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Multimodal Numerical Interactions during Mother-Child Picture Book Reading

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Title: Multimodal Numerical Interactions during Mother-Child Picture Book Reading
Language: English
Authors: Salsa, Analía, Gariboldi, María Belén, Rodríguez, Jimena
Source: Early Education and Development. 2022 33(6):997-1012.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 16
Publication Date: 2022
Document Type: Journal Articles
Reports - Research
Descriptors: Foreign Countries, Mothers, Preschool Children, Picture Books, Computation, Numbers, Interpersonal Communication, Age Differences, Reading Strategies, Interaction, Verbal Communication, Number Concepts
Geographic Terms: Argentina
DOI: 10.1080/10409289.2021.1936375
ISSN: 1040-9289
1556-6935
Abstract: Research Findings: The focus of the current study was on the frequency and type of number talk of 2.5- and 4-year-old Argentinean children and their mothers (N = 23 dyads) in shared counting-type picture book reading. The book included sets of animals in ascending order (from 1 to 9), with their corresponding numerals and the animals' written names. A finer-grained approach was used for identifying four types of numerical utterances (enumeration, quantification, comparison, and recognition of numerals); for each category, a subset of codes was created to describe how dyads used numerical information for different purposes, intertwining different semiotic modes of communication and reflection with and about numbers. Results showed distinct ways in which mothers and children express and elaborate numerical information, as a function of children's age and set size. Practice or Policy: Shared picture book reading is a simple, low-cost, and effective tool. The results can contribute to the design of books, intervention programs and policies that focus on multimodal contexts for early mathematical development, both in the family and educational environment, with a special emphasis on young children's active participation.
Abstractor: As Provided
Entry Date: 2022
Accession Number: EJ1357595
Database: ERIC
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  Value: <anid>AN0158177556;h4j01aug.22;2022Jul28.02:23;v2.2.500</anid> <title id="AN0158177556-1">Multimodal Numerical Interactions during Mother-Child Picture Book Reading </title> <p>Research Findings: The focus of the current study was on the frequency and type of number talk of 2.5- and 4-year-old Argentinean children and their mothers (N = 23 dyads) in shared counting-type picture book reading. The book included sets of animals in ascending order (from 1 to 9), with their corresponding numerals and the animals' written names. A finer-grained approach was used for identifying four types of numerical utterances (enumeration, quantification, comparison, and recognition of numerals); for each category, a subset of codes was created to describe how dyads used numerical information for different purposes, intertwining different semiotic modes of communication and reflection with and about numbers. Results showed distinct ways in which mothers and children express and elaborate numerical information, as a function of children's age and set size. Practice or Policy: Shared picture book reading is a simple, low-cost, and effective tool. The results can contribute to the design of books, intervention programs and policies that focus on multimodal contexts for early mathematical development, both in the family and educational environment, with a special emphasis on young children's active participation.</p> <p>Social interaction and semiotic mediation[<reflink idref="bib1" id="ref1">1</reflink>] are two intrinsically related factors that contribute to the ontogeny of key cognitive abilities (Vygotsky, [<reflink idref="bib39" id="ref2">39</reflink>]). Based on the sociocultural perspective, informal every day activities such as board games, cooking or shopping are unique opportunities for parents to promote, challenge, and extend numerical knowledge on young children (Anders et al., [<reflink idref="bib1" id="ref3">1</reflink>]; Cavalcante et al., [<reflink idref="bib6" id="ref4">6</reflink>]; Chan et al., [<reflink idref="bib7" id="ref5">7</reflink>]; Lefevre et al., [<reflink idref="bib20" id="ref6">20</reflink>]; Leyva et al., [<reflink idref="bib21" id="ref7">21</reflink>]; Vandermaas-Peeler & Pittard, [<reflink idref="bib38" id="ref8">38</reflink>]). Likewise, in these activities, spoken language is not the only important communication system; adults and children deploy a multiplicity of semiotic modes (Kress, [<reflink idref="bib19" id="ref9">19</reflink>]) (visual, gestural, written, three-dimensional, and others) in order to represent, communicate, and solve problems with and about numbers. One source of experiences in which social and semiotic mediation intertwine is shared picture book reading, a fairly universal routine for families from different cultural backgrounds living in urban settings. Picture book reading may offer a meaningful and playful context for communication and reflection about numbers through counting activities, labeling the size of collections, establishing comparisons of quantities, among others (Goldstein et al., [<reflink idref="bib13" id="ref10">13</reflink>]; Ramani et al., [<reflink idref="bib27" id="ref11">27</reflink>]; Uscianowski et al., [<reflink idref="bib34" id="ref12">34</reflink>]; Van den Heuvel-Panhuizen et al., [<reflink idref="bib36" id="ref13">36</reflink>]). The focus of the current study was on the frequency and type of number talk of Argentinean mothers and their 2.5- and 4-year-old children during counting-type picture book reading.</p> <p>Making use of picture books – and children's literature in general – for supporting mathematical understanding has become increasingly popular since the last two decades (Haury, [<reflink idref="bib16" id="ref14">16</reflink>]; Van den Heuvel-Panhuizen et al., [<reflink idref="bib36" id="ref15">36</reflink>]). However, there is still an imbalance in knowledge to support the development of early mathematics through picture book reading compared to early literacy: only a few empirical studies have been carried out to investigate the impact of reading books on preschoolers' mathematics performance (Hassinger-Das et al., [<reflink idref="bib15" id="ref16">15</reflink>]; Jennings et al., [<reflink idref="bib18" id="ref17">18</reflink>]; Van den Heuvel-Panhuizen et al., [<reflink idref="bib35" id="ref18">35</reflink>]). Moreover, a set of studies used book reading sessions but followed by other activities, such as playing with story-related mathematical materials (Hong, [<reflink idref="bib17" id="ref19">17</reflink>]; Vandermaas-Peeler et al., [<reflink idref="bib37" id="ref20">37</reflink>]; Young-Loveridge, [<reflink idref="bib42" id="ref21">42</reflink>]), singing rhymes (Young-Loveridge, [<reflink idref="bib42" id="ref22">42</reflink>]) or composing geometrical puzzles (Casey et al., [<reflink idref="bib5" id="ref23">5</reflink>]). The follow-up activities, rather than the book reading sessions themselves, were the focus of that research.</p> <p>Even less work has centered on the number concepts and skills that parents and/or their children spontaneously put into play within the context of shared reading interactions. On the one hand, Anderson et al. ([<reflink idref="bib2" id="ref24">2</reflink>]) explored how parents and their 4-year-old children attended to mathematical concepts as they read two story books. Through a qualitative analysis, the authors showed that almost all dyads engaged in mathematical talk with considerable diversity in the amount of talk and the ways in which mathematical concepts were shared. The concepts of size (e.g., using descriptors of size like "little" or "big" or comparing the size of objects in illustrations) and number (using "one" as a descriptor or global descriptors such as "lots" and "tons", counting) arose most frequently, while utterances about shape occurred most infrequently. Interestingly, most of the mathematical talk was centered on the pictures in the story books, not the text, which supported previous findings from studies of non-math book reading (Ezell & Justice, [<reflink idref="bib9" id="ref25">9</reflink>]; Fletcher & Reese, [<reflink idref="bib10" id="ref26">10</reflink>]).</p> <p>Using a different approach but also focusing on the prekindergarten years, Mix et al. ([<reflink idref="bib25" id="ref27">25</reflink>]) asked parents to read two books to their 3.5-year-olds, one book that was about numbers (counting book) and one that was not. Then, they coded parents' utterances in order to determine how often they provided a particular numerical input: cardinal labels ("three") immediately followed by counting ("one-two-<emph>three</emph>"). This study revealed that parents rarely elaborated on number and almost never labeled and counted the same set, even when they were asked to read the counting book.</p> <p>On the other hand, Goldstein et al. ([<reflink idref="bib13" id="ref28">13</reflink>]) were interested in exploring when parents begin to engage in these behaviors, specifically whether they elaborated on numerical information when reading a counting book to their infants, as young as 5 months of age. Parents' spontaneous statements rarely focused on number and those that did consisted primarily of counting, with little emphasis on labeling the cardinality of sets. Nevertheless, developmental differences were observed, such that parents were more likely to provide numerical information when reading to older infants (10 month olds).</p> <p>Our study builds upon the aforementioned studies in a number of ways. First, prior studies have focused on shared reading during the first year of life and around the fourth; consequently, a deep examination of the critical period between 1 and 4 years of age is missing. Most middle-class children's uptake of symbolic number forms is evident from approximately 1.5 years in the oral mode and from 2.5 years of age in the notational, written mode; in the second case, it takes place through the naming of surrounding written numerals by parents and daycare teachers ("That is a <emph>two</emph>") (Mix, [<reflink idref="bib23" id="ref29">23</reflink>]; Palmer & Baroody, [<reflink idref="bib26" id="ref30">26</reflink>]; Rudd et al., [<reflink idref="bib28" id="ref31">28</reflink>]). During these early years, children use the number words one, two, and three to label and/or to give the number for small sets (<reflink idref="bib1" id="ref32">1</reflink>, 2, or 3 things). Although they begin to learn the ordered list of number words, meaningful enumeration emerges by observing others counting small collections they can recognize. Progressively, children extend their repertoire of number words to larger sets and, by the age of 4, they can discern the purpose of enumeration (a way of determining the total number of items of a collection or its cardinal value) and the rationale of enumeration procedures (the how-to-count principles) (Baroody et al., [<reflink idref="bib3" id="ref33">3</reflink>]; Mix et al., [<reflink idref="bib24" id="ref34">24</reflink>]; Sarama & Clements, [<reflink idref="bib29" id="ref35">29</reflink>]).</p> <p>Second, the interest of previous studies has almost exclusively been centered in identifying parents' contribution to the reading sessions, as in Mix et al.'s ([<reflink idref="bib25" id="ref36">25</reflink>]) and Goldstein et al.'s ([<reflink idref="bib13" id="ref37">13</reflink>]) research. Nevertheless, from the sociocultural perspective, children's in-the-moment cognitive engagement, such as their spontaneous focus of attention and their ways and means to participate, is as important as adults' numerical input and support. In the present study, we focused precisely on both mothers and children numerical interventions during shared reading.</p> <p>In addition, this study provides an opportunity for extending prior research to Argentinean dyads, a sample outside the English-speaking groups commonly used in field. Taking a close look at whether and how Spanish-speaking young children and their parents actively engage in numerical talk during shared reading will contribute to a better understanding of how informal activities promote and challenge early numerical knowledge in diverse cultural settings.</p> <p>Finally, the numerical content of parent-child interactions is only part of the story: the ways in which numerical information is communicated also matter. Numerical activities are mediated by various semiotic modes (Kress, [<reflink idref="bib19" id="ref38">19</reflink>]) that children progressively appropriate in order to communicate and represent numbers, such as deictic and representational gestures (e.g., finger patterns), number words, verbal quantifiers, collections of objects and images of them, numerals and math notations, all of them with distinct potentials for meaning. People orchestrate meaning through their selection and configuration of semiotic modes. Semiotic mediation is not only a means of expressing already available meanings; rather, it constitutes a path to number elaboration and understanding. This is why children, from early stages, interact with these sign systems and use them to develop their number knowledge and thus participate more actively in their culture. In order to investigate children's numerical thinking, it is necessary to confront them with meaningful situations involving a variety of semiotic modes. However, most of the prior studies have focused only on the oral, mainly verbal mode; further research is needed to understand the complexity and interplay between different semiotic modes of number deployed by children and adults in everyday interactions.</p> <p>The study we report here sought to achieve a deeper understanding of mother-child interactions involving number concepts and skills during shared counting-type picture book reading. In particular, this study examined variations in the ways that Argentinean mothers and their young children express and elaborate about numbers, as a function of children's age (2.5 and 4 years) and the size of the sets depicted in the book (1–9). As noticed above, it seems critical to yield a more nuanced view of this activity as a multimodal mediated space of social interaction in which children younger than 4 years of age actively participated guided by maternal support.</p> <p>In the current study, we used a counting book designed to elicit talk about numbers under certain conditions. The book included sets of discrete elements (animals) in ascending order (from 1 to 9), each set with its corresponding Arabic numeral and the animal's written name (see Figure 1). This book offered an opportunity to engage in different numerical activities: enumeration of individual items in a collection, quantification of the collections of items, recognition of numerals and the ordinal relations of numbers, symbol-quantity mappings, numerical comparisons between collections and numerals. Besides, it allowed communicating and reflecting with and about numbers in oral, gestural and notational (pictorial and written) modes. Finally, as previous research has revealed that parents provided little input for number relative to other information (Mix et al., [<reflink idref="bib25" id="ref39">25</reflink>]), our book made it possible to focus on numerical or non-numerical contents (labeling or describing the pictures in the book), privileging pictures rather than text, which is especially suitable for children under 4 years.</p> <p>Graph: Figure 1. Examples of the pages of the book.</p> <p>Additionally, numerical input from parents varies as a function of set size, with some set sizes highlighted more than others. Longitudinal data revealed that the amount of number talk in the home referring to large sets (4–10 items) is a better predictor of cardinal number knowledge later in childhood than number talk referring to small sets (1–3 items) (Gunderson & Levine, [<reflink idref="bib14" id="ref40">14</reflink>]). Mix et al. ([<reflink idref="bib25" id="ref41">25</reflink>]) reported that parents were significantly more likely to count the sets 4–10 than they were to count set sizes 1–3 to their preschoolers. Exploring spontaneous counting behavior in mother-child dyads as a function of children's age and set sizes should help determine the factors that may compel the content of numerical interactions.</p> <p>Our study thus asks three questions: (<reflink idref="bib1" id="ref42">1</reflink>) How frequent is mother-child spontaneous talk about numbers during counting-type picture book reading when children are 2.5 and 4 years old?; (<reflink idref="bib2" id="ref43">2</reflink>) What is the nature of the numerical talk dyads put into play while reading a book that contains references to numbers in different semiotic modes?, and are there differences in numerical talk as a function of children's age?; (<reflink idref="bib3" id="ref44">3</reflink>) Does numerical talk during picture book reading varies as a function of set sizes, categorized as small (1–3), medium (4–6), and large (7–9)? These questions will be addressed by taking a finer-grained approach to mother-child shared numerical interactions.</p> <hd id="AN0158177556-2">Method</hd> <p></p> <hd id="AN0158177556-3">Participants</hd> <p>Participants were 23 Argentinean mothers and their children, 13 2.5-year-olds (<emph>M</emph><subs>age</subs> = 29 months; range = 28–32 months; seven females) and 10 4-year-olds (<emph>M</emph><subs>age</subs> = 48.10 months; range = 46–50 months; six females) recruited using an incidental non aleatory method (Clark-Carter, [<reflink idref="bib8" id="ref45">8</reflink>]). In Argentina, compulsory education starts at the age of 4, but the majority of the middle SES children already enrolls in a preschool program when they are about 2–3 years of age and focusing on non-mandatory learning goals. From the present sample, all children attended a part time preschool on a permanent basis and they had no history of special developing issues, according to the records of the educational institutions.</p> <p>The mothers' age ranged from 25 to 44 years (<emph>M</emph><subs>age</subs> = 32.22 years). The majority of the mothers had post-secondary education. Specifically, 44% had completed a high school diploma, 30% completed a college technical program, and 26% were professionals holding graduate or postgrad degrees; most of them (79%) worked in professional or commercial positions. Mothers completed a brief survey about their families' demographic information; their responses indicated that families were from middle SES and had the same cultural lineage. All of the mothers indicated that they had picture books at home and shared them with their children on a regular basis (at least twice a week). Counting-type picture books were not a frequent reading resource in these families. The sample size (<emph>N</emph> = 23 dyads) matched the sample size range reported in previous studies (<emph>N</emph> = between 14 and 39; see Anderson et al., [<reflink idref="bib2" id="ref46">2</reflink>]; Mix et al., [<reflink idref="bib25" id="ref47">25</reflink>]).</p> <hd id="AN0158177556-4">Materials and Procedure</hd> <p>The book had nine cardboard pages (20 × 20 cm) with drawings of familiar animals for children (e.g., dog, fish, rabbit) in a central position, their names in capital letters and the numerals denoting the number of animals, presented in consecutively ascending order (from 1 to 9). The words and numerals appeared in different positions on the pages interspersed above and below the illustrations (see Figure 1). On each page, the same color was used for the drawings (without filling the forms), the numerals and the written words, varying the colors per page. We decided to design the counting book specially for this research in an attempt to control the presence of distractors on book pages and some factors that may influence enumeration, such as item type (discrete, nameable and distinct), consistency of the item type (identical objects), size (exact same size), and set arrangement (randomly) (for a review of features of counting books, see Ward et al., [<reflink idref="bib40" id="ref48">40</reflink>]).</p> <p>Mother-child dyads were asked to "Share this book as you normally would", either at preschool (48%) or at home (52%), according to the mother's preference. Dyads did not receive any indications regarding how many times to read the book or how to interact with it: they were free to use and explore the book as they wished. Nevertheless, each dyad read the book only once. The dyads were observed individually in a quiet room, during drop-off or pick-up time when the session occurred at the child's preschool or at a time set by the mother at home. Mother-child reading sessions lasted approximately from 5 to 10 minutes and were videotaped with a video camera mounted on a tripod: the researcher, while being as inconspicuous as possible during the taping, kept field notes of any information that would aid in understanding and interpreting the data. Videos and field notes were incorporated in the Atlas-ti 7 software for data coding.</p> <p>The mothers signed a written informed consent form, also stating confidentiality of all information.</p> <hd id="AN0158177556-5">Coding</hd> <p>The reading sessions constituted the first unit of analysis. Within this unit, the conversational utterances of the mother and/or her child were considered. An utterance was defined as a conversational turn or series of turns referring to a same subject, with meaningful content in the context of shared reading. For the analysis of all the utterances pertaining to number, a system was developed considering, simultaneously, different categories that had been elaborated in previous research (Ramani et al., [<reflink idref="bib27" id="ref49">27</reflink>]; Saxe et al., [<reflink idref="bib30" id="ref50">30</reflink>]), as well as the analysis of the empirical evidence obtained by the constant comparative method (Glaser & Strauss, [<reflink idref="bib12" id="ref51">12</reflink>]; Strauss & Corbin, [<reflink idref="bib32" id="ref52">32</reflink>]). Four types of numerical utterances emerged from the reading sessions and constituted the basic categories of the observational code: (<reflink idref="bib1" id="ref53">1</reflink>) <emph>Enumeration</emph> (counting out the items on a particular page, labeling or not the cardinality of the set); (<reflink idref="bib2" id="ref54">2</reflink>) <emph>Quantification</emph> (labeling the cardinal value of the collection on a page, without counting); (<reflink idref="bib3" id="ref55">3</reflink>) <emph>Comparison</emph> (between two sets on different pages); and (<reflink idref="bib4" id="ref56">4</reflink>) <emph>Recognition of numerals</emph>. For each of these categories, we created a subset of codes that reflect: (a) the interplay between these numerical elaborations and the semiotic modes that support them; (b) who participated in the utterance (M: Mother; C: Child) and how they did it. Utterances about the ordinal relations of numbers, mappings among numerals and collections, and comparisons between numerals were not observed, therefore no categories were developed. A complete description (with examples) of each subcategory of the observational code is presented in the Results section.</p> <p>After two raters (the second and third authors) coded all transcripts, around 50% of the videos (<reflink idref="bib10" id="ref57">10</reflink>) were transcribed a second time and coded for the total numerical utterances by a third independent rater trained by the first author during three rounds of coding (each round entailed a different video). Inter-coder reliability between this third rater and the primary raters across all utterance types was found to be 94% (range 85–100%). Finally, those utterances subject to disagreement between raters were resolved at a coding meeting involving all raters.</p> <hd id="AN0158177556-6">Results</hd> <p>This section presents the results of quantitative and qualitative analyses for each of the three research questions: frequency of number talk, types of number talk as a function of age group and set size. In preliminary analyses, children's gender had non-significant effect in the main dependent variables (frequency and type of numerical utterances) (all <emph>p</emph>'s >.05) and was thus excluded from the analyses.</p> <hd id="AN0158177556-7">Frequency of Spontaneous Number Talk by Age Group</hd> <p>The focus of our first research question was the extent to which the dyads provided any numerical elaborations whatsoever. Numerical elaborations included the four basic types of numerical utterances described above (enumeration, quantification, comparison, and recognition of numerals). Non-numerical elaborations included utterances about the names of the animals and their characteristics (i.e., M: "How does the hen?", C: "Co-co-co-co"), relations between the book and children's experiences (M: "These pigs are just like the little pigs that we watch in the cartoons"), and mothers' invitations to identify letters (M: "Which letter is this?", C: "It's my letter", pointing to an A). The proportions of numerical and non-numerical utterances are reported in Table 1.</p> <p>Table 1. Number and non-number talk by age group.</p> <p> <ephtml> <table><thead><tr><td /><td>Numerical utterances</td><td>Non-numerical utterances</td><td /></tr><tr><td>Age groups</td><td><italic>n</italic> (%)</td><td><italic>n</italic> (%)</td><td>Total</td></tr></thead><tbody><tr><td>2.5 years</td><td>82 (27.7%)</td><td>214 (72.3%)</td><td>296</td></tr><tr><td>4 years</td><td>179 (50.4%)</td><td>176 (49.6%)</td><td>355</td></tr></tbody></table> </ephtml> </p> <p>1 Range of numerical utterances: 0 to 16 (2.5 years) and 9 to 29 (4 years).</p> <p>A mixed measures analysis of variance (ANOVA) looking at the within-subject factor of Utterance Type (numerical, non-numerical) and the between-subjects factor of Age Group (2.5 and 4 years) on the total number of utterances revealed a main effect of Utterance Type [<emph>F</emph>(<reflink idref="bib1" id="ref58">1</reflink>, 21) = 20.66, <emph>p</emph> <.001, η<subs>p</subs><sups>2</sups> =.496] showing that, across age groups, dyads made significantly more non-numerical (<emph>M</emph><subs>Non-numerical</subs> = 17.03, <emph>SE</emph> = 1.11) than numerical utterances (<emph>M</emph><subs>Numerical</subs> = 12.10, <emph>SE</emph> = 1.10). However, the Utterance Type x Age Group interaction [<emph>F</emph>(<reflink idref="bib1" id="ref59">1</reflink>, 21) = 23.25, <emph>p</emph> <.001, η<subs>p</subs><sups>2</sups> =.525] indicated that only 2.5-year-olds dyads made significantly more non-numerical utterances while reading the book (<emph>M</emph><subs>Non-numerical</subs> = 16.46; <emph>M</emph><subs>Numerical</subs> = 6.30) (Bonferroni, <emph>p</emph> <.001); 4-year-olds dyads made a comparable number of non-numerical and numerical utterances (<emph>M</emph><subs>Non-numerical</subs> = 17.60; <emph>M</emph><subs>Numerical</subs> = 17.90) (<emph>p</emph> =.856).</p> <p>We examined these patterns of results more closely carrying out analyses between age groups. A one-way ANOVA revealed that, as expected, the total number of utterances increased with age (<emph>M</emph><subs>2.5 years</subs> = 22.77, <emph>SE</emph> = 2.31; <emph>M</emph><subs>4 years</subs> = 35.50, <emph>SE</emph> = 3.25) [<emph>F</emph>(<reflink idref="bib1" id="ref60">1</reflink>, 21) = 10.75, <emph>p</emph> =.004]; the same pattern was observed in relation to numerical utterances (<emph>M</emph><subs>2.5 years</subs> = 6.30; <emph>M</emph><subs>4 years</subs> = 17.90) [<emph>F</emph>(<reflink idref="bib1" id="ref61">1</reflink>, 21) = 27.32, <emph>p</emph> <.001]. However, no significant effects were obtained in the number of non-numerical elaborations (<emph>M</emph><subs>2.5 years</subs> = 16.46; <emph>M</emph><subs>4 years</subs> = 17.60) [<emph>F</emph>(<reflink idref="bib1" id="ref62">1</reflink>, 21) = 0.261, <emph>p</emph> =.615]. Thus, results reveal that the counting book prompted 4-year-olds dyads to talk more in general and, foremost, to elaborate, communicate, and reflect more about numbers.</p> <hd id="AN0158177556-8">Types of Number Talk by Age Group</hd> <p>For the second research question, a mixed measures ANOVA was conducted to examine the within-subject factor of Number Utterance Type (enumeration, quantification, comparison, recognition of numerals) and the between-subjects factor of Age Group (2.5 and 4 years) on the total number of numerical utterances. A main effect of Number Utterance Type [<emph>F</emph>(<reflink idref="bib3" id="ref63">3</reflink>, 63) = 12.82, <emph>p</emph> <.001, η<subs>p</subs><sups>2</sups> =.379] indicated that, across age groups, mothers generally did not compare sets of different pages of the book. There were a very few instances of this type of utterance (<emph>M</emph><subs>Comparison</subs> = 0.27, <emph>SE</emph> = 0.11), significantly less than recognition of numerals (<emph>M</emph><subs>Numerals</subs> = 4.79, <emph>SE</emph> = 0.76), labeling the cardinality of sets (<emph>M</emph><subs>Quantification</subs> = 3.51, <emph>SE</emph> = 0.49), and counting utterances (<emph>M</emph><subs>Enumeration</subs> = 3.51, <emph>SE</emph> = 0.57) (Bonferroni, <emph>p</emph>'s <.001). There were not differences between the last three types of numerical elaborations (<emph>p</emph>'s >.05).</p> <p>The Number Utterance Type x Age Group interaction was significant [<emph>F</emph>(<reflink idref="bib3" id="ref64">3</reflink>, 63) = 2.85, <emph>p</emph> =.044, η<subs>p</subs><sups>2</sups> =.120], revealing interesting patterns of results within age groups (see Figure 2). In the 2.5-year-olds' group, of the total of 82 numerical utterances recorded across all 13 dyads, recognition of numerals was the most frequent type of utterance (35/82 = 43%), enumeration (<reflink idref="bib25" id="ref65">25</reflink>, 30%) and quantification (<reflink idref="bib20" id="ref66">20</reflink>, 24%) were next, and there were only 2 instances of comparison (3%). Follow-up analyses did not indicate significant differences between the four types of numerical talk (Bonferroni, <emph>p</emph>'s >.05).</p> <p>Graph: Figure 2. Mean number of the four types of numerical utterances as a function of age group.</p> <p>In the 4-year-olds' group, of the total of 179 numerical utterances (across 10 dyads), the majority of spontaneous numerical utterances also involved recognition of numerals (69/179 = 39%), with fewer instances of quantification (<reflink idref="bib55" id="ref67">55</reflink>, 31%) and counting items in sets (<reflink idref="bib51" id="ref68">51</reflink>, 28%). Similar to the findings of the younger dyads, comparison utterances were very infrequent (<reflink idref="bib4" id="ref69">4</reflink>, 2%) (Figure 2). Nevertheless, in this age group, there were significant differences between comparison and the other three types of number talk (Bonferroni, <emph>p</emph>'s <.001), without differences between recognition of numerals, quantification and enumeration (<emph>p</emph>'s >.05).</p> <p>Finally, and not surprisingly, comparisons between age groups confirmed that 4-year-olds dyads elaborated significantly more utterances about recognition of numerals [<emph>F</emph>(<reflink idref="bib1" id="ref70">1</reflink>, 21) = 7.56, <emph>p</emph> =.012], enumeration [<emph>F</emph>(<reflink idref="bib1" id="ref71">1</reflink>, 21) = 7.59, <emph>p</emph> =.012], and quantification [<emph>F</emph>(<reflink idref="bib1" id="ref72">1</reflink>, 21) = 15.82, <emph>p</emph> =.001] than 2.5-year-olds dyads. The averages of comparison were similar in both age groups [<emph>F</emph>(<reflink idref="bib1" id="ref73">1</reflink>, 21) = 1.18, <emph>p</emph> =.290].</p> <p>However, these basic categories did not adequately capture the nuanced manner in which mothers and children co-constructed numerical meanings in the context of shared reading. Consequently, we identified a subset of categories for each type of numerical utterance in order to examine more closely how mothers and children deployed different semiotic modes of communication and reflection about numbers, and used numerical information for different purposes.</p> <hd id="AN0158177556-9">Recognition of Numerals</hd> <p>In both age groups, dyads identified and read numerals most of the times they elaborated on number (2.5 years = 43% of utterances; 4 years = 39%). Dyads labeled numerals in two different ways: simply as "a number", regardless what specific numeral it was <emph>(Number)</emph>, or using the corresponding number word for each number symbol <emph>(Numeral)</emph> (see Table 2).</p> <p>Table 2. Recognition of numerals utterances: description and examples.</p> <p> <ephtml> <table><thead><tr><td>Recognition of numerals</td><td>Definition</td><td>Examples</td></tr></thead><tbody><tr><td><italic>Number</italic></td><td>Mothers or children use the word "number" to label any numeral</td><td><italic>Dyad 11 (2.5 years) (1 dog)</italic> M: "And what is this?" (pointing to the numeral 1) C: "A number" M: "Yes, a number"</td></tr><tr><td><italic>Numeral</italic></td><td>Mothers or children label a numeral with its corresponding number word <italic>(dyad 14)</italic>. Children usually label numerals up to 4, mapping the numeral with its number word and a representational gesture <italic>(dyad 17)</italic>. When mothers label numerals, they usually relate them with children's prior experiences <italic>(dyad 18)</italic></td><td><italic>Dyad 14 (4 years) (2 lions, 3 hens)</italic> M: "What's up here?" C: "Two lions, three hens. And they have the number 3" M: "Which is the number 3?" C: "This one" (pointing to 3) <italic>Dyad 17 (4 years) (1 dog)</italic> M: "And this one, which number is it?" (pointing to 1) C: "One" (showing 1 finger) <italic>Dyad 18 (4 years) (4 pigs)</italic> M: "This number is the age you are going to turn soon" (pointing to 4) C: (Nodding in agreement) M: "Four" (pointing to 4 again). It looks like a little chair"</td></tr></tbody></table> </ephtml> </p> <p>2 C: Child; M: Mother. The page number of the book (e.g., 1 dog) is included to contextualize the mother-child conversation.</p> <p>Two-and-a-half-year-olds' dyads used these two types of utterances with a similar frequency (<emph>M</emph><subs>Number</subs> = 0.85, <emph>SE</emph> = 0.29; <emph>M</emph><subs>Numeral</subs> = 1.85, <emph>SE</emph> = 0.90) [Paired samples <emph>t</emph> test, <emph>t</emph>(<reflink idref="bib12" id="ref74">12</reflink>) = −1.16, <emph>p</emph> =.269]. In contrast, the majority of 4-year-olds' utterances about numerals involved using the corresponding number word for each number symbol (<emph>M</emph><subs>Number</subs> = 1.20, <emph>SE</emph> = 0.29; <emph>M</emph><subs>Numeral</subs> = 5.70, <emph>SE</emph> = 1.15) [<emph>t</emph>(<reflink idref="bib9" id="ref75">9</reflink>) = −3.55, <emph>p</emph> =.006]; these dyads used significantly more numeral labels than 2.5-year-olds dyads [Independent samples <emph>t</emph> test, <emph>t</emph>(<reflink idref="bib21" id="ref76">21</reflink>) = −2.66, <emph>p</emph> =.014] ["number" as label = <emph>t</emph>(<reflink idref="bib21" id="ref77">21</reflink>) = −0.83, <emph>p</emph> =.413].</p> <hd id="AN0158177556-10">Enumeration</hd> <p>As shown in Table 3, we identified two types of enumeration utterances, <emph>Nominal</emph> and <emph>Cardinal</emph>. In the 2.5-year-olds' group, the frequencies of nominal (<emph>M</emph><subs>Nominal</subs> = 1, <emph>SE</emph> = 0.39) and cardinal enumeration (<emph>M</emph><subs>Cardinal</subs> = 0.92, <emph>SE</emph> = 0.36) were very similar [<emph>t</emph>(<reflink idref="bib12" id="ref78">12</reflink>) = 0.22, <emph>p</emph> =.829]. However, in the 4-year-olds' group, the data followed a different pattern, with fewer nominal enumerations (<emph>M</emph><subs>Nominal</subs> = 0.30, <emph>SE</emph> = 0.21) than cardinal enumerations (<emph>M</emph><subs>Cardinal</subs> = 4.80, <emph>SE</emph> = 1.04) [<emph>t</emph>(<reflink idref="bib9" id="ref79">9</reflink>) = −3.95, <emph>p</emph> =.003].</p> <p>Table 3. Enumeration utterances: description and examples.</p> <p> <ephtml> <table><thead><tr><td>Enumeration</td><td>Definition</td><td>Examples</td></tr></thead><tbody><tr><td><italic>Nominal</italic></td><td>Children use labels to serve an enumerative function, without an intention to quantify the set. The labels can be numerical <italic>(dyad 11)</italic> as non-numerical <italic>(dyad 4)</italic>. Children perform global sweeping gestures on segments of the collection while spelling out the labels, making one-to-many correspondences</td><td><italic>Dyad 11 (2.5 years) (7 cats)</italic> C: "Look, cats. One, two, three, four, five, six, seven, eight, nine, ten ... thirteen, fourteen, fifteen" (pointing to each cat without one-to-one correspondence) <italic>Dyad 4 (2.5 years) (8 rabbits)</italic> M: "And what is here?" C: "Rabbit, rabbit, rabbit, rabbit, rabbit" (pointing to each rabbit without one-to-one correspondence)</td></tr><tr><td><italic>Cardinal</italic></td><td>Mothers or children use number word-to-object correspondences in a count to refer to cardinal values of sets. Number words are accompanied by pointing gestures, which support and organize enumeration, facilitating a joint reference. Children use cardinal enumeration in response to mothers' how many questions or instruction to count <italic>(dyad 18)</italic>. Mothers usually use it as feedback, in order to correct children's errors <italic>(dyad 11)</italic></td><td><italic>Dyad 18 (4 years) (2 lions)</italic> M: "How many lions are there?" C: "One" (pointing to a lion) M: "One" (pointing to the same lion) C: "And two" (pointing to the other lion) M: "Two" (pointing to the same lion and emphasizing "two") <italic>Dyad 11 (2.5 years) (4 pigs)</italic> M: "What are they?" C: "Piggies" M: "And how many are there?" C: "One, two, three, four, five, six" (pointing to each lion but double-counting some items) M: "No, there are four. One, two, three and ... four" (pointing to with one-to-one correspondence between number words and objects and emphasizing the last word)</td></tr></tbody></table> </ephtml> </p> <p>Cardinal enumeration was used differently by children and mothers. Four-year-old's children rarely counted spontaneously (29% of these utterances), but used cardinal enumeration in response to mothers' how many questions or an explicit incentive to count (67%). Fifty percent of maternal interventions were feedback; mothers used cardinal enumeration to confirm or correct her child's previous enumeration.</p> <p>Lastly, comparisons between age groups indicated differences in cardinal enumeration due to significantly more cardinal enumerations in the older group [<emph>t</emph>(<reflink idref="bib21" id="ref80">21</reflink>) = −3.88, <emph>p</emph> =.001], but not in nominal enumeration [<emph>t</emph>(<reflink idref="bib21" id="ref81">21</reflink>) = 1.43, <emph>p</emph> =.165], which had a similar frequency in both groups.</p> <hd id="AN0158177556-11">Quantification</hd> <p>Three types of quantification utterances were observed during the reading sessions: <emph>Number words quantification, Bimodal</emph> (number word and gesture) and <emph>Global quantification</emph> (Table 4).</p> <p>Table 4. Quantification utterances: description and examples.</p> <p> <ephtml> <table><thead><tr><td>Quantification</td><td>Definition</td><td>Examples</td></tr></thead><tbody><tr><td><italic>Number words</italic></td><td>Mothers or children use number words to communicate the cardinality of a set, without counting. Children usually quantify with number words collections up to 4 items <italic>(dyad 16)</italic>. Mothers usually use number words to quantify a set immediately after their children's verbal counting <italic>(dyad 22)</italic></td><td><italic>Dyad 16 (4 years) (4 pigs)</italic> M: "Look here!" (pointing to a pig) C: "Four pigs" (pointing to each pig, without counting them) M: "Very good!" <italic>Dyad 22 (4 years) (3 hens)</italic> M: "How many hens are there?" C: "One, two, three" (pointing to each hen) M: "Three hens" (emphasizing the number word)</td></tr><tr><td><italic>Bimodal: number word and gesture</italic></td><td>Mothers or children use a number word together with a representational finger gesture to communicate the cardinality of a set. Mothers use this type of quantification as feedback, imitating the previous numerical intervention of their children (<italic>dyad 22</italic>) or emphasizing feedback correction <italic>(dyad 8)</italic></td><td><italic>Dyad 22 (4 years) (5 fish)</italic> M: "Do you want to count? How many fish are there?" C: "One, two, three, four, five" (pointing to each item) M: "Five" (pointing to the last item in the count) C: "They're five!" (raising and opening his hand) M: "They're five" (raising and opening her hand) <italic>Dyad 8 (2.5 years) (2 lions)</italic> M: "Look! Lions. One and ... " (pointing to a lion) C: "Three" (pointing to the other lion) M: "Two (pointing to the lion simultaneously with her son). Like this (showing two fingers), two"</td></tr><tr><td><italic>Global</italic></td><td>Mothers or children quantify a set as if it were a plurality, without communicating an exact cardinal value <italic>(dyad 18)</italic></td><td><italic>Dyad 18 (4 years) (8 rabbits)</italic> C: "A lot of rabbits!" M: "Yes! A lot of rabbits"</td></tr></tbody></table> </ephtml> </p> <p>Few quantification utterances were registered in the 2.5-year-olds' group, either using number words together with finger gestures (<emph>M</emph><subs>Bimodal</subs> = 0.31, <emph>SE</emph> = 0.17), number words alone (<emph>M</emph><subs>Number words</subs> = 0.46, <emph>SE</emph> = 0.18), or global quantifications (<emph>M</emph><subs>Global</subs> = 0.77, <emph>SE</emph> = 0.20). Significant differences were found between bimodal and global quantifications [<emph>t</emph>(<reflink idref="bib12" id="ref82">12</reflink>) = −2.52, <emph>p</emph> =.027], but not between number words and bimodal [<emph>t</emph>(<reflink idref="bib12" id="ref83">12</reflink>) = 0.56, <emph>p</emph> =.584] or number words and global quantifications [<emph>t</emph>(<reflink idref="bib12" id="ref84">12</reflink>) = −1.07, <emph>p</emph> =.303].</p> <p>There was a clear increase in the number of quantifications in the 4-year-olds' group, particularly bimodal (<emph>M</emph><subs>Bimodal</subs> = 4.80, <emph>SE</emph> = 1.04) and global quantifications (<emph>M</emph><subs>Global</subs> = 3.20, <emph>SE</emph> = 0.71). However, there was not an increase in the quantification utterances with number words (<emph>M</emph><subs>Number words</subs> = 0.30, <emph>SE</emph> = 0.21). In this age group, bimodal and global quantifications differed from number words quantification [<emph>t</emph>(<reflink idref="bib9" id="ref85">9</reflink>) = −3.95, <emph>p</emph> =.003 and <emph>t</emph>(<reflink idref="bib9" id="ref86">9</reflink>) = −3.93, <emph>p</emph> =.003, respectively], without differences between the first two types of quantifications [<emph>t</emph>(<reflink idref="bib9" id="ref87">9</reflink>) = 1.80, <emph>p</emph> =.104]. Comparisons between age groups showed that 4-year-olds dyads used more bimodal and global quantifications than 2.5-year-olds dyads [<emph>t</emph>(<reflink idref="bib21" id="ref88">21</reflink>) = −4.83, <emph>p</emph> <.001 and <emph>t</emph>(<reflink idref="bib21" id="ref89">21</reflink>) = −3.67, <emph>p</emph> =.001, respectively], without differences in the use of number word quantification [<emph>t</emph>(<reflink idref="bib21" id="ref90">21</reflink>) = 1.80, <emph>p</emph> =.104].</p> <p>Despite the scarce use of number word quantifications in both age groups, its use is particularly interesting in the 4-year-olds' group because when mothers putted into play number words in order to communicate the cardinality of sets, they did so immediately after their children had counted the items (11/13 utterances, 85%). In this way, mothers seemed to make clear the connection between counting and cardinality, a milestone in children's numerical learning path.</p> <hd id="AN0158177556-12">Comparison</hd> <p>Mothers displayed two types of comparisons during the reading sessions, <emph>Direct</emph> and <emph>Indirect</emph>. Their frequencies were so low in the two age groups (2.5 years = 2 utterances; 4 years = 4 utterances) that we chose to illustrate this numerical activity (see Table 5), without statistical analysis of the data.</p> <p>Table 5. Comparison utterances: description and examples.</p> <p> <ephtml> <table><thead><tr><td>Comparison</td><td>Definition</td><td>Examples</td></tr></thead><tbody><tr><td><italic>Direct</italic></td><td>Mothers compare or encourage their children to compare two sets in the book based on: (1) their exact cardinal values (to determine which has more or less items) (<italic>dyad 10</italic>); or (2) their global set sizes <italic>(dyad 14)</italic></td><td><italic>Dyad 10 (2.5 years) (4 pigs and 5 fish)</italic> M: "Would you like to count?" (pointing to a pig) C: "One, two, three, and four" (pointing to with one-to-one correspondence between number words and objects and emphasizing the last word) M: "Very good!" M: "And what is here?" (pointing to a fish on the other page). "Fish. Oops, there is more here than on the other page, we have to count them more slowly ... " C: "One" (pointing to a fish) M: "One" C: "Two" [...] <italic>Dyad 14 (4 years) (6 chicks and 7 cats)</italic> M: "What is this?" C: "A lot of chicks and a lot of cats" M: "Many, many?" C: "Yes!" M: "Are there more animals than before?" C: "Yes"</td></tr><tr><td><italic>Indirect</italic></td><td>Mothers compare or encourage their children to compare the cardinal value of a set depicted in the book with another cardinal value not depicted in the book. These comparisons are always of quantitative equivalence <italic>(dyad 22)</italic></td><td><italic>Dyad 22 (4 years) (4 pigs)</italic> C: "There are four" (after counting the pigs together with their mother) M: "And how old are you?" C: "Four" (showing four fingers) M: "Very good! The same number of pigs as the years you are old!"</td></tr></tbody></table> </ephtml> </p> <hd id="AN0158177556-13">Types of Number Talk by Set Size</hd> <p>Research question 3 sought to investigate the extent to which numerical talk during picture book reading varied as a function of set sizes. A mixed measures ANOVA was conducted to examine the effects of Set Size (small, medium, and large) and Number Utterance Type (using the eight codes identified above) (within-subject factors), and Age Group (2.5 and 4 years) on the total number of numerical utterances. A main effect of Set Size was obtained [<emph>F</emph>(<reflink idref="bib2" id="ref91">2</reflink>, 42) = 7.41, <emph>p</emph> =.002, η<subs>p</subs><sups>2</sups> =.261], showing that, across types of numerical utterances and age groups, dyads talk more about small collections (1 to 3) (<emph>M</emph><subs>Small</subs> = 0.63, <emph>SE</emph> = 0.07) than medium collections (4 to 6) (<emph>M</emph><subs>Medium</subs> = 0.43, <emph>SE</emph> = 0.05) (Bonferroni, <emph>p</emph> =.017) and large ones (<emph>M</emph><subs>Large</subs> = 0.44, <emph>SE</emph> = 0.04) (<emph>p</emph> =.022), without differences between medium and large sets (<emph>p</emph> >.999).</p> <p>The ANOVA also revealed a Set Size x Number Utterance Type interaction [<emph>F</emph>(<reflink idref="bib14" id="ref92">14</reflink>, 294) = 7.91, <emph>p</emph> <.001, η<subs>p</subs><sups>2</sups> =.274], a non-significant Set Size x Age Group interaction [<emph>F</emph>(<reflink idref="bib2" id="ref93">2</reflink>, 42) = 0.18, <emph>p</emph> =.982, η<subs>p</subs><sups>2</sups> =.001], but a significant interaction between Set Size, Number Utterance Type and Age Group [<emph>F</emph>(<reflink idref="bib14" id="ref94">14</reflink>, 294) = 2.44, <emph>p</emph> =.003, η<subs>p</subs><sups>2</sups> =.104]. Within the 2.5-year-olds' group, follow-up comparisons only yielded an impact of set size in recognition of numerals, particularly when the dyads used the label "number" for any numeral: this kind of utterance was more frequent with small sets (<emph>M</emph><subs>Small</subs> = 0.76, <emph>SE</emph> = 0.22) than with medium (<emph>M</emph><subs>Medium</subs> = 0.07, <emph>SE</emph> = 0.13) (Bonferroni, <emph>p</emph> =.024) and large sets (<emph>M</emph><subs>Large</subs> = 0) (<emph>p</emph> =.006).</p> <p>Conversely, in the 4-year-olds' group, effects of the set sizes were registered in recognition of numerals, enumeration and quantification. Regarding recognition of numerals utterances, the use of the label "number" was more frequent with small sets (<emph>M</emph><subs>Small</subs> = 0.90, <emph>SE</emph> = 0.25) than with large ones (<emph>M</emph><subs>Large</subs> = 0) (Bonferroni, <emph>p</emph> =.005); the recognition of each specific "numeral" was also displayed more frequently with small sets (<emph>M</emph><subs>Small</subs> = 3.30, <emph>SE</emph> = 0.67) but, in this case, with significant differences with medium (<emph>M</emph><subs>Medium</subs> = 1.30, <emph>SE</emph> = 0.41) (<emph>p</emph> =.016) and large collections (<emph>M</emph><subs>Large</subs> = 1.10, <emph>SE</emph> = 0.29) (<emph>p</emph> =.008). Four-year-olds' dyads used cardinal enumeration with the three sets sizes but more often with medium (<emph>M</emph><subs>Medium</subs> = 2, <emph>SE</emph> = 0.34) and large sets (<emph>M</emph><subs>Large</subs> = 2, <emph>SE</emph> = 0.30) than with small sets (<emph>M</emph><subs>Small</subs> = 0.80, <emph>SE</emph> = 0.26) (<emph>p</emph>'s =.001 and.007, respectively). Finally, in quantification utterances, there was only an impact of set size in global quantifications: this type of utterance was higher with large sets (<emph>M</emph><subs>Large</subs> = 1.10, <emph>SE</emph> = 0.29) than with small ones (<emph>M</emph><subs>Small</subs> = 0.10, <emph>SE</emph> = 0.06) (<emph>p</emph> =.004).</p> <p>At last, Table 6 resumes follows up analyses exploring the effects of Set Size and Number Utterance Type between age groups. Four-year-olds' dyads used more enumerations with medium and large sets than 2.5-year-olds, both nominal and cardinal. The older age group used number words more frequently to communicate the cardinality of small, medium and large sets. Numeral labels were also brought into play by 4-year-olds more frequently, especially small (1–3) and large (7–9) numerals.</p> <p>Table 6. Numerical utterances types as a function of set size: comparisons by age group.</p> <p> <ephtml> <table><thead><tr><td>Utterance type x Set size</td><td>2.5 years <italic>M</italic></td><td>4 years <italic>M</italic></td><td><italic>p</italic><sup>a</sup></td></tr></thead><tbody><tr><td><italic>Nominal Enumeration</italic></td><td /><td /><td /></tr><tr><td>Medium sets</td><td>0.30</td><td>2</td><td>.057</td></tr><tr><td><italic>Cardinal Enumeration</italic></td><td /><td /><td /></tr><tr><td>Medium sets</td><td>0.30</td><td>2</td><td>.001</td></tr><tr><td>Large sets</td><td>0.07</td><td>2</td><td>.001</td></tr><tr><td><italic>Number Words Quantification</italic></td><td /><td /><td /></tr><tr><td>Small sets</td><td>0.30</td><td>1.30</td><td>.004</td></tr><tr><td>Medium sets</td><td>0.07</td><td>1</td><td>.017</td></tr><tr><td>Large sets</td><td>0.07</td><td>0.90</td><td>.016</td></tr><tr><td><italic>Numerals</italic></td><td /><td /><td /></tr><tr><td>Small sets</td><td>1.23</td><td>3.30</td><td>.030</td></tr><tr><td>Large sets</td><td>0.15</td><td>1.10</td><td>.026</td></tr></tbody></table> </ephtml> </p> <p>3 This table only presents the comparisons with <emph>p</emph> ≤.05. <sups>a</sups>Bonferroni's adjustment for multiple comparisons.</p> <hd id="AN0158177556-14">Discussion</hd> <p>The present study expanded on the extant shared picture book literature to examine how Argentinean pairs of mothers and their 2.5- and 4-year-old children read a book that contained explicit references to number concepts and skills. It added to previous works the use of a finer-grained analysis that enabled a detailed description of the multimodal framework in which numerical activities such as enumeration, quantification, recognition of numerals, and comparison arose. More importantly, the study set out to highlight whether and how children (especially those younger than 4 years of age) actively participated in reading interactions involving numbers, since prior research tended to focus almost exclusively on parental interventions (e.g., Mix et al., [<reflink idref="bib25" id="ref95">25</reflink>]; Uscianowski et al., [<reflink idref="bib34" id="ref96">34</reflink>]). The description and analysis of different numerical activities revealed that children co-constructed number meanings together with their mothers.</p> <p>Providing children with opportunities to engage in numerical conversations and practice numeracy skills contributes to their math achievement (Gunderson & Levine, [<reflink idref="bib14" id="ref97">14</reflink>]; Ramani et al., [<reflink idref="bib27" id="ref98">27</reflink>]). The counting-type picture book designed for this study was considered to be a math tool for families at home, since specific features were controlled to facilitate numerical elaborations (such as presenting numbers in an ascending sequence, without distractors on pages with items to be counted) (Ward et al., [<reflink idref="bib40" id="ref99">40</reflink>]). Dyads of both age groups engaged in a similar proportion of non-numerical elaborations; however, 4-year-olds dyads elaborated, communicated, and reflected more about numbers. In fact, despite the simple nature of the book (picture and number), all dyads of this age group talked about numbers. This finding contrasted with Mix et al. ([<reflink idref="bib25" id="ref100">25</reflink>]), who found that parents of 3.5-year-old children commented on non-numerical information much more frequently than on numerical one. Nevertheless, that prior study did not explicitly code when children provided numerical elaborations, which is a noticeable difference with our research. As can be seen here, particularly at 4 years of age, children contributed spontaneously to numerical utterances.</p> <p>Our purpose was not only to identify the numerical content of mother-child interactions but also the distinct ways in which dyads communicate and reflect on numbers, as a function of children's age and set size, with special emphasis on language and other semiotic modes. This purpose was reflected in the richness of the coding system we have developed, revealing different forms of recognizing numerals, enumerating items and quantifying sets, across and within age groups. For example, in the two groups, dyads elaborated information about numerals most of the time during the reading sessions. Nonetheless, different patterns of interaction were found. In the 2.5-year-olds' group, numerals were recognized and labeled by mothers and children as "numbers", thus discriminating this system from the other graphic systems, writing and drawing. Prior studies showed that the first discriminations between graphic systems appear around 3 years of age (Mix, [<reflink idref="bib23" id="ref101">23</reflink>]; Yamagata, [<reflink idref="bib41" id="ref102">41</reflink>]). In contrast, 4-year-olds dyads went a step ahead. After recognizing and discriminating the number system, mothers and children labeled each number symbol with its corresponding number word, especially small (1 to 3) and large (7 to 9) numerals.</p> <p>Another example of the different ways in which dyads expressed and reflected on numbers in the context of the same numerical activity could be observed in the quantification utterances. With age, a significant increase in quantifications was registered; however, this pattern was mainly due to a clear rise in bimodal quantifications, combining finger gestures and number words to communicate set sizes. Furthermore, a close inspection not only of how numerical information was shared but also what it was done for, showed that when 4-year-olds' mothers used number words, they did so immediately after their children had counted the items of a set. In this way, mothers seemed to make clear the connection between counting and cardinality (Mix et al., [<reflink idref="bib25" id="ref103">25</reflink>]).</p> <p>The only numerical activity displayed during the reading sessions with similar averages in both age groups was comparison. Naturalistic observations of parents and young children during daily activities at home have found that parents rarely involved their children in comparing quantities (Ramani et al., [<reflink idref="bib27" id="ref104">27</reflink>]; Susperreguy & Davis-Kean, [<reflink idref="bib33" id="ref105">33</reflink>]), a fact similar to the one reported here (but with a relatively small sample size, as we will discuss below). Given the relevance of comparison activities to early number development, future research could include counting-type picture books with a distribution of the collections that encourages comparisons between quantities (for example, not using an ascending or descending order of numbers). Another interesting strategy could be to train parents to pose questions about comparisons when interact with their children in reading sessions.</p> <p>Early number understanding may provide a context for the differences reported in the frequency and type of number talk at 2.5 and 4 years; it is also possible that mothers have adjusted their interventions according to their children's ages. These developmental differences could explain, for example, the increase of the attention to numbers in general and the focus on cardinal enumeration of medium (4 to 6) and large (7 to 9) collections and number word quantification (of the three set sizes) in the older group. However, mothers' beliefs about their children's number skills may also have an influence on shared reading. Although parents' beliefs and attitudes about early math learning have been evaluated in several studies (e.g., Blevins-Knabe et al., [<reflink idref="bib4" id="ref106">4</reflink>]; Missall et al., [<reflink idref="bib22" id="ref107">22</reflink>]), future research can investigate this further by obtaining a measure of these beliefs and exploring their relationship with maternal behaviors during reading.</p> <p>There were several limitations of the study. One limitation was that the sample size was relatively small, it was overwhelmingly middle-class, and mothers had at least a high school degree. Research on math book shared reading should represent diverse populations, because if book accessibility and reading practices vary within and across cultures, this knowledge may insure that specific reading recommendations given to parents are culturally relevant. Families of varying social and educational contexts may have unique practices associated with their reading behaviors in general, and their ways of elaborating numerical information in particular (Vandermaas-Peeler et al., [<reflink idref="bib37" id="ref108">37</reflink>]). They may also use different semiotic modes (visual, spoken, gestural, and others) which realize communication and reflection on numbers in distinct ways – making the choice of a mode a central aspect of interaction and meaning. Further studies are needed that include a bigger Spanish-speaking sample and a diversity of socio-educational contexts within that culture. Additional mother characteristics that can be incorporated in future studies include mothers' math abilities and enjoyment of math, which have been associated with aspects of the home numerical environment in previous studies (e.g., Missall et al., [<reflink idref="bib22" id="ref109">22</reflink>]; Skwarchuk, [<reflink idref="bib31" id="ref110">31</reflink>]).</p> <p>Another suggestion for future research may be to examine father-child dyads in addition to mother-child dyads. This inclusion would offer an informative and interesting opportunity to examine any differences in mothers' and fathers' language while reading a counting book with their young children, as well as an occasion to explore how the unique characteristics of father-child dyads are related to children's mathematical skills at varying ages.</p> <p>A further limitation of the current research was that mother-child dyads were only observed reading one picture book with explicit numerical content. Future studies can incorporate a range of books from basic counting books, such as the one presented here, to those with a narrative structure and/or variations in how number concepts were presented in the illustrations in order to see how mothers address the numerical content based on the type of math book. The ways parents use counting books may depend, among other factors, on the particular counting books they use (Gaylord et al., [<reflink idref="bib11" id="ref111">11</reflink>]). Furthermore, it is possible that the outcomes will be influenced by children's interest in the book: Perhaps children who were more interested and engaged would prompt their mothers to provide more support or discuss more the number concepts in the book than disinterested children. The role of children's interest in books with distinct characteristics should be explored in futures studies.</p> <p>In addition, although this study identified how mothers supported children's numerical participation by sharing different numerical activities (enumeration, quantification, comparison, and recognition of numerals), with variations within activities, it did not address which type of maternal supports were more effective in advancing children's number knowledge. Longitudinal studies could help clarify whether certain types of support are advantageous by capturing how mothers put into play numerical information at various time points and measuring children's later numerical skills. Alternatively, studies in which mothers are trained to provide certain types of supports during counting-type picture book reading can help uncover which supportive responses might predict number outcomes. This will be especially important with some number inputs rarely put into play during the reading sessions, such as comparisons or mappings between sets and numerals, for example.</p> <p>Children learn mathematics from meaningful contexts, and teaching should build on the informal knowledge children have acquired both before starting school and outside school hours. It is thus essential that intervention programs and policies promote and support aspects of adult-child interaction that have been empirically demonstrated to boost early number learning. In this sense, results of the current study have implications for researchers and practitioners who create instructional materials and strategies for families and teachers. Shared picture book reading is a simple, low-cost, and effective tool. By knowing the various ways that mothers and/or caregivers are already using books, materials can use a strength-based approach and build on what parents belonging to different socio-educational backgrounds are already doing to support their children's number knowledge while suggesting additional supportive strategies parents may not have considered. For example, in the present study, 2.5-year-olds' mothers tended to label numbers while 4-year-old children and their mothers spent more time focusing on enumeration and cardinality. Parents of children under 4 years can be provided with case examples to illustrate the kinds of numerical activities children are likely to involve during shared reading of counting books.</p> <p>In the current study, mothers were allowed to choose the setting (home or preschool) in which they engaged in book reading with their children. As carried out in the study, preschools could offer parents an opportunity to read books with their children at drop off and pick up. Preschools could also allow families to check out books to take home to further children's opportunities to learn from dyadic book reading. This could be especially important for counting-type picture books since, for example, in the present sample the families had very few of these books.</p> <p>Workshops or materials intended for parents can demonstrate that picture books may be a fun and engaging way to facilitate young children's exploration and understanding of numbers. In different socio-educational contexts, efforts can be made to help parents realize the potential of reading for math learning. For instance, parents and/or caregivers could be invited to preschools in order to share with their children specific activities that promote positive math interactions with books.</p> <p>In sum, this study suggests that a careful examination of the social and multimodal contexts in which numerical cognition takes place is important. This work provides crucial insights on the active role young children play in numerical problems that emerge in an everyday life practice as picture book reading. A fine-grained approach that captures how and what for number is communicated and elaborated in daily interactions is important when investigating the processes involved in numerical cognition, and even more so when seeking ways to support and improve numerical performance in educational contexts.</p> <hd id="AN0158177556-15">Disclosure Statement</hd> <p>No potential conflict of interest was reported by the author(s).</p> <ref id="AN0158177556-16"> <title> Note </title> <blist> <bibl id="bib1" idref="ref1" type="bt">1</bibl> <bibtext> Semiotic mediation refers to cultural resources of signs that play a crucial role in mediating individuals' construction of knowledge during the course of ontogenetic development.</bibtext> </blist> </ref> <ref id="AN0158177556-17"> <title> References </title> <blist> <bibtext> Anders, Y., Rossbach, H.-G., Weinert, S., Ebert, S., Kuger, S., Lehrl, S., & Von Maurice, J (2012). 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Early Childhood Research Quarterly, 19 (1), 82 – 98. https://doi.org/10.1016/j.ecresq.2004.01.001</bibtext> </blist> </ref> <aug> <p>By Analía Salsa; María Belén Gariboldi and Jimena Rodríguez</p> <p>Reported by Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib39" firstref="ref2"></nolink> <nolink nlid="nl2" bibid="bib20" firstref="ref6"></nolink> <nolink nlid="nl3" bibid="bib21" firstref="ref7"></nolink> <nolink nlid="nl4" bibid="bib38" firstref="ref8"></nolink> <nolink nlid="nl5" bibid="bib19" firstref="ref9"></nolink> <nolink nlid="nl6" bibid="bib13" firstref="ref10"></nolink> <nolink nlid="nl7" bibid="bib27" firstref="ref11"></nolink> <nolink nlid="nl8" bibid="bib34" firstref="ref12"></nolink> <nolink nlid="nl9" bibid="bib36" firstref="ref13"></nolink> <nolink nlid="nl10" bibid="bib16" firstref="ref14"></nolink> <nolink nlid="nl11" bibid="bib15" firstref="ref16"></nolink> <nolink nlid="nl12" bibid="bib18" firstref="ref17"></nolink> <nolink nlid="nl13" bibid="bib35" firstref="ref18"></nolink> <nolink nlid="nl14" bibid="bib17" firstref="ref19"></nolink> <nolink nlid="nl15" bibid="bib37" firstref="ref20"></nolink> <nolink nlid="nl16" bibid="bib42" firstref="ref21"></nolink> <nolink nlid="nl17" bibid="bib10" firstref="ref26"></nolink> <nolink nlid="nl18" bibid="bib25" firstref="ref27"></nolink> <nolink nlid="nl19" bibid="bib23" firstref="ref29"></nolink> <nolink nlid="nl20" bibid="bib26" firstref="ref30"></nolink> <nolink nlid="nl21" bibid="bib28" firstref="ref31"></nolink> <nolink nlid="nl22" bibid="bib24" firstref="ref34"></nolink> <nolink nlid="nl23" bibid="bib29" firstref="ref35"></nolink> <nolink nlid="nl24" bibid="bib14" firstref="ref40"></nolink> <nolink nlid="nl25" bibid="bib40" firstref="ref48"></nolink> <nolink nlid="nl26" bibid="bib30" firstref="ref50"></nolink> <nolink nlid="nl27" bibid="bib12" firstref="ref51"></nolink> <nolink nlid="nl28" bibid="bib32" firstref="ref52"></nolink> <nolink nlid="nl29" bibid="bib55" firstref="ref67"></nolink> <nolink nlid="nl30" bibid="bib51" firstref="ref68"></nolink> <nolink nlid="nl31" bibid="bib41" firstref="ref102"></nolink> <nolink nlid="nl32" bibid="bib33" firstref="ref105"></nolink> <nolink nlid="nl33" bibid="bib22" firstref="ref107"></nolink> <nolink nlid="nl34" bibid="bib31" firstref="ref110"></nolink> <nolink nlid="nl35" bibid="bib11" firstref="ref111"></nolink>
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  Data: Multimodal Numerical Interactions during Mother-Child Picture Book Reading
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  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Foreign+Countries%22">Foreign Countries</searchLink><br /><searchLink fieldCode="DE" term="%22Mothers%22">Mothers</searchLink><br /><searchLink fieldCode="DE" term="%22Preschool+Children%22">Preschool Children</searchLink><br /><searchLink fieldCode="DE" term="%22Picture+Books%22">Picture Books</searchLink><br /><searchLink fieldCode="DE" term="%22Computation%22">Computation</searchLink><br /><searchLink fieldCode="DE" term="%22Numbers%22">Numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Interpersonal+Communication%22">Interpersonal Communication</searchLink><br /><searchLink fieldCode="DE" term="%22Age+Differences%22">Age Differences</searchLink><br /><searchLink fieldCode="DE" term="%22Reading+Strategies%22">Reading Strategies</searchLink><br /><searchLink fieldCode="DE" term="%22Interaction%22">Interaction</searchLink><br /><searchLink fieldCode="DE" term="%22Verbal+Communication%22">Verbal Communication</searchLink><br /><searchLink fieldCode="DE" term="%22Number+Concepts%22">Number Concepts</searchLink>
– Name: Subject
  Label: Geographic Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Argentina%22">Argentina</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1080/10409289.2021.1936375
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 1040-9289<br />1556-6935
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Research Findings: The focus of the current study was on the frequency and type of number talk of 2.5- and 4-year-old Argentinean children and their mothers (N = 23 dyads) in shared counting-type picture book reading. The book included sets of animals in ascending order (from 1 to 9), with their corresponding numerals and the animals' written names. A finer-grained approach was used for identifying four types of numerical utterances (enumeration, quantification, comparison, and recognition of numerals); for each category, a subset of codes was created to describe how dyads used numerical information for different purposes, intertwining different semiotic modes of communication and reflection with and about numbers. Results showed distinct ways in which mothers and children express and elaborate numerical information, as a function of children's age and set size. Practice or Policy: Shared picture book reading is a simple, low-cost, and effective tool. The results can contribute to the design of books, intervention programs and policies that focus on multimodal contexts for early mathematical development, both in the family and educational environment, with a special emphasis on young children's active participation.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2022
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1357595
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1357595
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/10409289.2021.1936375
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 16
        StartPage: 997
    Subjects:
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Mothers
        Type: general
      – SubjectFull: Preschool Children
        Type: general
      – SubjectFull: Picture Books
        Type: general
      – SubjectFull: Computation
        Type: general
      – SubjectFull: Numbers
        Type: general
      – SubjectFull: Interpersonal Communication
        Type: general
      – SubjectFull: Age Differences
        Type: general
      – SubjectFull: Reading Strategies
        Type: general
      – SubjectFull: Interaction
        Type: general
      – SubjectFull: Verbal Communication
        Type: general
      – SubjectFull: Number Concepts
        Type: general
      – SubjectFull: Argentina
        Type: general
    Titles:
      – TitleFull: Multimodal Numerical Interactions during Mother-Child Picture Book Reading
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Salsa, Analía
      – PersonEntity:
          Name:
            NameFull: Gariboldi, María Belén
      – PersonEntity:
          Name:
            NameFull: Rodríguez, Jimena
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2022
          Identifiers:
            – Type: issn-print
              Value: 1040-9289
            – Type: issn-electronic
              Value: 1556-6935
          Numbering:
            – Type: volume
              Value: 33
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: Early Education and Development
              Type: main
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