Almost Means Less Than Preschoolers Comprehension of Scalar Adverbs

Almost means `less than': preschoolers' comprehension of scalar adverbs 1 1 Introduction Children proudly produce sentences like `I'm almost 5'. This is an important concept to them, as it means that they are close to an age they perceive as a threshold, and almost is quite complex: being `almost 5' means not being ve (yet) and being an age close to ve (e.g. 4 and ten months). Does a 4 year-old understand the components of the meaning of almost ? And does the child grasp the meaning of almost when it occurs with expressions other than number words? In fact, almost may modify expressions of dierent syntactic children care about growing up. But the meaning of categories: verbs, adjectives, prepositions, other adverbs. Do children understand its meaning in all cases? Previous studies claim that children aged 4  6 have diculties with interpreting almost, and only reach adult-like interpretation of the adverb by age 7 or 8. According to these studies, children understand the `proximity' component of the meaning of the adverb (being `close to' ve) but not its `scalar' component (i.e. if you are `almost 5' you are `less than' 5). almost as a modier of number almost ve ), directional prepositional phrases (e.g. almost to the lilypad ) equative comparative phrases (e.g. almost as far as ). I am interested in the In this paper I focus on children's interpretation of words (e.g. and following research questions: almost ˆ Do children interpret ˆ How do children acquire the dierent components of the meaning of ˆ How do children generalize from the cross-categorial instances of modication by dierently from adults across the board? almost ? almost ? My study explores the hypothesis that early diculties with the interpretation of almost almost reported in the literature result from diculties in identifying the scale that operates on, not from late acquisition of the scalar component of the adverb. I show that children grasp both components of the meaning of almost when the adverb modies linguistic expressions that provide a scale that the child understands (e.g. number words). This paper is organized as follows. In section 2 I describe the meaning of In section 3, I summarize the ndings of previous studies. aims and methods of my experimental study. Section 5 presents the results of the experiment and section 6 provides a discussion of the results. 2 almost. Section 4 describes the Scalarity of almost 2 The meaning of almost can be analyzed as involving two implications or meaning components: a Polar component and a Proximal component ([1], [2]), exemplied below for (1). (1) John is almost ve years old. A sentence with almost entails the negation of the expression that is modied by the adverb (Polar component). For example, (1) means that John is not ve years old. ˆ Polar component: [. . . [almost [x] . . .] The meaning of almost entails [. . . [NOT[x] . . .] requires that the modied expression, possibly with the sup- port of the conversational context, provides a scale, i.e. a set of alternatives to the value of the modied expression with a linear order on it, and a value on that scale, which I will call `the endpoint'. A linearly ordered set is dened by a relation that is transitive, antisymmetric, reexive, and connected, for which I use the notation < ([3]). almost ve is the numeric order, the almost ), and scalar alternatives to ve In (1), the scale needed to interpret `endpoint' is ve (the expression modied by are e.g. two, three, four, six, seven, etc. A sentence containing almost(S) entails a related sentence S', where S' expresses a proposition in which existential quantication is made over scalar alternatives to the expression modied by to it on the scale. almost that are ranked lower than the endpoint and are close How close an alternative must be to the endpoint is context- dependent. This entailment relation can be schematized as follows: ˆ Proximal component: [. . . [almost [x] . . .] entails [for some d < [[x]]∧CLOSE(d, [[x]])(...d...)] To exemplify, (1) means that there is an age close to five and ranked lower than ve on the numeric order, i.e. less than five, and that John is this age (Proximal component). The notion of a scale or ordered set has proven useful in dierent domains of semantics and pragmatics and their acquisition, e.g. in the study of the meaning of gradable predicates and in the study of conversational implicature ([4], [5], [6], [7]). For language acquisition, the meaning of almost provides an excellent test case for studying the relation between language and scalar knowledge: in order to understand the proximal component of the adverb, children must retrieve the scale relevant to the specic instance of modication by almost. Thus, children's understanding of may be used to investigate what children know about scales. 3 almost n almost n Figure 1: Interpretation of 3 almost without the scalar implication. Previous studies To my knowledge, the only experimental studies on the acquisition of terms like almost have been done on French ([8], [9]). These studies have argued that children aged 4 to 7 interpret French presque `almost' dierently from adults across the board presque n seems to indicate a value which may be less than n , more than n , equal to n  (i.e. same as the modied expression), or simultaneously less than n  and more than n ([8]). This has been taken as evidence that children rst interpret presque as `close to' and ([8]). A study with 4 to 11 year-olds shows that for young children, later acquire its scalar meaning `less than'. On the basis of these ndings, the authors presque ; from 4 to 7, children interpret presque n as denoting an area around the value n, this value included. This propose a developmental path in the comprehension of proposal suggests an initial interpretation of `almost' as depicted in Figure 1, i.e. meaning `close to', in contrast to the scalar interpretation I described in the previous section. The ndings of this study dier from [9]. In a study on the acquisition of dierent degree modiers (e.g. presque presque n as equivalent to `almost', n (i.e. à peine `barely'), children did not interpret as having the same meaning as the modied expression). In terms of the semantic analysis of almost given above, this suggests that children have acquired the Polar component of the meaning of the adverb: The value n was almost never selected in the statements containing presque. This dierentiates presque from all the other items studied and seems to uncover an essential peculiarity of the meaning of presque . . . (p. 615). This study reports the following response types for the group of 6 year-olds, the youngest age group in [9]: slightly less than n (60%), less and more than n (18%), any value less than n (10%). The disparate ndings of these two studies may stem from possible confounds in their methodologies. In both studies, children were tested on isolated sentences containing almost. The scale that was relevant to each specic utterance was not clear in the context of the task, so dierent children may have identied dierent scales and interpreted almost accordingly. 4 4 This study The current experimental study aims to address the acquisition of the two implications of almost by providing children with rich contextual information about the scale that is relevant to each instance of modication. Participants heard sentences with almost as a modier of number words, directional prepositional phrases (PP's), and equative comparative constructions. These expressions were chosen for two reasons. First, they were used in previous studies, so this allows for comparison with previous ndings. Second, with these expressions one can test the comprehension of the scalar meaning of discrete scalar alternatives to the value of ther ranked higher or lower than n n almost, since it is possible to provide almost ) ei- (the expression modied by on the scale, and the order of the alternatives can be contextually manipulated. The predictions of this study are the following. If children acquire the scalar component of almost only by age 7 or 8 ([8]), and young children interpret almost as equivalent to close to (cf. Figure 1), then young children are expected to interpret almost n as less than n , more than n , or simultaneously less than n  and more than n . The expected response pattern is that children are equally likely to choose either of these alternatives, and this should happen regardless of the expression that is modied by almost. On the other hand, if children have acquired the two compo- nents of the meaning of almost, and hence have grasped the scalar meaning of the adverb, they should tend to choose the less than n n alternative over the more than alternative. 4.1 4.1.1 Method Participants Two groups of children and one group of adults participated in this study: 4;0-4;11 year-olds (N = 22, mean age 4;7), 5;0-5;11 year-olds (N = 23, mean age 5;5) and 14 adults, undergraduate students at Stanford University. 4.1.2 Materials and Procedure Children were pre-tested for their ability to count to 8; children who could not count did not participate in the experiment. Children sat next to the experimenter at a small table and saw slides on a computer screen. with several characters (animals or people). The slides depicted a situation In the number words condition, the experimenter presented slides with people or animals, as in (2): 5 (2) The boys are playing with blocks. Can you count the blocks? ( has almost n Let's see how many blocks each boy has. Child counts the blocks for each boy ) Which boy blocks? The child was asked to choose from the alternatives on the screen; the alternatives consisted of 4 blocks ?, n, n−1 and n+1. For example, for the question Which boy has almost the alternatives were a boy with 4 blocks, a boy with 3 blocks, and a boy with 5 blocks. In the 4 experimental stimuli in the number words condition, the value of n ranged from 4 to 7. In the directional PP's condition, the experimenter presented a sequence of slides telling a short story about a set of animals. This is exemplied in (3); the slides show a garden path with a vase on it. (3) There are three snails in the garden. The snails want to get to the vase. Let's see if they can do it. ( The snails move along the path, one by one ) There! Which snail got almost to the vase? The sequence of the slides showed the motion of the snails along the path until they reached their nal position with respect to the vase. The child was asked to choose from the snails on the last slide of the sequence. In the slide, there was a snail who got to the vase (i.e. the scalar value corresponding to the meaning of the expression modied by almost ), a snail that was close to the vase but did not get to it, and a snail that was close to and beyond the vase. In the sentences containing an equative comparative, children saw slides with 4 animals and a jumping board. The sequence of slides presented a jumping contest and the experimenter described the sequence as in (4): Zebra jumps ) Now (The animals jump on the board, one by (4) This is a jumping contest. The zebra is going to jump rst. ( the zebra's friends are going to jump. one ) There! Which animal jumped almost as far as the zebra? The length of the jump of the rst animal (here, the zebra) provides the standard of comparison. The child had to choose from the three animals that jumped after the zebra (described as the zebra's friends by the experimenter). For each animal, the length of his/her jump corresponded to one of the scalar alternatives: the animals jumped as far as the zebra (i.e. meaning of the expression modied by one of the scalar value corresponding to the almost ), another animal jumped a bit less far than the zebra, and another animal jumped a bit farther than the zebra. The board was divided in stripes of equal width, so that the measure of closeness to the animal providing the standard of comparison (1 stripe in all the cases) remained the same and could be easily perceived. 6 In the situations depicted on the slides, for all the experimental conditions, there n-1, i.e. less n , another character corresponded to n (the value of the expression modied by almost ), and another character corresponded to n+1, i.e. more than n . was one character per scalar alternative: one character corresponded to than The dependent variable is the response type: less than n and less and more than n n, more than n, same as if the child chose both the characters corresponding n and more than n . The independent variables are the modied by almost (within subjects) and age group (between subjects). to less than expression There were 4 experimental items per condition, with a total of 12 experimental stimuli, and 16 ller items. All the llers were similar to the experimental items, with three alternative responses, and were designed to unbias the response type in the critical items. Given that in the experimental items the adult-like response was less than n , in order to unbias subjects towards this response, 8 llers were biased towards the response same as n and 8 llers were biased towards the response more than n . The items were pseudorandomized (both for order of item and order of condition) for each child. Each session lasted approximately 15 minutes and was videotaped in order to record the responses, gestures and spontaneous comments provided by the children about their choices. 5 Results Overall, the data show that there is continuity in the interpretation of almost by the three age groups, with greater variability in response from the younger group. The only exception to this pattern is the behavior of the youngest group (4;0-4;11) in the Equative comparatives condition: than n, as shown in Fig. 2. here, the more common response type is more There is almost no variability in the adult results: adults never chose two scalar alternatives (less than had a clear preference for the less than n n and more than n) and response. A mixed-eects binary logistic regression model predicting the `other than less' re- n vs `other than less') revealed a main almost with number words and with directional PP's diers signicantly from the interpretation of almost with comparatives in sponse (conating responses into less than eect of condition: the interpretation of = −2.17, SE = 0.39, odds = 0.11, p < 0.001; Directional PP's Condition: B = −1.59, SE = 0.38, odds = 0.20, p < 0.001). The odds of a less than n response in the Number words disfavoring the `other than less' response (Number words Condition: B condition, when compared to the Comparatives condition, is 9 to 1. a less than n The odds of response in the Directional PP's condition, when compared to the Comparatives condition, is 5 to 1. The dierence between the Number words and the Directional PP's conditions was not statistically signicant but I will return to this nding later. 7 5;0−5;11 Adults 100 80 60 40 Percentage of response types 0 20 80 60 40 Percentage of response types 0 20 80 60 40 Percentage of response types 20 0 4;0−4;11 5;0−5;11 ResponseAdults types 4;0−4;11 5;0−5;11 per condition (Children_4to5) Adults 100 Response types per condition (Children_4to5) Response types per condition (Children_4to5) s per condition (Children_4to5) (a) Number words 80 100 4;0−4;11 more same Percentage of responses per condition 80 less Percentage of responses per condition Response types for condition C per age group 100 Response types for condition P per age group 100 Response types for condition N per age group (b) Directional PP's less (c) Equative Comparatives more less less more same more same less and more same less and more less and more 60 60 Figure less and more 2: Percentages of response types per age group for each condition. n scalar alternative was 40 In the Number words condition, the choice of the less than the relevant scale: 20 20 40 accompanied by spontaneous comments by the children showing they have identied (5) Experimenter: Which boy has almost 4 blocks? 0 Child: I think it's this one [Points to 3], because it goes 1,2,3,4. N 0 C N In other cases, children pointed Nto the value C P N n+1 P and said: It's not this one, because P P this one has more/because this one has the most. Only two children chose both scalar alternatives less than n and more than n (a response type found in previous studies), but they did not do so consistently during the whole experiment. For one child, this response was given only in the Directional PP's condition. The child gave the following justication: (6) Experimenter: Which frog got almost to the lilypad? Child: I think these two did [Points to both more than n and less than n alternatives] 'cause they're close to it. For the other child, this response (less than n and more than n ) was given both in the Directional PP's and Comparatives conditions. 5.1 Patterns in the acquisition of almost The children were sorted into groups according to their response patterns. The individual response patterns were coded as a triple of 0 and 1, with one digit per condition, 8 in the order NPC (Number words  Directional PP's  Equative comparatives). The responses were coded in binary terms: 1 stands for `adult-like' response, 0 for `nonadult-like'. If children had three or four (out of four) `adult-like' responses in one condition, this was coded as a 1, otherwise as a 0, following the criteria adopted in [10]. Of all the possible combinations of response types (a total of 8), only the pattern 0 01 (i.e. `non-adult-like' responses in Number words and Directional PP's conditions, and `adult-like' response in Comparatives condition) is not attested in the data. This means that children understand the sentences with almost comparatives after they have understood the sentences with as a modier of equative almost modifying number words and directional PP's. The patterns obtained were then grouped as reecting no comprehension (i.e. `non-adult-like' responses in all the conditions), partial comprehension (i.e. `adult-like' responses in one or two conditions) and adult-like. The results of this coding scheme are shown in Table 1. Pattern (NPC) Nr of children Mean age (range) No comprehension 0 0 0 6 4;8 (4;05;2) Partial comprehension 1 0 0 0 1 0 11 7 4;11 (4;05;11) 5 1 1 5;5 (4;85;11) (2 domains) 1 1 0 0 1 1 1 0 1 Adult-like 1 1 1 14 5;1 (4;65;11) (one domain) Partial comprehension 4;11 (4;65;5) 4;1 5;0 Table 1: Individual response patterns for the total number of children (N=45). The distribution of the four patterns (No comprehension, 1, Partial comprehension in one domain, 2, Partial comprehension in two domains, 3, Adult-like, 4) across ages is presented in Figure 3. The plot shows that there is much variability in the distribution of the patterns across ages. Pattern 1 (No comprehension) and pattern 4 (Adult-like comprehension) present more limited age ranges, corresponding, as one would expect, to younger children and older children, respectively. Patterns 3 and 4 correspond to transitional stages, and are found across a wider range of ages. Overall, there is an upward trend in the data suggesting a developmental path from pattern 1 to pattern 4. However, the existence of such a path can only be conrmed by a longitudinal study. remains for further research. 9 This 70 65 60 55 50 Age in months 1 2 3 4 Pattern Figure 3: Distribution of patterns of interpretation of 6 almost over age. Discussion The ndings of this study demonstrate that children as young as 4;6 years-old can identify the two meaning components of almost and hence that they have acquired the scalar meaning of the adverb. In sentences with number words and directional prepositional phrases, children retrieve the scales that the adverb operates on. In the Number words condition, the scale is the numeric order, and in the Directional PP's condition, the scale is the endpoint-oriented spatial path. In the sentences with comparatives, children had more diculties. Here, the scale underlying the interpretation of almost and the relevant elements of the scale (the scalar alternatives and the endpoint) can only be retrieved from contextual information. This information is provided by the experimental setting of the study: the scalar alternatives are the positions of the animals on the jumping board and the endpoint of the scale is the position, on the jumping board, of the animal that provides the standard of comparison (e.g. the zebra in (4)). The regression results show that the dierence between the Number words condition and the Directional PP's condition was not statistically signicant. However, there is an indication that children made a distinction between the interpretation of almost with number words vs. PP's. The regression coecient for the Number words condition was almost twice the value of the coecient for the Directional PP's condition. One explanation for why the interpretation of the modied sentences with number words might have been easier is that, with small numbers, the measure of closeness to n is given in advance: the scalar alternatives to 10 n would always be n-1 and n+1, i.e., there is no variability in how close a value is to the reference point n. On the other hand, in the Directional PP's condition, the child had to assess the closeness to n on the basis of the visual setting. The results reveal a dierence in children's understanding of the scales underlying the Number words and Directional PP's conditions, on the one hand, and the Comparatives, on the other hand. Why do children have diculty accessing the scale to interpret the sentence with the comparative? Given the semantics of almost, a scale must be somehow accessible here too since those sentences are perfectly acceptable for adults. Children understood the unmodied equative comparative, as shown by the accurate responses in the ller items containing such expressions (e.g. the elephant that is as big as the house ). Point to Semantically, an equative comparative con- struction introduces a relation between sets of degrees. In the case of modication by almost, the child must identify an order between such relations, e.g. 2 cm less than, 1 cm less than, as much as, 1 cm more than, etc.. It is possible that children have diculty understanding `almost as far as' because such scales are hard to access. The results of this study suggest a developmental path: the meaning of almost is understood rst in one domain, then generalizes to others, but further work is required to conrm this. My results are consistent with earlier ndings that children's understanding of scales diers across domains ([5], [11]). One question for further research may be to compare the domain of scalar representations with numbers or spatial paths to the domain of scalar representations with relations between sets of degrees. Are there dierent types of scales? And why are some scales understood earlier than others by children? Possible hypotheses to be pursued in further work include: quency of the expressions (and respective scales) modied by dierences in the fre- almost in child directed speech, and the cognitive availability of certain scales (e.g. the representations of telic events and spatial paths oriented towards an endpoint). In sentences containing directional PP's, it is possible that goal-oriented motion may help children understand the meaning of almost and guide them in retrieving the relevant scale; for example, children understand early on the notion of a failed attempt and form representations of probable endings of motion events ([12]). The developmental pattern suggests that the type of scale encoded by the meaning of the expression modied by almost inu- ences the way children generalize from cross-categorial instances of modication by . almost 11