Babies who are years away from being able to say “one,” “two,” and “three” actually already have a sense of what counting means, Johns Hopkins University researchers have discovered.
The findings reveal that very early on, years earlier than previously believed, babies who hear counting realize that it’s about quantity.
“Although they are years away from understanding the exact meanings of number words, babies are already in the business of recognizing that counting is about number,” said senior author Lisa Feigenson, a cognitive scientist at Johns Hopkins who specializes in the development of numeric ability in children.
“Research like ours shows that babies actually have a pretty sophisticated understanding of the world – they’re already trying to make sense of what adults around them are saying, and that includes this domain of counting and numbers.”
The findings are newly published in Developmental Science.
Most children don’t understand the full meaning of number words until they’re about four years old.
That’s surprising, Feigenson said, considering how much counting young children are exposed to.
“We buy counting books for babies and we count aloud with toddlers. All of that raises the question: Are kids really clueless about what counting means until they’re in the preschool years?”
To find out, Feigenson and first author Jenny Wang, a former graduate student at Johns Hopkins who is slated to become an assistant professor at Rutgers University, worked with 14 and 18-month-old infants.
The babies watched as toys, little dogs or cars, were hidden in a box that they couldn’t see inside of, but could reach into.
Sometimes the researchers counted each toy aloud as they dropped them into the box, saying, “Look! One, two, three, four – four dogs!” Other times the researchers simply dropped each toy into the box, saying, “This, this, this and this – these dogs.”
Babies who are years away from being able to say ‘one,’ ‘two,’ and ‘three’ actually already have a sense of what counting means, Johns Hopkins University researchers have discovered. The findings reveal that very early on, years earlier than previously believed, babies who hear counting realize that it’s about quantity. The image is credited to Johns Hopkins University.
Without counting, the babies had a hard time remembering that the box held four things.
They tended to become distracted after the researchers pulled just one out – as if there was nothing else to see. But when the toys were counted, the babies clearly expected more than one to be pulled from the box. T
hey didn’t remember the exact but they did remember the approximate number.
“When we counted the toys for the babies before we hid them, the babies were much better at remembering how many toys there were,” Wang said.
“As a researcher these results were really surprising. And our results are the first to show that very young infants have a sense that when other people are counting it is tied to the rough dimension of quantity in the world.”
The team is now conducting several follow-up studies, trying to determine if early counting practice leads to later number skills land if English-speaking babies react to counting in a foreign language.
The current study examines variation in parent talk about number during naturalistic interactions with their 14 to 30 month olds, and the relation of this variation to children’s subsequent numerical understanding.
By the time children enter preschool, there are marked individual differences in their mathematical knowledge, as shown by their performance on standardized mathematics tests (e.g., Starkey, Klein, & Wakeley, 2004) as well as experimental tasks (Clements & Sarama, 2007; Entwisle & Alexander, 1990; Ginsburg & Russell, 1981; Griffin, Case, & Siegler, 1994; Jordan, Huttenlocher, & Levine, 1992; Klibanoff, Levine, Huttenlocher, Vasilyeva & Hedges, 2006; Lee & Burkham, 2002; Saxe, Guberman & Gearheart, 1987; Starkey, Klein, & Wakeley, 2004).
These early differences in mathematics knowledge are concerning for several reasons. First, levels of mathematics knowledge at the time of school entry have been shown to predict later school achievement (e.g., Duncan et al., 2007; Lee & Burkham, 2002).
For example, a meta-analysis of six longitudinal data sets shows that the level of children’s early mathematics skills (at about the time of school entry) predicts subsequent mathematics achievement through at least the 5th grade (Duncan et al., 2007). Second, there is increased demand for high levels of mathematical skill as demands for a scientifically and technologically sophisticated workforce increase (National Research Council, 2009).
Finally, level of mathematics skill is associated with socioeonomic status, raising issues of equity in terms of employment opportunity (e.g., Ehrlich, 2007, Klibanoff et al., 2006, Starkey et al., 2004).
The existence of early variations in mathematics knowledge motivates our investigation of how particular aspects of early parent-child interactions may contribute to these variations. Here we examine whether differential exposure to number talk in the early home environment is an important factor in setting the course for children’s school achievement in mathematics.
Although many studies have shown that specific early language and literacy practices predict later language and reading achievement (e.g., Dickinson & Tabors, 2001; Evans, Shaw & Bell, 2000; Griffin & Morrison, 1997; Hart & Risley, 1995; Huttenlocher, Haight, Bryk, Seltzer, & Lyons, 1991; Sénéchal & LeFevre, 2002; Snow, Burns & Griffin, 1998; Whitehurst & Lonigan, 1998) much less is known about the nature and frequency of early mathematical interactions, nor about the extent to which these interactions predict the development of children’s mathematical knowledge.
Findings from these studies indicate that the frequency, range, and complexity of mathematical activities that parents engage in with their preschool children vary widely, and that these variations are associated with the socioeconomic background of families (Saxe et al., 1987; Blevins-Knabe & Musun-Miller, 1996; Starkey et al., 1999).
In one study, Saxe et al. (1987) found that although the numerical activities engaged in by low- and middle-SES families did not differ in frequency, they did differ in complexity.
For example, middle SES mothers reported more frequently engaging in activities involving the comparison of set sizes and calculation than lower-SES mothers, whereas the reverse was true for rote counting, recognizing number symbols, and labeling the numerosity of a single set.
Although information from questionnaires and checklists is informative, it is also potentially problematic. First, because these measures rely on memory, parents may under-report certain kinds of number input, notably numerically relevant input that occurs incidentally, e.g., “Do you want one cookie or two cookies?”
Second, parents may over-report certain kinds of input, such as reading their child number books, because of demand characteristics of the instruments.
Observation of parent-child interactions provides a more direct way to gauge the frequency and nature of number input, and avoids memory limitations and biases. Several observational studies have reported the number-related input parents provide their preschoolers in the context of prescribed numerical activities given in a laboratory setting (e.g., Fluck, 1995; Saxe et al., 1987).
For example, Saxe et al. (1987) observed mothers assisting 2- and 4-year-olds on a counting task and on a numerosity matching task that involved producing a set of pennies that matched the number of Cookie Monster cards on the table.
Consistent with their questionnaire findings, results showed that the complexity of maternal instruction was highly related to children’s knowledge level, but that even when children’s knowledge level was controlled, middle-class mothers set more challenging goals for their children than working-class mothers. Another study described the number words mothers provided to their children (9 months to 36 months) while sitting in a laboratory room with minimal materials (Durkin, Shire, Riem, Rowther, & Rutter, 1986).
Findings showed that the frequency of mothers’ number words increased between child ages 9 to 27 months and then leveled off. Number words were largely confined to the first four numbers, with some increase in number magnitude with the child’s age.
Durkin et al. (1986) suggested that parent number word usages may be confusing to children. For example, numbers were frequently uttered in the context of routines such as “one, two, three, go” or “one, two, three, tickly”, which contrasts with “one, two, three, four.”
Further, mothers sometimes asked children to repeat the number she had said, resulting in the following jointly constructed number string: “one, one, two, two, three, three.” At other times, mothers asked children to alternate with her in producing the next number word, resulting in the jointly constructed number string, “one, two, three, etc.”
On the other hand, Bloom and Wynn (1997) suggest that linguistic regularities in parental number input, such as the use of number words to exclusively modify count nouns (as opposed to mass nouns) could help children infer that number words apply to countable sets and are distinct from other quantifiers.
In any case, noise in the input, and the documented difficulty children have in learning the cardinal meanings of the number words (e.g., Wynn, 1990, 1992), make it likely that children who receive higher amounts of exposure to number talk may be better able to figure out these meanings.
In the current study, carry out an exploratory study examining the frequency of “number talk” engaged in by parents and children at home and the relation of this talk to the child’s later number knowledge.
First, we report on the findings of a longitudinal study that directly examines parent and child “number talk” during naturalistic interactions at home, beginning when the children are 14 months of age and continuing every four months until they are 30 months of age. Second, we examine the relation of this “number talk” to the development of a central number concept – understanding the cardinal meanings of the number words. Cardinal numbers are used to quantify sets, e.g., “two jumps,” “three babies,” “four ice cream cones” (e.g., Piaget 1941/1965; Gelman & Gallistel, 1978; Sophian, 1996). Although children typically can recite the count list in a rote manner and begin to use number words to refer to the cardinal value of sets as early as 2 years of age (e.g., Fuson, 1988; Wynn, 1990), these instances typically occur in familiar, frequently repeated routines, e.g., Spencer’s “Two shoes. One, two” (Mix, 2009; Mix, Sandhofer, & Baroody, 2005).
However, understanding that the purpose of counting is enumeration and achievement of a more decontextualized understanding of cardinal number – one that extends to any set in the child’s count list – is a protracted developmental process (Wynn 1990, 1992). Thus, on the Give-A-Number task, which involves producing sets containing a specified number of elements, children typically show that they understand the meaning of “one” sometime between 2 and 3 years of age, and over the next year, gradually learn the meanings of “two,” “three”, and “four“, at which point they generalize their understanding of cardinal meanings to all the numbers in their count list and become “cardinal principle knowers” (Le Corre, Van de Walle, Brannon, & Carey, 2006; Wynn, 1990, 1992).
We focus on children’s understanding of the cardinal meanings of the number words because this understanding reflects a deep and important mathematical insight that lies at the core of the ability to exactly quantify set size for sets with more than three items, to compare the numerosity of different sets in an efficient manner, and to perform calculations to obtain an exact answer (e.g., Huttenlocher, Jordan, & Levine, 1994; Mix, Huttenlocher, & Levine, 2002; National Research Council, 2009; Sarnecka & Carey, 2008; Spelke, 2003; Spelke & Tsivkin, 2001). Further, several findings indicate that once children understand the cardinal meanings of the number words, they recognize equivalence relations not only across highly similar sets but also across dissimilar sets such as visual dots and auditory claps (Mix, 2008; Mix, Huttenlocher, & Levine, 1996, 2002).
Carey and colleagues argue that acquiring the cardinal principle allows children to construct a representation of the natural numbers, i.e., to understand that each successive number in their count string maps onto a set with one more element than the preceding number (Carey, 2004; Le Corre et al., 2006; Le Corre & Carey, 2007).
The more advanced knowledge of “cardinal principle knowers” is reflected in their counting behavior. For example, such children usually count to produce a set size larger than 3 and if their count yields the wrong number, they correctly adjust the set. In contrast, children who have not reached this milestone do not typically count to produce sets of objects and if they do, fail to adjust the set size when their count indicates an error (e.g., Le Corre et al., 2006; Wynn, 1990, 1992).
In addition, only cardinal principle knowers understand that adding one item to a set changes its numerosity by exactly one number in the count list (Sarnecka & Carey, 2008).
Several different measures have been used to assess this knowledge. These include the Point-to-X task (Wynn, 1992), the What’s on this Card task (Gelman, 1993), and the Give-A Number Task (Wynn, 1990, 1992). Children’s performance on these different measures is highly correlated (Le Corre et al., 2006; Wynn, 1992).
In the current study we used the Point-to-X task to examine children’s understanding of the cardinal meanings of the number words. Prior findings indicate that there is considerable individual variation in when children understand these cardinal meanings. For example, by age 4, some children understand the cardinal meanings of the number words up through four and beyond, whereas others have not even mapped the words “one” and “two” (Klibanoff, Levine, Huttenlocher, Vasilyeva, & Hedges, 2006; Ehrlich & Levine, 2007; Ehrlich, 2007).
A notable omission from the literature on the acquisition of cardinal number knowledge is an exploration of the kinds of environmental supports that impact the acquisition of this important aspect of mathematical understanding.
Exposure to talk involving number words is implicated by findings showing that knowledge of the exact cardinal value of sets is not universal, and seems to depend on the existence of an elaborated counting system in the culture (e.g., Gordon, 2004; Pica, Lemer, Izard, & Dehaene, 2004). The present study examines children’s exposure to number talk within a culture in order to determine whether variation in the amount of number talk is related to children’s development of cardinal number knowledge.
We purposely chose to focus on early parent input (at child ages 14 to 30 months), prior to the time when most children have mapped any but perhaps the smallest numbers onto the cardinal value of sets, because we wanted to obtain a measure of parent input that was less influenced by the child’s prior knowledge than later parent input would be.
In other words, our particular interest is whether the number talk that parents engage in prior to the child acquiring cardinal number knowledge influences the acquisition of that knowledge at a later time point. We assess child understanding at 46 months because this is an age at which some but not all children have become cardinal principle knowers. Testing 3, 4, and 5-year olds, Le Corre & Carey (2007) found that the age range of one-knowers through CP-knowers all included 46-month-olds.
Thus, there should be ample variation in child cardinal number knowledge at the 46-month time point to allow us to detect a relation between early parent number talk and later child cardinal number knowledge if such a relation exists.
Because our study takes place in the context of a broader investigation of parent input and children’s language development, we are able to examine the extent to which parent number talk co-varies with child number talk as well as with more general aspects of parent and child talk. It is possible that parent number talk is highly correlated with parents’ overall talk, and therefore is not a good specific predictor of children’s cardinal number knowledge.
Alternatively, parents who provide their children with a lot of linguistic input may not necessarily provide them with a lot of number input. Further, because our sample is socioeconomically diverse, we are able to examine whether the frequency of parent and child number talk varies with family income and education of the primary caregiver, and whether it predicts the child’s cardinal number knowledge once these socioeconomic variables are controlled.
Finally, as a point of comparison, we also examine the relation of parent and child number talk and other talk to children’s later vocabulary comprehension to further examine the specificity of number talk as a predictor of cardinal number knowledge versus more general knowledge. Thus, our specific goals are:
1) to examine the variability in parent talk about number with their children between 14–30 months,
2) to determine whether parent talk about number during the toddler period, when children have little or no knowledge about the cardinal value of numbers, predicts children’s performance on the Point-to-X task at 46 months, a task that measures the child’s knowledge of the cardinal meanings of the number words, and whether this is the case even controlling for child talk about number, parent other talk, child other talk, and SES, and
3) to examine similar relations between parent-child talk about number (versus other talk) and children’s later vocabulary skill as measured by the Peabody Picture Vocabulary Test, 3rd edition (Dunn & Dunn, 1997).
Johns Hopkins University
Jill Rosen – Johns Hopkins University
The image is credited to Johns Hopkins University.
Original Research: Closed access
“Infants recognize counting as numerically relevant”. Jinjing (Jenny) Wang and Lisa Feigenson.
Developmental Science doi:10.1111/desc.12805.