familiar test taking activities. Building on the foundation this work provides, the auditory ERP experiment in the current study is designed to probe its claims more directly. A key strength of the ERP method is that it provides researchers with a real-time correlate of the brain’s electrophysiological activity as it responds to sensory and cognitive events. The technique’s high temporal resolution–its ability to take millisecond by millisecond recordings–makes it especially well-suited for the study of language processing as it progresses throughout time (for reviews, see e.g., [27–38]). In the current context, supplementing previous sentence-level behavioral results with ERP data offers the opportunity to support arguments that verbal–s can cause sentence processing difficulties for AAE speaking children with observations of the neurophysiological effect this morpheme has on them at the very time and place of its utterance. Further, collecting such data makes it possible to draw connections between verbal–s’ role in AAE grammar and specific processing mechanisms.

Important to the topic at hand–how AAE speaking children cope with SCE verbal–s morphology–three functionally distinct ERP effects related to processing syntactic and morphosyntactic anomalies have been identified in the literature. In response to word-level syntactic category errors, errors that disrupt local structure building, an Early Left Anterior Negativity (ELAN) occurs approximately 120–200 ms after the onset of the offending word (e.g., [39–48]). A different response is triggered by sub-word errors that preserve basic syntactic structure, but violate rules of tense, number or gender agreement. For instance, replacing the neuter article das with the masculine den in the German sentence Sie bereist das Land auf einem kraftigen Kamel (“She travels the_neuter land_neuter on a strong Camel”), results in a sentence that preserves the original’s basic structure, Sie bereist den Land auf einem kraftigen Kamel. However, the change introduces an agreement error as the neuter noun land requires a neuter article das (adapted from [49]). Errors of this type induce a Left Anterior Negativity (LAN) that occurs slightly later than the previously discussed ELAN, between approximately 300 and 500 ms post onset of the critical morpheme (e.g., [43, 50–57]). Both of these effects are typically followed by a late central-posterior positivity (P600) (for reviews, see e.g., [58–63]). This late positive deflection is often argued to result from either the reanalysis or the repair of structures initially assigned in error (e.g., [30, 35, 44, 45, 47, 62, 64–70]), both of these processes likely a part of some more general integration process required to complete sentence comprehension (e.g., [60, 62, 71–74]).

Each of the established ERP patterns described above (e.g., LAN followed by P600) results from familiar linguistic material being used in unfamiliar ways. However, a chief claim of this paper is that although AAE speaking children recognize SCE verbal–s as inflectional morphology, the morpheme itself is, in an important sense, unfamiliar to them. The linguistic landscape of the United States is such that all AAE speakers receive some exposure to verbal–s. Be that as it may, we contended that for many, especially children, this morpheme is not integrated into a tense and agreement system that they control, and is therefore less cognitively available to them than, say, past tense–ed or some other morpheme that is a part of AAE grammar. Thus, in encountering it, they face a different type of morphological error than investigated in the studies from which the reported patterns emerge–a type of error commonly encountered by non-mainstream dialect speaking children, but not directly addressed in this literature or the literature that investigates how second language learners cope with similarly misused morphology in their non-native language (cf. [75, 76]). These previous studies are nonetheless suggestive, providing a starting point for predicting AAE speaking children’s neurophysiological responses to different types of SCE sentences that use verbal–s.

Although still a matter of debate, data from both behavioral and neuroimaging studies suggest that regular inflectional morphemes like verbal–s are accessed separately from their stems, with stem and affix being fused together in a subsequent syntactic operation (for an overview, see e.g., [77]). Consequently, affixing verbal–s to the end of a verb can be viewed as a structure building operation similar to that of adding a new word to a syntactic structure. The similarity of the two tree structures in Fig 1 –one syntactic, the other morphosyntactic underscore the point. As discussed in greater detail in the section to follow, due to the lack of integration of the morpheme into their tense and agreement system, we expect AAE speaking children’s encounters with verbal–s, then, to signal a morphosyntactic structure building error and induce a response similar but not identical to the type triggered by phrase structure errors. Further, we expect verbal–s to be met with some measurable effect of the processing load the children incur as a result.

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Fig 1. Syntactic and morphosyntactic similarity.

The similarity of syntactic and morphosyntactic tree diagrams suggests that the two result from similar structure building operations. “Af” stands for Affix, “N” for Noun, “NP” for Noun Phrase, “V” for Verb, and “VP” for Verb Phrase.

https://doi.org/10.1371/journal.pone.0273926.g001

Participants.

Thirty-two AAE speaking 2nd graders participated in the auditory ERP experiment described below. The data for twenty-two participants (10 male and 12 female; mean age 7.55 years and 6.32 months) were included in the final data analysis. The remaining ten participants either did not complete the experiment (six participants) or had their data excluded from final analysis due to excessive EEG artifacts (four participants). All participants were right-handed, had normal or corrected-to-normal vision, and were free of any known neurological or hearing disorders.

The dialect-speaking status of each participant was supported by results from the Diagnostic Evaluation of Language Variation (DELV) Screening Test [81] and a modified version of the Third Person Present Tense subtest of the Wiig Criterion Referenced Inventory of Language (Wiig CRIL) [82]. Twenty-one of the final twenty-two participants’ screening test results fell into the DELV category of “strong variation from Mainstream American English”, supporting the conclusion that they were indeed speakers of AAE. (We treat Mainstream American English here as a synonym for SCE.) The remaining one participant was identified by the DELV as having “some variation from Mainstream American English”, again suggesting that this participant was an AAE speaker. No participants fell into the DELV category of Mainstream American English speaker.

In contrast to the DELV screener’s more global evaluation of dialect status, the CRIL subtest was used specifically to measure the participants’ production of verbal–s. The verbal–s morpheme is a part of SCE but not AAE grammar; thus, it follows that low levels of its production are consistent with AAE use. We assume that when a child whose primary dialect is AAE does produce verbal–s, that production reflects either emerging SCE or code-switching/mixing on the part of the child. Because the goal in administering the CRIL subtest was to assist in evaluating participants’ dialect-speaking status, as opposed to their ability to produce an unfamiliar grammatical pattern, we modified the test’s instructions so that when modeling answers in the demonstration, the test administrator only used sentences that paired a plural subject with a suffix-less verb, sentences like “The ballerinas dance”. As a result, no sentence used to model a potential test answer ever contained verbal–s, and all model answers were consistent with both AAE and SCE grammar. No other modifications to the test were made. The CRIL subtest consisted of a total of 10 items. The mean percentage of verbal–s use on this test and its SD were 39.09 ± 33.08%. Anecdotal evidence suggests that the large standard of deviation here is due, at least in part, to the classroom-test-like format of the CRIL subtest coupled with participants’ awareness that classroom teachers expect students to use verbal–s. When asked to repeat an answer so that it could be better heard, one participant remarked “Oh, do you want me to put that–s on it?” The test administrator remained neutral in response and asked him to simply do his best to answer. Further, we note that the one participant the DELV identified as having only “some variation from Mainstream American English” scored 20%, for the use of verbal–s on the CRIL subtest (well below SCE mastery levels), providing additional evidence that this participant was indeed an AAE speaker.

Stimuli.

As exemplified by the sentence “One kid from Swan Village eats chocolate cake”, test sentences for the auditory ERP experiment fit the following sentential frame: NUMBER kid(s) from NAME Village VERB OBJECT. Following a 2 x 2 factorial design, the stimuli varied first in whether the subject noun phrase (NP) was the singular “One kid” (conditions SS and SN, the leading “S” standing for singular) or the plural “Six kids” (conditions PS and PN, the leading “P” standing for plural). Second, the stimuli varied in whether the sentence’s verb carried an–s suffix (SS and PS conditions, the trailing “S” standing for suffixed) or did not carry an–s suffix (SN and PN conditions, the trailing “N” standing for no suffix). Example sentences for each condition are provided in Table 1. Condition SS (a singular subject NP paired with a verb with–s) is consistent with SCE, but not AAE grammar. Condition SN (a singular subject NP paired with a verb without–s) is consistent with AAE, but not SCE grammar. Condition PS (a plural subject NP paired with a verb–s) is not consistent with either SCE or AAE grammar, while condition PN (a plural subject NP paired with a verb without–s) is consistent with both grammars. Thirty-six sets of test sentences were created, each set containing four sentences (one sentence per condition), for a total of 144 sentences. The test sentences were all spoken by a bidialectal African American woman, who at the time they were recorded, had been a life-long member of the community from which the participants were drawn.

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Table 1. Example stimuli for the four experimental conditions tested in the auditory ERP experiment and their grammatical statuses in AAE and SCE grammar.

https://doi.org/10.1371/journal.pone.0273926.t001

To monitor participants’ attention throughout this ERP portion of the experiment, a behavioral task was introduced into the experimental design. Each ERP test sentence was matched with a “comparison sentence” for which no ERP data were analyzed. These sentences were spoken by a bidialectal African American man, who although not a member himself, has close ties to the participants’ community through family and friends. The resulting test-comparison sentence pairs served as stimuli for the behavioral task, a sentence discrimination task in which participants were asked to indicate whether or not the two sentences in a given pair were identical. Of the 144 comparison sentences created, half matched their corresponding test sentences word for word. The other half differed from their corresponding test sentences by one word, changing either the number of kids, village name, verb or the verb’s object from test sentence to comparison sentence. The sentences always differed such that these words could not be misinterpreted as being semantically equivalent. For example, “One kid from Swan Village bakes chocolate cake” would serve as a suitable comparison sentence for the test sentence “One kid from Swan Village eats chocolate cake”. Given the pair, participants would be expected to recognize that these two sentences are different due to their different verbs, bakes and eats. The test sentence-comparison sentence differences were evenly distributed across the manipulated parts of the test sentence. The condition of the test sentence-comparison sentence pair is defined by the test-sentence condition.

Based on Thomas (2007, 2010, 2015) [83–85], the segmental and prosodic features of the stimuli (both the test and comparison sentences) were controlled to avoid any dialectical bias in their phonology. Stimuli sentences were constructed so that they only contained segments pronounced the same in African American and more mainstream varieties of English, and speakers were instructed in how to control their prosody to avoid ethnically identifiable patterns. Thus, while the sentences may have retained some phonological characteristics reflective of geographic region, they were designed to be phonologically consistent with both AAE as spoken by the study participants and other more mainstream varieties of Southern American English spoken in the area. All sentences were digitally recorded in stereo at a 16-bit/44.1-kHz sampling rate.

Audio files for the test sentences were constructed using a splicing (i.e., audio “copy and paste”) procedure to ensure that across all four test conditions and across all sentences within those conditions, instances of the same words were acoustically identical. Similarly, a single audio recording of the verbal–s morpheme was created, copied, and then spliced onto the verbs on which the morpheme occurred, thus guaranteeing that all instances of this critical feature were also acoustically identical. Once put together in this manner, each test sentence audio file was reviewed to make sure that it maintained the qualities of natural speech. Fig 2 presents pitchtracks for the example test sentences given in Table 1 along with indications of where the sentences were spliced. Tables 2 and 3 present the mean f0 maxima and duration of each phrase for the test stimuli. All stimuli were normalized to an intensity level of 70 dB. All audio editing was done using Adobe Audition CS6 (San Jose, CA). Acoustic measurements of the stimuli were taken with Praat [86].

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Fig 2. Example pitchtracks and illustration of the splicing procedure applied to the four experimental conditions tested in the auditory ERP experiment.

Scissors indicate the positions where auditory files were appended. A 100 ms period of silence was inserted after “one kid” and “six kids”, and a 200 ms period of silence was inserted after “from Swan village” and “eat(s)”.

https://doi.org/10.1371/journal.pone.0273926.g002

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Table 2. Mean max pitch (Hz) for each phrase of the sentences tested in the auditory ERP experiment with their SDs (in parentheses).

https://doi.org/10.1371/journal.pone.0273926.t002

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Table 3. Mean duration (ms) for each phrase of the sentences tested in the auditory ERP experiment with their SDs (in parentheses).

https://doi.org/10.1371/journal.pone.0273926.t003

To make the task more engaging for the participants, all of whom were children, the auditory stimuli described above were embedded inside animated video clips so that the recorded sentences appeared to be spoken by two animal-like cartoon characters. After a female cartoon character spoke a test sentence, a male character would speak a comparison sentence. A separate video clip was prepared for each of the stimulus sentence pairs (144 video clips in total). The GoAnimate™ (now Vyond™) software package (GoAnimate, Inc, San Mateo, CA) was used to create the animated video clips (for more details, see Procedures).

Procedures.

All ERP experimental sessions took place in a quiet room at the participants’ elementary school. Each participant individually completed one approximately one hour-long ERP session, separate from all other testing, which took place on different days. Participants were randomly assigned to one of four counterbalanced lists of stimuli, with each list divided into eight experimental blocks, each block containing 18 test sentences. The stimuli within each block were pseudorandomized so that no two sentences of the same condition ever appeared in more than two trials per sequence.

At the start of each session, a participant was seated in a chair placed approximately 100 cm away from the computer screen and loudspeakers that played the video clip and auditory stimuli. Before the stimuli were presented, participants were told that they would be listening to a series of paired sentences spoken by two cartoon characters. They were instructed to listen to each sentence and indicate whether the two sentences were identical. Each participant heard five pairs of practice sentences before the eight experimental blocks began. At the end of each block, participants were asked to take a short break. However, they were also advised that they could request a break at any time during the experiment.

At the beginning of each trial within a block, the female character appeared in the middle of the computer screen (see Fig 3). 500 ms after her appearance she spoke a test sentence approximately 3500 ms in length (see Table 3). After completing the sentence, she remained on screen for 1500 ms before disappearing and being replaced by the male character. 500 ms after his appearance, the male character then spoke a comparison sentence. 3500 ms after doing so, he disappeared and 2000 ms later, a question mark appeared on the screen. The question mark remained on screen until either the participant pressed one of two buttons on a response pad to indicate whether or not the sentences the cartoon characters spoke were identical, or until a 5000 ms time-out interval passed. No feedback was given to participants after they registered their responses. An inter-trial interval of 2000 ms during which a blank screen was shown occurred before the next trial began.

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Fig 3. Trial sequence in the auditory ERP experiment.

The appearance of the female cartoon character on the computer screen marked the beginning of each trial. After a participant gave his or her response to the task, a blank screen appeared for 2000 ms before the next trial started.

https://doi.org/10.1371/journal.pone.0273926.g003

Electrophysiological recording and preprocessing. During the presentation of the test sentences, electroencephalograms (EEG) were recorded from 32 Ag/AgCl scalp electrodes via an EASYCAP EEG recording cap (Brain Vision, Herrsching, Germany). In compliance with the standard 10–20 system for electrode positioning (cf. [87]), EEG signals were recorded from the following scalp positions: F1/F2, F3/4, F7/8, FC1/2, FC5/6, C3/4, T7/8, CP1/2, CP5/6, TP9/10, P3/4, P7/8, PO3/4, O1/2, FZ, CZ, PZ, and OZ, with the FPZ channel serving as the ground electrode. To control for artifacts resulting from ocular movements, the FP1 and FP2 channels were used to record electrooculograms (EOG). All scalp electrodes were referenced online to the left mastoid and re-referenced offline to linked mastoids. Electrode impedances were kept below 10 kΩ. EEG and EOG channels were amplified using an actiCHamp amplifier (Brain Vision, Herrsching, Germany). Both EEG and EOG were continuously recorded at a sampling rate of 1000 Hz. To remove slow signal drifts, EEG data were filtered with a 0.3–20 Hz band pass filter. Trials contaminated by EOG saturation, amplifier saturation, or other artifacts were identified by a semi-automatic artifact rejection using an automatic criterion of 40 μV standard deviations (calculated in 200 ms sliding windows) and were manually checked afterwards. Trials containing artifacts (39.71% of all trials) were eliminated from further analyses. Likewise, the data points of participants with fewer than 18 trials in one or more than one condition (data points of four participants) were not analyzed.

Data analysis procedures. Data for the behavioral task–the sentence discrimination task used to monitor participants’ attention during the collection of ERP data–were analyzed as follows: incorrect response rates and reaction times were calculated for each of the four experimental conditions. A response was considered incorrect if it was either false (i.e., the wrong answer) or was supplied after the time allotted to answer had elapsed. Incorrect responses were not included in the reaction time analysis. To investigate the effect of experimental condition on incorrect response rate and reaction time, separate one-way ANOVAs were carried out using the factor CONDITION (SS, SN, PS, PN) and error terms based on participant (F₁) and item variability (F₂). Following the one-way ANOVAs, two critical pairwise comparisons of the conditions were performed: SS vs. SN and PS vs. PN. In addition, contrast tests were conducted where appropriate.

All EEG data for test sentences were analyzed regardless of participants responses in the behavioral task. ERPs were time-locked to the onset of the end of the verb, the position where verbal–s attaches in SCE grammar, and average ERPs were computed for a time epoch that ranged from 0 ms to 1500 ms beginning from that target position (see Table 1). For each electrode, ERPs were averaged per participant per condition before grand averages were calculated across all participants across all conditions. On the basis of visual inspection, two time windows (200–400 ms and 400–900 ms) were chosen for statistical analysis. For each of these time windows, two critical pairwise comparisons were made to test our specific predictions: SS vs. SN and PS vs. PN. To examine the effect of experimental condition on the ERP signatures within each time window, prior to these condition comparisons, a repeated measures 4 x 3 x 2 Global ANOVA was performed with the experimental variable of COND (SS, SN, PS, PN) and the following topographical variables: REG (Anterior, Central, Posterior) and HEM (Left, Right). For the lateral electrodes, the topographical variables (REG and HEM) were fully crossed yielding six Regions Of Interest (ROIs); left anterior (F3, F7, FC1, FC5), right anterior (F4, F8, FC2, FC6), left central (C3, T7, CP1, CP5), right central (C4, T8, CP2, CP6), left posterior (P3, P7, PO3, O1), and right posterior (P4, P8, PO4, O2). (For the complete results of the repeated measures 4 x 3 x 2 Global ANOVA, see S1 and S2 Figs). In addition, to examine the effect of the presence or absence of verbal–s and its interaction with the subject NP while keeping other factors constant, a repeated measures 2 x 2 x 3 x 2 Global ANOVA was also conducted for each of the two time windows. In the repeated measures 2 x 2 x 3 x 2 Global ANOVA, the experimental variable was treated as a 2 x 2 factorial design, with the first variable VERB (SS, PS vs. SN, PN, i.e.,–s on verb vs. No–s on verb) and the second variable SUBJ (SS, SN vs. PS, PN, i.e., singular subject NP vs. plural subject NP). The topographical variables REG and HEM of the 2 x 2 x 3 x 2 Global ANOVA remained the same as the 4 x 3 x 2 Global ANOVA. Midline electrode analyses for the two Global ANOVAs (4 x 3 x 2 Global ANOVA and 2 x 2 x 3 x 2 Global ANOVA) are not reported below, however, they yielded results comparable to those obtained in the lateral electrodes. Statistical analyses were carried out in a hierarchical manner, i.e., only significant interactions (P < 0.05) were resolved. Whenever a variable included more than one degree of freedom in the numerator, corrected values were reported [88]. Effects attributed to the topographical variables alone (i.e., a main effect of REG and HEM or an interaction between two topographical variables, REG x HEM) are not reported. Only significant effects (P < 0.05) are reported.

Behavioral data.

Table 4 presents mean correct response percentages and mean response times for each condition of the behavioral task. Overall, performance on the task was high (mean correct response across all conditions 80.05%), suggesting that participants paid sufficient enough attention to the sentences in this behavioral task for the ERP data collected at the same time to be meaningfully analyzed. Statistical analyses show that participants performed best when the test sentence-comparison sentence pair being evaluated was in the SS condition, that is, when the two sentences participants were comparing both made use of a singular subject paired with verbal–s. Specifically, a one-way ANOVA showed that this effect of CONDITION on correct response was significant for the participant analysis (F₁(3,63) = 3.68, P < 0.05, F₂(3,105) = 2.06, P = 0.11). The significant result stemmed from participants’ performing better on the SS condition than the other two conditions (SN and PS). Pairwise comparisons showed significantly better performance in the SS condition than the SN and PS conditions in the participant analysis (SS vs. SN: F₁(1,21) = 11.44, P < 0.005, F₂(1,35) = 2.74, P = 0.11; SS vs. PS: F₁(1,21) = 15.71, P < 0.001, F₂(1,35) = 8.09, P < 0.01; SS vs. PN did not reach significance: F’s < 4.10). No other pairwise comparisons produced significant results (F’s < 1.00). A contrast test comparing SS and the mean of the other three conditions (SN, PS, and PN) was also conducted. Consistent with those of the pairwise tests, the results of this test indicated that SS yielded significantly better performance than the mean of all other conditions in the participant analysis (F₁(1,21) = 16.30, P < 0.001, F₂(1,35) = 0.15, P = 0.71). It is notable that SS, one of the two sentence types that are ungrammatical in AAE, and of them, the only one that is grammatical in SCE, gave rise to the strongest performance by the AAE speaking 2nd graders on this task. These results likely suggest that the combination of the ungrammaticality of the sentences and the fact that this construction is taught in school garnered the participants’ attention in a way that was beneficial to the task. For completeness, statistical analyses were carried out for the response time data. No significant results were found (F’s < 1.85).

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Table 4. Mean percent correct response (%), response times (ms), and their SDs (in parentheses) for each condition in the behavioral task for the auditory ERP experiment.

https://doi.org/10.1371/journal.pone.0273926.t004

ERP data.

Fig 4 visually depicts the grand averaged ERPs for each of the four experimental conditions given in Table 1. Each ERP was time-locked to its target position–the right edge of its sentence’s verb–as indicated in that same table. Tables 5 and 6 give the ERPs’ mean values and SDs in microvolts for the two time windows described in the Methods section (200–400 ms and 400–900 ms). Visual inspection of the data revealed the following patterns. First, compared to those sentences that paired a singular subject NP with a suffix-less verb (SN, Grammatical in AAE), sentences that contained a singular subject with an–s marked verb (SS, Ungrammatical in AAE) elicited a bilateral anterior-central negativity in both 200–400 ms and 400–900 ms post the target position. Second, compared to plural subject sentences with suffix-less verbs (PN, Grammatical in AAE), plural subject sentences that contained–s marked verbs (PS, Ungrammatical in AAE) showed a bilateral early anterior negativity from 200 to 400 ms, followed by a bilateral late central-posterior positivity that lasted from 400 to 900 ms. These data patterns are supported by the statistical analyses that follow.

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Fig 4. Grand average ERPs for the four experimental conditions.

ERPs were time-locked to the onset of the target position, i.e., at the right edge of the underlined word in Table 1. Negativity is plotted upwards. Left plot (SS vs. SN): Compared to AAE grammatical sentences that pair a singular NP subject with a suffix-less verb (green), AAE ungrammatical sentences with singular NP subjects and–s marked verbs (red) showed a bilateral anterior-central negativity in both the 200–400 ms and 400–900 ms time windows (Zoom-in plots (a) and (b)). Right plot (PS vs. PN): Compared to AAE grammatical sentences that pair a plural subject NP with a suffix-less verb (blue), AAE ungrammatical sentences with plural subject NPs and–s marked verbs (black) showed a bilateral anterior negativity (200–400 ms), followed by a bilateral central-posterior positivity (400–900 ms) (Zoom-in plots (c) and (d)).

https://doi.org/10.1371/journal.pone.0273926.g004

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Table 5. Mean ERP amplitudes (μV) and their SDs for the four experimental conditions in the 200–400 ms time window.

https://doi.org/10.1371/journal.pone.0273926.t005

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Table 6. Mean ERP amplitudes (μV) and their SDs for the four experimental conditions in the 400–900 ms time window.

https://doi.org/10.1371/journal.pone.0273926.t006

Results of critical pairwise comparisons of the experimental conditions. Table 7 presents the statistical results of the critical condition comparisons. As predicted, the comparison of single subject sentences with and without verbal–s (SS vs. SN) and the comparison of plural subject sentences with and without verbal–s (PS vs. PN) were both significant in the 200–400 ms and 400–900 time windows. More precisely, the comparison SS vs. SN was significant in both the anterior and central regions in both the 200–400 ms and 400–900 ms time windows. The comparison PN vs. PS reached significance in both the anterior and central regions in the 200–400 ms time window and in the central and posterior regions in the 400–900 ms time window. In addition, comparing SS and PS showed that SS was significantly more negative than PS in the anterior region in the 200–400 ms time window (F(1,21) = 4.84, P < 0.05). Together, the results of these comparisons support the data pattern observed via visual inspection. (See S1 and S2 Figs for the results of the complete statistical analyses of the ERP data).

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Table 7. Results of critical pairwise comparisons.

https://doi.org/10.1371/journal.pone.0273926.t007

2 x 2 x 3 x 2 Global ANOVA. In line with the study hypothesis, the statistical analyses presented above showed a difference in participants’ ERP responses to those sentences that contained a verbal–s, ungrammatical in AAE, and those that did not, grammatical in AAE. Still, rather than stemming from anything to do with grammar, it is possible that this difference merely reflects the differences in the test sentences’ lengths and acoustic properties that were introduced by the presence or absence of the–s marker itself. Unlike grammatical accounts, however, this explanation does not predict significant interactions between the presence or absence of the–s marker and other grammatical characteristics of the test sentences. To test whether such interactions occurred, as described in the Methods section, a 2 x 2 x 3 x 2 Global ANOVA with the first factor VERB (–s marker on the verb, No–s marker on the verb), the second factor SUBJ (Singular subject NP, Plural subject NP), the third factor REG (Anterior, Central, Posterior), and the fourth factor HEM (Left, Right), was performed for both selected time windows. The results of these analyses support both the ERP effects reported so far and the more grammatical account of them. A significant VERB x SUBJ interaction was found for all of the critical analyses. The 2 x 2 x 3 x 2 Global ANOVA showed a significant interaction of VERB x SUBJ in both selected time windows (see Table 8). (For completeness, all significant interactions found in the 2 x 2 x 3 x 2 Global ANOVA were resolved. For the results, see S3 Fig.)

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Table 8. Results of 2 x 2 x 3 x 2 Global ANOVA for the two selected time windows (200–400 ms and 400–900 ms).

https://doi.org/10.1371/journal.pone.0273926.t008

Participants.

Eighteen of the twenty-two study participants took part in the experiment. Participant selection was based solely on prior participation in the ERP experiment and availability. No other selection criteria were used.

Stimuli.

As noted above, the stimuli for the mathematical reasoning experiment were constructed so as to resemble the “word problems” commonly given to elementary school students. Such problems are given both orally and in written form on classroom tests, homework assignments, and as a part of psychoeducational batteries like the Woodcock Johnson [26]. Presented orally, the stimuli for the current experiment comprised 60 pre-recorded mathematical word problems, examples of which are provided in Tables 9 and 10. Following a 2 x 3 factorial design, the stimuli varied in 1) Problem Type, whether the problem was an addition or subtraction problem (Tables 9 and 10, respectively), and 2) Sentence Type, the grammar of sentences used to pose the problem. Consistent with SCE, but not AAE grammar, a third of the questions– 20 problems total, 10 addition, 10 subtraction–used sentences that paired singular subject NPs with–s suffixed verbs (MSS in Tables 9 and 10). Consistent with AAE, but not SCE grammar, a third of the questions–again, 10 addition and 10 subtraction–used sentences that paired singular subject NPs with suffix-less verbs (MSN in Tables 9 and 10). Finally, consistent with both SCE and AAE grammar, the remaining 10 addition and 10 subtraction questions used sentences that paired plural subject NPs with suffix-less verbs (MPN in Tables 9 and 10). To distinguish them from those in the auditory ERP experiment, the condition labels used here (MSS, MSN and MPN) all begin with “M” for math. Like the ERP labels, however, the following “P” or “S” stands for plural or singular subject, and the trailing “S” or “N” stands for–s suffix on verb or no suffix. In addition to the linguistic controls just described, the difficulty level of the math questions was controlled so that they would match that of problems the participants–all 2nd graders–would typically encounter in school. Specifically, solving each problem required either the addition or subtraction of two single digit numbers each ranging from 1 to 9, with the resulting sum or difference also being a single digit number that ranged from 1 to 9 (see Tables 9 and 10 for examples).

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Table 9. Example auditory stimuli for the mathematical reasoning experiment (addition Problems).

https://doi.org/10.1371/journal.pone.0273926.t009

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Table 10. Example auditory stimuli for the mathematical reasoning experiment (subtraction Problems).

https://doi.org/10.1371/journal.pone.0273926.t010

The methods used to record the questions were the same as those used in the previously described auditory ERP experiment. A female speaker, different from the speaker that recorded the target ERP stimuli, spoke the math question stimuli. Across all conditions, both pitch and duration of the questions were matched as much as possible. Due to necessary differences in their wording, the subtraction problems were significantly longer than the addition problems (F(1,9) = 75.58, P < 0.0001) (see Table 11). No other difference was found between the different conditions in Sentence Type, and there was no significant interaction between Sentence Type and Problem Type (F’s < 1.80).

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Table 11. Mean durations of the auditory stimuli for the mathematical reasoning experiment (seconds) with their SDs (in parentheses).

https://doi.org/10.1371/journal.pone.0273926.t011

Procedures.

Sessions for the ERP and mathematical reasoning experiments took place on separate days in the same quiet room at the participants’ elementary school. The order of experiments was kept constant for all participants: ERP session first, followed by the mathematical reasoning session. Ahead of the mathematical reasoning sessions, each participant was randomly assigned to one of four counterbalanced lists of stimuli. Each list was divided into two blocks, a block of addition problems and a block of subtraction problems. Half of the participants answered the addition problems first, and the subtraction problems second. The other half answered the subtraction problems first followed by the addition problems. In each session, after ensuring that the participant was ready to begin, the experimenter played pre-recorded versions of the math questions to be answered. After hearing a question, the participant spoke his or her answer, and the experimenter recorded it on a scoring sheet. Participants were permitted to listen to the same question up to three times. If a participant could not arrive at an answer to a question, he or she could respond “I don’t know” and the experimenter would move on to the next question. No feedback was provided to participants after answering questions.

The mathematical reasoning data were analyzed as follows. For each participant, percent correct response measures were calculated for each problem type for each sentence type. Unanswered questions and those answered with “I don’t know” were included in the data analysis as false responses. Note that response times were not recorded in the mathematical reasoning experiment and therefore not included in the analysis. To examine the effects of problem type, whether the question a participant was asked required addition or subtraction to solve; and sentence type, whether the problem was posed in a manner consistent with SCE (but not AAE) grammar, AAE (but not SCE) grammar, or both grammars; repeated measures 2 x 3 ANOVAs with the first factor PROBLEM TYPE (addition, subtraction) and the second factor SENTENCE TYPE (MSS, MSN, MPN) were carried out using error terms based on participant (F₁) and item variability (F₂). In addition to these statistical tests, based on our predictions, planned contrast tests were conducted to compare the percent correct response for MSS, the sentence type ungrammatical in AAE, to the percent correct response for the mean of MSN and MPN, the sentence types grammatical in AAE.

The bilateral early anterior-central negativities.

We initially predicted that due to its limited cognitive accessibility and ungrammaticality in their home dialect, AAE speaking children would identify the verbal–s in both singular subject sentences like Mary drinks coffee (SS) and plural subject sentences like The workers drinks coffee (PS) as an error. In both cases, we assumed that compared to their closest error-free counterparts, error detection would be reflected in the children’s producing a relatively early anterior negativity (SS vs SN and PS vs. PN). However, we also expected the two negativities to differ from one another, and in the case of the singular subject sentences (SS) to differ from the LAN most commonly associated with morphosyntactic error detection (e.g., [55]). This electrophysiological signature, normally part of a bi-phasic pattern of LAN followed by P600, is associated with the misuse of familiar morphology that results, for example, from morphological agreement errors (for an overview, see e.g., [32]). In contrast, the verbal–s that AAE speaking children encounter in a sentence like Mary drinks coffee is unfamiliar in the sense that it is less cognitively accessible to them. As previously noted, we believe this type of error is more akin to the kind of structure building error associated with a phrase structure violation than an agreement error. Unable to give it a semantic representation, AAE speaking children presented with verbal–s in this context are, in effect, given a building block of morphosyntactic structure without a blueprint for its use. A sentence like The workers drinks coffee, on the other hand, differs in that the plural–s on the subject, the workers in this case, makes that fully accessible morpheme and its rules of use salient. We hypothesized that hearing sentences of this type, the young AAE speakers in our study would be “tricked” into thinking that verbal–s was a misplaced plural. Thus, it would be detected as a morphological agreement error rather than a morphosyntactic structure building error, a distinction that should be visible in the ERP signatures.

The above expectations were largely met. Although neither type of ungrammatical sentence (SS or PS) elicited an ELAN, both did elicit a bilateral early anterior-central negativity. The broader than expected distributions–bilateral rather than left-lateralized, and anterior-central rather than anterior–are likely due to the young ages of our study participants. Compared to adults, children often need to use a greater proportion of their cognitive resources to perform the same linguistic tasks (e.g., for an overview, see [79, 80]). Our ERP predictions were based on adult processing studies; all our participants, however, were 2nd graders.

Although the verbal–s in both sentence types under discussion triggered a bilateral early anterior-central negativity, the two negativities were predicted and found to be different from one another. Statistical analysis showed that the amplitude of the negativity triggered by the verbal–s in singular subject sentences like Mary drinks coffee (SS) was higher than that that triggered by the–s in plural subject sentences like The workers drinks coffee (PS) (see the results of all condition comparisons in S2 Fig). We interpret this difference in ERP amplitude as reflecting different morphosyntactic processes, the former the detection of a morphosyntactic structure building error, the latter the detection of a misplaced morpheme.

At 200 ms, the bilateral anterior-central negativity we associate with the detection of misplaced/misused morphology (PS) is slightly earlier than the LAN we equate it with in the literature (e.g., [43, 44, 51–59]). The earlier onset time is most likely due to a difference in where the ERPs were time-locked: in the current ERP experiment, the ERPs were time-locked directly to the critical morpheme onset (verbal–s), whereas they were time-locked to the critical word onset in the previous studies.

The late ERP effects.

Further evidence that the bilateral anterior-central negativity that verbal–s induced in plural subject sentences (the PS condition) reflects the detection of an agreement-like morphological error comes from the late time window ERP effects. Compared to their grammatical counterparts (PN), sentences of this type elicited a bilateral late central-posterior positivity in the 400–900 ms time window. We identify this late positivity with the P600 effect often found in adult studies of morphological error. Following a LAN, the P600 effect has been taken to reflect either the repair of a misidentified morpheme or the engagement of a general integration process associated with the repair of some element within in an ungrammatical sentence.

In contrast, the verbal–s in singular subject sentences (the SS condition) did not elicit a P600. In line with our predictions, the bilateral early anterior-negativity (200–400 ms) in these sentences was followed by a longer lasting bilateral anterior-central negativity in the 400–900 ms time window. We view this second negativity as an indicator of the increased working memory load the children incurred as a result of not having a full representation for verbal–s in their morphological inventories and therefore not having a clear procedure for coping with its presence. Long lasting (or sustained) negativities have been found in previous studies that tested both the online processing of sentences (e.g., [71, 89–92] and other experimental tasks that required increased working memory loads (for an overview, see e.g., [93]). Both the early and late time window effects, then, suggest that AAE speaking children can approach verbal–s in two ways: they can misidentify it as a plural marker (the case of PS) or they can fail to identify it as a part of a system they control at all (the case of SS).

One might imagine a different explanation for the ERP pattern we observed in the PS condition. Instead of misidentifying verbal–s as a plural marker, the same or a similar pattern might be thought to arise due to the children’s misidentifying the plural–s on the subject noun as a possessive (e.g., the worker’s for the workers), only to have this initial hypothesis disconfirmed by the verb phrase. As is the case with verbal–s, it has been argued that possessive–s (in the attributive position) is not a part of AAE grammar. Sentences like This is John cup (in SCE, This is John’s cup) are grammatical and common in both adult and child AAE [4, 25]. However, unlike with verbal–s, comprehension studies suggest that, in the main, young AAE speaking children give this–s an SCE interpretation [94]. Although unlikely, it is possible, then, that AAE children’s first impression of the plural would be that it is a properly placed SCE possessive, and with that morphology not fully a part of their grammar, they would produce a LAN-like effect. A P600 would, then, follow the verbal–s, as the verb phrase makes it clear that the initial–s is not a possessive and, therefore, must be reanalyzed reanalysis must occur. This account, however, will not explain the results of the current experiment, as in the sentences presented to the children, the subject noun phrase was always separated from the verb phase by a prepositional phrase (e.g., from Durham in the sentence Six kids from Durham eats chocolate cake), the prepositional phrase making clear that the initial–s is not a possessive well before the verb phrase containing verbal–s is introduced. Misidentification of verbal–s as the plural remains the most plausible account of the ERP effects that we observed.