Tapping into the interplay of lexical and number knowledge using fast mapping: A longitudinal eye-tracking study with two-year-olds

Highlights

• Fast mapping and retention ability correlates with number knowledge at 30 but not at 36 months.

• Vocabulary size is associated with number acquisition at 36 months but not earlier.

• A cross-domain link between early language and natural number skills exists.

Abstract

Language skills and mathematical competencies are argued to influence each other during development. While a relation between the development of vocabulary size and mathematical skills is already documented in the literature, this study further examines how children’s ability to map a novel word to an unknown object as well as their ability to retain this word from memory may be related to their knowledge of number words. Twenty-five children were tested longitudinally (at 30 and at 36 months of age) using an eye-tracking-based fast mapping task, the Give-a-Number task, and standardized measures of vocabulary. The results reveal that children’s ability to create and retain a mental representation of a novel word was related to number knowledge at 30 months, but not at 36 months while vocabulary size correlated with number knowledge only at 36 months. These results show that even specific mapping processes are initially related to the acquisition of number words and they speak for a parallelism between the development of lexical and number-concept knowledge despite their semantic and syntactic differences.

Introduction

Language skills and mathematical competencies are argued to influence each other during development (Miura & Okamoto, 2003; Spelke, 2003; Spelke & Tsivkin, 2001), whereby vocabulary size is often taken as a proxy of language skills more generally (LeFevre et al., 2010). Both the domain of natural number and the language domain utilize language to convey meanings through symbols, i.e., a sequence of sounds in spoken language. The acquisition of number words (e.g., “one”, “two”, “three”) is a first milestone achievement in early mathematics learning (Shusterman, Slusser, Halberda, & Odic, 2016) and gives rise to a more precise understanding of number knowledge (Spelke, 2003). While Bloom and Wynn (1997) proposed a syntactic bootstrapping approach in which children’s number word acquisition is guided by linguistic cues in the input, Syrett, Musolino, and Gelman (2012) refine the original proposal by arguing that these kinds of bootstrapping accounts in fact combine two domains: the language domain and the domain of natural number. Certainly, the acquisition of early numeracy skills does not develop in isolation, but is rather interrelated with other cognitive skills (Purpura & Reid, 2016). In the ‘three precursor pathway model to mathematics’ by LeFevre et al. (2010) the linguistic pathway (measured by vocabulary size) was the most consistent and strongest predictor of early mathematical competencies in 4.5- to 7.5-year-olds. Since then, numerous studies have investigated and attested a cross-domain link between language and numeracy skills in 3- to 6-year-old children, using various linguistic measures like receptive and expressive language abilities (Gjicali, Astuto, & Lipnevich, 2019), reading skills (Purpura, Logan, Hassinger-Das, & Napoli, 2017), vocabulary size (Negen & Sarnecka, 2012), specific mathematical language (Purpura & Reid, 2016) or grammatical number (singular/plural) marking (Barner, Thalwitz, Wood, Yang, & Carey, 2007; Odic, Pietroski, Hunter, Lidz, & Halberda, 2013; Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina, 2007). Although the successive acquisition of small number words is assumed to exemplify fast and extended mapping (Carey, 2011), it has not yet been investigated whether performance in fast mapping and immediate retention is related to the process of number word acquisition. Building up on this, this study addresses the question, to what extent a relationship exists between mathematical development measured by the commonly used Give-a-Number task (Wynn, 1990) and specific mapping skills that support word learning (Bion, Borovsky, & Fernald, 2013). In addition, the contribution of general language skills (vocabulary size) is also examined.

As it is known from studies and theories on lexical development, word learning is a gradual process and words are learned slowly (Bion et al., 2013; Carey & Bartlett, 1978; Horst & Samuelson, 2008; Horst, 2018; Kucker, McMurray, & Samuelson, 2015). With each word encounter, children accumulate different bits of information about the word’s meaning, ultimately resulting in a robust and nuanced memory representation (Kucker et al., 2015). The beginning of this extended process is marked by a first association of a word with its referent (Horst, 2018). Initial guesses of word-meaning associations are defined by an in-the-moment behavior often referred to as fast mapping (Carey & Bartlett, 1978). Over the years a number of converging studies have shown that children as young as 17 months are able to select a novel object rather than a known one after hearing a novel name (for a summary see Halberda, 2003). Several cognitive factors are argued to drive this response behavior, e.g., mutual exclusivity (Markman & Wachtel, 1988), disjunctive syllogism (Halberda, 2003; 2006), novelty bias (Kucker, McMurray, & Samuelson, 2018) or Novel-name nameless-category principle (Mervis & Bertrand, 1994). Although fast mapping contributes to word learning, it must not be confused with full word learning (Bion et al., 2013). Several reiterations of hypothesis testing as well as of strengthening correct word-object associations and pruning false ones are necessary to gather a qualitative representation of a word and its meaning (Kucker et al., 2015; Yu & Smith, 2007; but see also Trueswell, Medina, Hafri, & Gleitman, 2013). The word learning process is considered completed when a representation of the word-object association is retained in memory and is also retrievable after a certain delay (Horst, 2018). This longer process is typically referred to as slow mapping (Swingley, 2010) or extended mapping (Carey, 2011). Bion et al. (2013) investigated fast mapping and immediate retention abilities in 18-, 24-, and 30-month-olds and the relation of these skills to the children’s concurrent vocabulary size. In this study, children as young as 24 months demonstrated fast word-object mappings by looking at a novel object rather than to a known object after hearing a novel name but only 30-month-olds showed a fragile evidence of retention (p = 0.049, Bion et al., 2013). Children’s ability to link a novel word to a novel object was positively related to their productive vocabulary size.

Interestingly, a similar picture emerges when studying the acquisition of number words or as Carey (2011):6) states it: “learning verbal numerals, like any word learning, exemplifies both fast and extended mapping”. Albeit children are argued to be endowed with an innate, non-symbolic, approximate number system (Dehaene, 1992), several studies on number acquisition reveal the same gradual developmental pattern for the acquisition of number words. Children as young as two years are able to recite a stably ordered number list (e.g., one, two, three, four, …) demonstrating at least some familiarity with number words (Barner, 2017). However, when testing the comprehension of the number words that two-year-olds use in a count list, they revealed little to no knowledge of the words’ meaning and thus no precise cardinal value of the quantities (Barner, 2017; Le Corre, Van de Walle, Brannon, & Carey, 2006; Wynn, 1990, 1992). Two-year-olds only appear to recite the number word list like a rehearsed rhyme but are unable to count or count out a single object (Fuson, Richards, & Briars, 1982). As a next step this number word series is broken up so that individual number words can be used for counting. Children begin to count by using the one-to-one correspondence that requires a child to assign the number words only once to each item in a list and rules out using the same label for two distinct numbers (Fuson et al., 1982). A particular counting procedure ends with the last number word recited or when the last item of the set is reached (Steffe, Cobb, & von Glasersfeld, 1988). The final number that children reach with the last item of a set is tied to the counting process but is not yet connected to the quantity (Steffe, 1992). Subsequently, children gain an early insight into the quantity of one, then two, then three, in an ordered sequence. The steps children take to acquire small numbers are described as so-called “knower levels” (Carey, 2011; Le Corre & Carey, 2007; Sarnecka & Carey, 2008). Children develop from “pre-numeral knowers” (being unable to assign a number word to an exact meaning) to “one-knowers” around the age of two. Six to eight months later children figure out the meaning of “two” (Carey, 2011). Subsequently, children acquire the meaning of “three” and sometimes undergo a “four”-knower level (Sarnecka & Carey, 2008). It seems that at this stage children have comprehensively grasped the principle of the one-to-one correspondence of number words and objects. However, they have not yet acquired the concept of cardinality. As soon as they acquire the meaning of four, they also comprehend the meaning of the other number words in their number-word sequence (five and above), and can use them to count as well as to count out quantities (Le Corre et al., 2006). Shusterman et al. (2016) investigated children’s number word acquisition in a six-month longitudinal design with children between 36 and 60 months of age. Results showed a significant increase in children’s knower level with age (Shusterman et al., 2016). This gradual development suggests that children deduce the meaning of number words from the verbal input (Syrett et al., 2012).

As for the investigation into the language domain, Bion et al. (2013) have shown that 30-month-olds reveal only fragile evidence of retaining newly established word-object mappings in an experimental set up. Hence, using a six-month longitudinal design, the present study strived to combine for the first time the testing of children’s individual number word acquisition as early as possible and, simultaneously, children’s potentially more consolidated retention abilities.

In the present study, we replicated the design of Bion et al. (2013) and extended the age range of participants by investigating fast mapping and retention abilities in the same group of children at 30 and 36 months. Therefore, the first aim was to replicate the method used by Bion et al. (2013) with German-learning 30-month-olds as well as to investigate whether their retention abilities consolidate in the transition between 30 and 36 months. Towards this end, this study examined whether the development of children’s mapping skills in the language domain and the mathematical domain are related. Should this be the case, we expect a significant positive correlation between children’s ability to initially map new words to novel objects and the individual knower level as well as a significant correlation between children’s ability to retain the newly formed word-object association and their individual knower level. We take the ability of forming and retaining a new object-word association as an indicator of initial word learning, which is followed by an extended mapping phase. The age groups of 30 and 36 months allowed us to assess children during the acquisition of their very first number words (Wynn, 1990, 1992). Moreover, it was explored whether changes involving fast mapping and retention abilities and the knower level become visible longitudinally. Next, the study investigated the relation between lexical development and mathematical competencies in children as young as 30 months as well as six months later, thereby evaluating whether the findings of LeFevre et al. (2010) also hold at a younger age. Should this be the case, we predict a positive correlation between children’s vocabulary size (and therefore the conceptual understanding of a given word) and the individual knower level.