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Parent-Child Math Talk and Early Math Interest: Comparing the Effects of Written versus Hands-On Materials

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Title: Parent-Child Math Talk and Early Math Interest: Comparing the Effects of Written versus Hands-On Materials
Language: English
Authors: Hsin-Hui Huang (ORCID 0000-0002-8121-5665), Peiyi Lee
Source: International Journal of Early Years Education. 2026 34(1):76-90.
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: 15
Publication Date: 2026
Document Type: Journal Articles
Reports - Research
Descriptors: Instructional Materials, Foreign Countries, Student Interests, Mathematics Instruction, Parent Child Relationship, Preschool Children, Childhood Interests, Manipulative Materials, Play, Written Language, Communication (Thought Transfer), Mathematical Concepts
Geographic Terms: Taiwan (Taipei)
DOI: 10.1080/09669760.2024.2389820
ISSN: 0966-9760
1469-8463
Abstract: This study investigated the impact of written and hands-on teaching materials on parent-child math talk and children's interest in mathematics. Thirty parents and their preschool children participated in two play sessions, one using written material and the other using hands-on material, each lasting 12 min. At the end of each session, the children's interest levels were assessed, and the frequency of math-related conversations was analysed. Regardless of the materials used, discussions primarily revolved around fundamental numerical concepts, with little mention of practical measurement units and conventional nominatives or number comparisons involving the application of mental representation. Ordinal and division concepts were only mentioned by parents in the written scenario rather than in the hands-on one. Overall, using written material led to doubling math discourse compared to hands-on material. However, children showed slightly higher interest levels in the hands-on scenario, where parent-child math talk categories also exhibited greater synchrony. The study highlights the complementary nature of written and hands-on teaching materials and provides recommendations for their future application.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1504024
Database: ERIC
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  Value: <anid>AN0192005932;54r01mar.26;2026Mar06.00:45;v2.2.500</anid> <title id="AN0192005932-1">Parent–child math talk and early math interest: comparing the effects of written versus hands-on materials </title> <p>This study investigated the impact of written and hands-on teaching materials on parent–child math talk and children's interest in mathematics. Thirty parents and their preschool children participated in two play sessions, one using written material and the other using hands-on material, each lasting 12 min. At the end of each session, the children's interest levels were assessed, and the frequency of math-related conversations was analysed. Regardless of the materials used, discussions primarily revolved around fundamental numerical concepts, with little mention of practical measurement units and conventional nominatives or number comparisons involving the application of mental representation. Ordinal and division concepts were only mentioned by parents in the written scenario rather than in the hands-on one. Overall, using written material led to doubling math discourse compared to hands-on material. However, children showed slightly higher interest levels in the hands-on scenario, where parent–child math talk categories also exhibited greater synchrony. The study highlights the complementary nature of written and hands-on teaching materials and provides recommendations for their future application.</p> <p>Keywords: Math talk; math interest; written material; hands-on material; dyadic synchrony</p> <hd id="AN0192005932-2">Introduction</hd> <p>Math talk refers to using general and math language to conduct math-related discussions (Ramani et al. [<reflink idref="bib21" id="ref1">21</reflink>]; Susperreguy and Davis-Kean [<reflink idref="bib25" id="ref2">25</reflink>]). Adult–child math talk facilitates children's development of math language and skills (Levine et al. [<reflink idref="bib18" id="ref3">18</reflink>]; Ramani et al. [<reflink idref="bib21" id="ref4">21</reflink>]; Susperreguy and Davis-Kean [<reflink idref="bib25" id="ref5">25</reflink>]). Since some adults rarely express math-related vocabulary in natural contexts (Ramani et al. [<reflink idref="bib21" id="ref6">21</reflink>]; Susperreguy and Davis-Kean [<reflink idref="bib25" id="ref7">25</reflink>]), many studies have used teaching materials, such as picture books, toys, and board games, to elicit mathematical discussions (DePascale, Prather, and Ramani [<reflink idref="bib7" id="ref8">7</reflink>]; Huang [<reflink idref="bib15" id="ref9">15</reflink>]; Purpura et al. [<reflink idref="bib20" id="ref10">20</reflink>]).</p> <p>Two important conclusions emerge from the study of adult–child math talk. One is that specific categories of adult mathematical discourse (e.g. cardinality, ordinal relations, and conventional nominatives) can predict children's mathematical language and skills (Boonen, Kolkman, and Kroesbergen [<reflink idref="bib4" id="ref11">4</reflink>]; Levine et al. [<reflink idref="bib18" id="ref12">18</reflink>]; Purpura et al. [<reflink idref="bib20" id="ref13">20</reflink>]; Ramani et al. [<reflink idref="bib21" id="ref14">21</reflink>]). However, the interactive materials or contexts used in these studies vary, prompting different contents of the mathematical discourse. Currently, there is no research comparing the links between teaching materials and mathematical discourse. Investigating this connection in detail would aid in designing appropriate mathematical language environments.</p> <p>Another important conclusion is that there is a high correlation between the frequency of mathematical speech in adult–child conversations (Huang [<reflink idref="bib15" id="ref15">15</reflink>]; Ramani et al. [<reflink idref="bib21" id="ref16">21</reflink>]). This association can be considered an indicator of synchrony, which refers to the dynamic and reciprocal verbal and non-verbal communication and emotional behaviour between two interacting partners over time (Leclère et al. [<reflink idref="bib16" id="ref17">16</reflink>]). Synchronicity between parents and children is significantly related to positive child development, including cognition, language, intelligence, and adaptation (Harrist and Waugh [<reflink idref="bib13" id="ref18">13</reflink>]; Leclère et al. [<reflink idref="bib16" id="ref19">16</reflink>]).</p> <p>Parent–child synchrony can be gauged through observation-based scales or by measuring behavioural and physiological indicators in interactions (Leclère et al. [<reflink idref="bib16" id="ref20">16</reflink>]). Given preschoolers' advancement in verbal expression, investigating the alignment of mathematical speech categories between parents and children in interactive settings offers insights into their synchrony. This study aims to expand the investigation of parent–child mathematical discourse by examining dyadic synchrony across different teaching materials. It will shed light on how these materials influence the degree of active dialogue, content matching, and focus on conversation topics.</p> <p>In addition, this study aims to investigate a less explored aspect of mathematical performance in the preschool stage: mathematical interest. 'Interest' manifests motivations that guide student learning behaviour and effort (Wigfield and Wentzel [<reflink idref="bib30" id="ref21">30</reflink>]). Individuals more interested in a task tend to engage and derive personal meaning from it for extended periods. Understanding the impact of teaching materials on children's math interests can assist in selecting the appropriate intervention tools to increase children's motivation and enrich mathematical language environment.</p> <hd id="AN0192005932-3">Teaching materials and math talk</hd> <p>The constructive alignment framework emphasises the correspondence of learning objectives, teaching methods and activities, and assessment as three essential elements to guide educators in designing effective curricula (Biggs [<reflink idref="bib3" id="ref22">3</reflink>]). Teaching materials serve as vital mediums within learning activities. The present study classified teaching materials as written and hands-on materials. Written materials refer to content expressed in written form, such as textbooks, handouts, worksheets, activity sheets, and storybooks. Hands-on materials refer to instructional resources or objects that require physical interaction and manipulation by learners, fostering practical engagement and experiential learning, such as blocks, puzzles, and board games. Both written and hands-on materials are used at home and in preschools, but the frequency of using written materials is relatively lower (Cave [<reflink idref="bib5" id="ref23">5</reflink>]; Soto-Calvo et al. [<reflink idref="bib24" id="ref24">24</reflink>]).</p> <p>The use of teaching materials affects the occurrence of adult–child math talk. Compared to everyday activities such as quiet reading, cooking, and shopping, parents engage in more parent–child math talk when they use picture books, toy blocks, or worksheets (Anderson [<reflink idref="bib1" id="ref25">1</reflink>]; Anderson, Anderson, and Shapiro [<reflink idref="bib2" id="ref26">2</reflink>]). The format and characteristics of teaching materials play a crucial role in how children are involved. Research indicates that children participate in more math-related discussions while playing pretend games than reading storybooks (Vandermaas-Peeler et al. [<reflink idref="bib29" id="ref27">29</reflink>]). Moreover, children initiate more math talk during grocery store play than post office play (Vandermaas-Peeler et al. [<reflink idref="bib29" id="ref28">29</reflink>]; Vandermaas-Peeler, Nelson, and Bumpass [<reflink idref="bib28" id="ref29">28</reflink>]).</p> <p>Although using certain teaching materials increased the likelihood that parents and children engaged in mathematical discussions, most math talk was confined to fundamental concepts such as counting and number recognition (Ramani et al. [<reflink idref="bib21" id="ref30">21</reflink>]; Susperreguy and Davis-Kean [<reflink idref="bib25" id="ref31">25</reflink>]). More advanced math concepts, such as number comparison or adding and subtracting, are rarely addressed (Vandermaas-Peeler et al. [<reflink idref="bib26" id="ref32">26</reflink>]; Vandermaas-Peeler, Ferretti, and Loving [<reflink idref="bib27" id="ref33">27</reflink>]).</p> <p>Guidance on teaching materials can address this issue. Vandermaas-Peeler et al. ([<reflink idref="bib26" id="ref34">26</reflink>]) found that providing recipe cards with mathematical activity suggestions increased discussions on addition, subtraction, and shape identification. Without such guidance, the control group had fewer spontaneous mathematical discussions despite the cooking activity involving various mathematical concepts (Vandermaas-Peeler et al. [<reflink idref="bib26" id="ref35">26</reflink>]). Therefore, it is worth investigating whether teaching materials with specific task guidelines, such as workbooks, can broaden the scope of adult verbalisation in mathematics.</p> <hd id="AN0192005932-4">Teaching materials and math interest</hd> <p>Interest in mathematics correlates with math skills, leading to a mutually beneficial association and a successful learning cycle (Fisher et al. [<reflink idref="bib11" id="ref36">11</reflink>]). A positive attitude toward math can increase interest in math activities and improve math skills. Excelling in math can further boost interest in the subject. A review by Schiefele, Krapp, and Winteler ([<reflink idref="bib22" id="ref37">22</reflink>]) revealed that the association becomes more pronounced with increasing grade levels. Therefore, considering the factors affecting early math proficiency, including interest in math in the equation, is essential.</p> <p>Children begin to exhibit an interest in mathematics from a young age, which is related to the context of play. Several studies by Vandermaas-Peeler et al. indicate that parents and young children are more actively engaged in numeracy exchanges during pretend play than when reading stories; furthermore, in role-playing games, children initiate more mathematical talk during grocery store play than post-office play (Vandermaas-Peeler et al. [<reflink idref="bib29" id="ref38">29</reflink>]; Vandermaas-Peeler, Nelson, and Bumpass [<reflink idref="bib28" id="ref39">28</reflink>]). These findings suggest that interest in mathematics may be related to the type of material being used and warrant further investigation.</p> <hd id="AN0192005932-5">Current study</hd> <p>To date, no studies have investigated the role of teaching material types in children's math interest or parent–child math talk. This study represents a critical next step in establishing the optimal intervention design for mathematical learning in home and preschool settings. Specifically, our research investigates whether the frequency and categories of parent–child math talk and children's math interest differ when using written or hands-on materials. Additionally, we explore the dyadic synchrony of math talk in both written and hands-on contexts.</p> <hd id="AN0192005932-6">Methods</hd> <p></p> <hd id="AN0192005932-7">Participants</hd> <p>After seeking permission from three preschools in New Taipei City, Taiwan, the researchers asked preschool teachers to help send recruitment notices to parents of kindergarteners who had been enroled for one year or more. Parents were contacted to explain the study process and ethical principles, and informed consent was obtained. A total of 30 dyads of parents (26 mothers and four fathers) and children (14 girls and 16 boys) participated in the study. The mean child age was 70 months (standard deviation [<emph>SD</emph>] = 3.4, range = 65–75). Among parents, 11 had a vocational school diploma, 16 had a bachelor's degree, and three had a graduate school or higher. The sample size was determined based on power analysis, which was conducted using G*Power (3.1; Faul et al. [<reflink idref="bib10" id="ref40">10</reflink>]). The results indicated that a sample with <emph>N</emph> = 27 was required to achieve 80% power for detecting a medium effect at a significance level of <emph>α</emph> =.05 for paired t-tests (one-tailed).</p> <hd id="AN0192005932-8">Measures</hd> <p></p> <hd id="AN0192005932-9">Math teaching materials</hd> <p>For comparison purposes, written and hands-on materials should convey similar mathematical concepts but differ only in format. As such, the present study selected a commercially available mathematics product for young children, the 'Hsin-Yi New Math Treasure Chest' (Hsin Yi Foundation [<reflink idref="bib14" id="ref41">14</reflink>]). The product, featuring a considerable quantity of picture books, teaching aids, etc., and sold as a complete set, is therefore not commonly found in typical households. The three preschools in the study did not have them, and parents did not report that their children had played with them. Therefore, it is assumed that the children were not exposed to the materials before the study.</p> <p>The product was developed based on the four domains of mathematics: number, quantity, logical relation, and shapes and space, and is suitable for children 3–8 years of age. The product comprises 13 picture books, 15 manipulative toys, 10 workbooks, a parent guide, and a VCD demonstration.</p> <p>The hands-on material was selected from the 15 manipulative toys. Selection criteria included covering number and quantity and having the most open-ended play possibilities. Two experts with 12 and 20 years of experience in preschool teaching were consulted, and the final decision was made to use 'Cubes' as hands-on teaching material for this study. The Cubes comprise 155 three-dimensional cubes (2 × 2 × 2 cm<sups>3</sups>) in five colours, a square play tray (21 × 21 cm<sups>2</sups>) that could hold 100 cubes, 10 bar-shaped slots that could each have 1–10 cubes, and five types of play cards that provide references to organise the cubes in various ways. The researchers also designed eight number and quantity games and produced a guide with illustrations for parents and children to refer to.</p> <p>Written material was selected from the 10 workbooks. These workbooks have pages with math questions suitable for preschoolers, each with a picture and brief text. For example, a picture might show a row of books, and the question would ask children to find the third book with a specific title and colour it green. Two experts selected 10 pages and bound them into a booklet as written material based on the criteria that covered number and quantity, had questions corresponding to the games in the hands-on material, and required dialogue to complete.</p> <p>A two-way cross-check was performed using the coding schema developed by Susperreguy and Davis-Kean ([<reflink idref="bib25" id="ref42">25</reflink>]) to check whether the two materials cover the nine categories of mathematical discourse. The results showed that both teaching materials could allow participants to discuss most categories, except conventional nominatives. This category is retained, as conventional nominatives refer to numerical labelling of objects or dates, which may occur in general conversation and not necessarily in mathematical contexts.</p> <p>The Cubes and the play guide were neatly arranged on a tray for clear visibility. Each parent–child dyad received a workbook, collected after use to maintain result integrity and prevent peer-sharing interference.</p> <hd id="AN0192005932-10">Math interest assessment</hd> <p>The Math Interest Scale, adapted from Lerkkanen et al. ([<reflink idref="bib17" id="ref43">17</reflink>]), consisted of three practice items and two formal items. The practice items, 'Do you like ... (ice cream/snakes/onions),' assessed children's ability to express preferences. The formal items assessed their interest levels in the activity, such as 'Do you like the activity just now?' and 'Do you like to do the same activity at home?' Children rated their enjoyment using a scale of five faces ranging from 'did not like it at all' (1 point) to 'liked it very much' (5 points). The sum of their responses to the formal items indicated overall interest in the activity, with higher scores reflecting greater interest. Lerkkanen et al. ([<reflink idref="bib17" id="ref44">17</reflink>]) reported a reliability of.72 for this scale.</p> <hd id="AN0192005932-11">Math talk coding schema</hd> <p>We adopted the math talk coding schema that Susperreguy and Davis-Kean ([<reflink idref="bib25" id="ref45">25</reflink>]) developed to analyse transcripts. This coding system, centring on numeracy concepts, demonstrated a high interrater agreement (intraclass correlation coefficient =.99, range =.92–.99). Table 1 provides detailed definitions and examples of the nine categories of math talk.</p> <p>Table 1. Math talk coding categories.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td>Categories</td><td>Definition and example</td></tr></thead><tbody><tr><td>Number recognition</td><td>Referring to numbers, reading numerals on paper and in other forms of media, recognising names of written numbers when seen, or writing numbers. <italic>Example: (Point at the text) This is three.</italic></td></tr><tr><td>Cardinal values</td><td>Mentioning or asking for the number of objects immediately without counting. <italic>Example: Please give me two cubes.</italic></td></tr><tr><td>Counting</td><td>Counting objects or listing numbers in increasing order of regular intervals. <italic>Example: Please count how many apples are here.</italic></td></tr><tr><td>Adding/subtracting</td><td>Performing or asking for addition and subtraction calculations using counting-based strategies. <italic>Example: How much do two plus two equal?</italic></td></tr><tr><td>Ordinal numbers</td><td>Using ordinal numbers, such as first, second, etc. <italic>Example: This is the first one; this is the second one.</italic></td></tr><tr><td>Division</td><td>Performing or asking to perform division calculations or using fractional values or percentages. <italic>Example: What is four divided by two?</italic></td></tr><tr><td>Units of measure</td><td>Using numbers to refer to units of measure. <italic>Example: (Point to the thermometer on the wall) To what degree is it?</italic></td></tr><tr><td>Conventional nominatives</td><td>Using numbers as labels for things or dates. <italic>Example: Today is 8 July.</italic></td></tr><tr><td>Number comparisons</td><td>Comparing numbers in sequence. <italic>Example: What is the number after five?</italic></td></tr></tbody></table> </ephtml> </p> <p>The dialogue between parents and children in the two play sessions was transcribed at the utterance level and coded according to the definitions in Table 1. An utterance is a sequence of words before or after pausing or conversational turns (Eason and Ramani [<reflink idref="bib9" id="ref46">9</reflink>]; Hanner et al. [<reflink idref="bib12" id="ref47">12</reflink>]). Each category of math talk was coded once per utterance, but multiple codes could be assigned. For example, 'one, two, three, there are three elephants' is coded for counting and cardinal values. Two coders independently coded 25% of the data, achieving an intercoder reliability of.89 (Cronbach's alpha). Any coding disagreements were resolved through discussion.</p> <hd id="AN0192005932-12">Procedure</hd> <p>The study was conducted in an unoccupied classroom on a prearranged date with the parents. An experimenter explained the procedure for two play sessions, and then the children were directed to a specific corner to read storybooks while the parents completed a brief survey on background information. After completing the form, the parents were directed to a preparation area where two types of teaching materials were introduced. The experiment was carried out on a table with blank sheets and pencils. Parents were reminded two minutes before the end of each 12-minute session.</p> <p>Following the explanation, parents had time to familiarise themselves with the two teaching materials, and the experimenter recorded video sessions while assessing the children's interest level at the end of each session. Half of the parent–child dyads started with hands-on material, while the other half began with written material. Finally, each child received a toy as a token of gratitude for their participation.</p> <hd id="AN0192005932-13">Data processing and analysis</hd> <p>The recordings from the two play sessions were transcribed into verbatim scripts and analysed at the utterance level. Descriptive statistics, including means (<emph>Ms</emph>) and <emph>SDs,</emph> were calculated for each category of math talk. Additionally, <emph>Ms</emph> and <emph>SD</emph>s of children's math interests were determined during interactions with written and hands-on materials.</p> <p>Paired sample <emph>t-</emph>tests were performed to determine potential differences in parent and child math talk and child math interest according to the teaching material used. Using Pearson's correlation coefficients, the interrelations between parent math talk, child math talk, and child math interest were calculated separately for written and hands-on contexts. Finally, Fisher's <emph>z</emph>-tests were used to compare correlation coefficients, evaluating whether associations varied depending on the types of teaching material.</p> <hd id="AN0192005932-14">Results</hd> <p></p> <hd id="AN0192005932-15">Descriptive statistics</hd> <p>Table 2 shows descriptive statistics and paired sample <emph>t-</emph>tests for parent math talk, child math talk, and child math interest in scenarios involving written and hands-on teaching materials. Parents and children frequently referred to number recognition, cardinal values, counting, and adding and subtracting in both scenarios. Categories of units of measure, conventional nominatives, and number comparisons were rarely mentioned in either scenario. Parents' ordinal numbers and division speech occurred more frequently in the written scenario. The children's mean math interest score in the hands-on scenario was 8.93 (<emph>SD</emph> = 1.36), slightly higher than that of the written scenario (<emph>M </emph>= 8.33, <emph>SD</emph> = 1.47).</p> <p>Table 2. Descriptive statistics and paired sample <emph>t</emph>-tests of math talk and math interest.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>Written</td><td>Hands-on</td><td><italic>t</italic></td><td><italic>d</italic></td></tr><tr><td><italic>M</italic></td><td><italic>SD</italic></td><td><italic>M</italic></td><td><italic>SD</italic></td></tr></thead><tbody><tr><td>Parent math talk</td></tr><tr><td> Number recognition</td><td char=".">11.93</td><td char=".">14.01</td><td char=".">6.30</td><td char=".">6.96</td><td char=".">2.84**</td><td char=".">0.51</td></tr><tr><td> Cardinal values</td><td char=".">8.13</td><td char=".">9.86</td><td char=".">5.77</td><td char=".">5.19</td><td char=".">1.32</td><td char=".">0.30</td></tr><tr><td> Counting</td><td char=".">7.83</td><td char=".">8.00</td><td char=".">3.30</td><td char=".">4.04</td><td char=".">2.93**</td><td char=".">0.72</td></tr><tr><td> Adding/subtracting</td><td char=".">6.53</td><td char=".">5.13</td><td char=".">6.13</td><td char=".">9.44</td><td char=".">0.21</td><td char=".">0.05</td></tr><tr><td> Ordinal numbers</td><td char=".">2.67</td><td char=".">2.92</td><td char=".">0.93</td><td char=".">1.86</td><td char=".">3.02**</td><td char=".">0.71</td></tr><tr><td> Division</td><td char=".">7.30</td><td char=".">6.87</td><td char=".">0.17</td><td char=".">0.65</td><td char=".">5.55***</td><td char=".">1.46</td></tr><tr><td> Units of measure</td><td char=".">0.73</td><td char=".">1.48</td><td char=".">0.20</td><td char=".">0.55</td><td char=".">1.89<xref ref-type="table-fn" rid="tfn1">+</xref></td><td char=".">0.48</td></tr><tr><td> Conventional nominatives</td><td char=".">0.60</td><td char=".">1.40</td><td char=".">0.30</td><td char=".">0.88</td><td char=".">1.27</td><td char=".">0.26</td></tr><tr><td> Number comparisons</td><td char=".">0.13</td><td char=".">0.43</td><td char=".">0.17</td><td char=".">0.59</td><td char=".">–0.24</td><td char=".">–0.08</td></tr><tr><td> Total</td><td char=".">47.10</td><td char=".">25.20</td><td char=".">24.57</td><td char=".">18.99</td><td char=".">4.94***</td><td char=".">1.01</td></tr><tr><td>Child math talk</td></tr><tr><td> Number recognition</td><td char=".">10.90</td><td char=".">9.57</td><td char=".">6.60</td><td char=".">8.54</td><td char=".">2.97**</td><td char=".">0.47</td></tr><tr><td> Cardinal values</td><td char=".">7.77</td><td char=".">10.72</td><td char=".">4.47</td><td char=".">5.92</td><td char=".">2.05*</td><td char=".">0.38</td></tr><tr><td> Counting</td><td char=".">18.00</td><td char=".">9.15</td><td char=".">7.13</td><td char=".">6.22</td><td char=".">5.64***</td><td char=".">1.39</td></tr><tr><td> Additing/subtracting</td><td char=".">2.30</td><td char=".">2.41</td><td char=".">3.00</td><td char=".">4.70</td><td char=".">–0.67</td><td char=".">–0.19</td></tr><tr><td> Ordinal numbers</td><td char=".">0.47</td><td char=".">1.11</td><td char=".">0.77</td><td char=".">1.36</td><td char=".">–1.80<xref ref-type="table-fn" rid="tfn1">+</xref></td><td char=".">–0.24</td></tr><tr><td> Division</td><td char=".">1.07</td><td char=".">1.78</td><td char=".">0.00</td><td char=".">0.00</td><td char=".">3.28**</td><td char=".">0.85</td></tr><tr><td> Units of measure</td><td char=".">0.07</td><td char=".">0.25</td><td char=".">0.10</td><td char=".">0.40</td><td char=".">–0.37</td><td char=".">–0.09</td></tr><tr><td> Conventional nominatives</td><td char=".">0.03</td><td char=".">0.18</td><td char=".">0.23</td><td char=".">0.82</td><td char=".">–1.29</td><td char=".">–0.34</td></tr><tr><td> Number comparisons</td><td char=".">0.07</td><td char=".">0.25</td><td char=".">0.13</td><td char=".">0.51</td><td char=".">–0.63</td><td char=".">–0.15</td></tr><tr><td> Total</td><td char=".">40.73</td><td char=".">13.83</td><td char=".">22.80</td><td char=".">14.31</td><td char=".">5.21***</td><td char=".">1.27</td></tr><tr><td>Math interest</td><td char=".">8.33</td><td char=".">1.47</td><td char=".">8.93</td><td char=".">1.36</td><td char=".">–1.94<xref ref-type="table-fn" rid="tfn1">+</xref></td><td char=".">–0.42</td></tr></tbody></table> </ephtml> </p> <p>1 <emph>p</emph> <.10. *<emph>p </emph><.05. **<emph>p </emph><.01. ***<emph>p</emph> <.001.</p> <p>We used paired sample <emph>t</emph>-tests to compare whether the variables differed between the two scenarios. Parents produced more mathematical talk in the written scenario, with significant differences in four categories: number recognition (<emph>t </emph>= 2.84, <emph>p</emph> =.008, <emph>d </emph>= 0.51), counting (<emph>t</emph> = 2.93, <emph>p</emph> =.006, <emph>d </emph>= 0.72), ordinal numbers (<emph>t </emph>= 3.02, <emph>p</emph> =.005, d = 0.71), and division (<emph>t</emph> = 5.55, <emph>p</emph> <.001, <emph>d </emph>= 1.46). The overall parent math talk also exhibited a significant difference (<emph>t</emph> = 4.94, <emph>p</emph> <.001, <emph>d </emph>= 1.01) with a large effect size (Cohen [<reflink idref="bib6" id="ref48">6</reflink>]).</p> <p>Similarly, children were more likely to engage in mathematical conversation when using written material, particularly for the four categories of number recognition (<emph>t</emph> = 2.97, <emph>p</emph> =.006, <emph>d </emph>= 0.47), cardinal values (<emph>t </emph>= 2.05, <emph>p</emph> =.050, <emph>d</emph> = 0.38), counting (<emph>t</emph> = 5.64, <emph>p</emph> <.001, <emph>d </emph>= 1.39), and division (<emph>t </emph>= 3.28, <emph>p</emph> =.003, <emph>d</emph> = 0.85). There was also a significant difference in overall child math talk (<emph>t</emph> = 5.21, <emph>p</emph> <.001, <emph>d</emph> = 1.27), which had a large effect size (Cohen [<reflink idref="bib6" id="ref49">6</reflink>]).</p> <p>A Pearson's correlation analysis was conducted on the mathematical interest in written and hands-on scenarios to eliminate the possibility that children's original math interest influenced their interest in math activities. The results did not show a significant correlation between the two (<emph>r </emph>=.287, <emph>p</emph> =.124), indicating that children had different attitudes in the two contexts. When comparing children's interest in mathematics in two scenarios using the paired sample <emph>t</emph>-test, the results showed marginal statistical significance (<emph>t</emph> = –1.94, <emph>p</emph> =.062, <emph>d</emph> = –0.42). Overall, children showed high interest in both scenarios, with a slightly higher interest score in the hands-on scenario compared to the written one.</p> <hd id="AN0192005932-16">Relations between parent math talk, child math talk, and math interest</hd> <p>Pearson's correlations were used to examine the associations between parent math talk, child math talk, and child math interest, as shown in Table 3. The analysis excluded math talk categories of units of measure, conventional nominatives, and number comparison due to their low frequency.</p> <p>Table 3. Correlation coefficients and Fisher's <emph>z</emph>-tests for math talk and math interest.</p> <p> <ephtml> <table><thead valign="bottom"><tr><td /><td>Written</td><td>Hands-on</td><td><italic>z</italic></td></tr><tr><td><italic>r</italic></td><td><italic>r</italic></td></tr></thead><tbody><tr><td>Parent math talk vs. Child math talk</td><td char="." /><td char="." /><td char="." /></tr><tr><td> Number recognition</td><td char=".">.68***</td><td char=".">.73***</td><td char=".">–0.33</td></tr><tr><td> Cardinal values</td><td char=".">.87***</td><td char=".">.60***</td><td char=".">2.27*</td></tr><tr><td> Counting</td><td char=".">.02</td><td char=".">.65***</td><td char=".">–2.75**</td></tr><tr><td> Adding/subtracting</td><td char=".">.51**</td><td char=".">.90***</td><td char=".">–3.27**</td></tr><tr><td> Ordinal numbers</td><td char=".">–.07</td><td char=".">.18</td><td char=".">–0.97</td></tr><tr><td> Division</td><td char=".">.43*</td><td char="." /><td char="." /></tr><tr><td> Total</td><td char=".">.40*</td><td char=".">.74***</td><td char=".">–1.97*</td></tr><tr><td>Parent math talk vs. Math interest</td><td char=".">–.24</td><td char=".">–.06</td><td char=".">–0.69</td></tr><tr><td>Child math talk vs. Math interest</td><td char=".">–.14</td><td char=".">–.07</td><td char=".">–0.27</td></tr></tbody></table> </ephtml> </p> <p>2 *<emph>p </emph><.05. **<emph>p </emph><.01. ***<emph>p</emph> <.001.</p> <p>In the written scenario, this study identified significant positive correlations for parent–child math talk related to number recognition (<emph>r</emph> =.68, <emph>p</emph> <.001), cardinal values (<emph>r</emph> =.87, <emph>p</emph> <.001), adding and subtracting (<emph>r</emph> =.51, <emph>p</emph> =.004), and division (<emph>r</emph> =.43, <emph>p</emph> =.018). A significant positive correlation was also identified for the overall math talk between parents and children (<emph>r</emph> =.40, <emph>p</emph> =.031). No significant associations were observed between parents and children for the counting and ordinal numbers categories of math talk.</p> <p>Regarding the hands-on scenario, we identified significant positive correlations for parent–child math talk related to number recognition (<emph>r</emph> =.73, <emph>p</emph> <.001), cardinal values (<emph>r</emph> =.60, <emph>p</emph> <.001), counting (<emph>r</emph> =.65, <emph>p</emph> <.001), and adding and subtracting (<emph>r</emph> =.90, <emph>p</emph> <.001). A significant positive correlation was identified for the overall math talk (<emph>r</emph> =.74, <emph>p</emph> <.001). A positive but nonsignificant correlation related to ordinal numbers was found for the parent–child math talk. Since children did not display division talk in the hands-on scenario, no further calculations were made to correlate this with parents' division talk.</p> <p>The present study found no significant correlation between child math interest and math talk (<emph>r</emph> = –.06 to –.24, <emph>p</emph> =.203 to.770). Specifically, in the hands-on scenario, math interest did not correlate with math talk by parents or children. In the written scenario, math interest showed negative but nonsignificant correlations with parent and child math talk.</p> <hd id="AN0192005932-17">Contextual differences in correlations between variables</hd> <p>This study conducted Fisher's <emph>z</emph>-tests to determine whether the above correlation coefficients differed between the two scenarios. The findings indicate that the correlation coefficient for parent–child math talk associated with cardinal values was significantly higher in the written scenario (<emph>z</emph> = 2.27, <emph>p</emph> =.023). In contrast, the correlation coefficients for parent–child math talk associated with counting (<emph>z</emph> = –2.75, <emph>p</emph> =.006), adding and subtracting (<emph>z</emph> = 3.27, <emph>p</emph> =.001), and overall math talk (<emph>z</emph> = 1.97, <emph>p</emph> =.049) were significantly higher in the hands-on scenario.</p> <p>Regarding the correlation coefficients between child math interest and overall math talk of parents, no significant differences were found between the scenarios (<emph>z</emph> = 0.69, <emph>p</emph> =.491). Similarly, there was no contextual variation in the correlation coefficients between child math interest and overall math talk of children (<emph>z</emph> = 0.27, <emph>p</emph> =.789).</p> <hd id="AN0192005932-18">Discussion</hd> <p>The nine categories of math talk were classified according to the parents' performance into groups for ease of interpretation. (<reflink idref="bib1" id="ref50">1</reflink>) A high-frequency group, which comprised four categories: number recognition, cardinal values, counting, and adding and subtracting; (<reflink idref="bib2" id="ref51">2</reflink>) A low-frequency group, which consisted of units of measure, conventional nominatives, and number comparisons; (<reflink idref="bib3" id="ref52">3</reflink>) The remaining two categories of math talk, ordinal numbers and division, were classified into a scenario-specific group as the scenarios influenced their performance.</p> <hd id="AN0192005932-19">Math talk and math interest in two scenarios</hd> <p>Parents and children were predominantly engaged in the high-frequency group of math talk across the two scenarios, consistent with prior research (de Vries, Polk, and Missall [<reflink idref="bib8" id="ref53">8</reflink>]; Huang [<reflink idref="bib15" id="ref54">15</reflink>]; Levine et al. [<reflink idref="bib18" id="ref55">18</reflink>]; Ramani et al. [<reflink idref="bib21" id="ref56">21</reflink>]). The four categories within the high-frequency group encompass commonly encountered numerical concepts. When comparing contextual differences within the high-frequency group, we observed that parents and children had higher mathematical expressions in the written scenario than in the hands-on scenario, particularly regarding number recognition and counting. This observation could be attributed to the nature of the workbook, where parents aimed to ensure that their children recognised the numerals and completed the counting tasks prompted by the questions. Alternatively, parents may have anticipated that the workbook exercises required problem solving, potentially posing greater challenges and less appealing to young children. Consequently, they may have invested more effort in verbally engaging their children to encourage participation. On the contrary, during the hands-on scenario, parents and children spent more time manipulating the cubes, reducing verbal communication.</p> <p>The results of the current study on math talk categories in the low-frequency group are consistent with previous research (Huang [<reflink idref="bib15" id="ref57">15</reflink>]; Levine et al. [<reflink idref="bib18" id="ref58">18</reflink>]; Susperreguy and Davis-Kean [<reflink idref="bib25" id="ref59">25</reflink>]). However, the study by Susperreguy and Davis-Kean ([<reflink idref="bib25" id="ref60">25</reflink>]) observed a higher incidence of measurement units as parent–child conversations were collected during mealtimes. These categories were less frequently observed in two scenarios because they involve real-life situations and more abstract applications of mental number lines that may be unfamiliar to some parents. Nevertheless, using numbers in various contexts can significantly contribute to children's understanding of the meaning and significance of numbers in our daily lives (Levine et al. [<reflink idref="bib18" id="ref61">18</reflink>]). To improve this understanding, incorporating these low-frequency math concepts into guidelines for hands-on teaching materials or integrating them into written materials to provide opportunities for parents and children to discuss them would be beneficial.</p> <p>Different scenarios exert varying influences on specific categories of mathematical discourse. This study noted that parents' utilisation of ordinal numbers and division was more prevalent in the written scenario but less common in the hands-on scenario. This observation may be attributed to explicit distributional questions in the workbook. Questions such as 'How many of these hot dogs will each be given to four people?' enabled parents to elucidate the concept of division and employ ordinal numbers to aid children in problem solving. For example, parents might say, 'Let us use the checkmark method, see the first person, the second person ... , is it divided between four people?' The parents' explicit prompts and explanations likely facilitated mathematical discourse about ordinal numbers and division in the written scenario.</p> <p>The children's performance in the two scenario-specific categories differed slightly from their parents. There was a significant contextual difference in division talks but not in ordinal discourse. During the written scenario, children displayed division speech to answer distribution questions in response to parental prompts. On the contrary, children did not speak about division in the hands-on scenario, possibly because they were more in control of the play direction in the hands-on scenario or because division was a more advanced concept.</p> <p>As for the other scenario-specific category, ordinal numbers, children rarely produced in both scenarios. This could be attributed to the absence of queueing and sorting tasks in these scenarios, which limits children's opportunities for such discussions. However, children can easily engage in ordinal talk with suitable materials, such as sequential picture cards (Huang [<reflink idref="bib15" id="ref62">15</reflink>]).</p> <p>The children exhibited considerable interest in mathematics in both scenarios, with a slightly higher level observed in the hands-on setting. They demonstrated enthusiasm for drawing and writing, actively participating in problem-solving activities in the workbook. Additionally, their focus and participation were evident during cube-based play. In the hands-on scenario, where specific mathematical responses were not required, parents did not interfere with their children's imaginative play, resulting in discussions that included building a house, assembling a car, or creating shapes. This observation indicates that the hands-on approach stimulated children's creativity and imagination, fostering diverse mathematical conversations beyond purely numeracy topics.</p> <hd id="AN0192005932-20">Correlations between math talk and math interest</hd> <p>The high-frequency group and overall math talk between parents and children showed positive correlations in both scenarios, except for the counting category in the written scenario. This alignment in math discourse echoes previous research findings (Huang [<reflink idref="bib15" id="ref63">15</reflink>]; Ramani et al. [<reflink idref="bib21" id="ref64">21</reflink>]), highlighting the dyadic synchronicity between parents and children. When parents introduce mathematical concepts or prompt discussions, children often respond with the corresponding mathematical discourse to facilitate communication.</p> <p>The lack of correlation in the counting category in the written scenario can be attributed to children's consistent use of counting as the primary problem-solving strategy, irrespective of their parents' specific types of questions. For instance, whether posed with questions regarding cardinality ('How many are there?'), counting ('Count how many?'), or division ('How many of these are there for each person if you cut them in half?'), children generally resorted to counting to arrive at answers. This observation is supported by the prevalence of counting as the most frequent category of children's speech in the written scenario. Since counting was not merely a response to counting prompts but rather a pervasive strategy, no significant parent–child correlation was detected in this category.</p> <p>No correlations were found between parent–child discourse in the scenario-specific category of ordinal numbers in either scenario. This may be due to disparities between the categories of children's responses and the specific instructions given by parents. For instance, when a parent asks a question about ordinal numbers, such as 'Is this the first or the second?' and the child responds with 'two,' an answer that does not align with the definition of ordinal numbers in this study. Although the child's response 'two' may functionally refer to 'the second,' when the child cannot orally distinguish between 'two' and 'the second,' it is not possible to confirm whether they understand the difference between ordinal and cardinal numbers. Therefore, this study adopted a more stringent coding definition. As a result, it leads to a lack of correlation in ordinal number discourse between parents and children.</p> <p>An alternative explanation could be that when parents or children mentioned ordinal numbers, it was not necessarily expected that the other party would provide a corresponding response. For instance, a parent might say, 'We have completed the second level,' or point to a page in the workbook and say, 'Look, there are six of them, right? This is the first, and this is the second ... ' These instances suggest that ordinal numbers were often used descriptively rather than to elicit a specific response from children.</p> <p>In the other scenario-specific category, division, a positive correlation was observed between parent–child expressions during the written scenario. This finding can be ascribed to the workbook's distributional questions requiring division-related responses. On the contrary, despite parents' suggestions to divide the cubes into parts during the hands-on scenario, children often played according to their own ideas without responding to parental guidance. Therefore, there was a complete absence of division discourse among children in the hands-on scenario, resulting in no correlation between parent–child division discourse.</p> <p>We found no correlation between child math interest and the frequency of parent or child math talk in the hands-on scenario. However, we observed negative but nonsignificant associations between child math interest and the frequency of parent or child math talk in the written scenario. This finding suggests that in the written scenario, as the frequency of parent or child math talk increased, there was a tendency for children's math interests to decrease. This observation could be attributed to the nature of the written context. In the written scenario, when a child did not fully understand a question, the parent needed to break down the question and provide step-by-step explanations, leading to prolonged discussions that potentially diminished enjoyment during the activity. Another reason could be that parents anticipated that the workbook exercises required problem-solving skills, which could be perceived as more challenging and less appealing to young children. Therefore, they may have exerted more effort to involve children orally to encourage participation.</p> <hd id="AN0192005932-21">Comparing correlation coefficients across scenarios</hd> <p>The current study further investigated whether the correlations mentioned above differed between the two scenarios. We first examined the correlations of parent–child math talk, revealing that the correlation of cardinal talk was higher in the written scenario. Conversely, the correlations between parent–child talk concerning counting, adding and subtracting, and overall math talk were higher in the hands-on scenario. It can be speculated that despite the lower frequency of parent–child math talk in the hands-on scenario, there was a greater degree of synchronisation or mutual responsiveness in the verbal interactions between parents and children. This finding may be attributed to the more relaxed nature of the interaction, as the play was not task-specific and allowed child-driven exploration and participation.</p> <p>The correlation coefficients between math talk and math interest showed no differences between scenarios. We observed high levels of engagement and interest among children in both scenarios. This indicates that both written and hands-on teaching materials are equally effective in capturing children's attention and fostering their interest in mathematics.</p> <hd id="AN0192005932-22">Limitations and future directions</hd> <p>One limitation of the present study is its exclusive focus on numeracy concepts, overlooking spatial concepts such as patterning and shapes that emerged during cube play. Future research should investigate various domains of mathematical language performance, particularly when employing low-structure teaching materials. Another limitation is the concentration of the written teaching material on fundamental mathematical concepts such as cardinal values, counting, and adding and subtracting, which are essential for elementary school readiness. Future teaching materials should incorporate a broader range of mathematical concepts, such as number line estimation and number comparisons, which have been shown to predict future mathematics achievement (Libertus [<reflink idref="bib19" id="ref65">19</reflink>]; Schneider et al. [<reflink idref="bib23" id="ref66">23</reflink>]).</p> <p>Two recommendations are proposed for future research. Firstly, explore how various teaching materials can enhance young children's mathematical learning. For example, integrating low-frequency numerical concepts into written materials, encouraging children to use hands-on materials to solve questions presented in written materials, and assessing the impact on mathematical learning. Secondly, investigate the sustainability of mathematical interest as children transition to elementary school, where textbooks and worksheets are predominant. Continued monitoring of children's mathematical interests can provide valuable insights for educators and policymakers, enabling them to make informed decisions regarding the use of diverse teaching materials and their effects on children's mathematical interests and performance.</p> <hd id="AN0192005932-23">Conclusions</hd> <p>This study marks the first exploration of the connections between parent–child mathematics talk and children's mathematics interest, alongside comparing these correlations in two different teaching material contexts. Moreover, this study introduces an innovative method to assess the synchronicity of mathematical discourse between parents and children.</p> <p>The findings reveal that parents and children engage in more frequent mathematical discourse in the written scenario, with parents displaying higher frequencies of ordinal and division expressions. In contrast, interest scores are marginally elevated in the hands-on scenario, coupled with enhanced synchronicity in verbal interactions between parents and children. These outcomes imply that hands-on materials hold a particular allure for young children while fostering a more fluid and focused parent–child communication style. Furthermore, specific categories of mathematical discourse were infrequent in both contexts, underscoring a limited familiarity with these concepts.</p> <p>Educators can refer to the constructive alignment framework to develop teaching activities based on instructional objectives, leveraging the strengths of both types of teaching materials to enhance teaching effectiveness. Written materials, such as workbooks, provide structured approaches to teaching specific math objectives by employing symbols and representations to aid children's understanding. In contrast, hands-on materials align with young children's natural inclination to learn through play, allowing them to explore and manipulate objects, thereby fostering a deeper grasp of abstract mathematical concepts. While hands-on materials may not explicitly address mathematical concepts, they create a relaxed, child-driven learning environment that adults can utilise to shape children's learning experiences. By combining hands-on materials with purpose-planned written content, adults can guide children's use of hands-on materials while engaging in math-focused discussions. This approach enriches children's math vocabulary, nurtures their interest and enthusiasm for mathematics, and supports the successful development of their mathematical skills.</p> <hd id="AN0192005932-24">Disclosure statement</hd> <p>No potential conflict of interest was reported by the author(s).</p> <hd id="AN0192005932-25">Ethical statement</hd> <p>This study was conducted according to the guidelines of the Declaration of Helsinki. Informed consent was obtained from all subjects involved in the study and their guardians.</p> <ref id="AN0192005932-26"> <title> References </title> <blist> <bibl id="bib1" idref="ref25" type="bt">1</bibl> <bibtext> Anderson, Ann. 1997. " Families and Mathematics: A Study of Parent-Child Interactions." Journal for Research in Mathematics Education 28 (4): 484 – 511. https://doi.org/10.2307/749684.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref26" type="bt">2</bibl> <bibtext> Anderson, Ann, Jim Anderson, and Jon Shapiro. 2004. 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  Data: Parent-Child Math Talk and Early Math Interest: Comparing the Effects of Written versus Hands-On Materials
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  Data: <searchLink fieldCode="AR" term="%22Hsin-Hui+Huang%22">Hsin-Hui Huang</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-8121-5665">0000-0002-8121-5665</externalLink>)<br /><searchLink fieldCode="AR" term="%22Peiyi+Lee%22">Peiyi Lee</searchLink>
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  Data: 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
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  Data: 10.1080/09669760.2024.2389820
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  Data: This study investigated the impact of written and hands-on teaching materials on parent-child math talk and children's interest in mathematics. Thirty parents and their preschool children participated in two play sessions, one using written material and the other using hands-on material, each lasting 12 min. At the end of each session, the children's interest levels were assessed, and the frequency of math-related conversations was analysed. Regardless of the materials used, discussions primarily revolved around fundamental numerical concepts, with little mention of practical measurement units and conventional nominatives or number comparisons involving the application of mental representation. Ordinal and division concepts were only mentioned by parents in the written scenario rather than in the hands-on one. Overall, using written material led to doubling math discourse compared to hands-on material. However, children showed slightly higher interest levels in the hands-on scenario, where parent-child math talk categories also exhibited greater synchrony. The study highlights the complementary nature of written and hands-on teaching materials and provides recommendations for their future application.
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