Who Is a Deaf Learner of English?

It is often assumed that a deaf person’s L1 is American Sign Language (ASL). ASL is estimated to be the “primary” language of between 100,000 and 300,000 deaf individuals in the United States and English-speaking parts of Canada (see Padden & Humphries, Reference Padden and Humphries2005). For deaf persons exposed to ASL, it is a natural and accessible visual-spatial language, and it is an icon of Deaf cultural identity.Footnote ² Therefore, it is often assumed that, with respect to language acquisition, a deaf person’s L1 is in fact ASL. In actuality, the learning of ASL may occur at various points in a deaf person’s lifetime, if at all, but rarely as early as a L1 in the conventional sense. Only between 5% and 10% of deaf children are born to two deaf parents for whom ASL might be their L1, in which case the child’s L1 would be ASL. Otherwise, the vast majority (more than 90%) of deaf children are born to two hearing parents who do not know ASL (Marschark, Lang, & Albertini, Reference Marschark, Lang and Albertini2002). If hearing parents learn to sign, the reality is that any early signed input to the child would likely be fragmentary, inconsistent, and not at all nativelike. For deaf individuals who learn ASL later, ASL can become their preferred or better language (relative to English), given its natural access in the visual-spatial modality. Depending on age of exposure and other personal and situational factors, ASL proficiency will vary, often up to nativelike proficiency. The number of actual L1 signers of ASL is nevertheless proportionately very small within the deaf population.

English is also not the L1, as conventionally conceived, of the majority of deaf individuals in the United States and English-speaking Canada. Depending on the deaf child’s degree of hearing loss (Levitt, Reference Levitt, Wang, Reynolds and Walberg1989), access to English language input is typically delayed for months and sometimes years, as auditory access to the input is severely or totally restricted.Footnote ³ Compensatory visual access to English input can occur through face-to-face communication but only to the extent that the learner is able to lip-read and capitalize on facial expression, gesture, and other contextual cues. If sign language skills are acquired, then the deaf learner will eventually be able to access signed representations of English input, including finger spelling. As literacy skills develop, reading serves as a vital source of supplementary (and lifelong) English input; however, reading does not serve as a naturalistic source of primary English input for deaf children (Bochner & Bochner, Reference Bochner and Bochner2009). Thus, English acquisition by deaf learners (a) is typically delayed in onset, (b) proceeds under conditions of severely restricted access to the input, (c) is protracted and gradual over their lifespan, (d) is highly variable, and (e) rarely reaches the ultimate attainment as that of hearing L1 English speakers (with many exceptions, however; see Toscano, McKee, & Lepoutre, Reference Toscano, McKee and Lepoutre2002).

Given all these factors, English acquisition for a large majority of deaf learners is, in essence, L2 acquisition in the absence of an (intact) L1 (Berent & Kelly, Reference Berent, Kelly and Han2008). Moreover, because deaf learners’ English acquisition proceeds over the course of many years, it is recognizably influenced by the same factors that otherwise guide hearing learners’ L2 acquisition—maturational constraints, memory limitations, processing capacity, implicit and explicit learning procedures as well as sociolinguistic and cultural factors, and so on (see Doughty & Long, Reference Doughty and Long2003; Ritchie & Bhatia, Reference Ritchie and Bhatia2009). It is this later language learning under conditions of restricted input access and intake (whether the restriction is cognitive or auditory) that presumably yields so many L2 learner–deaf learner interlanguage parallels. As argued in Berent (Reference Berent, Ritchie and Bhatia2009) and Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009), it is the restricted input access that renders L2 and deaf learners more vulnerable (than L1 speakers) to the pressures of derivational economy and that shapes the acquisitional parallels.

One fundamental distinction to note in this study of hearing and deaf learners is that, with respect to deaf learners, speaking skills can be factored out of the discussion of internalized English acquisition. Whether a deaf person learns and uses speech (e.g., via speech therapy) depends on early parental decisions, individual preferences and inclinations, educational environment, and social or cultural factors. English language acquisition and knowledge for a deaf learner refers to the learner’s knowledge of the lexical, morphosyntactic, syntactic, semantic, and other properties of English (i.e., the mental lexicon and grammar) as communicated or revealed through any medium—reading, writing, signing, finger spelling, and so forth—irrespective of whether that person has learned and uses speech (for further details on deaf learners’ acquisition of English language and literacy, see Marschark et al., Reference Marschark, Lang and Albertini2002; Paul, Reference Paul2001; and Strong, Reference Strong1988).

Theoretical Context

Much of the extant research on quantifier knowledge and acquisition has been conducted within the context of generative theories such as the theory of principles and parameters (P&P; Chomsky, Reference Chomsky1981, Reference Chomsky1986) and its successor framework, the minimalist program (MP; Chomsky, Reference Chomsky1995, Reference Chomsky, Martin, Michaels and Uriagereka2000). These theories assume the existence of universal grammar (UG), or an innate human language faculty, which includes tacit knowledge of universal principles and parametric options that constrain language acquisition.Footnote ⁴ Prior to and within P&P theory, quantifier raising (QR; May, Reference May1977, Reference May1985) was proposed as the fundamental operation provided by UG by which scope relations among elements in quantificational sentences are established. Because of the theoretical centrality of QR in accounting for quantifier interpretation, the present research is conducted within the P&P and MP context. This context provides explicit constructs and processes for assessing learnability factors that may constrain acquisition amid restricted input access.Footnote ⁵

Quantifier raising has been challenged within the MP because it differs from other widely employed movement operations that combine lexical entries and check agreement features. Various proposals within the MP have thus attempted to eliminate or reduce the need for QR (e.g., Fox, Reference Fox2000). To the extent that QR must be retained as an explanatory construct, it has been shown to impose a heavy burden on the computational system for human language (Reinhart, Reference Reinhart2006). Given that computational burden, the present study explores the extent to which QR imposes an even higher computational burden on L2 and deaf learners of English.

L2 and Deaf Learners’ Universal Quantifier Knowledge

This study builds on the results of Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009), which explored L2 and deaf learners’ English universal quantifier knowledge. A summary of those results provides appropriate background for the present study’s focus on Num QP knowledge. The research employed a multiple-picture sentence interpretation task, the English Sentence Picture Task–Quantifiers (ESPT-Q; Berent, Kelly, Porter, & Fonzi, Reference Berent, Kelly, Porter and Fonzi2008), described in the Method section. Both Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009) and the present study employed the ESPT-Q.

The ambiguity of universally quantified sentences as in (2) has long been explained as a result of the manner in which QR adjusts relative scope relations at the syntactic-semantic interface level of logical form (LF). For example, the collective and distributive LF derivations of sentence (2a), Every boy is climbing a tree, can be represented as in (3).

1. (3) a. [[a tree_j [every boy_i] [t_i is climbing t_j]]].

2. b. [[every boy_i [a tree_j] [t_i is climbing t_j]]].

In (3a), the collective derivation, the NP—a tree—raises via QR (leaving a trace, t) to a position from which it takes scope over the universal quantifier phrase (QP) every boy; thus, its interpretation is the logical equivalent of there is a tree, j, such that every boy, i, is climbing it (i.e., one specific tree). In the distributive derivation (3b), in which every boy takes scope over a tree, the sentence means that for every boy, i, there is some tree, j, such that i is climbing j (i.e., the members of the set of boys are climbing different trees).

As noted, the reduction of the role of QR is theoretically desirable. Two proposals, Reinhart’s (Reference Reinhart1997) choice function analysis and Schwarzschild’s (Reference Schwarzschild2002) theory of singleton indefinites, provide semantic-based mechanisms that reduce the need for QR by restricting the scope of singular indefinite NPs, such as a tree in (3), in their surface positions, without the need to adjust such scope relations via movement. These proposals capitalize on the flexibility with which the domain of an indefinite NP is reducible to a one-member set, free from the scope effects of other quantifiers. For example, when a speaker freely restricts the domain of a tree in (4a) to a singleton indefinite (the set of trees, |T|, has one member), a collective interpretation results.

1. (4) a. Every boy is climbing a tree _{|T| = 1.}

2. b. Every boy is climbing a tree_x.

In contrast, when a tree does not receive a singleton indefinite restriction, as in (4b), the NP receives its restriction as a variable (a tree_x) within the scope of every boy, yielding a distributive interpretation. In this case, a tree is morphologically singular but semantically plural (designating a multimember set of trees), unlike a tree in (4a), which is singular both morphologically and semantically.

In the case of a universally quantified sentence in which a singular indefinite NP precedes the universal QP, as in (2b) (A woman is smelling every flower), a singleton indefinite restriction of the NP, as in (5a), again yields a collective interpretation: one specific woman smelling all members of a set of flowers. However, despite the interpretive flexibility of indefinite NPs, the only means of deriving a distributive interpretation of (2b) is via QR, as in (5b), where every flower must raise to a position from which it takes scope over a woman.

1. (5) a. A woman _{|W| = 1}is smelling every flower.

2. b. Every flower_i [a woman_x is smelling t_i].

Within the scope of the universal QP every flower, a woman now denotes a multimember set of women who, cumulatively, are smelling all the members of the set of flowers. Thus, a woman in (5b) is morphologically singular but semantically plural. Where QR is forced as the only derivational alternative for obtaining a required contextual meaning, it is viewed as a high-cost, last resort operation. Reinhart (Reference Reinhart2006) argued that QR extends the options permitted by the human computational system to yield derivations that are “harder to obtain,” even by L1 speakers (p. 105). Among such derivations is the distributive interpretation illustrated in (5b).

Assuming these derivational processes, Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009) predicted that learners who acquire English under conditions of restricted input access (i.e., L2 learners and deaf learners) would exhibit interlanguage knowledge that results from the relative degrees of acquisitional pressure tied to derivational economy and complexity (see Yusa, Reference Yusa, Flynn, Martohardjono and O’Neil1998). Thus, the learners’ predicted order of success would be as shown in (6), where the label QP-NP refers to universally quantified sentences in which the QP precedes the singular indefinite NP and NP-QP refers to the opposite order.

1. (6) a. QP-NP collective = NP-QP collective

2. b. QP-NP distributive

3. c. NP-QP distributive

There were four learner groups in Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009) and one control group of hearing L1 speakers of English (L1). There were two participant groups of hearing L2 learners: the L2-L group with lower overall English proficiency and the L2-H group with higher overall English proficiency. Parallel to these groups were two groups of deaf learners (DF) with lower and higher overall English proficiency: the DF-L group and the DF-H group, respectively. Results of the study confirmed the predicted success order in (6); this is illustrated in Figure 1. The figure also shows that even the L1 group accepted fewer NP-QP distributive interpretations of sentences like (2b) in view of the computational cost associated with derivations involving QR (Reinhart, Reference Reinhart2006).

Figure 1.

Acceptance of collective and distributive depictions of universal quantifier sentence types by group, based on the results of Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009).

In addition to assessing semantic knowledge of universally quantified English sentences, the ESPT-Q was designed to assess pragmatic factors that affect sentence-picture matching when a sentence is underinformative relative to its depicted discourse context. In the child L1 acquisition literature, children have long been observed to reject a universally quantified sentence as a match to a depiction containing an extraneous uninvolved entity. For example, children often reject a sentence like (2a), Every boy is climbing a tree, as a match to a distributive depiction showing all members of a set of boys (e.g., four boys), each climbing a distinct tree, when there is an additional fifth tree not being climbed. Despite the presence of the extra tree, the sentence is still true in that context, because every boy is, in fact, climbing a tree. The claim has been that children, unlike adults, require exhaustive pairing between the members of the agent set and the members of the object set, also described as a symmetry preference (argued to involve quantifier spreading; Philip, Reference Philip1995). The study of this phenomenon has resulted in diverse explanations implicating methodological, maturational, cognitive, or linguistic factors (see summary discussions in Berent et al., Reference Berent, Kelly, Porter and Fonzi2008; Berent et al., Reference Berent, Kelly and Schueler-Choukairi2009; Rakhlin, Reference Rakhlin, Takita and Fuji2007).

More recent research has established that a symmetry preference is not limited to child L1 acquisition but is observed in picture tasks that assess knowledge of universally quantified English sentences by both deaf and hearing students at the middle school, high school, and college levels (Berent et al., Reference Berent, Kelly, Porter and Fonzi2008) as well as by adult L2 learners and L1 speakers (Berent et al., Reference Berent, Kelly and Schueler-Choukairi2009; Brooks & Sekerina, 2005/2006; DelliCarpini, Reference DelliCarpini, Liceras, Zobl and Goodluck2003). The explanation of the observed symmetry preference in Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009) expanded on Rakhlin’s (Reference Rakhlin, Takita and Fuji2007) analysis of the same effect in her studies of young children. Rakhlin’s novel explanation drew on Schwarzschild’s (Reference Schwarzschild2002) semantic theory of singleton indefinites. As noted, any singular indefinite NP may be freely restricted to a singleton set, where the NP denotes one specific entity. Rakhlin argued that the symmetry preference appeared under pragmatic pressures when a child’s visual attention was diverted to a depicted extra entity (e.g., an extra tree) and thus prompted the child to interpret the singular indefinite NP in the target sentence—for example, a tree in sentence (2a)—as a singleton indefinite referring to the extra tree itself. In such a case, every boy is not climbing a specific tree, and the sentence-picture match is legitimately rejected. Rakhlin attributed this phenomenon to a lack of pragmatic flexibility in managing contextual information in discourse.

Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009) argued that older learners whose course of English acquisition has been constrained by restricted input access are also challenged in their management of discourse-pragmatic factors such that they too sometimes prefer exhaustive pairing between members of the agent and object sets. This can now be understood on principled grounds as resulting from a singleton effect. The present study further explores and explains the symmetry preference in adult learners’ and L1 speakers’ interpretations of numerically quantified sentences.

Properties of Numerically Quantified Sentences

English Numeral Quantifier Sentences. Like the analogous QP-NP sentences in Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009), Num-NP sentences like (1a), containing a Num QP followed by a singular indefinite NP, also typically permit a collective and a distributive interpretation as in (7).

1. (7) a. Three guys _{|G| = 3}are carrying a box _{|B| = 1}.

2. b. Three guys _{|G| = 3}are carrying a box_x.

Following the same minimalist assumptions as in the universal quantifier study, including Schwarzschild’s (Reference Schwarzschild2002) singleton indefinites analysis, when a box is restricted to a singleton set as in derivation (7a), it is free from the scope effects of the Num QP three guys. Accordingly, (7a) is the collective derivation, indicating that three guys are carrying one specific box. When a box is not restricted to a singleton set, as in derivation (7b), a box is a variable within the scope of three guys and therefore provides the distributive interpretation in which three guys are carrying different boxes.

Unlike universally quantified NP-QP sentences, NP-Num sentences like (1b) permit a collective derivation as in (8a) but not a distributive derivation as in (8b).

1. (8) a. A mother _{|M| = 1}is bathing three babies _{|B| = 3}.

2. b. *[[three babies_{|B| = 3}]_i [a mother_x] is bathing t_i].

Collective derivation (8a), in which a mother is a singleton indefinite, is interpreted to mean that one specific mother is bathing all three members of a set of three babies. In view of the lexical-semantic properties of Num QPs, the distributive derivation of sentence (1b) is not available. If it were, it would require QR as shown in (8b), resulting in a mother being within the scope of three babies. Such a derivation would be interpreted to mean that three mothers are each bathing one member of a set of three babies.

Numeral Quantifier Sentences in Other Languages. Numeral quantifiers have different properties across languages, but in a given language there are typically ambiguous and unambiguous Num QP sentence types. Like English, ASL has such options. However, because ASL is a visual-spatial language, it employs many morphosyntactic processes that appear to have no correlates in spoken languages. For example, ASL marks agreement through the manual movement of a sign toward or from referents set up in the signing space or through the use of indexical pointing or eye gaze toward spatially designated referents (Fischer & van der Hulst, Reference Fischer, van der Hulst, Marschark and Spencer2003). Additionally, ASL uses nonmanual grammatical mechanisms involving head position, body position, eyebrow and forehead position, eye gaze, nose position, and the mouth, tongue, and cheek. These mechanisms are layered in that they sometimes co-occur simultaneously or overlap (Wilbur, Reference Wilbur, Emmorey and Lane2000).

The ASL sentence in (9a) from Petronio (Reference Petronio, Bach, Jelinek, Kratzer and Partee1995) can have a collective interpretation as in (9b) or a distributive interpretation as in (9c). The capitalized words in (9a), and henceforth, represent manual ASL signs, and the line above CAR and the letter t indicate eyebrow raising during the signing of CAR, grammatically marking CAR as the sentence topic (t).

1. (9) a. TWO STUDENT BUY.

2. b. Two students together bought a car.

3. c. Two students each bought a car.

As with an English sentence like (1a), Three guys are carrying a box, the intended interpretation is determined by discourse context. As the translations illustrate, languages can specify an explicit meaning through the use of adverbials (e.g., together in 9b) or floating quantifiers (e.g., each in 9c), or by other means. For example, ASL can also disambiguate Num QP sentences through the employment of its modality-specific morphological marking, as in sentence (10a), also from Petronio (Reference Petronio, Bach, Jelinek, Kratzer and Partee1995). The subscript a—marking both _aSTUDENT and SHOW_a—indicates morphological agreement between the verb and its (indirect) object.

(10)

1. a. PICTURE ANN SHOW_a – [_AGR exhaustive].

2. b. Ann showed each student the picture(s).

It is the exhaustive morpheme articulated in the signing of SHOW that unambiguously establishes a distributive interpretation for the sentence, as indicated in translation (10b). In (10a), the sign SHOW is articulated in the direction in which STUDENT has been set up in the signing space and with repeated and slightly sweeping movements, as if counting out the members of the set of students.

With regard to other spoken languages, Japanese, like English, is a language that has numeral phrases in which the numeral occurs within the Num QP, as in (11). Japanese, however, can also license floating numerals, which behave like floating quantifiers, as in (12), based on Kobuchi-Philip (Reference Kobuchi-Philip2007).Footnote ⁶

1. (11) a. San-nin-no gakusei-ga peepaa-o kaita.

2. 3.cl.gen student.nom paper.acc wrote

3. b. [Three students] wrote a paper.

4. (12) a. Gakusei-ga san-nin peepaa-o kaita.

5. Student.nom 3.cl paper.acc wrote

6. b. *Students [three wrote a paper].

Sentence (11a), like its English analogue (11b), can receive either a collective or a distributive interpretation. However, sentence (12a), in which the floating numeral is actually within the scopal domain of the verb phrase (ungrammatical in English as in 12b), typically receives a distributive interpretation.

Issues of L1 Transfer

Despite any crosslinguistic typological variation, the present study was not designed as an investigation of the role of L1 transfer in the L2 acquisition of numerically quantified English sentences. It is, rather, an investigation of whether—and, if so, the extent to which—issues of derivational economy and complexity impose observable pressures on the computational system of human language under the constraints of non-L1 acquisition. The target structures are simple subject-verb-object (SVO) sentences, for which both a collective and a distributive derivation are anticipated. However, as noted for a NP-Num sentence like (1b), its distributive derivation is illicit, as indicated in (8b). Because the L2 learners and DF learners who participated in this study, given their proficiency levels, know that English has SVO word order, this study simply assesses their interpretive knowledge of syntactically unexceptional sentences containing Num QPs and indefinite NPs in subject and object positions (relative to the interpretations of hearing L1 English speakers).

Even so, transfer effects can show up in subtle ways in almost any domain of the L2 (Odlin, Reference Odlin, Doughty and Long2003). Therefore, this study includes a crosscheck of L2 learner performance by L1 background to see if there are any striking group differences suggestive of a subtle transfer effect. With respect to ASL, however, finding transfer effects among any deaf participants who might have native or nativelike ASL proficiency is confounded by two factors. First, the type of ASL a given individual uses will vary in the extent to which it reflects native ASL properties (e.g., it could be more English-driven signing or could be contact signing, which is a bilingual blend of ASL and English often used by deaf adults; see Lucas & Valli, Reference Lucas and Valli1992). Second, with regard to modality-specific morphological processes of native ASL, such as the articulation of the exhaustive morpheme on the verb in sentence (10a), it is simply not known how such properties would be transferred and in what form they may manifest themselves in an auditory-spoken language.Footnote ⁷

Participant Groups

The present study involved five participant groups of students (the same participants whose performance was reported in Berent et al., Reference Berent, Kelly and Schueler-Choukairi2009) at the Rochester Institute of Technology (RIT) in Rochester, New York. There were two groups of hearing L2 learners taking English courses in RIT’s English Language Center, two groups of DF RIT students, and one control group of hearing RIT students who were L1 speakers of English. The L2 and DF learner groups were distinguished according to overall English language proficiency (L = lower, H = higher) as assessed by the Michigan Test of English Language Proficiency (2003). The L2-L and L2-H groups’ mean Michigan test scores (and standard deviations) were 50.5 (8.0) and 74.2 (6.1), respectively. The DF-L and DF-H groups’ Michigan test scores were 59.5 (8.4) and 76.6 (9.3), respectively. The DF-L group included students enrolled in—no higher than—associate’s degree programs at the National Technical Institute for the Deaf (NTID), one of RIT’s eight colleges. The DF-H group included NTID students enrolled in bachelor’s degree programs in RIT’s other seven colleges. The hearing L1 group included students also enrolled in bachelor’s degree programs at RIT.

A total of 53 L2 learners of English represented 12 different L1 backgrounds. There were 12 native speakers of Korean, 8 native speakers of Arabic, 7 native speakers of Turkish, 7 native speakers of Japanese, 5 native speakers of Chinese, 5 native speakers of Spanish, 5 bilingual speakers of Kazakh and Russian, 1 bilingual speaker of Tibetan and Chinese, and 1 native speaker of each of the following languages: German, Italian, and Tamil. Table 1 provides available demographic information for the five participant groups, including number of participants per group, mean age, and gender distribution. For the DF participant groups, the table also provides the mean pure tone average (PTA) hearing loss in the better ear in decibels (dB) measured at 500, 1,000, and 2,000 Hz (Levitt, Reference Levitt, Wang, Reynolds and Walberg1989). Of the four standard categories of hearing loss (mild, moderate, severe, profound), the mean PTA values reported in Table 1 reflect severe to profound deafness. Severely and profoundly deaf individuals rely largely on vision for language processing and thus represent learners who are more likely to have experienced the greatest acquisitional restriction on access to English spoken-language input.

Table 1.

Demographic information on participant groups

Note

PTA = pure tone average; Michigan = Michigan Test of English Language Proficiency (2003).

^a Hearing loss measured in the better ear at 500, 1,000, and 2,000 Hz (Levitt, Reference Levitt, Wang, Reynolds and Walberg1989).

English Sentence Picture Task–Quantifiers

The ESPT-Q (Berent et al., Reference Berent, Kelly, Porter and Fonzi2008) was developed to assess students’ knowledge of English quantifier sentences containing the universal quantifiers each, every, and all (10 items each) as well as sentences containing Num QP (10 items). There were an additional 10 filler items that contained only NPs and no universal or Num QPs. The picture task contained a total of 50 items and 250 depictions. Four randomized versions of the task were developed to address any potential order effects among task items. The present study reports and analyzes participants’ performance on the 10 Num QP items. Half of these items target Num-NP sentences and half target NP-Num sentences.

Each item on the ESPT-Q consists of a target sentence accompanied by five pictures that either do or do not represent a possible depicted discourse compatible with the meaning of the sentence. Each of the five pictures within an item requires a separate judgment. Participants received simplified instructions that explained the task format and procedures. They were instructed to read an item’s target sentence, study the five accompanying pictures, and circle either no under any picture that they felt did not represent a possible meaning of the target sentence or yes under any picture they felt did represent a possible meaning of the sentence.

The Appendix contains ESPT-Q items targeting the Num-NP sentence type (as in [1a]) and the NP-Num sentence type (as in [1b]), along with their associated picture sets. These items and sentence types are referred to by Roman numeral designations listed in the Appendix. Specific depictions in an item will be referred to by the Roman numeral and letter designation of the picture (picture I.C, picture II.E, etc.). It is important to note that the words no and yes that appear vertically under each picture on the ESPT-Q are not shown in the Appendix. Because the results of this study are discussed in conjunction with some of the results of Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009), items targeting QP-NP and NP-QP sentences in that study are also included in the Appendix as item types III and IV, respectively.

Num-NP Depictions. With respect to item type I in the Appendix, the five depiction types to be considered as possible matches to the meaning of the target Num-NP sentence are listed in (13). The response no or yes, to the right of each depiction type, indicates the correct response; that is, whether or not that depiction is a possible match to the target sentence.

1. (13) I.A Distributive Yes

2. I.B Insufficient No

3. I.C No object No

4. I.D Extra object Yes

5. I.E Collective Yes

The no-object depiction, as in I.C, is not a possible match to the target sentence because there are three guys but no boxes. A participant’s no response to this match indicates fundamental knowledge of the semantics of Num-NP sentences—namely, the requirement that the depicted discourse must contain members of both the agent set and the object set. The insufficient depiction I.B, showing two guys carrying a box and a third guy not carrying a box, further tests semantic knowledge of the target sentences in that, specifically, no fewer than the number of agents designated by the Num QP must participate in the event described by the sentence. The collective depiction I.E shows three guys carrying one unique box, an acceptable interpretation of the sentence. The distributive depiction I.A, which shows three guys, each carrying his own separate box, is also an acceptable interpretation. Finally, the extra-object depiction I.D also represents an acceptable distributive interpretation, but there is an additional member of the object set, in this case a fourth box.

NP-Num Depictions. The five depiction types for NP-Num item type II in the Appendix are listed in (14).

1. (14) II.A Superfluous Yes

2. II.B Collective Yes

3. II.C No object No

4. II.D Extra object Yes

5. II.E Distributive No

The different semantic properties of NP-Num sentences, relative to Num-NP sentences, motivate a somewhat different set of depiction types. The no-object depiction II.C shows no members of the object set of babies and thus is not an acceptable match. Unlike the Num-NP distributive interpretation, the NP-Num distributive interpretation is underivable for ESPT-Q items, such that II.E—showing three mother-baby pairs—is not a possible match. The acceptable collective depiction II.B shows one mother bathing three babies. The extra-object depiction II.D is also a collective depiction but includes an extra member of the object set, a baby, not being bathed. A yes response is permitted because the uninvolved extra object does not affect the truth value of the sentence-picture match. Finally, the superfluous depiction II.A shows one mother bathing three babies but also an additional mother-baby pair. Inclusion of this depiction type provided balance between Num-NP and NP-Num items in that all item sets allow two no responses and three yes responses, and it assumes the possibility of a yes response on the basis of the compatible portion of a superfluous depiction (e.g., the one mother–three baby pairing in II.A).

Hypotheses

The same factors that contribute to relative derivational economy and learnability predictions for universally quantified sentences in English, as in (6), similarly define learnability predictions for Num QP sentences as well. With respect to collective and distributive derivations, the Num-NP collective derivation (7a) and the NP-Num collective derivation (8a) involve singleton indefinites, interpreted in their surface position, and Num QPs of fixed cardinality. In contrast, in the Num-NP distributive derivation (7b), the indefinite singular NP is not a singleton indefinite and accordingly receives its plural set restriction within the scope of the Num QP. This introduces added derivational complexity. Consequently, learner judgments should conform to a learnability order parallel to that of universally quantified sentences: Num-NP collective = NP-Num collective > Num-NP distributive (see (6a)–(6b)). The semantic properties of Num QPs are such that a distributive derivation of an NP-Num sentence is underivable.

In addition to hypotheses related to derivational economy, it is argued that participants’ performance on extra-object depictions will activate discourse-pragmatic factors. With respect to universally quantified sentences, the results of Berent et al. (Reference Berent, Kelly and Schueler-Choukairi2009) revealed that the four learner groups (and to some extent the L1 English group) accepted fewer distributive depictions containing extra entities than distributive depictions with no extra entities. Specifically, they accepted fewer extra-object depictions like III.D than depictions like III.B and fewer extra-agent depictions like IV.E than depictions like IV.D. The authors attributed this performance pattern to the singleton effect. When attention is diverted to the extra entity, the extra object in III.D and the extra agent in IV.E, the singular indefinite NP in the sentence is interpreted as a singleton indefinite referring to that extra entity. The sentence-picture match thus receives a no response.

With respect to Num QP sentences, the singleton effect can explain any observed higher rejection of Num-NP extra object depictions, because the distributive extra-object depiction I.D contains an extra box, whereas the basic distributive depiction I.A does not. However, the singleton effect cannot be invoked to explain any observed greater rejection of a NP-Num extra-object depiction such as II.D. The reason for this is that the NP-Num extra-object depiction is associated with the collective depiction of sentence type II rather than a distributive depiction; that is, the extra baby in picture II.D is an entity associated with the members of the set of three babies that a mother is bathing. Because three babies in the target sentence is a plural phrase and not a singular indefinite NP, there is no option for a singleton restriction referring to the extra object.

The assumptions guiding the hypotheses are that, relative to learners, hearing native speakers of English will (a) exhibit greater overall knowledge of numerically quantified English sentences, (b) be less influenced by the pressures of derivational economy on sentence interpretation, and (c) be less derailed by the influences of discourse-pragmatic factors that presumably suppress the acceptance of extra-entity depictions. In the context of these assumptions, the study predicts the following:

1. 1. The L1 group will outperform the L2 and DF learner groups in the overall interpretation of English Num QP sentences.

2. 2. The L2-H group will outperform the L2-L group and the DF-H group will outperform the DF-L group in the overall interpretation of English Num QP sentences.

3. 3. All participant groups will reject sentence-picture matches with (a) Num-NP and NP-Num no-object depictions and (b) Num-NP insufficient depictions.

4. 4. In association with relative derivational economy, (a) the learner groups will accept more Num-NP and NP-Num collective interpretations than Num-NP distributive interpretations, (b) the L2-H and DF-H groups will accept relatively more Num-NP distributive interpretations than the L2-L and DF-L groups, respectively, and (c) the L1 group will be less influenced by these economy pressures than the L2 and deaf learner groups.

5. 5. All participant groups will fully reject the underivable NP-Num distributive interpretations.

6. 6. With the discourse-pragmatic resources available to hearing speakers of English, the L1 group will accept more extra object depictions than the L2 and DF learner groups. However, each of the learner groups (a) will accept more Num-NP basic distributive depictions than extra-object (distributive) depictions, which are vulnerable to the singleton effect, but (b) will exhibit equal acceptance of NP-Num basic collective depictions and extra-object (collective) depictions, to which the singleton effect is irrelevant.

7. 7. The L1 group will accept more NP-Num superfluous depictions than the L2 and DF learner groups. However, to whatever extent NP-Num extra-object depictions are accepted, the learner groups will accept more extra-object depictions than superfluous depictions, which have contextual elements confounding truth value judgments for matching these depictions to target sentences.