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. Author manuscript; available in PMC: 2011 Sep 1.
Published in final edited form as: Dev Psychol. 2010 Sep;46(5):1309–1319. doi: 10.1037/a0019671

What counts in the development of young children’s number knowledge?

Susan C Levine 1, Linda Whealton Suriyakham 2,1, Meredith L Rowe 3,2, Janellen Huttenlocher 4, Elizabeth A Gunderson 5
PMCID: PMC2998540  NIHMSID: NIHMS232624  PMID: 20822240

Abstract

Prior studies indicate that children vary widely in their mathematical knowledge by the time they enter preschool and that this variation predicts levels of achievement in elementary school. In a longitudinal study of a diverse sample of 44 preschool children, we examined the extent to which their understanding of the cardinal meanings of the number words (e.g., knowing that “four” refers to sets with four items) is predicted by the number talk they hear from their primary caregiver in the early home environment. Results showed substantial variation in parent “number talk” during five visits between child ages 14 and 30 months. Moreover, this variation predicted children’s knowledge of the cardinal meanings of number words at 46 months of age, even when socioeconomic status and other measures of parent and child talk were controlled. These findings suggest that encouraging parents to talk about number with their toddlers, and providing them with effective ways to do so, may positively impact children’s school achievement.

Keywords: Parent input, number, cardinality, mathematical skill, parent-child interaction

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.

Existing studies have mainly relied on parental interviews and surveys to obtain information about number relevant input (Saxe et al., 1987; Blevins-Knabe & Musun-Miller, 1996; Starkey et al., 1999). 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).

Method

Participants

Forty-four typically-developing children (24 males, 20 females) participated in the study. Children were drawn from a larger sample of 63 families in a longitudinal study of language development. Recruitment was based on direct mailings to families in targeted zip codes and an advertisement in a free monthly parenting magazine. Parents who responded participated in a screening questionnaire over the phone during which information was gathered on race, ethnicity, income, education, language(s) spoken in the home, and child gender. Sixty-three English-speaking families were selected to match as closely as possible the 2000 census data on family income and ethnicity in the greater Chicago area. Children were included in the present study if they had data for all five visits between 14 and 30 months, if they interacted with the same caregiver during those visits, and if they completed the Point-to-X task at 46 months (see task description below). From the larger sample of 63 families, 10 were eliminated because the caregiver changed over the course of the study or two caregivers were present at one or more sessions, and 2 were eliminated because the children did not complete the Point-to-X task. Due to the cumulative nature of the predictor variables, 7 additional families were eliminated because they were missing one or more of the visits between 14 and 30 months. The 44 remaining dyads (after we eliminate 19 for various reasons) are still representative of the original sample in terms of income and education. That is, of the 19 we removed, 9 had incomes and/or education levels below the mean of the larger sample and 10 had incomes and/or education levels above the mean. We measured socioeconomic status (SES) as the education level of the primary caregiver who interacted with the child during the visits, and the annual family income level. In both cases, data were collected categorically from parents on a questionnaire at or before the first visit. Parental education was transformed into a continuous scale by using the total number of years of schooling (e.g., “high school or GED” was scored as 12 years, “Bachelor’s degree” as 16 years, etc.). On this scale, parental education ranged from 10 to 18 years (M = 15.9, SD =2.1). Income was transformed into a continuous scale by using the midpoint of each category (e.g, the category $15,000 – $35,000 was scored as $25,000). The average family income level ranged from less than $15,000 per year to over $100,000 (M = $61,818, SD = $31,542) (see Table 1 for frequencies of family income and education). Thirty-one of the 44 children included in this study are White, 6 are African American, 3 are Hispanic, 2 are Asian, and 2 are of mixed race.

Table 1.

Frequencies of income by education levels for the 44 families in the study. Income and education were collected categorically and transformed into continuous variables. Parental education was transformed into a continuous scale by using the total number of years of schooling (e.g., “high school or GED” was scored as 12 years, “Bachelor’s degree” as 16 years, etc.). Income was transformed into a continuous scale by using the midpoint of each category (e.g, the category $15,000 – $35,000 was scored as $25,000).

Parent Education (years) Family Income (Thousands $US)
 Total
7.5 25.0 42.5 62.5 87.5 100.0
10 1 1 0 0 0 0 2
12 1 0 0 0 1 0 2
14 1 3 2 0 0 1 7
16 1 0 4 6 4 3 18
18 0 2 2 2 3 6 15
Total 4 6 8 8 8 10 44
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Procedure

At the time of recruitment, families were told that they were participating in a study of language development. There was no mention of the particular aspects of language that we were examining, and importantly, no mention of our interest in parent and child number talk.

Parent-child dyads were visited in the home every four months between child ages 14 and 30 months. Appointment times for the visits were arranged at the convenience of the family. At each visit, dyads were videotaped for 90 minutes engaging in their ordinary activities. Parents were asked to interact with their child as they normally would. Our decision to carry out visits in the home environment was motivated by our goal of obtaining parent-child language samples that were as naturalistic as possible. Toy play, book reading, and meal or snack time were common activities during visits although no direction was given about engaging in any particular activities. Following the observations of naturalistic interactions, children were given the Point-to-X task at age 46 months, and were given a measure of vocabulary comprehension, the Peabody Picture Vocabulary Test (Dunn & Dunn, 1997), at age 54 months.

All speech was transcribed. The unit of transcription was the utterance, defined as any sequence of words preceded and followed by a pause, a change in conversational turn, or a change in intonational pattern. All dictionary words, as well as onomatopoeic sounds (e.g., woof-woof) and evaluative sounds (e.g., uh-oh), were counted as words. Transcription reliability was established by having a second coder transcribe 20% of the videotapes; reliability was assessed at the utterance level and was achieved when coders agreed on 95% of transcription decisions.

Measures

Measures of number and other talk

Cumulative number word tokens

Transcripts were searched by computer for uses of the number words one through ten. Each use of a number word was coded as a number word token. Thus, if a child or parent said “two ducks” this would be coded as one number word token and if a child or parent said “one, two, three” this would be coded as three number word tokens. As the word “one” can be used numerically and non-numerically, all uses of the word “one” were identified, and were manually coded by a research assistant as either numerical or non-numerical. A second researcher coded 20% of the sessions and achieved 99% reliability. Numerical uses of “one” included references to number symbols (e.g., “That’s the number one”), counting (e.g., “one, two three”), cardinal values (e.g., “one of these”, “one truck”), reference to time or age (e.g., “one minute”, “when you turned one”) and uses of “one” with an emphasis of numerosity or individuation (e.g., “you can only have one”, “just one”, “one per day”, “one more”, “one at a time”). Although some uses of “one” were ambiguous with respect to their numerical content, we imposed relatively strict criteria and considered all other uses of one to be non-numerical. These uses included deictics (e.g., “this one”, “that one”), “one” as a direct object (e.g., “that’s the pretty one”, “do you want one”), and some idioms (e.g., “one day”, “one morning”, “one of these days”). All uses of number words (e.g., all number word tokens) over the five sessions were summed to form the measure of cumulative number word tokens for parent and child.

Parent elicitation of child number talk

We also searched transcripts by computer for parent uses of the words “count”, “how many” and “number” in order to identify their elicitations of counting, calculating, set size responses and numeral identification. These uses were then manually coded to ensure that they were used in a numerical context. All numerical elicitations were summed over the five sessions to form a measure of cumulative number elicitations for each parent.

Cumulative other word tokens

Other talk consisted of the cumulative word tokens produced by the child or parent over the five sessions minus the cumulative number word tokens. We controlled for other talk in our analyses that examined the relation between cumulative number talk and child cardinal number knowledge.

Measures of child number and other word knowledge

Child comprehension of cardinal meaning of number words: Point-to-X task

In the Point-to-X task children were administered 16 items. On each item, the child was presented with an 8.5 × 11 piece of paper that had two vertically arrayed sets of squares, one on the left and one on the right half of the paper, with the two halves separated by a vertical line. On each item, children were asked to point to X, where X equaled 2 to 6. The foil alternatives included arrays consisting of adjacent numbers such as 2 vs. 3 (10 items) and also non-adjacent numbers such as 2 vs. 4 (6 items). The foil choice on the non-adjacent items differed from the target by no more than three, and by no more than a 2:1 ratio. Children indicated their response by pointing to the set on the left side or the right side of the page (the location of the target set was counterbalanced across children). The items administered on this test are listed in Table 2. In addition, a sample item is provided in Figure 1.

Table 2.

Percentage of children responding correctly to each item on the Point-to-X task (N=44). Items were presented in a single random order, and the location of the target numerosity (left versus right) was counterbalanced across children.

Item Target Percent Correct
1 vs. 2 1 95
1 vs. 2 2 91
2 vs. 3 2 82
2 vs. 3 3 89
2 vs. 4 2 86
2 vs. 4 4 82
3 vs. 4 3 73
3 vs. 4 4 73
3 vs. 5 3 77
3 vs. 5 5 95
3 vs. 6 3 73
3 vs. 6 6 84
4 vs. 5 4 66
4 vs. 5 5 82
5 vs. 6 5 32
5 vs. 6 6 75
Total 78
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Figure 1.

Figure 1

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Sample item from the Point-to-X task.

Vocabulary Comprehension: PPVT, 3rd edition

Children’s scores on the Peabody Picture Vocabulary Test (Dunn & Dunn, 1997), administered at 54 months, served as the outcome measure for later vocabulary skill. In this measure children are presented with a verbal stimulus (i.e. a word) and are asked to indicate the picture (out of four possible pictures) that best depicts the verbal stimulus. The PPVT was chosen as it is a widely used measure of vocabulary comprehension with published norms, and because it is similar in administration format to the Point-to-X task, the measure of cardinal number knowledge used in this study.

Socioeconomic Status (SES)

As noted earlier, parent education and family income served as measures of socioeconomic status. Because parent education and family income were moderately related to one another (r = 0.48, p<.01) they were combined into one variable of socioeconomic status (SES) using Principal Components Analysis. The first principle component weighted education and income positively and equally and accounted for 74 percent of the original variance. The mean score of the composite is 0 (SD = 1). Families that score high on the SES composite have high annual income levels and the primary caregiver has a high level of education.

Results

Variation in number talk

Descriptive statistics on amount of parent and child cumulative number talk and other talk during the five home visits (7.5 hours from 14 to 30 months) showed marked individual variation. On average, parents produced a total of 90.8 number words during interactions with their children over the five sessions (SD = 61.3), with a minimum of 4 and a maximum of 257. Mean cumulative child number word tokens was 35.3 and also varied widely (SD = 31.2), with a minimum of 0 and a maximum of 126. Parents averaged 18,118 cumulative other word tokens (all word tokens beside number words) (SD = 8,217) and children averaged 3,229 cumulative other word tokens (SD = 1,866). In addition, during the five home visits parents produced an average of only 6.3 prompts (i.e., “how many”, “count” and “number”) to elicit number talk from their children (SD = 6.5), with a minimum of 0 and a maximum of 30. Because these elicitations were quite rare and were highly collinear with overall parent number talk (r = 0.62, p < .001), they are not considered further in our analyses

Parent cumulative number word tokens were related to parent cumulative other word tokens (r = 0.56, p <.001). Similarly, child cumulative number word tokens were related to child cumulative other word tokens (r = 0.55, p < .001). That is, parents and children who talked more overall also talked more about number. Not surprisingly, parent and child cumulative number word tokens produced over this period were positively related (r = 0.35, p = .05), as dyads often engaged in joint conversations about number. Parents’ cumulative number word tokens1 were positively related to the SES composite (r = 0.30, p <. 05), yet children’s cumulative number word tokens were not significantly related to the SES composite (r = 0.05, ns).

Nature of parent and child number talk

All uses of number words from 1 to 10 (number word tokens) were coded according to context at the 30-month session for both parents and children (i.e. counting, cardinal values of sets, numeral naming, etc.). The two most common types of parent input were cardinal values (50% of the number token input) and counting (32% of the input). The rest of the input (18%) consisted of interactions involving naming digits, using numbers with a unit of measure, conventional nominatives, and number comparisons (see Table 3 for examples and proportions of each type of utterance). There was much variability in the input that parents provided (mean cardinal value inputs = 9.35, SD = 10.56; mean counting inputs = 9.16, SD = 14.60).

Table 3.

Examples of each type of number talk and proportions of total number talk at 30 months (parents, N=44; children, N=41).

Type of Number Talk Parent Example Child Example Parent % of Number Talk Mean (SD) Child % of Number Talk Mean (SD)
Cardinal values “Five little monkeys wake up with the sun.” [Reading a book] Eight arms. [Referring to a picture of an octopus] 50.0 (29.3) 27.5 (32.0)
Counting Let’s count the balloons. Ready? One, two, three, four, five. Mommy hiding. Two. Three. Four. Five. Six. Seven. Eight. Nine. [Playing hide and seek] 31.7 (30.6) 61.5 (36.9)
Naming digits There’s a five. [Playing with a toy with the number symbol 5 on it] A four. A Y. [Playing with an alphabet/number toy] 7.9 (16.7) 4.3 (16.7)
Units of measure You were about, uh - think you were five months old here. [Looking at pictures] I pick up one second. [Cleaning up toys] 6.0 (11.6) 2.3 (9.3)
Conventional nominatives Oh, give me a high five. Five oh five? [Referring to an account number] 1.0 (3.4) 0.4 (2.2)
Number Comparisons Three is after four. One! [Response to “What is after one?”] 0.3 (1.3) 0.1 (0.8)
Other I’ll start it from disc two. Two. [Response to “What color is that?”] 3.2 (7.7) 4.0 (10.3)
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Although children’s number words also consisted predominantly of counting (61% of number tokens) and reference to the cardinal values of sets (28% of number tokens), children, unlike their parents, counted much more than they talked about the cardinal values of sets. Other uses of number were much less frequent (11% of number tokens) (see Table 3 for examples and proportions). As for parents, children showed marked variability in their use of number words (mean cardinal value production = 2.51, SD = 3.56; mean counting production = 9.85, SD = 11.36).

For both parents and children, we expected an increase in the use of number words over the 14 to 30 month period, as children typically begin to talk about number and to learn the meanings of the first number words during this period (e.g., Wynn, 1990, 1992; Fuson, 1988). Figure 2 shows the average use of number words over time for parents and children. Contrast analyses were conducted and supported our hypothesis that there was a steady increase in number word use across the 14–30 month period for both parents and children (t(43) = 2.67, p < .05 and t(43) = 6.80, p < .001, respectively) (Furr, 2008; Rosenthal, Rosnow & Rubin, 2000). Overall, parents produced an average of 12.5 number words at 14 months compared to 23.1 at 30 months. Overall, children produced an average of one number word at 18 months compared to 14.3 at 30 months. Only one child said a single number word, “two”, at 14 months and it wasn’t until 22 months that the majority of the children (61%) produced at least one number word (see Figure 3). At all five sessions between 14 and 30 months, parents and children produced more low than high numbers. For example, cumulatively across the five sessions, parents produced the words “one” and “two” an average of 31 and 26 times each, “three” an average of 12 times, and “five” an average of 5.7 times compared to “nine” and “ten” which were produced an average of 1.1 and 1.6 times respectively. Cumulatively, children who produced number words (43 of 44 children) produced “one”, “two”, ”three” and “five” an average of 7.2, 9.8, 5.1, and 2.3 times, compared to “nine” and “ten”, which were produced an average of 1.5 and 1.3 times respectively (see Figure 4).

Figure 2.

Figure 2

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Change over time in use of number words for parents and children

Figure 3.

Figure 3

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Percentage of parents and children producing number words at each session

Figure 4.

Figure 4

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Cumulative production of each numerosity for parents and children

Point-to-X task performance

Children’s knowledge of the cardinal meanings of the number words, as indexed by performance on the Point-to-X task at age 46 months, varied considerably with an average score of 12.55 (range 6 to 16; SD = 2.96). Table 2 reports the percent of children who answered correctly on each item administered. Children showed a higher number bias (i.e., performance was greater when the target was the higher number of the pair, t(43)=2.48, p<.05), as would be expected based on reports that children in this age range generally have a “more” bias on choice tasks (e.g., Carey, 1978).

As would be expected based on prior research showing that children map the number words onto their cardinal values in order, one by one, children’s performance level decreased as the numerosity of the items in the pair increased. (e.g., Wynn, 1990; Condry & Spelke, 2008; LeCorre & Carey, 2007). In particular, children performed better on items involving smaller rather than larger numbers. This trend can be seen most easily by examining performance on the ten items (out of 16) that involved a target and distractor that were one digit apart (e.g., 1 vs. 2, 2 vs. 3, 3 vs. 4, 4 vs. 5 and 5 vs. 6, each with the lower and higher number as targets on different items). For example, averaging across the two items with the same number pair we found that the average percent correct for 1 versus 2 was 93%, compared with 73% for 3 versus 4, and 53% for 5 versus 6. The correlation between item numerosity and percent correct was significant, r=−0.96, p<.05. Considering all sixteen items on the test, children performed better when at least one of two choice sets was a small number (1 to 3) than when both choice sets were greater than or equal to 4. Specifically, when the lower number in a pair was less than or equal to 3 (12 items), children answered correctly 83% of the time (SD=20.2). In contrast, when the lower number in a pair was greater than 3 (4 items), children answered correctly only 64% of the time (SD=25.5). This difference in performance levels on the lower and higher numerosity items was highly significant (t(43)=5.04, p<.001) (see Table 2 for the percent of children who answered each item correctly).

Relation between number talk and Point-to-X performance

We next examined the main question of interest, whether children’s performance on the Point-to-X task at 46 months of age was significantly related to parent number talk at child ages 14 to 30 months. In fact this was the case. Children’s Point-to-X task performance was positively related to parent cumulative number talk2 (r = 0.47, p < .01). This relationship is displayed in Figure 5. Children’s Point-to-X performance also was positively related to parent cumulative other talk (r = 0.39, p < .01) and child cumulative number talk (r = 0.34, p < .05), but not to child cumulative other talk. Further, Point-to-X performance was related to the SES composite (r = 0.50, p < .001).

Figure 5.

Figure 5

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Scatter plot displaying the relation between parent cumulative number word tokens (log) between 14–30 months and child cardinal number knowledge at 46 months (n = 44).

We conducted multiple regression analyses to examine the relation between parent cumulative number talk and child Point-to-X performance, controlling for socioeconomic status and other talk measures. The results of these models are displayed in Table 4. Our approach to model fitting was as follows. We started by fitting a model showing just the relation between SES and Point-to-X performance. This model (Model 1) thus serves as a baseline for comparison to other models containing talk predictors. In the next model (Model 2) we address our primary question of the role of parent number talk in child cardinality skill, by including the effect of parent cumulative number talk, controlling for SES. In Model 3 we add the additional control of parent other talk, and then the final two models (4 and 5) address the role of child number talk and child other talk. This analytic approach allows us to build our models based on our theoretical questions and to look at the effect of our variable of interest (number talk), controlling for SES and other talk. We explain the results of these models in more detail below.

Table 4.

Multiple regression models predicting child cardinal number knowledge at 46 months based on parent and child cumulative number talk and other talk between 14–30 months, controlling for SES (n = 44).

Child Cardinal Number Knowledge – 46 months Parameter estimate (standardized)
Model 1 Model 2 Model 3 Model 4 Model 5
SES 0.50*** 0.39** 0.39** 0.39** 0.40**
Parent number word tokensa 0.35** 0.34* 0.28* 0.29*
Parent other word tokens 0.03
Child number word tokensa 0.23~ 0.29~
Child other word tokens −0.11
R-squared stat (%) 24.8 36.2 36.2 40.8 41.5
F-stat 13.8** 11.6*** 7.6*** 9.2*** 6.9***
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~p<.10;

*

p<.05;

**

p<.01;

***

p<.001

a

The natural log of parent and child number word tokens was used in analyses to ensure linear relations with cardinal number knowledge. The SES composite, and parent and child other word tokens did not require transformation.

Model 1 in Table 4 shows that the SES composite is a significant predictor of children’s Point-to-X performance, explaining 24.8 percent of the variation in children’s scores. Model 2 shows that, controlling for SES, parent cumulative number word tokens is a significant positive predictor of children’s Point-to-X performance. In comparing Model 2 to Model 1 we see that when parent cumulative number word tokens is included in the model with SES, the effect of SES reduces by 22% (the parameter estimate reduces from 0.50 to 0.39), but is still significant. Taken together, SES and parent cumulative number word tokens combine to explain 36.2 percent of the variance in child Point-to-X performance.3

Importantly, in Model 3 (Table 4) we add in parent other word tokens and see that the relation between parent cumulative number word tokens and child Point-to-X performance holds even when controlling for parent cumulative other word tokens in addition to SES. Thus, controlling for SES, parents who talked more about number over the early childhood period, not necessarily parents who talked more in general, had children with more knowledge of the cardinal meaning of the number words at age 46 months.

Further, Model 4 (Table 4) shows that child cumulative number word tokens relate to their Point-to-X performance at the p < .10 level, explaining an additional 4.5 percent of the variance in Point-to-X performance after controlling for SES and parent cumulative number tokens. Finally, in Model 5 we find that controlling for SES and parent and child cumulative number word tokens, child other word tokens is not related to Point-to-X performance.

In sum, controlling for SES, parental cumulative talk to children about number during the early childhood years positively related to children’s later cardinal number knowledge, over and above parental talk in general4. Further, children’s own cumulative experience talking about number also contributed to their later cardinal number knowledge, yet children’s talkativeness in general did not. Thus, controlling for SES, talk about number in particular during early childhood predicted later cardinal number knowledge.

Relation between parent talk and PPVT

The average normed PPVT score for our sample at 54 months5 was 111.4 (SD=17.8), which is about 2/3 of a standard deviation above the standardized mean score of 100. There was a significant, positive relationship between children’s scores on the cardinal number knowledge task at 46 months and on the vocabulary comprehension task (PPVT) at 54 months (r = 0.65, p < .001). Here we examine relations between parent and child cumulative number tokens and other tokens and children’s later vocabulary skill to test the specificity of our input predictors. That is, one might expect children’s early experience with number talk to relate to cardinal number knowledge skill, not overall vocabulary. Similarly, we know from previous work that overall experience with verbal input relates to vocabulary, yet experience with number input might not. Not surprisingly, SES also relates to children’s PPVT scores (r = 0.58, p < .001), thus we use partial correlations to look at relations between early number and other talk and later PPVT scores, controlling for the SES composite. Interestingly, we find that children’s normed scores on the PPVT at 54 months are marginally positively related to parent cumulative other input (r = 0.27, p =.08) and child cumulative other talk (r = 0.25, p = .10), yet are not related to parent cumulative number input nor child cumulative number talk6, controlling for SES. Thus, it is not the case that number input predicts comprehension of the cardinal meanings of the number words and general vocabulary knowledge. Instead, parent number input specifically predicts children’s cardinal number knowledge, whereas parents’ overall talkativeness predicts children’s word comprehension as assessed by the PPVT-III.

Discussion

Our findings show some commonalities in the number talk of parent-child dyads during everyday interactions from 14–30 months. First, low numbers predominated in both children’s and parents’ number talk at all time points. Second, at 30 months, the time point at which we carried out detailed qualitative coding, the majority of children’s and parents’ number talk concerned counting and labeling cardinal values of sets. However, whereas the most common type of parent number talk was labeling set size followed by counting, the opposite was true of children. Thus, children’s number word utterances did not directly mirror those of their parents. The preponderance of child counting at 30 months is consistent with findings showing that children learn to recite the count string before they understand the cardinal meaning of the number words (e.g., Fuson, 1988; Wynn, 1990, 1992).

Against this backdrop of commonality in the nature of number talk, there was marked variability in the frequency of parent and child number talk during everyday interactions between 14 and 30 months. Some parents produced as few as four number words in over 7.5 hours of interaction whereas others produced as many as 257. This amount of variation would amount to a range of approximately 28 to 1,799 number word tokens over a week! Thus, it is not surprising that variation in parental number talk to their toddlers relates strongly to children’s cardinal number knowledge at 46 months, even when socioeconomic status is controlled. Further, despite a moderate correlation between parent cumulative other word tokens and child cardinal number knowledge, when parental talk about number and parents’ cumulative other word tokens were pitted against each other, only number talk remained a significant predictor of later cardinal number knowledge. Finally, the relation between parent number talk and child cardinal number knowledge remained robust even when controlling for child number talk in addition to socioeconomic-status. Thus, the relation of parent number talk and child cardinal number knowledge held regardless of the child’s own use of number words. This shows that parent number talk is not merely related to greater amounts of number talk by children. Rather, it is related to children’s greater understanding of the cardinal value of the number words as assessed on the Point-to-X task.

Why does early parent number talk show such a strong relation to children’s later understanding of the cardinal values of the number words? Clearly, linguistic input is crucial for a child to learn words. Moreover, a large body of research indicates that verbal labels promote category formation by orienting attention to a labeled dimension and by inviting comparisons between sets (e.g., Loewenstein & Gentner, 2005; Lupyan, Rakison, & McClelland, 2007; Mix, 2008; Waxman & Markow, 1995; Yoshida & Smith, 2005). Thus, the role of number words in promoting children’s understanding of cardinal number may be similar to the role of labels for other categories (e.g., Mix et al., 2005). However, language may be particularly important in supporting children’s learning of the cardinal meanings of number words as this mapping poses several unique challenges, discussed by Mix and colleagues (Mix, 2008; Mix et al., 2005). First, unlike other early categories, cardinal number does not refer to an object or a characteristic of an object but rather to a property of sets, and sets may be more difficult for parents to point out and for children to conceptualize than objects. Second, number words select sets that vary widely, only sharing numerosity (e.g., two claps, two dogs, two cookies), Thus, it may be difficult for children to grasp the meaning of “two” as there is only one possible dimension, rather than multiple dimensions, on which to align to extract commonalities (e.g., this contrasts with categories such as “cat”, which share many features) (e.g., Gentner & Ratterman, 1991; Kotovsky & Gentner, 1996). If children focus on the wrong dimension (e.g., shape of the objects in the set or length of the entire set), they may fail to abstract the numerical commonality of dissimilar sets. Finally, number words are special in that they are not only used in a cardinal sense to label set size but are also used as part of a count string, as labels for number symbols, and as labels for ordinal position (e.g., Hughes, 1986; Gelman & Gallistel, 1978; Mix, 2008). Thus, for number words, frequent exposure may be especially important in helping children coordinate these various uses and to understand the cardinal meaning of these words.

A final point concerns the correlational nature of our study. Because of this, it is possible that parent number talk is not causally related to children’s number knowledge. That is, parents who talk more about number may have children who are more interested in this topic or who are better at understanding number words and concepts. A follow-up study that randomly assigns young children to receive different amounts (as well as types) of number talk could shed light on the question of whether parent number talk is causally related to children’s mathematical development. Further, such a study could investigate whether certain kinds of number talk are most effective in promoting children’s mathematical development. Another direction for future research would be to investigate why parents vary in their use of number talk with their young children. For example, some parents may be uncertain how to foster their children’s numerical development, or may view numerical development as the responsibility of the school and not the home (e.g., Cannon & Ginsburg, 2008; Evans, Fox, Cremaso, & McKinnon, 2004). In the meantime, the finding of a strong relation between parents’ early number talk and children’s later understanding of the cardinal meaning of number words opens up the possibility that children’s developmental trajectories can be positively impacted by this simple but important kind of input.

Footnotes

1

We use the natural log of parent cumulative number word tokens here to ensure a linear relation with parent education. In its raw form the relation was curvilinear.

2

We use the natural log of parent cumulative number word tokens to ensure a linear relationship with 46 month Point-to-X performance. Child cumulative number word tokens was logged as well (after adding 1), as it also showed a learning curve shape relation with Point-to-X performance. None of the other variables (family income, education, parent other talk, child other talk) were transformed because they showed linear relations with Point-to-X in their original form.

3

Residuals from all regression models were examined and did not violate model assumptions.

4

We had verbal and spatial IQ data (based on the vocabulary and block design subscales of the WAIS) from a subset of the parents (n=37). We ran the same analyses for this subset and the regression findings hold even when controlling for parent verbal and spatial IQ (which were not significant predictors).

5

One child did not complete the PPVT, thus the sample size for this analysis is 43.

6

Raw forms of all parent and child talk measures showed linear relations with PPVT and were not transformed for correlational analyses.

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Contributor Information

Susan C. Levine, University of Chicago

Linda Whealton Suriyakham, University of Chicago.

Meredith L. Rowe, University of Chicago.

Janellen Huttenlocher, University of Chicago.

Elizabeth A. Gunderson, University of Chicago

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