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Racing Dragons and Remembering Aliens: Benefits of Playing Number and Working Memory Games on Kindergartners' Numerical Knowledge

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Title: Racing Dragons and Remembering Aliens: Benefits of Playing Number and Working Memory Games on Kindergartners' Numerical Knowledge
Language: English
Authors: Ramani, Geetha B., Daubert, Emily N., Lin, Grace C., Kamarsu, Snigdha, Wodzinski, Alaina, Jaeggi, Susanne M.
Source: Developmental Science. Jul 2020 23(4).
Availability: Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA
Peer Reviewed: Y
Page Count: 17
Publication Date: 2020
Sponsoring Agency: National Science Foundation (NSF)
Contract Number: 1561447
1561404
Document Type: Journal Articles
Reports - Research
Education Level: Early Childhood Education
Elementary Education
Kindergarten
Primary Education
Descriptors: Educational Games, Mathematics Education, Number Concepts, Short Term Memory, Kindergarten, Young Children, Handheld Devices, Mathematics Skills, Skill Development, Mathematics Achievement, Computer Games
DOI: 10.1111/desc.12908
ISSN: 1467-7687
Abstract: Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet-based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten-age children. We hypothesized that playing a number-based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; M[subscript age] = 71.87 months) were randomly assigned to either play a number-based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain-specific and domain-general skills can benefit a broad range of kindergarten-aged children.
Abstractor: As Provided
Entry Date: 2020
Accession Number: EJ1257547
Database: ERIC
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  Value: <anid>AN0144200760;5g501jul.20;2020Jun25.01:53;v2.2.500</anid> <title id="AN0144200760-1">Racing dragons and remembering aliens: Benefits of playing number and working memory games on kindergartners' numerical knowledge </title> <p>Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet‐based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten‐age children. We hypothesized that playing a number‐based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; Mage = 71.87 months) were randomly assigned to either play a number‐based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain‐specific and domain‐general skills can benefit a broad range of kindergarten‐aged children.</p> <p>Keywords: domain‐general skills; long‐term effects; mathematics; working memory</p> <p>We tested the benefits of engaging in tablet‐based games that target either domain‐specific or domaingeneral skills in a diverse population of kindergarten‐aged children. Structural equation modeling was used to determine children's learning gains in mathematics and working memory across time. The results suggest that computerized games that target both domain‐specific and domain‐general skills can lead to broad and longitudinal benefits that go beyond the trained task.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01jul20/desc12908-toc-0001.jpg?ephost1=dGJyMMvl7ESepq84yOvsOLCmsE6epq5Srqa4SK6WxWXS" alt="desc12908-toc-0001.jpg" title="." /> </p> <p></p> <hd id="AN0144200760-3">Research Highlights</hd> <p></p> <ulist> <item> We tested the benefits of engaging in tablet‐based games that target either domain‐specific or domain‐general skills in a diverse population of kindergarten‐aged children.</item> <p></p> <item> Training domain‐specific skills (numerical knowledge) led to improvements in numerical knowledge on a latent level, and in addition, in working memory.</item> <p></p> <item> Training domain‐general skills (working memory) led to improvements in working memory on a latent level.</item> <p></p> <item> The observed transfer effects were observed over and above an active control, and furthermore, the gains were maintained for several weeks.</item> </ulist> <hd id="AN0144200760-4">INTRODUCTION</hd> <p>Over the last decade, efforts to improve the numerical knowledge of young children has grown tremendously because substantial evidence has demonstrated a strong relation between children's early mathematical knowledge and their later mathematical achievement (Claessens & Engel, [<reflink idref="bib12" id="ref1">12</reflink>]; Geary, Hoard, Nugent, & Bailey, [<reflink idref="bib23" id="ref2">23</reflink>]; Watts, Duncan, Siegler, & Davis‐Kean, [<reflink idref="bib66" id="ref3">66</reflink>]). Effective avenues to improve young children's mathematics include games and activities that target specific numerical skills (Laski & Siegler, [<reflink idref="bib37" id="ref4">37</reflink>]; Navarrete, Gómez, & Dartnell, [<reflink idref="bib45" id="ref5">45</reflink>]; Scalise, Daubert, & Ramani, [<reflink idref="bib52" id="ref6">52</reflink>]), as well as comprehensive mathematics curricula (Clements, Sarama, Spitler, Lange, & Wolfe, [<reflink idref="bib13" id="ref7">13</reflink>]). Additionally, there have been attempts to improve children's domain‐general skills by targeting working memory (WM) and executive function skills, which are thought to underlie both numerical knowledge and the acquisition thereof (Kroesbergen, Noordende, & Kolkman, [<reflink idref="bib35" id="ref8">35</reflink>]; Ramani, Jaeggi, Daubert, & Buschkuehl, [<reflink idref="bib48" id="ref9">48</reflink>]; Wang et al., [<reflink idref="bib65" id="ref10">65</reflink>]). Individual differences in such underlying characteristics are considered critical for later mathematical achievement (Bailey, Watts, Littlefield, & Geary, [<reflink idref="bib3" id="ref11">3</reflink>]). Thus, targeting precursors to help children learn mathematics, which include both numerical knowledge and underlying cognitive processing abilities, could have important implications for later mathematical achievement.</p> <p>The current study tested the benefits of tablet‐based training games that targeted either domain‐specific or domain‐general skills in a diverse population of kindergarten‐aged children. Even though there is evidence that targeting either domain‐specific and domain‐general skills through computerized interventions boost aspects of numerical knowledge in early childhood, little is known about how these interventions promote children's boarder numerical knowledge and whether there are longer term benefits of training activities. Importantly, we used structural equation modeling (SEM) to model children's gains in numerical knowledge and in WM across time. This approach allows for the examination of relations between latent factors in order to minimize task‐specific error variance and family‐wise error inflation. We compared the benefits of each intervention with an active control that did not intend to focus on either numerical skills or WM to control for non‐specific factors, such as familiarity with tablet use or interaction with experimenters.</p> <hd id="AN0144200760-5">Role of domain‐specific and domain‐general skills in mathematical achievement</hd> <p>Both domain‐specific numerical knowledge and domain‐general underlying cognitive processes play a critical role in children's mathematical development. During early childhood children acquire foundational numerical knowledge, and one of the key areas within that domain is the understanding of numerical magnitudes. According to the integrated theory of numerical development, an increased understanding of numerical magnitudes is critical for learning mathematical concepts (Siegler, [<reflink idref="bib56" id="ref12">56</reflink>]; Siegler, Thompson, & Schneider, [<reflink idref="bib59" id="ref13">59</reflink>]). Numerical magnitude knowledge is represented by a mental number line, which is a hypothesized cognitive structure where numbers are represented in a horizontal line with increasing magnitude from left to right (Dehaene, [<reflink idref="bib18" id="ref14">18</reflink>]). During the preschool years, children acquire an understanding of the magnitudes of small symbolic numbers in the number range 0–10 (Berteletti, Lucangeli, Piazza, Dehaene, & Zorzi, [<reflink idref="bib5" id="ref15">5</reflink>]). Through kindergarten and first grade, children begin to acquire numerical magnitude knowledge of the numbers 0–100, although there is variability to children's knowledge of this number range (Booth & Siegler, [<reflink idref="bib8" id="ref16">8</reflink>]).</p> <p>The acquisition of numerical knowledge in early childhood is critical because there is evidence linking these early mathematical skills to later achievement. For example, magnitude understanding at age 6 was predictive of fraction magnitudes and fractions arithmetic, traditionally difficult mathematical concepts, at age 13 (Bailey et al., [<reflink idref="bib3" id="ref17">3</reflink>]). These relations held even after controlling for various factors such as children's executive function, IQ, race, gender, and SES. Similarly, variability in numerical magnitude knowledge predicts children's math achievement in later elementary school (Booth & Siegler, [<reflink idref="bib8" id="ref18">8</reflink>]; Kolkman, Hoijtink, Kroesbergen, & Leseman, [<reflink idref="bib32" id="ref19">32</reflink>]; Sasanguie, De Smedt, Defever, & Reynvoet, [<reflink idref="bib51" id="ref20">51</reflink>]).</p> <p>Early mathematical achievement is also linked to underlying domain‐general knowledge. One critical area of domain‐general skills is WM, which is an essential cognitive mechanism for storing and processing information (Miyake & Shah, [<reflink idref="bib42" id="ref21">42</reflink>]). WM is critical in the development of numerical knowledge and mathematics more generally as it facilitates learning through maintenance processes, for example, when information has to be kept in memory during the process of problem‐solving, such as carry operations (e.g. Geary, [<reflink idref="bib21" id="ref22">21</reflink>]; Krajewski & Schneider, [<reflink idref="bib33" id="ref23">33</reflink>]). But even precursors of later mathematical skills require WM, such as counting or number line estimation, by allowing children to keep track of where they are in the process of counting, or by facilitating retrieval and associations between the representation of number symbols and the corresponding quantity or magnitude (Kolkman et al., [<reflink idref="bib32" id="ref24">32</reflink>]; Noël, [<reflink idref="bib46" id="ref25">46</reflink>]). Indeed, a vast body of correlational literature demonstrates the strong link of WM skills and math achievement (for reviews, see Bull & Lee, [<reflink idref="bib10" id="ref26">10</reflink>]; Cragg & Gilmore, [<reflink idref="bib15" id="ref27">15</reflink>]; Jacob & Parkinson, [<reflink idref="bib26" id="ref28">26</reflink>]; Peng, Namkung, Barnes, & Sun, [<reflink idref="bib47" id="ref29">47</reflink>]). For example, in a longitudinal study tracking children from kindergarten to third grade, researchers found that WM affects children's early and later quantity–number competencies, which in turn contributes to their math achievement (Krajewski & Schneider, [<reflink idref="bib33" id="ref30">33</reflink>]). Another longitudinal study also finds WM to be predictive of later math performance beyond the contributions of number sense (Toll, Kroesbergen, & Luit, [<reflink idref="bib61" id="ref31">61</reflink>]). Both findings are consistent with earlier work demonstrating that WM predicts children's academic attainment, including their scores on mathematics tests (Jarvis & Gathercole, [<reflink idref="bib29" id="ref32">29</reflink>]), and that younger children rely on WM when performing math‐related tasks (Best, Miller, & Naglieri, [<reflink idref="bib6" id="ref33">6</reflink>]).</p> <hd id="AN0144200760-6">Training domain‐specific and domain‐general skills for improving numerical knowledge</hd> <p>Children's numerical magnitude knowledge can be improved through both domain‐specific and domain‐general training games. For example, empirical work with preschool children from lower income backgrounds improved their numerical magnitude knowledge through playing linear number board games, which provide both a visual representation of the mental number line as well as practice with number skills (Ramani & Siegler, [<reflink idref="bib49" id="ref34">49</reflink>]; Siegler & Ramani, [<reflink idref="bib58" id="ref35">58</reflink>]). Board games have been shown to be equally effective with kindergarteners. Specifically, playing a board game with the numbers 0–100 arranged in a 10 × 10 matrix for four sessions improved children's numerical magnitude knowledge (Laski & Siegler, [<reflink idref="bib37" id="ref36">37</reflink>]). In another study training kindergarten children using activities focused on categorizing the numbers between 0 and 100 by their magnitudes improved their numerical magnitude knowledge (Kolkman et al., [<reflink idref="bib32" id="ref37">32</reflink>]).</p> <p>In addition to traditional games, numerous technology‐based games have been shown to improve young children's numerical magnitude knowledge. For example, playing adaptive and computerized number games involving numerical magnitude comparisons using dots, numbers, or arithmetic problems improved preschool‐ and kindergarten‐age children's numerical magnitude knowledge (Sella, Tressoldi, Lucangeli, & Zorzi, [<reflink idref="bib54" id="ref38">54</reflink>]; Wilson, Dehaene, Dubois, & Fayol, [<reflink idref="bib68" id="ref39">68</reflink>]). Thus, playing computer‐based games that directly target numerical magnitude knowledge can benefit young children's mathematical development.</p> <p>Similarly for domain‐general skills, empirical work has targeted WM as an area of intervention to improve mathematics performance and learning. However, it has been difficult to demonstrate that training WM is beneficial for mathematics and related academic domains (e.g., Titz & Karbach, [<reflink idref="bib60" id="ref40">60</reflink>]). Although a meta‐analysis of 47 studies with WM training found effect sizes of near‐transfer improvements on short‐term and WM skills that ranged from <emph>g</emph> = 0.37 to <emph>g</emph> = 0.72, only minimal transfer effects were reported on mathematical abilities (effect sizes ranged from <emph>g</emph> = 0.04 to <emph>g</emph> = 0.13; Schwaighofer, Fischer, & Bühner, [<reflink idref="bib53" id="ref41">53</reflink>]). Nonetheless, some WM training studies have been successful in improving children's mathematical knowledge. For example, Kroesbergen, Van't Noordende, and Kolkman ([<reflink idref="bib34" id="ref42">34</reflink>]) showed that training WM improved kindergarten children's counting skills, and WM games that include both numerical and non‐numerical information improved children's counting and numerical comparison skills (Kroesbergen et al., [<reflink idref="bib35" id="ref43">35</reflink>]). Similarly, Bergman‐Nutley and Klingberg ([<reflink idref="bib4" id="ref44">4</reflink>]) found that computerized WM training improved older children's speed on an arithmetic task. WM training can also improve basic numeracy and arithmetic skills in adolescents with attentional problems and other learning difficulties (Alloway, [<reflink idref="bib1" id="ref45">1</reflink>]; Dahlin, [<reflink idref="bib16" id="ref46">16</reflink>]), and there is some limited evidence that WM training might improve school‐related performance including math in typically developing middle school–aged children (Holmes & Gathercole, [<reflink idref="bib25" id="ref47">25</reflink>]).</p> <p>Finally, most closely related to the present study, kindergarten children from predominantly lower income backgrounds played one of two computerized tablet games: one targeting their understanding of numerical magnitudes and the other targeting their WM skills (Ramani et al., [<reflink idref="bib48" id="ref48">48</reflink>]). The numerical magnitude knowledge tablet game was a 0–100 number board game linearly arranged in a 10 × 10 array (Laski & Siegler, [<reflink idref="bib37" id="ref49">37</reflink>]) and the WM training tablet required children to recall an increasing amount of items. After 10 sessions of gameplay, children's numerical magnitude knowledge improved in both experimental groups as compared to a no‐contact control group, suggesting that both domain‐specific and domain‐general interventions can facilitate mathematical skills.</p> <hd id="AN0144200760-7">The present study</hd> <p>The present study had four main goals aiming to replicate and extend previous research in several ways. Our first goal was to replicate previous findings (Ramani et al., [<reflink idref="bib48" id="ref50">48</reflink>]) with a larger and more diverse sample of kindergarten‐age children using the same domain‐specific and domain‐general tasks as used earlier. This seems critical given the overall mixed empirical work of WM training on children's mathematical performance.</p> <p>The second goal was to extend the previous work by including an active control condition given that previous work primarily relied only on a no‐contact control group. It might be that playing a tablet game regardless of the content could have improved children's numerical knowledge, thus, incorporating an active control condition can help to further disentangle the specificity of the effects of the two games. To pursue this goal, we developed an active control condition that was a board game similar to the numerical game except the numbers were replaced with colors similar to the active control groups used in previous research (Ramani & Siegler, [<reflink idref="bib49" id="ref51">49</reflink>]; Siegler & Ramani, [<reflink idref="bib58" id="ref52">58</reflink>]).</p> <p>A third goal was to examine stability of improvements over time. Very few training studies to date incorporate follow‐up assessments. This is critical since many successful educational intervention effects for mathematics appear temporary when the longer term benefits are examined (e.g. Bailey, Duncan, Odgers, & Yu, [<reflink idref="bib2" id="ref53">2</reflink>]). Conversely, it has been shown that it can take some time for learning to express itself in other domains, and there might be continued learning even after the intervention (e.g., Feuerstein, Rand, Hoffman, & Miller, [<reflink idref="bib19" id="ref54">19</reflink>]). Overall, it is important to examine the influence of an intervention after a shorter time to determine whether the results are stable, whether fade‐out is already beginning to occur, or whether there is even continued growth by children in the experimental condition.</p> <p>Our final goal was to use SEM to model children's learning gains in WM and mathematics across time. We chose SEM because there are several advantages over more traditional analyses of experimental data. First, SEM techniques allow us to combine several measures of numerical knowledge and WM into two latent constructs. Second, SEM also allows for comparing the outcomes of each of the two experimental conditions compared to the active control condition, and finally, we can include all three measurement points into one single analysis (Grimm, Mazza, & Mazzocco, [<reflink idref="bib24" id="ref55">24</reflink>]).</p> <hd id="AN0144200760-8">METHOD</hd> <p></p> <hd id="AN0144200760-9">Participants</hd> <p>Participants were 163 kindergarten children recruited from elementary schools on the east and west coast of the United States. Fifteen participants were excluded because of technical issues with the training game (<emph>n</emph> = 5), excessive absences resulting in not completing seven or more training sessions (<emph>n</emph> = 5), or not completing at least two or more math and WM measures during pretest and posttest (<emph>n</emph> = 5). The resulting 148 participants (<emph>M</emph><subs>age</subs> = 71.87 months, <emph>SD</emph> = 4.42; 52% girls) were ethnically and socioeconomically diverse (see Table).</p> <p>Descriptive statistics of demographic variables</p> <p> <ephtml> <table><thead valign="top"><tr><th align="left"> </th><th align="left">Total analysis sample (<italic>n</italic> = 148)</th><th align="left">Math (<italic>n</italic> = 47)</th><th align="left">WM (<italic>n</italic> = 48)</th><th align="left">Control (<italic>n</italic> = 53)</th></tr></thead><tbody><tr><td align="left">Age in months, M (SD) [min, max]</td><td align="char" char="(">71.87 (4.42) [62.00, 86.02]</td><td align="char" char="(">72.24 (3.94) [63.04, 78.04]</td><td align="char" char="(">72.09 (5.35) [62.00, 86.02]</td><td align="char" char="(">71.36 (3.89) [63.02, 79.03]</td></tr><tr><td align="left">Gender, n (%)</td></tr><tr><td align="left">Female</td><td align="char" char="(">77 (52)</td><td align="char" char="(">21 (45)</td><td align="char" char="(">27 (56)</td><td align="char" char="(">29 (55)</td></tr><tr><td align="left">Male</td><td align="char" char="(">68 (46)</td><td align="char" char="(">26 (55)</td><td align="char" char="(">20 (42)</td><td align="char" char="(">22 (42)</td></tr><tr><td align="left">Ethnicity, n (%)</td></tr><tr><td align="left">Hispanic/Latino</td><td align="char" char="(">61 (41)</td><td align="char" char="(">21 (45)</td><td align="char" char="(">20 (42)</td><td align="char" char="(">20 (38)</td></tr><tr><td align="left">Not Hispanic/Latino</td><td align="char" char="(">53 (36)</td><td align="char" char="(">17 (36)</td><td align="char" char="(">16 (33)</td><td align="char" char="(">20 (38)</td></tr><tr><td align="left">Other</td><td align="char" char="(">18 (12)</td><td align="char" char="(">7 (15)</td><td align="char" char="(">7 (15)</td><td align="char" char="(">4 (8)</td></tr><tr><td align="left">Race, n (%)</td></tr><tr><td align="left">African American/Black</td><td align="char" char="(">34 (23)</td><td align="char" char="(">11 (23)</td><td align="char" char="(">11 (23)</td><td align="char" char="(">12 (23)</td></tr><tr><td align="left">Caucasian/White</td><td align="char" char="(">56 (38)</td><td align="char" char="(">17 (36)</td><td align="char" char="(">15 (31)</td><td align="char" char="(">24 (45)</td></tr><tr><td align="left">Asian or Pacific Islander</td><td align="char" char="(">4 (3)</td><td align="char" char="(">0 (0)</td><td align="char" char="(">3 (6)</td><td align="char" char="(">1 (2)</td></tr><tr><td align="left">American Indian or Alaskan Native</td><td align="char" char="(">2 (1)</td><td align="char" char="(">1 (2)</td><td align="char" char="(">1 (2)</td><td align="char" char="(">0 (0)</td></tr><tr><td align="left">Biracial/Mixed Race</td><td align="char" char="(">14 (9)</td><td align="char" char="(">7 (15)</td><td align="char" char="(">6 (13)</td><td align="char" char="(">1 (2)</td></tr><tr><td align="left">Other</td><td align="char" char="(">3 (2)</td><td align="char" char="(">1 (2)</td><td align="char" char="(">0 (0)</td><td align="char" char="(">2 (4)</td></tr><tr><td align="left">Maternal education, n (%)</td></tr><tr><td align="left">Some High School Coursework</td><td align="char" char="(">14 (9)</td><td align="char" char="(">4 (9)</td><td align="char" char="(">10 (21)</td><td align="char" char="(">3 (6)</td></tr><tr><td align="left">High School Diploma/GED</td><td align="char" char="(">33 (22)</td><td align="char" char="(">10 (21)</td><td align="char" char="(">8 (17)</td><td align="char" char="(">15 (28)</td></tr><tr><td align="left">Some College Coursework/Vocational Training</td><td align="char" char="(">28 (19)</td><td align="char" char="(">7 (15)</td><td align="char" char="(">10 (21)</td><td align="char" char="(">11 (21)</td></tr><tr><td align="left">2‐year College Degree (Associates)</td><td align="char" char="(">12 (8)</td><td align="char" char="(">9 (19)</td><td align="char" char="(">2 (4)</td><td align="char" char="(">1 (2)</td></tr><tr><td align="left">4‐year College Degree (BA/BS)</td><td align="char" char="(">20 (14)</td><td align="char" char="(">9 (19)</td><td align="char" char="(">5 (10)</td><td align="char" char="(">6 (11)</td></tr><tr><td align="left">Postgraduate or Professional Degree</td><td align="char" char="(">27 (18)</td><td align="char" char="(">5 (11)</td><td align="char" char="(">11 (23)</td><td align="char" char="(">11 (21)</td></tr><tr><td align="left">Annual Household Income, n (%)</td></tr><tr><td align="left">Less than $15,000</td><td align="char" char="(">21 (14)</td><td align="char" char="(">5 (11)</td><td align="char" char="(">9 (19)</td><td align="char" char="(">7 (13)</td></tr><tr><td align="left">$15,000–$30,000</td><td align="char" char="(">25 (17)</td><td align="char" char="(">9 (19)</td><td align="char" char="(">3 (6)</td><td align="char" char="(">13 (25)</td></tr><tr><td align="left">$31,000–$45,000</td><td align="char" char="(">13 (9)</td><td align="char" char="(">3 (6)</td><td align="char" char="(">7 (15)</td><td align="char" char="(">3 (6)</td></tr><tr><td align="left">$46,000–$59,000</td><td align="char" char="(">11 (7)</td><td align="char" char="(">7 (15)</td><td align="char" char="(">2 (4)</td><td align="char" char="(">2 (4)</td></tr><tr><td align="left">$60,000–$75,000</td><td align="char" char="(">16 (11)</td><td align="char" char="(">5 (11)</td><td align="char" char="(">7 (15)</td><td align="char" char="(">4 (8)</td></tr><tr><td align="left">$76,000–$100,000</td><td align="char" char="(">9 (6)</td><td align="char" char="(">5 (11)</td><td align="char" char="(">1 (2)</td><td align="char" char="(">3 (6)</td></tr><tr><td align="left">$101,000–$150,000</td><td align="char" char="(">13 (9)</td><td align="char" char="(">3 (6)</td><td align="char" char="(">8 (17)</td><td align="char" char="(">2 (4)</td></tr><tr><td align="left">$151,000 or more</td><td align="char" char="(">18 (12)</td><td align="char" char="(">6 (13)</td><td align="char" char="(">4 (8)</td><td align="char" char="(">8 (15)</td></tr><tr><td align="left">Household language, n (%)</td></tr><tr><td align="left">Monolingual English speakers</td><td align="char" char="(">65 (44)</td><td align="char" char="(">21 (45)</td><td align="char" char="(">18 (38)</td><td align="char" char="(">26 (49)</td></tr><tr><td align="left">Exposed to more than one language</td></tr><tr><td align="left">Spanish</td><td align="char" char="(">58 (39)</td><td align="char" char="(">21 (45)</td><td align="char" char="(">18 (38)</td><td align="char" char="(">19 (36)</td></tr><tr><td align="left">Other</td><td align="char" char="(">8 (5)</td><td align="char" char="(">1 (2)</td><td align="char" char="(">4 (8)</td><td align="char" char="(">3 (6)</td></tr></tbody></table> </ephtml> </p> <p>1 Note</p> <p>2 Percentages are calculated out of total in each category (e.g., out of 148 for total analysis sample). They do not always add up to 100 because some participants did not receive the questionnaire or did not fill out the question(s)..</p> <hd id="AN0144200760-10">Overview of procedure</hd> <p>The study consisted of 16 sessions. During sessions 1–2, 13–14, and 15–16, experimenters administered numerical knowledge, WM, and control measures one‐on‐one with each child. Each session lasted approximately 25–30 min. Sessions 15 and 16 were conducted 4–6 weeks after the last training session to assess long‐term benefits of the training (see Figure S1). Children were randomly assigned within classroom to one of three training conditions: domain specific (numerical knowledge), domain general (WM), and active control. During sessions 3 through 12 (10 sessions total), children played the training tablet games and the session lasted approximately 10–15 min. At least half of the experimenters conducting the posttest and follow‐up assessments were blind to the condition of the child.</p> <hd id="AN0144200760-11">Training conditions</hd> <p>The training games were played on Lenovo Tab 2 A10 tablets with participant responses being recorded on the tablet. The games incorporated stories and themes to mimic a video game–like setting (see Figures S2–S4). During the first training session, children were given the game playing instructions using a storyline. Each of the interventions included eight themes to maintain engagement (see Figure S5). All children cycled through one theme per session during the first eight sessions, and then picked the theme of their choice for the remaining two training sessions. Each training session was conducted in small groups with one to two experimenters supervising the game play.</p> <p>After each training session, children were asked to indicate (a) how much they liked playing the game, and (b) how much effort they put into the game by using a 3‐point Likert scale in which the anchor points were represented with smiley faces and cartoon characters (Figure S6). The dependent variables were the average ratings for each of the questions per training session.</p> <hd id="AN0144200760-12">Domain‐specific condition (numerical knowledge training): "The Great Race"</hd> <p>Children were presented with a 10 × 10 grid of numbers ranging from 1 to 100 and increasing in value from left to right (Ramani et al., [<reflink idref="bib48" id="ref56">48</reflink>]; Figure S2). Children moved their character along the board by tapping a spinner numbered from 1 to 6 and then moving the appropriate number of spaces by tapping each numbered space. When finished, they tapped the 'done' button to indicate the end of their turn. The computer player would then repeat the process for its turn. As each character moved along the board, the game narrator would read the number in each space. Feedback was provided when children made an error (e.g., moving too many or too few spaces). After three turns, the characters were removed from the board and displayed on the left of the board indicating the number each character was on underneath. Children were prompted to answer the question "Which character is leading?" by tapping on the correct character/number combination. Coins were earned for each correct answer and totaled at the end of the game. The game ended when either the computer or the participant reached 100.</p> <p>The dependent variables were the percentage of questions answered correctly for the magnitude comparisons questions ('Who is leading'?), the number of error prompts with respect to counting ('you moved too few/many spaces'), and the number of other error prompts (failure to touch done button, etc.).</p> <hd id="AN0144200760-13">Domain‐general condition (WM training): "Recall Them All"</hd> <p>Children had to complete two stages for each of the trials (Ramani et al., [<reflink idref="bib48" id="ref57">48</reflink>]; Figure S3): They were first presented with a series of characters (e.g., aliens) that varied in color and that were shown either right‐side up or upside down. For each character, children had to decide the orientation of the character by touching the corresponding button at the bottom of the screen. If they pressed the incorrect orientation button or took too long to decide, children would receive feedback indicating that their response was incorrect, and they had to provide the correct answer before the game continued. In the second part, the character was presented in all four possible colors. Children had to recall the order in which the characters were presented by tapping on the respective colored characters. Children's progression in the game was adaptive: the more accurate children were in the orientation and recall trials, the longer the sequence they had to recall. At the end of each trial (i.e., after the recall part), children received feedback in the form of gold coins, with the amount of coins increasing with higher levels. To prevent fatigue, children played two rounds of 5 min each per session, with a break in between the rounds.</p> <p>The average recall accuracy, the largest set size recalled, as well as the average reaction time during the recall part of the game across the two rounds per session served as the dependent variables (Ramani et al., [<reflink idref="bib48" id="ref58">48</reflink>]).</p> <hd id="AN0144200760-14">Active control condition: "Rainbow Race"</hd> <p>Children were presented with a 10 × 10 grid similar to the one featured in the Great Race except that the numbered spaces were replaced with a repeating pattern of six colors (red, orange, yellow, green, blue, purple; Figure S4). Each theme had a different sequence of these colors. Children moved their character along the board by tapping a colored spinner and then tapping each colored space until they reached the required colored space. They tapped the 'done' button to end their turn. The computer player would then take its turn. Feedback was provided when children moved to the incorrect color. Similar to the "Great Race," once every three turns, the game pieces were removed from the game board, the screen showed the colors the two characters were on, and children were prompted to indicate which character was leading by touching the color. Children earned coins for each correct answer. The game ended when either the computer or the user reached the star at the end of the grid.</p> <p>The dependent variables were the percentage of questions answered correctly for the leader questions ('Who is leading'?), the number of error prompts with respect to moving ('you moved too few/many spaces'), and the number of other error prompts (failure to touch done button, etc.).</p> <hd id="AN0144200760-15">Outcome measures</hd> <p></p> <hd id="AN0144200760-16">Mathematical knowledge measures</hd> <p></p> <hd id="AN0144200760-17">Counting principles</hd> <p>Children were presented with two bags one at a time containing star‐shaped erasers. Each bag was emptied and the child was prompted to count the stars (Figure S7). The experimenter recorded whether the child used one‐to‐one correspondence while counting. To determine cardinality understanding, the experimenter hid the stars and asked the child, "How many stars did you count?" If the child answered correctly, they received one point. The procedure was repeated with a second bag. The bag amounts (10 and 16; 14 and 10) were counterbalanced across participants and sessions. Counting accuracy, cardinality, and one‐to‐one correspondence served as indicators of performance.</p> <p>In the second counting task, children were asked to start counting on from a particular number (i.e., 1, 28/38, 87, 100) and continue counting until the experimenter asked them to stop counting at a predetermined endpoint (i.e., 25, 40/50, 100, 125). All children were administered the first two trials. The task ended if children failed to count the first three numbers in a given sequence. The number of correctly counted numerals indicated their performance. The scores from the two counting measures were standardized and summed to create a composite score, which served as dependent variable representing counting principles.</p> <hd id="AN0144200760-18">Numeral identification</hd> <p>Children were shown 24 flashcards containing Arabic numerals one at a time presented in random order and asked to label the number on each card (adapted from Ramani & Siegler, [<reflink idref="bib49" id="ref59">49</reflink>]; Figure S7a). The cards included eight numbers less than 20 (<reflink idref="bib1" id="ref60">1</reflink>, 5, 8, 10, 11, 13, 15, 18), and two numbers from each subsequent decade (<reflink idref="bib20" id="ref61">20</reflink>, 26, 31, 37, 41, 44, 53, 59, 62, 64, 75, 78, 83, 86, 92, 95). The dependent variable was the number of numerals correctly identified.</p> <hd id="AN0144200760-19">Number line estimation</hd> <p>Children were presented with a 20‐cm number line on a tablet screen with 0 on the left end of the line and 100 on the right end (Ramani et al., [<reflink idref="bib48" id="ref62">48</reflink>]). A number was shown about 4 cm from the top of the screen and the child was asked to make a mark on the number line where they thought "the right place for the number is" on the line by tapping on it (Figure S8a). There were 26 trials of the following numbers 3, 4, 6, 8, 12, 14, 17, 18, 21, 24, 25, 29, 33, 39, 42, 48, 52, 57, 61, 64, 72, 79, 81, 84, 90, and 96 (Booth & Siegler, [<reflink idref="bib8" id="ref63">8</reflink>]). The numbers were presented in random order for each assessment session. The dependent variable was the accuracy of children's estimates, measured by percentage of absolute error (PAE), which is computed using the formula: PAE = (|estimate − estimated quantity|/scale of estimates) × 100 (Siegler & Booth, [<reflink idref="bib57" id="ref64">57</reflink>]). Because lower scores for the number line estimation task indicate higher accuracy, we reversed this score to ease interpretability.</p> <hd id="AN0144200760-20">Magnitude comparison</hd> <p>Children were shown 26 pairs of numbers in flipbook and asked to identify the larger number in each pair (adapted from Laski & Siegler, [<reflink idref="bib36" id="ref65">36</reflink>]; Figure S8b). Children were given 2 practice trials with feedback followed by 24 experimental trials. To create experimental pairs, we chose 11 of the 26 numbers from the number line estimation task; 2 numbers from the first decade and 1 number from each of the subsequent decades (i.e., 3, 8, 12, 25, 33, 42, 57, 64, 79, 84, 96). Of the 55 possible pairs, we chose 24 pairs with ratios ranging from 1.27 (e.g., 33|42) to 3.16 (e.g., 25|79). The larger number was presented on the left in half of the pairs. Half of the children within each condition were presented a given pair in one order and half in the opposite order (counterbalanced across sessions). The dependent variable was the number of pairs in which the larger number was correctly chosen.</p> <hd id="AN0144200760-21">Addition</hd> <p>Children were shown 12 addition problems presented horizontally on a computer screen one at a time. Children were asked to solve each problem without using pencil and paper and to say the answer aloud as soon as they had an answer (adapted from Geary, Hoard, Byrd‐Craven, & DeSoto, [<reflink idref="bib22" id="ref66">22</reflink>]; Figure S9). Children were first administered a simple example problem (2 + 2) with feedback followed by eight single‐digit simple problems and four complex problems. The simple problems involved the integers 2 through 9, although the same integer did not appear in the same problem. For 4 of these simple problems, the sum was 10 or less. The complex problems included one single‐digit and one double‐digit number (ranging from 14 to 19), and the sums ranged between 21 and 24. In half of the problems, the integer with the larger value was presented first. Two sets of problems following the same specifications were counterbalanced across the conditions and sessions. The dependent variable was the percentage of problems solved correctly.</p> <hd id="AN0144200760-22">Working memory measures</hd> <p></p> <hd id="AN0144200760-23">Complex span (Counting Sheep)</hd> <p>In this child‐friendly version of the counting span task (Case, Kurland, & Goldberg, [<reflink idref="bib11" id="ref67">11</reflink>]) programmed in E‐Prime 2, children were presented with a series of pictures containing a green meadow with two to five sheep as well as two to six wolves on a laptop computer (Figure S10). For each of the pictures, they were asked to count the number of sheep while ignoring the wolves, after which the next picture was presented. After two, three, or four pictures (= set size), they were asked to recall the number of sheep they counted from each picture in the correct order. Children were administered three blocks of trials, containing one trial per set size each in randomized order for a total amount of nine trials. Each block ended with a break screen to prevent fatigue. The dependent variable was the percentage of trials children recalled correctly.</p> <hd id="AN0144200760-24">Following instructions</hd> <p>We used a modified version of the Following Instructions (FI) task (Gathercole, Durling, Evans, Jeffcock, & Stone, [<reflink idref="bib20" id="ref68">20</reflink>]). Given that our population struggled verbally with the standard set of items (ruler, eraser, etc.; Ramani et al., [<reflink idref="bib48" id="ref69">48</reflink>]), here we used five child‐friendly items (car, fish, plane, cup, and box) each in three different colors (blue, red, and yellow), see Figure S11. Children were asked to perform actions that were verbally given by the experimenter (e.g., "touch the blue fish"). The number of actions increased as the task progressed. There were four trials for each set of actions. The task ended when the child made mistakes on two or more trials in a particular action set. Two forms (differentiated by different colors and objects) were counterbalanced among all three conditions and sessions. The dependent variable was the total number of trials answered correctly.</p> <hd id="AN0144200760-25">Spatial span (Touch Base)</hd> <p>We used a tablet‐based child‐friendly version of the Corsi Block Tapping Task (Corsi, [<reflink idref="bib14" id="ref70">14</reflink>]) to assess spatial WM. Instead of squares that light up as in typical eCorsi tasks (e.g., Brunetti, Del Gatto, & Delogu, [<reflink idref="bib9" id="ref71">9</reflink>]), in our version of the game, the tablet displayed nine planet craters and a character, Alvin the Alien, appeared at the craters in a particular sequence (Figure S12). Children were asked to tap on the craters in the same (forward version) or reverse (backward version) order as the alien appeared. The task started with set size two and increased in difficulty. There were two trials per set size, and children advanced to the next set size as long as they answered one trial correctly. The game ended when children answered both trials in a particular set size incorrectly. Children first played the forward version, followed by the backward version. The sequences presented to the children were counterbalanced across the conditions and sessions. The dependent variables for both versions were the total number of questions answered correctly.</p> <hd id="AN0144200760-26">Control measure</hd> <p>In order to account for potential pre‐existing individual differences and non‐specific improvements associated with tablet use, we implemented a control measure to assess processing speed and general executive function (inhibitory control, set shifting).</p> <hd id="AN0144200760-27">Dogs and monkeys</hd> <p>We used a tablet‐based control measure that was adapted from Davidson, Amso, Anderson, and Diamond ([<reflink idref="bib17" id="ref72">17</reflink>]). The task included three separate phases. In the first (congruent) phase, children saw a dog displayed on either the left or right of the screen and had to tap one of two buttons, here, the one that was on the same side as the dog (12 trials). In the second (incongruent) phase, children saw a monkey and had to tap the button that was on the opposite side of the monkey (12 trials). In the third (mixed) phase, children saw 24 dogs and 24 monkeys in randomized order and had to follow the same rule as in the previous phases (same side for dogs, opposite for monkeys; Figure S13). The dependent variables for this measure were reaction times (median) on accurate trials in the mixed block (third phase) for (a) congruent trials (processing speed), (b) incongruent trials (inhibitory control), and (c) switch trials (set shifting), that is, trials for which the rule changed from incongruent to congruent or vice versa (~50% of the trials).</p> <hd id="AN0144200760-28">Task order</hd> <p>The outcome measures were administered in the same order during the pretest, posttest, and follow‐up sessions. Counting principles, FI, addition, and complex WM span (counting sheep) were administered on the first day. Number line estimation, spatial span (touch base), numeral identification, magnitude comparison, and control task (dogs and monkeys) were administered on the second day.</p> <hd id="AN0144200760-29">Analytic approach</hd> <p></p> <hd id="AN0144200760-30">Primary analyses</hd> <p>Structural equation modeling conducted using Mplus Version 8.3 was used to answer the primary research questions. SEM is an analytic approach which models linear relations among latent variables and produces two regression models: (a) a measurement model that describes the relations between observed indicator variables and latent variables (i.e., factors; see Supporting Information, p. 15), and (b) a structural model which elucidates the effects of the latent factors on the latent outcome variables. In the present study, a latent change score model (LCS model; McArdle, [<reflink idref="bib39" id="ref73">39</reflink>], [<reflink idref="bib40" id="ref74">40</reflink>]; McArdle & Hamagami, [<reflink idref="bib41" id="ref75">41</reflink>]) was used to model change in numerical knowledge and WM over the course of the intervention. Furthermore, multigroup comparisons were conducted to test the effect of the condition on growth over time.</p> <p>Figure shows the LCS model used for the subsequent analysis of growth in numerical knowledge or WM. The observed variable indicators for numerical knowledge collected at pretest, posttest, and follow‐up are shown in rectangular boxes. All latent factors are shown in circles. The first‐order factors, pretest, posttest, and follow‐up, represent children's numerical knowledge skills at those three time points. The second‐order factors, D‐12 and D‐23, indicate the change in children's numerical knowledge performance from pretest to posttest and the change in numerical knowledge performance from posttest to follow‐up, respectively. Other parameters in the model include the factor loadings (λ), and the means of the change score factors (D‐12 and D‐23; <emph>μ</emph><subs>α</subs> and <emph>μ</emph><subs>β</subs>). Curved, two‐headed arrows represent variances, covariances, and straight, one‐headed arrows represent direct effects. For WM, the observed variable indicators include four measures. Otherwise, the model used for the subsequent analysis of WM growth is the same as described above for numerical knowledge.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01jul20/desc12908-fig-0001.jpg?ephost1=dGJyMMvl7ESepq84yOvsOLCmsE6epq5Srqa4SK6WxWXS" alt="desc12908-fig-0001.jpg" title="Latent change score (LCS) model defining the effect of numerical knowledge indicators on the latent variables representing the change in numerical knowledge from pretest to posttest and the change in numerical knowledge from posttest to follow‐up. The intercepts of the variable indicators (τ), error variances of the indicators (σ2), and the covariances between the same indicators at different time points (σx,y) are not shown above but are included in the model. The LCS model representing the change in working memory over time is identical except the indicators at each time point in the working memory model include four measures, that is, Touch base forward, Touch base backward, Counting sheep, and Following instructions" /> </p> <p></p> <p>The primary goal of the subsequent analyses is to estimate the change from pretest to posttest (D‐12) and from posttest to follow‐up (D‐23) and to compare the change estimates (<emph>μ</emph><subs>α</subs> and <emph>μ</emph><subs>β</subs>) of children in the domain‐specific (numerical knowledge) or the domain‐general (WM) condition with the estimates of the children in the active control condition (Figure). Prior to comparing change over time, the invariance of the measurement portion of the models for numerical knowledge and for WM must be established. It is important to determine if there is stability in the measurement of the constructs over time in order to ensure that any growth in latent numerical knowledge or latent WM reflects change in the underlying phenomena and not due to any change in the measurement model.</p> <p>To test the measurement invariance of numerical knowledge and WM over time, two separate confirmatory factor analysis models were fit to the data at each time point to evaluate whether the form of the observed latent variable relation is the same across time points. In service of this goal, a series of subsequently more stringent constraints were applied to the factor loadings and intercepts of the measured variables. Beginning with an unconstrained model, constraints were first applied to factor loadings to test their invariance at the three different time points and next to observed variable intercept values across time. These competing models were tested against each other to determine the most appropriate measurement model for the data. See Figure for the final numerical knowledge and WM measurement models. The established measurement models are presented in the Supporting Information (p. 16) and were retained for subsequent analyses in which the structural model is applied.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01jul20/desc12908-fig-0002.jpg?ephost1=dGJyMMvl7ESepq84yOvsOLCmsE6epq5Srqa4SK6WxWXS" alt="desc12908-fig-0002.jpg" title="Measurement model for Pretest, Posttest, and Follow‐up numerical knowledge. Count, counting principles; NumID, numeral identification; NumLine, number line; MagComp, magnitude comparison; Add, addition. The measurement model for Pretest, Posttest, and Follow‐up working memory is identical except that the indicators are TBF, Touch base forward; TBB, Touch base backward; Sheep, Counting sheep; FI, Following instructions. Single‐headed arrows pointing to the indicators denote error variances (σ2)" /> </p> <p></p> <p>Once appropriate measurement models were identified, the structural models were constructed. In the numerical knowledge structural model (Figure), the latent variable representing children's numerical knowledge at posttest was predicted by pretest and some amount of change, which was estimated in the model. Follow‐up was predicted by posttest and some amount of change, which was estimated in the model. Figure also applies to the WM structural model, in which the latent variable representing WM at posttest was predicted by pretest and some amount of change, which was estimated in the model. Follow‐up was predicted by posttest and some amount of change, which was estimated in the model.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/5G5/01jul20/desc12908-fig-0003.jpg?ephost1=dGJyMMvl7ESepq84yOvsOLCmsE6epq5Srqa4SK6WxWXS" alt="desc12908-fig-0003.jpg" title="Structural model representing the change in children's numerical knowledge or working memory from pretest to posttest to follow‐up" /> </p> <p></p> <hd id="AN0144200760-34">Additional analyses</hd> <p>For the analysis of the control measure that was not part of the SEM model, we used analyses of covariance (ANCOVAs) with group as the between‐subject variable and pretest performance as the covariate for each of the dependent measures, after testing for pretest differences using one‐way ANOVAs. We report effect sizes as well as Bayes factors (BF) using a Cauchy prior (γ = 0.707) as the scale invariant, information consistent prior is more conservative and theoretically desirable (Rouder, Morey, Speckman, & Province, [<reflink idref="bib50" id="ref76">50</reflink>]; Wagenmakers et al., [<reflink idref="bib64" id="ref77">64</reflink>]). Finally, we also analyzed training performance for each of the interventions using gains comparing the first and the last training session. The results of both of these analyses are presented in the Supporting Information (p. 12).</p> <hd id="AN0144200760-35">RESULTS</hd> <p></p> <hd id="AN0144200760-36">Preliminary analyses</hd> <p>Preliminary analyses were conducted using JASP version 0.8.6 (JASP Team, [<reflink idref="bib30" id="ref78">30</reflink>]) . Analyses of demographic data revealed no age, gender, ethnicity, race, or home language differences between groups (all <emph>p</emph>s > .22 and BF<subs>10</subs>s < 0.14; see Table). Group differences in maternal education and household income were marginally significant with classical tests (χ<sups>2</sups>(<reflink idref="bib10" id="ref79">10</reflink>) = 18.47, <emph>p</emph> = .048 and χ<sups>2</sups>(<reflink idref="bib14" id="ref80">14</reflink>) = 23.98, <emph>p</emph> = .046, respectively), however, Bayesian analyses revealed that there is only anecdotal, weak evidence for group differences in maternal education (BF<subs>10</subs> = 1.21), and more evidence showing a <emph>lack</emph> of group differences in household income (BF<subs>10</subs> = 0.29). Therefore, demographic variables were not included in the subsequent analyses. A MANOVA using the five math outcomes as dependent variables showed no difference in baseline math performance across the three conditions (<emph>F</emph>(<reflink idref="bib10" id="ref81">10</reflink>, 274) = 1.72, <emph>p</emph> = .075, η<subs>p</subs><sups>2</sups> = 0.059). Likewise, a MANOVA using the four WM tasks as dependent variables revealed no difference in baseline WM performance across the three conditions (<emph>F</emph>(<reflink idref="bib8" id="ref82">8</reflink>, 270) = 0.92, <emph>p</emph> = .50, η<subs>p</subs><sups>2</sups> = 0.026). Finally, there were no group differences at baseline in any of the three control variables either (all BF<subs>10</subs> < 0.33; see Supporting Information, pp. 20–21).</p> <p>Descriptive data as well as reliability estimates, effect sizes and BF for each of the outcome measures as a function of testing session and intervention are provided in Table.</p> <p>Descriptive data for outcome measures as a function of group and testing session, along with within‐group comparisons for pre versus post and post versus follow‐up</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Group, measure</th><th align="left">Pretest</th><th align="left">Posttest</th><th align="left">Follow‐up test</th><th align="left">Pre versus post</th><th align="left">Post versus follow‐up</th></tr><tr><th align="left"><italic>n</italic></th><th align="left">Mean</th><th align="left"><italic>SD</italic></th><th align="left">Min</th><th align="left">Max</th><th align="left"><italic>n</italic></th><th align="left">Mean</th><th align="left"><italic>SD</italic></th><th align="left">Min</th><th align="left">Max</th><th align="left"><italic>n</italic></th><th align="left">Mean</th><th align="left"><italic>SD</italic></th><th align="left">Min</th><th align="left">Max</th><th align="left"><italic>p</italic></th><th align="left"><italic>r</italic></th><th align="left">ES</th><th align="left">BF10</th><th align="left"><italic>p</italic></th><th align="left"><italic>r</italic></th><th align="left">ES</th><th align="left">BF10</th></tr></thead><tbody><tr><td align="left">Number game group</td></tr><tr><td align="left">Math</td></tr><tr><td align="left">Number line</td><td align="char" char=".">47</td><td align="left">0.78</td><td align="left">0.07</td><td align="left">0.66</td><td align="left">0.96</td><td align="char" char=".">45</td><td align="left">0.80</td><td align="left">0.10</td><td align="left">0.35</td><td align="left">0.95</td><td align="char" char=".">43</td><td align="left">0.82</td><td align="left">0.08</td><td align="left">0.56</td><td align="left">0.94</td><td align="char" char=".">.138</td><td align="char" char=".">.59</td><td align="char" char=".">0.21</td><td align="char" char=".">0.47</td><td align="char" char=".">.771</td><td align="char" char=".">.81</td><td align="char" char=".">0.31</td><td align="char" char=".">0.18</td></tr><tr><td align="left">Addition</td><td align="char" char=".">46</td><td align="left">4.50</td><td align="left">3.30</td><td align="left">0</td><td align="left">11</td><td align="char" char=".">46</td><td align="left">5.70</td><td align="left">3.67</td><td align="left">0</td><td align="left">12</td><td align="char" char=".">45</td><td align="left">5.53</td><td align="left">3.27</td><td align="left">0</td><td align="left">12</td><td align="char" char=".">.001</td><td align="char" char=".">.82</td><td align="char" char=".">0.56</td><td align="char" char=".">22.27</td><td align="char" char=".">.114</td><td align="char" char=".">.90</td><td align="char" char=".">−0.10</td><td align="char" char=".">0.54</td></tr><tr><td align="left">Magnitude Comp.</td><td align="char" char=".">46</td><td align="left">20.17</td><td align="left">4.04</td><td align="left">9</td><td align="left">24</td><td align="char" char=".">45</td><td align="left">20.89</td><td align="left">3.80</td><td align="left">10</td><td align="left">24</td><td align="char" char=".">46</td><td align="left">20.93</td><td align="left">3.67</td><td align="left">13</td><td align="left">24</td><td align="char" char=".">.036</td><td align="char" char=".">.79</td><td align="char" char=".">0.28</td><td align="char" char=".">1.36</td><td align="char" char=".">.727</td><td align="char" char=".">.46</td><td align="char" char=".">0.01</td><td align="char" char=".">0.17</td></tr><tr><td align="left">Numeral ID</td><td align="char" char=".">47</td><td align="left">20.34</td><td align="left">5.60</td><td align="left">3</td><td align="left">24</td><td align="char" char=".">45</td><td align="left">20.36</td><td align="left">5.69</td><td align="left">3</td><td align="left">24</td><td align="char" char=".">46</td><td align="left">21.35</td><td align="left">4.38</td><td align="left">5</td><td align="left">24</td><td align="char" char=".">.806</td><td align="char" char=".">.64</td><td align="char" char=".">0.00</td><td align="char" char=".">0.17</td><td align="char" char=".">.220</td><td align="char" char=".">.62</td><td align="char" char=".">0.22</td><td align="char" char=".">0.34</td></tr><tr><td align="left">Counting</td><td align="char" char=".">47</td><td align="left">0.26</td><td align="left">1.52</td><td align="left">−2.66</td><td align="left">2.12</td><td align="char" char=".">47</td><td align="left">0.20</td><td align="left">1.54</td><td align="left">−4.84</td><td align="left">1.81</td><td align="char" char=".">46</td><td align="left">0.27</td><td align="left">1.43</td><td align="left">−3.48</td><td align="left">1.75</td><td align="char" char=".">.820</td><td align="char" char=".">.45</td><td align="char" char=".">−0.03</td><td align="char" char=".">0.16</td><td align="char" char=".">.864</td><td align="char" char=".">.35</td><td align="char" char=".">0.04</td><td align="char" char=".">0.16</td></tr><tr><td align="left">Working memory</td></tr><tr><td align="left">Touch Base Fwd.</td><td align="char" char=".">47</td><td align="left">3.57</td><td align="left">2.04</td><td align="left">0</td><td align="left">7</td><td align="char" char=".">44</td><td align="left">4.34</td><td align="left">2.00</td><td align="left">0</td><td align="left">8</td><td align="char" char=".">42</td><td align="left">4.29</td><td align="left">2.06</td><td align="left">0</td><td align="left">8</td><td align="char" char=".">.008</td><td align="char" char=".">.57</td><td align="char" char=".">0.41</td><td align="char" char=".">4.55</td><td align="char" char=".">.722</td><td align="char" char=".">.59</td><td align="char" char=".">−0.03</td><td align="char" char=".">0.18</td></tr><tr><td align="left">Touch Base Bw.</td><td align="char" char=".">46</td><td align="left">1.87</td><td align="left">1.59</td><td align="left">0</td><td align="left">6</td><td align="char" char=".">42</td><td align="left">2.50</td><td align="left">1.58</td><td align="left">0</td><td align="left">7</td><td align="char" char=".">42</td><td align="left">2.98</td><td align="left">1.59</td><td align="left">0</td><td align="left">5</td><td align="char" char=".">.019</td><td align="char" char=".">.51</td><td align="char" char=".">0.40</td><td align="char" char=".">2.36</td><td align="char" char=".">.320</td><td align="char" char=".">.35</td><td align="char" char=".">0.27</td><td align="char" char=".">0.28</td></tr><tr><td align="left">Counting Sheep</td><td align="char" char=".">46</td><td align="left">14.73</td><td align="left">20.69</td><td align="left">0</td><td align="left">100</td><td align="char" char=".">46</td><td align="left">26.67</td><td align="left">25.67</td><td align="left">0</td><td align="left">77.78</td><td align="char" char=".">45</td><td align="left">27.16</td><td align="left">28.78</td><td align="left">0</td><td align="left">100</td><td align="char" char=".">.012</td><td align="char" char=".">.29</td><td align="char" char=".">0.43</td><td align="char" char=".">3.33</td><td align="char" char=".">1.00</td><td align="char" char=".">.55</td><td align="char" char=".">0.02</td><td align="char" char=".">0.17</td></tr><tr><td align="left">Following Instr.</td><td align="char" char=".">47</td><td align="left">8.72</td><td align="left">3.01</td><td align="left">2</td><td align="left">16</td><td align="char" char=".">46</td><td align="left">8.54</td><td align="left">3.24</td><td align="left">0</td><td align="left">16</td><td align="char" char=".">45</td><td align="left">9.09</td><td align="left">2.62</td><td align="left">2</td><td align="left">15</td><td align="char" char=".">.564</td><td align="char" char=".">.44</td><td align="char" char=".">−0.05</td><td align="char" char=".">0.19</td><td align="char" char=".">.427</td><td align="char" char=".">.45</td><td align="char" char=".">0.18</td><td align="char" char=".">0.22</td></tr><tr><td align="left">Control</td></tr><tr><td align="left">Processing speed</td><td align="char" char=".">44</td><td align="left">1,448</td><td align="left">259</td><td align="left">1,004</td><td align="left">2,255</td><td align="char" char=".">43</td><td align="left">1,421</td><td align="left">297</td><td align="left">703</td><td align="left">1,977</td><td align="char" char=".">42</td><td align="left">1,341</td><td align="left">302</td><td align="left">563</td><td align="left">2,458</td><td align="char" char=".">.655</td><td align="char" char=".">.63</td><td align="char" char=".">−0.11</td><td align="char" char=".">0.19</td><td align="char" char=".">.029</td><td align="char" char=".">.59</td><td align="char" char=".">−0.29</td><td align="char" char=".">1.72</td></tr><tr><td align="left">Inhibitory control</td><td align="char" char=".">44</td><td align="left">1,541</td><td align="left">320</td><td align="left">862</td><td align="left">2,308</td><td align="char" char=".">43</td><td align="left">1,445</td><td align="left">229</td><td align="left">1,038</td><td align="left">2,036</td><td align="char" char=".">42</td><td align="left">1,374</td><td align="left">319</td><td align="left">280</td><td align="left">2,313</td><td align="char" char=".">.086</td><td align="char" char=".">.35</td><td align="char" char=".">−0.30</td><td align="char" char=".">0.70</td><td align="char" char=".">.291</td><td align="char" char=".">.41</td><td align="char" char=".">−0.23</td><td align="char" char=".">0.30</td></tr><tr><td align="left">Set shifting</td><td align="char" char=".">44</td><td align="left">1,558</td><td align="left">287</td><td align="left">985</td><td align="left">2,255</td><td align="char" char=".">43</td><td align="left">1,476</td><td align="left">242</td><td align="left">892</td><td align="left">2,123</td><td align="char" char=".">42</td><td align="left">1,418</td><td align="left">356</td><td align="left">280</td><td align="left">2,562</td><td align="char" char=".">.046</td><td align="char" char=".">.58</td><td align="char" char=".">−0.33</td><td align="char" char=".">1.15</td><td align="char" char=".">.221</td><td align="char" char=".">.48</td><td align="char" char=".">−0.18</td><td align="char" char=".">0.36</td></tr><tr><td align="left">Working memory game group</td></tr><tr><td align="left">Math</td></tr><tr><td align="left">Number Line</td><td align="char" char=".">48</td><td align="left">0.75</td><td align="left">0.12</td><td align="left">0.39</td><td align="left">0.95</td><td align="char" char=".">47</td><td align="left">0.76</td><td align="left">0.12</td><td align="left">0.41</td><td align="left">0.95</td><td align="char" char=".">42</td><td align="left">0.78</td><td align="left">0.13</td><td align="left">0.46</td><td align="left">0.96</td><td align="char" char=".">.411</td><td align="char" char=".">.77</td><td align="char" char=".">0.13</td><td align="char" char=".">0.22</td><td align="char" char=".">.833</td><td align="char" char=".">.91</td><td align="char" char=".">0.23</td><td align="char" char=".">0.17</td></tr><tr><td align="left">Addition</td><td align="char" char=".">48</td><td align="left">4.50</td><td align="left">3.82</td><td align="left">0</td><td align="left">12</td><td align="char" char=".">48</td><td align="left">4.90</td><td align="left">4.21</td><td align="left">0</td><td align="left">12</td><td align="char" char=".">45</td><td align="left">4.60</td><td align="left">3.77</td><td align="left">0</td><td align="left">12</td><td align="char" char=".">.198</td><td align="char" char=".">.87</td><td align="char" char=".">0.19</td><td align="char" char=".">0.35</td><td align="char" char=".">.452</td><td align="char" char=".">.84</td><td align="char" char=".">−0.13</td><td align="char" char=".">0.21</td></tr><tr><td align="left">Magnitude Comp.</td><td align="char" char=".">48</td><td align="left">18.71</td><td align="left">4.73</td><td align="left">10</td><td align="left">24</td><td align="char" char=".">47</td><td align="left">19.15</td><td align="left">5.14</td><td align="left">6</td><td align="left">24</td><td align="char" char=".">45</td><td align="left">19.58</td><td align="left">4.84</td><td align="left">10</td><td align="left">24</td><td align="char" char=".">.193</td><td align="char" char=".">.95</td><td align="char" char=".">0.27</td><td align="char" char=".">0.36</td><td align="char" char=".">.357</td><td align="char" char=".">.80</td><td align="char" char=".">0.14</td><td align="char" char=".">0.24</td></tr><tr><td align="left">Numeral ID</td><td align="char" char=".">48</td><td align="left">15.92</td><td align="left">8.31</td><td align="left">0</td><td align="left">24</td><td align="char" char=".">48</td><td align="left">16.71</td><td align="left">7.85</td><td align="left">0</td><td align="left">24</td><td align="char" char=".">45</td><td align="left">17.58</td><td align="left">7.50</td><td align="left">0</td><td align="left">24</td><td align="char" char=".">.062</td><td align="char" char=".">.94</td><td align="char" char=".">0.28</td><td align="char" char=".">0.83</td><td align="char" char=".">.013</td><td align="char" char=".">.96</td><td align="char" char=".">0.40</td><td align="char" char=".">3.12</td></tr><tr><td align="left">Counting</td><td align="char" char=".">47</td><td align="left">0.00</td><td align="left">1.89</td><td align="left">−6.31</td><td align="left">2.12</td><td align="char" char=".">48</td><td align="left">−0.29</td><td align="left">1.98</td><td align="left">−6.73</td><td align="left">1.81</td><td align="char" char=".">45</td><td align="left">−0.15</td><td align="left">2.05</td><td align="left">−5.15</td><td align="left">1.75</td><td align="char" char=".">.125</td><td align="char" char=".">.77</td><td align="char" char=".">−0.22</td><td align="char" char=".">0.49</td><td align="char" char=".">.640</td><td align="char" char=".">.67</td><td align="char" char=".">0.09</td><td align="char" char=".">0.18</td></tr><tr><td align="left">Working memory</td></tr><tr><td align="left">Touch Base Fwd.</td><td align="char" char=".">48</td><td align="left">2.94</td><td align="left">2.23</td><td align="left">0</td><td align="left">7</td><td align="char" char=".">45</td><td align="left">3.44</td><td align="left">2.19</td><td align="left">0</td><td align="left">8</td><td align="char" char=".">42</td><td align="left">4.38</td><td align="left">1.62</td><td align="left">1</td><td align="left">8</td><td align="char" char=".">.125</td><td align="char" char=".">.40</td><td align="char" char=".">0.21</td><td align="char" char=".">0.53</td><td align="char" char=".">.060</td><td align="char" char=".">.48</td><td align="char" char=".">0.47</td><td align="char" char=".">0.96</td></tr><tr><td align="left">Touch Base Bw.</td><td align="char" char=".">47</td><td align="left">1.92</td><td align="left">1.43</td><td align="left">0</td><td align="left">5</td><td align="char" char=".">46</td><td align="left">2.15</td><td align="left">1.96</td><td align="left">0</td><td align="left">7</td><td align="char" char=".">41</td><td align="left">2.22</td><td align="left">1.86</td><td align="left">0</td><td align="left">7</td><td align="char" char=".">.440</td><td align="char" char=".">.27</td><td align="char" char=".">0.11</td><td align="char" char=".">0.21</td><td align="char" char=".">.650</td><td align="char" char=".">.42</td><td align="char" char=".">0.03</td><td align="char" char=".">0.19</td></tr><tr><td align="left">Counting sheep</td><td align="char" char=".">47</td><td align="left">16.31</td><td align="left">22.68</td><td align="left">0</td><td align="left">100</td><td align="char" char=".">45</td><td align="left">22.47</td><td align="left">26.64</td><td align="left">0</td><td align="left">100</td><td align="char" char=".">43</td><td align="left">26.1</td><td align="left">25.76</td><td align="left">0</td><td align="left">100</td><td align="char" char=".">.080</td><td align="char" char=".">.38</td><td align="char" char=".">0.22</td><td align="char" char=".">0.74</td><td align="char" char=".">.550</td><td align="char" char=".">.54</td><td align="char" char=".">0.14</td><td align="char" char=".">0.20</td></tr><tr><td align="left">Following Inst.</td><td align="char" char=".">48</td><td align="left">8.06</td><td align="left">3.19</td><td align="left">0</td><td align="left">15</td><td align="char" char=".">48</td><td align="left">8.48</td><td align="left">2.62</td><td align="left">1</td><td align="left">13</td><td align="char" char=".">45</td><td align="left">8.58</td><td align="left">2.55</td><td align="left">1</td><td align="left">15</td><td align="char" char=".">.270</td><td align="char" char=".">.62</td><td align="char" char=".">0.16</td><td align="char" char=".">0.28</td><td align="char" char=".">.940</td><td align="char" char=".">.69</td><td align="char" char=".">0.05</td><td align="char" char=".">0.16</td></tr><tr><td align="left">Control</td></tr><tr><td align="left">Processing speed</td><td align="char" char=".">46</td><td align="left">1,470</td><td align="left">391</td><td align="left">884</td><td align="left">3,176</td><td align="char" char=".">47</td><td align="left">1,517</td><td align="left">533</td><td align="left">904</td><td align="left">3,721</td><td align="char" char=".">41</td><td align="left">1,486</td><td align="left">745</td><td align="left">953</td><td align="left">5,605</td><td align="char" char=".">.518</td><td align="char" char=".">.25</td><td align="char" char=".">0.08</td><td align="char" char=".">0.20</td><td align="char" char=".">.857</td><td align="char" char=".">.53</td><td align="char" char=".">−0.05</td><td align="char" char=".">0.17</td></tr><tr><td align="left">Inhibitory control</td><td align="char" char=".">46</td><td align="left">1,420</td><td align="left">293</td><td align="left">933</td><td align="left">1979</td><td align="char" char=".">47</td><td align="left">1,576</td><td align="left">476</td><td align="left">951</td><td align="left">2,698</td><td align="char" char=".">41</td><td align="left">1,451</td><td align="left">412</td><td align="left">966</td><td align="left">2,744</td><td align="char" char=".">.033</td><td align="char" char=".">.27</td><td align="char" char=".">0.32</td><td align="char" char=".">1.43</td><td align="char" char=".">.037</td><td align="char" char=".">.71</td><td align="char" char=".">−0.36</td><td align="char" char=".">1.35</td></tr><tr><td align="left">Set shifting</td><td align="char" char=".">46</td><td align="left">1,519</td><td align="left">305</td><td align="left">984</td><td align="left">2,395</td><td align="char" char=".">47</td><td align="left">1,686</td><td align="left">783</td><td align="left">945</td><td align="left">5,591</td><td align="char" char=".">41</td><td align="left">1518</td><td align="left">467</td><td align="left">984</td><td align="left">3,259</td><td align="char" char=".">.172</td><td align="char" char=".">.14</td><td align="char" char=".">0.21</td><td align="char" char=".">0.40</td><td align="char" char=".">.120</td><td align="char" char=".">.54</td><td align="char" char=".">−0.25</td><td align="char" char=".">0.54</td></tr><tr><td align="left">Control game group</td></tr><tr><td align="left">Math</td></tr><tr><td align="left">Number line</td><td align="char" char=".">53</td><td align="left">0.77</td><td align="left">0.09</td><td align="left">0.53</td><td align="left">0.90</td><td align="char" char=".">51</td><td align="left">0.78</td><td align="left">0.09</td><td align="left">0.56</td><td align="left">0.92</td><td align="char" char=".">45</td><td align="left">0.80</td><td align="left">0.09</td><td align="left">0.53</td><td align="left">0.93</td><td align="char" char=".">.123</td><td align="char" char=".">.74</td><td align="char" char=".">0.22</td><td align="char" char=".">0.48</td><td align="char" char=".">.425</td><td align="char" char=".">.71</td><td align="char" char=".">0.21</td><td align="char" char=".">0.22</td></tr><tr><td align="left">Addition</td><td align="char" char=".">53</td><td align="left">3.76</td><td align="left">3.04</td><td align="left">0</td><td align="left">12</td><td align="char" char=".">53</td><td align="left">4.13</td><td align="left">2.96</td><td align="left">0</td><td align="left">11</td><td align="char" char=".">49</td><td align="left">4.25</td><td align="left">2.93</td><td align="left">0</td><td align="left">11</td><td align="char" char=".">.232</td><td align="char" char=".">.71</td><td align="char" char=".">0.16</td><td align="char" char=".">0.30</td><td align="char" char=".">.898</td><td align="char" char=".">.72</td><td align="char" char=".">0.05</td><td align="char" char=".">0.16</td></tr><tr><td align="left">Magnitude Comp.</td><td align="char" char=".">52</td><td align="left">19.58</td><td align="left">4.65</td><td align="left">3</td><td align="left">24</td><td align="char" char=".">52</td><td align="left">19.06</td><td align="left">5.77</td><td align="left">0</td><td align="left">24</td><td align="char" char=".">48</td><td align="left">19.60</td><td align="left">5.18</td><td align="left">0</td><td align="left">24</td><td align="char" char=".">.559</td><td align="char" char=".">.56</td><td align="char" char=".">−0.10</td><td align="char" char=".">0.18</td><td align="char" char=".">.305</td><td align="char" char=".">.41</td><td align="char" char=".">0.09</td><td align="char" char=".">0.26</td></tr><tr><td align="left">Numeral ID</td><td align="char" char=".">52</td><td align="left">18.25</td><td align="left">6.51</td><td align="left">4</td><td align="left">24</td><td align="char" char=".">52</td><td align="left">19.81</td><td align="left">5.84</td><td align="left">3</td><td align="left">24</td><td align="char" char=".">48</td><td align="left">19.81</td><td align="left">5.93</td><td align="left">4</td><td align="left">24</td><td align="char" char=".">.013</td><td align="char" char=".">.85</td><td align="char" char=".">0.45</td><td align="char" char=".">3.03</td><td align="char" char=".">.339</td><td align="char" char=".">.93</td><td align="char" char=".">0.00</td><td align="char" char=".">0.25</td></tr><tr><td align="left">Counting</td><td align="char" char=".">53</td><td align="left">−0.11</td><td align="left">1.45</td><td align="left">−4.48</td><td align="left">2.12</td><td align="char" char=".">53</td><td align="left">0.10</td><td align="left">1.47</td><td align="left">−4.84</td><td align="left">1.81</td><td align="char" char=".">49</td><td align="left">−0.05</td><td align="left">1.53</td><td align="left">−3.99</td><td align="left">1.75</td><td align="char" char=".">.271</td><td align="char" char=".">.58</td><td align="char" char=".">0.15</td><td align="char" char=".">0.27</td><td align="char" char=".">.525</td><td align="char" char=".">.59</td><td align="char" char=".">−0.11</td><td align="char" char=".">0.19</td></tr><tr><td align="left">Working memory</td></tr><tr><td align="left">Touch Base Fwd.</td><td align="char" char=".">51</td><td align="left">3.73</td><td align="left">1.92</td><td align="left">0</td><td align="left">8</td><td align="char" char=".">51</td><td align="left">3.84</td><td align="left">2.16</td><td align="left">0</td><td align="left">8</td><td align="char" char=".">45</td><td align="left">4.02</td><td align="left">2.01</td><td align="left">0</td><td align="left">8</td><td align="char" char=".">.730</td><td align="char" char=".">.50</td><td align="char" char=".">0.05</td><td align="char" char=".">0.17</td><td align="char" char=".">.670</td><td align="char" char=".">.49</td><td align="char" char=".">0.09</td><td align="char" char=".">0.18</td></tr><tr><td align="left">Touch base Bw.</td><td align="char" char=".">50</td><td align="left">1.72</td><td align="left">1.47</td><td align="left">0</td><td align="left">6</td><td align="char" char=".">49</td><td align="left">2.27</td><td align="left">1.68</td><td align="left">0</td><td align="left">7</td><td align="char" char=".">44</td><td align="left">2.34</td><td align="left">1.74</td><td align="left">0</td><td align="left">7</td><td align="char" char=".">.003</td><td align="char" char=".">.63</td><td align="char" char=".">0.40</td><td align="char" char=".">12.60</td><td align="char" char=".">.530</td><td align="char" char=".">.36</td><td align="char" char=".">0.04</td><td align="char" char=".">0.20</td></tr><tr><td align="left">Counting sheep</td><td align="char" char=".">53</td><td align="left">13.52</td><td align="left">16.51</td><td align="left">0</td><td align="left">55.56</td><td align="char" char=".">51</td><td align="left">20.48</td><td align="left">19.67</td><td align="left">0</td><td align="left">77.78</td><td align="char" char=".">47</td><td align="left">23.64</td><td align="left">24.8</td><td align="left">0</td><td align="left">88.89</td><td align="char" char=".">.013</td><td align="char" char=".">.32</td><td align="char" char=".">0.33</td><td align="char" char=".">2.98</td><td align="char" char=".">.840</td><td align="char" char=".">.42</td><td align="char" char=".">0.13</td><td align="char" char=".">0.16</td></tr><tr><td align="left">Following Inst.</td><td align="char" char=".">53</td><td align="left">8.45</td><td align="left">2.61</td><td align="left">4</td><td align="left">17</td><td align="char" char=".">52</td><td align="left">8.42</td><td align="left">2.91</td><td align="left">1</td><td align="left">17</td><td align="char" char=".">49</td><td align="left">8.41</td><td align="left">2.42</td><td align="left">4</td><td align="left">14</td><td align="char" char=".">.960</td><td align="char" char=".">.54</td><td align="char" char=".">−0.01</td><td align="char" char=".">0.15</td><td align="char" char=".">.400</td><td align="char" char=".">.64</td><td align="char" char=".">0.00</td><td align="char" char=".">0.22</td></tr><tr><td align="left">Control</td></tr><tr><td align="left">Processing speed</td><td align="char" char=".">50</td><td align="left">1,513</td><td align="left">367</td><td align="left">950</td><td align="left">2,924</td><td align="char" char=".">50</td><td align="left">1,432</td><td align="left">366</td><td align="left">699</td><td align="left">2,515</td><td align="char" char=".">45</td><td align="left">1,408</td><td align="left">358</td><td align="left">1,023</td><td align="left">2,716</td><td align="char" char=".">.087</td><td align="char" char=".">.52</td><td align="char" char=".">−0.23</td><td align="char" char=".">0.64</td><td align="char" char=".">.380</td><td align="char" char=".">.48</td><td align="char" char=".">−0.07</td><td align="char" char=".">0.24</td></tr><tr><td align="left">Inhibitory control</td><td align="char" char=".">50</td><td align="left">1,503</td><td align="left">307</td><td align="left">982</td><td align="left">2,472</td><td align="char" char=".">50</td><td align="left">1,534</td><td align="left">527</td><td align="left">823</td><td align="left">3,710</td><td align="char" char=".">45</td><td align="left">1,484</td><td align="left">372</td><td align="left">1,029</td><td align="left">2,537</td><td align="char" char=".">.847</td><td align="char" char=".">.57</td><td align="char" char=".">0.07</td><td align="char" char=".">0.16</td><td align="char" char=".">.845</td><td align="char" char=".">.43</td><td align="char" char=".">−0.10</td><td align="char" char=".">0.17</td></tr><tr><td align="left">Set shifting</td><td align="char" char=".">50</td><td align="left">1,536</td><td align="left">298</td><td align="left">1,041</td><td align="left">2,584</td><td align="char" char=".">50</td><td align="left">1,545</td><td align="left">461</td><td align="left">699</td><td align="left">3,381</td><td align="char" char=".">45</td><td align="left">1,455</td><td align="left">335</td><td align="left">1,029</td><td align="left">2,437</td><td align="char" char=".">.670</td><td align="char" char=".">.48</td><td align="char" char=".">0.02</td><td align="char" char=".">0.17</td><td align="char" char=".">.186</td><td align="char" char=".">.42</td><td align="char" char=".">−0.20</td><td align="char" char=".">0.39</td></tr></tbody></table> </ephtml> </p> <ulist> <item>3 Note</item> <item>4 <emph>r</emph> = retest reliability (Pearson correlation); ES = effect size that accounts for the correlation between pre‐ and posttest or post‐ and follow‐up measures: <ephtml> <math altimg="urn:x-wiley:1363755X:media:desc12908:desc12908-math-0001" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext>ES</mtext><mo>=</mo><mrow><mo>(</mo><msub><mtext>Mean</mtext><mtext>post</mtext></msub><mo>-</mo><msub><mtext>Mean</mtext><mtext>pre</mtext></msub><mo>)</mo></mrow><mo>/</mo><msqrt><mrow><mo>(</mo><mi>S</mi><msubsup><mi>D</mi><mtext>pre</mtext><mn>2</mn></msubsup><mo>+</mo><mi>S</mi><msubsup><mi>D</mi><mtext>post</mtext><mn>2</mn></msubsup><mo>-</mo><mn>2</mn><mi>r</mi><mo>×</mo><mi>S</mi><msub><mi>D</mi><mtext>pre</mtext></msub><mo>×</mo><mi>S</mi><msub><mi>D</mi><mtext>post</mtext></msub><mo>)</mo></mrow></msqrt></mrow></math> </ephtml> . BF<subs>10</subs> = Bayes factor in favor of the alternative hypothesis calculated with a non‐informative, conservative Cauchy prior of 0.707. For the control measures (reaction times), smaller values are indicative of better performance, for all other measures, higher values indicate better performance.</item> </ulist> <hd id="AN0144200760-37">Missing data</hd> <p>As would be expected, missing data increased as the study progressed with the greatest amount at the follow‐up visit due to attrition, technical issues, and restrictions from the data collection sites (1.05% missing at pretest; 3.07% missing at posttest; 8.63% missing at follow‐up). The data were missing at random across the three conditions (chi‐square tests of missing data and conditions were not significant for all measures, <emph>p</emph>s range from.16 to.83). Given that the Full Information Maximum Likelihood (FIML) estimation method for the SEM is particularly suited for dealing with missing values, FIML was used in the subsequent analyses.</p> <hd id="AN0144200760-38">Primary analyses</hd> <p></p> <hd id="AN0144200760-39">Numerical knowledge</hd> <p></p> <hd id="AN0144200760-40">The structural model</hd> <p>Retaining the established measurement model (Supporting Information, pp. 14–16), the structural portion of the model was constructed. The latent variable representing children's numerical knowledge at posttest was predicted by pretest and some amount of change, which was estimated in the model. Follow‐up was predicted by posttest and some amount of change, which was estimated in the model. According to absolute (SRMR = 0.078), parsimonious (RMSEA = 0.000), and incremental (CFI = 1.000) fit indices, the structural model had excellent fit, χ<sups>2</sups>(<reflink idref="bib91" id="ref83">91</reflink>) = 79.654, <emph>p =</emph> .490.</p> <hd id="AN0144200760-41">Multigroup comparison</hd> <p>A multigroup comparison using an LCS model was conducted using repeated measures of children's numerical knowledge. In the final multigroup model, all paths of interest (i.e., <emph>μ</emph><subs>α</subs>, the path representing the amount of change from pretest to posttest, and <emph>μ</emph><subs>β</subs>, the path representing the amount of change from posttest to follow‐up) were allowed to vary across groups. In this way, the differential change between groups was assessed. In addition, the intercepts for the pretest variable were allowed to vary across groups in order to control for (non‐significant) differences in numerical knowledge at pretest. The fit indices for the final multigroup model showed that the model had adequate fit (RMSEA = 0.062, CFI = 0.967, SRMR = 0.131, χ<sups>2</sups>(<reflink idref="bib282" id="ref84">282</reflink>) = 333.077, <emph>p < </emph>.05).</p> <p>Controlling for numerical knowledge at pretest, children who played the number game significantly improved their numerical knowledge from pretest to posttest above and beyond the improvements during the same time period for children in the control group, <emph>μ</emph><subs>α</subs> = 0.852, <emph>p</emph> < .001. There was no statistically significant difference in the amount of change in numerical knowledge from posttest to follow‐up between children in the number and control groups, <emph>μ</emph><subs>β</subs> = −0.029, <emph>p</emph>s = .888. Children who played the WM game did not improve significantly as compared with the children in the control group between pretest and posttest, <emph>μ</emph><subs>α</subs> = 0.138, <emph>p</emph>s = .321, nor did they show significantly greater gains than children in the control group in numerical knowledge between posttest and follow‐up, <emph>μ</emph><subs>β</subs> = 0.213, <emph>p</emph>s = .190.</p> <hd id="AN0144200760-42">Working memory</hd> <p></p> <hd id="AN0144200760-43">The structural model</hd> <p>Retaining the established measurement model (Supporting Information, pp. 16–17), the structural portion of the model was constructed. The latent variable representing children's WM at posttest was predicted by pretest and some amount of change, which was estimated in the model. Follow‐up was predicted by posttest and some amount of change, which was estimated in the model. According to absolute (SRMR = 0.063), parsimonious (RMSEA = 0.000), and incremental (CFI = 1.000) fit indices, the structural model had excellent fit, χ<sups>2</sups>(<reflink idref="bib42" id="ref85">42</reflink>) = 39.933, <emph>p =</emph> .473.</p> <hd id="AN0144200760-44">Multigroup comparison</hd> <p>As with the numerical knowledge analysis, a multigroup comparison using an LCS model was conducted using repeated measures of children's WM. In the final multigroup model, all paths of interest (i.e., <emph>μ</emph><subs>α</subs>, the path representing the amount of change from pretest to posttest and <emph>μ</emph><subs>β</subs>, the path representing the amount of change from posttest to follow‐up) were allowed to vary across groups. In this way, differential change between groups was assessed. In addition, the intercepts for the pretest variable were allowed to vary across groups in order to control for non‐significant differences in WM at pretest. The fit indices for the final multigroup model showed that the model had very good fit (RMSEA = 0.050, CFI = 0.968, SRMR = 0.109, χ<sups>2</sups>(<reflink idref="bib148" id="ref86">148</reflink>) = 166.205, <emph>p</emph>s = .146).</p> <p>Controlling for WM at pretest, children who played the number game significantly improved their WM from pretest to posttest above and beyond the improvements during the same time period for children in the control group, <emph>μ</emph><subs>α</subs> = 0.771, <emph>p</emph> < .05. There was no significant difference in the amount of change in WM from posttest to follow‐up between children in the number and control groups, <emph>μ</emph><subs>β</subs> = 0.100, <emph>p</emph>s = .609. Children who played the WM game also improved significantly more than children in the control group between pretest and posttest, <emph>μ</emph><subs>α</subs> = 0.415, <emph>p</emph> < .05. Additionally, these gains in WM continued to increase between posttest and follow‐up, <emph>μ</emph><subs>β</subs> = 0.391, <emph>p</emph> < .05.</p> <hd id="AN0144200760-45">DISCUSSION</hd> <p>We examined whether playing tablet games that focused on domain‐specific and domain‐general skills has beneficial short‐ and longer term effects for a racially, ethnically, and socioeconomically diverse population of kindergarten children's numerical knowledge and WM.</p> <hd id="AN0144200760-46">Improving children's numerical knowledge and WM through tablet games</hd> <p>Children who played the domain‐specific game targeting their numerical knowledge improved their performance on the mathematical tasks from pretest to posttest above and beyond the improvements during the same time period for those who played the active control game. Importantly, these improvements for children who played the domain‐specific game were observed on a latent level and were maintained for approximately a month period after not having played the game. These findings replicate previous work using traditional board games to improve kindergarten children's numerical magnitude knowledge (Laski & Siegler, [<reflink idref="bib37" id="ref87">37</reflink>]), as well as work with numerical board games adapted for a tablet (Ramani et al., [<reflink idref="bib48" id="ref88">48</reflink>]). The results also extend previous work demonstrating that improvements in children's numerical knowledge from playing computer‐based games can be maintained over time.</p> <p>Using LCS models to demonstrate changes in numerical knowledge and WM can have numerous advantages, such as preventing task‐specific error variance (Grimm et al., [<reflink idref="bib24" id="ref89">24</reflink>]). It is interesting to note though that the effects were mostly driven by the addition task, which was purposefully modified for the present study to also include more difficult problems (Ramani et al., [<reflink idref="bib48" id="ref90">48</reflink>]). Gains were also observed in magnitude comparison, a domain that was specifically targeted by the 'who is leading' questions throughout the game. The gains in number line estimation were less pronounced in the current study as compared with the previous study (Ramani et al., [<reflink idref="bib48" id="ref91">48</reflink>]), which might be explained by the differences in populations. This type of replication using diverse samples is important to add to the generalizability of our findings.</p> <p>Although we expected that targeting domain‐general skills would benefit children's numerical knowledge, playing the WM game did not significantly improve children's numerical knowledge compared to children in the control condition, although the gains were in the expected direction. These findings were unexpected given the consistent correlational evidence that WM plays a critical role in mathematical development (Bull & Lee, [<reflink idref="bib10" id="ref92">10</reflink>]), and because previous experimental work has found that playing WM can improve children's numerical magnitude knowledge (Kroesbergen et al., [<reflink idref="bib35" id="ref93">35</reflink>], [<reflink idref="bib34" id="ref94">34</reflink>]; Ramani et al., [<reflink idref="bib48" id="ref95">48</reflink>]). Several reasons could account for why improvements were minimal in the WM group here. It is likely that because the active control game included rows and columns, children in this group were counting and comparing these features. Indeed, observation field notes revealed that children from the active control group would count the colored squares and rows during the game (e.g., a child exclaimed, "I need 3 more!" for needing to proceed three more rows to get to the star). The opportunity to count and the practice may have contributed to increased numerical knowledge among the active control group, and as such, minimizing the potential differences between the WM and the active control group. Overall, the WM training group did improve on some aspects of numerical cognition, but that improvement was not over and above the active control group in which the children were actively counting the colored grids.</p> <p>Children who played the domain‐specific number game or the domain‐general WM game on the tablet improved their performance on the WM measures on a latent level compared to children who played an active control game. Although previous research has found that training can improve WM, many studies have primarily focused on older children and adults (Jaeggi, Buschkuehl, Jonides, & Perrig, [<reflink idref="bib27" id="ref96">27</reflink>]; Jaeggi et al., [<reflink idref="bib28" id="ref97">28</reflink>]; Loosli, Buschkuehl, Perrig, & Jaeggi, [<reflink idref="bib38" id="ref98">38</reflink>]). The present study demonstrates that WM training can benefit younger kindergarten children as well. Although previous research has attempted WM training with younger children, the results were not as successful as in the present study (Ramani et al., [<reflink idref="bib48" id="ref99">48</reflink>]; but see Wang et al., [<reflink idref="bib65" id="ref100">65</reflink>]). One likely reason is that the present study aimed to extend our previous work by revising or adding several measures that are more appropriate for the kindergarten‐aged group. Specifically, the previous study utilized several WM measures that were linguistically challenging, whereas the present study used measures that required less linguistically demanding responses or vocabulary that was more familiar for the children, many of whom had an English learner background (cf. Table). As a result, the strongest effects were observed in the complex span and the forward spatial span, both of which have the most similarities with the trained game.</p> <p>Interestingly, we found that playing the WM game continued to improve children's WM even after not having played the game for a month. There is evidence from the literature indicating that some learning occurs after a delay during which children might start to implement their learned skills into other tasks or domains. Such effects have been described as cumulative, 'snowball' or 'sleeper' effects (Feuerstein et al., [<reflink idref="bib19" id="ref101">19</reflink>]), and they seem to occur not only in cognitive training (Blair & Raver, [<reflink idref="bib7" id="ref102">7</reflink>]; van der Molen, Luit, Molen, Klugkist, & Jongmans, [<reflink idref="bib63" id="ref103">63</reflink>]) but also in other domains, such as psychotherapy (e.g., van Aar, Leijten, Orobio de Castro, & Overbeek, [<reflink idref="bib62" id="ref104">62</reflink>]; Moritz et al., [<reflink idref="bib44" id="ref105">44</reflink>]). Furthermore, two recent studies by our group that trained children in a similar age range using slight variants of the game also showed continued growth in WM and reasoning 3 months after the intervention was completed, thus, providing converging evidence that training domain‐general skills might not only lead to immediate short‐term effects but that the effects continue to increase as children learn to implement their newly acquired skills (Wang et al., [<reflink idref="bib65" id="ref106">65</reflink>]; Zhang et al., [<reflink idref="bib69" id="ref107">69</reflink>]).</p> <p>In addition to the WM game, playing the domain‐specific number game also improved children's WM performance. The numerical board game was chosen because theoretically it provides a visual representation that should help children learn numerical magnitude knowledge and practice numerical skills. There are, however, WM components to playing the numerical tablet game. For example, when children are moving their game piece they are required to tap each space as they move and the spaces are highlighted in yellow. As they are tapping a space, the tablet verbally indicates the number in the space (e.g., if they are on space 50 and need to move 3 spaces, the game narrator will count 51, 52, and 53). This feature was included in the tablet game because children learn more about numerical magnitude from playing a board game when they "count‐on" in this way (Laski & Siegler, [<reflink idref="bib37" id="ref108">37</reflink>]). However, this can be taxing on children's WM because as they move and count the numbers in the spaces, they also need to keep in mind the number of spaces they need to move as indicated on the spinner. In that sense, it is not surprising that we did find improvements in WM after playing the number game, and furthermore, as discussed earlier, the strongest effects in numerical knowledge were observed in a task that arguably is most taxing on WM (addition). Overall, even though we attempted to primarily train domain‐specific skills with our number game, given the integral role that WM has in math, it can be challenging to design mathematical games that do not involve a WM component.</p> <hd id="AN0144200760-47">Limitations</hd> <p>Overall, even though we did find significant improvements on the latent level, the improvements in the individual tasks were numerically small, which underscores the importance of including adequate sample sizes for such training work, especially in young children, where variability might be especially pronounced. Even though our sample size is larger than most cognitive training studies to date, it is still on the lower end when it comes to the application of SEM. Despite this limitation, it should be noted that the fit indices of the measurement and structural models were adequate to excellent.</p> <p>Another limitation that became increasingly apparent throughout our study was that our active control task was less than ideal as a comparison game for several reasons. As discussed, the children in the active control group were often actively engaged in counting and number comparisons (although to a lesser extent than the number group, but more so than the WM group). Furthermore, similar to the number game, the active control game also required spatial WM skills when answering the 'who is leading' question. As such, there were clear WM demands when playing the control game. A challenge for future research is to continue to design control tasks that (a) are as engaging as the intervention groups, and (b) do not require any of the processes that are targeted by the intervention groups (Green et al., [<reflink idref="bib55" id="ref109">55</reflink>]).</p> <p>In a related design issue of the interventions, although we found improvements in children's WM, the current design of the WM training game may have also 'backfired' for some of the children, which could further explain why the games did not improve children's numerical knowledge. In trying to prevent children from being bored, we designed eight visually appealing themes with different characters, and children played with a new theme each training session. Unfortunately, the visual changes might have been distracting, and as such, detrimental for learning (see also Katz, Jaeggi, Buschkuehl, Stegman, & Shah, [<reflink idref="bib31" id="ref110">31</reflink>]; Mohammed et al., [<reflink idref="bib43" id="ref111">43</reflink>]). It is possible that each new theme appeared to be a different game for the children, which is especially apparent when comparing the training performance between the current sample and another population with similar age who played the game without any theme changes (Wang et al., [<reflink idref="bib65" id="ref112">65</reflink>]). While the children in the present study remained at set size 4 throughout the 10 sessions, the other population improved their performance by almost 1.5 set sizes across 10 sessions (from 3.7 to 5.15). Indeed, many children in the present study still required a lot of assistance and instructions from experimenters even well into the fifth session.</p> <hd id="AN0144200760-48">CONCLUSION AND IMPLICATIONS</hd> <p>Overall, our findings add to the literature by demonstrating that computerized games that target both domain‐specific and domain‐general skills can have beneficial effects in a broad range of kindergarten‐aged children. In particular, both our games were effective in improving WM processes over and above an active control group, and given the importance of WM and related skills for school readiness and in classroom behavior, our findings indicate promising avenues for improving those skills in children who are at a particular risk for developing deficits in WM and related executive function skills (e.g., Welsh, Nix, Blair, Bierman, & Nelson, [<reflink idref="bib67" id="ref113">67</reflink>]).</p> <p>Critically, playing the number game led to improvements in a range of foundational number skills, offering similar opportunities for future research and practice, such as targeting children who struggle with early numeracy skills who have been shown to be at a high risk for developing learning disabilities. Importantly, even though the time spent playing the games was minimal (~10 min/day), the benefits lasted for at least a month, suggesting that the changes in number knowledge and WM might last beyond just the intervention period, and hopefully having downstream effects into other domains where those skills are required.</p> <p>Finally, our easy‐to‐administer and low‐cost tablet games could also be easily implemented in other classrooms and complement kindergarten activities – they are fun and well‐liked by children, and as such, they add to the domain of educational games that can be beneficial for early learning.</p> <hd id="AN0144200760-49">ACKNOWLEDGEMENTS</hd> <p>This research was supported by the National Science Foundation Awards DRL 1561447 and DRL 1561404 to Geetha B. Ramani and Susanne M. Jaeggi. We thank the schools and children who participated in this research, as well as Jeffrey R. Harring and Gregory R. Hancock for their contributions to the statistical analyses.</p> <hd id="AN0144200760-50">CONFLICT OF INTEREST</hd> <p>Susanne M. Jaeggi has an indirect financial interest in the MIND Research Institute, Irvine, CA, whose interests are related to this work.</p> <hd id="AN0144200760-51">DATA AVAILABILITY STATEMENT</hd> <p>The data that support the findings of this study are available from the corresponding authors upon reasonable request. Please contact Geetha B. Ramani, Department of Human Development and Quantitative Methodology, University of Maryland, College Park, MD; email address: gramani@umd.edu or Susanne M. Jaeggi, School of Education, University of California, Irvine, Irvine, CA; e‐mail address: smjaeggi@uci.edu.</p> <p>GRAPH</p> <ref id="AN0144200760-52"> <title> REFERENCES </title> <blist> <bibl id="bib1" idref="ref45" type="bt">1</bibl> <bibtext> Alloway, T. (2012). Can interactive working memory training improving learning? 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DbLabel: ERIC
An: EJ1257547
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PubType: Academic Journal
PubTypeId: academicJournal
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Items – Name: Title
  Label: Title
  Group: Ti
  Data: Racing Dragons and Remembering Aliens: Benefits of Playing Number and Working Memory Games on Kindergartners' Numerical Knowledge
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Ramani%2C+Geetha+B%2E%22">Ramani, Geetha B.</searchLink><br /><searchLink fieldCode="AR" term="%22Daubert%2C+Emily+N%2E%22">Daubert, Emily N.</searchLink><br /><searchLink fieldCode="AR" term="%22Lin%2C+Grace+C%2E%22">Lin, Grace C.</searchLink><br /><searchLink fieldCode="AR" term="%22Kamarsu%2C+Snigdha%22">Kamarsu, Snigdha</searchLink><br /><searchLink fieldCode="AR" term="%22Wodzinski%2C+Alaina%22">Wodzinski, Alaina</searchLink><br /><searchLink fieldCode="AR" term="%22Jaeggi%2C+Susanne+M%2E%22">Jaeggi, Susanne M.</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Developmental+Science%22"><i>Developmental Science</i></searchLink>. Jul 2020 23(4).
– Name: Avail
  Label: Availability
  Group: Avail
  Data: Wiley-Blackwell. 350 Main Street, Malden, MA 02148. Tel: 800-835-6770; Tel: 781-388-8598; Fax: 781-388-8232; e-mail: cs-journals@wiley.com; Web site: http://www.wiley.com/WileyCDA
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 17
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2020
– Name: SourceSuprt
  Label: Sponsoring Agency
  Group: SrcSuprt
  Data: National Science Foundation (NSF)
– Name: NumberContract
  Label: Contract Number
  Group: NumCntrct
  Data: 1561447<br />1561404
– Name: TypeDocument
  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
– Name: Audience
  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Early+Childhood+Education%22">Early Childhood Education</searchLink><br /><searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Kindergarten%22">Kindergarten</searchLink><br /><searchLink fieldCode="EL" term="%22Primary+Education%22">Primary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Educational+Games%22">Educational Games</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink><br /><searchLink fieldCode="DE" term="%22Number+Concepts%22">Number Concepts</searchLink><br /><searchLink fieldCode="DE" term="%22Short+Term+Memory%22">Short Term Memory</searchLink><br /><searchLink fieldCode="DE" term="%22Kindergarten%22">Kindergarten</searchLink><br /><searchLink fieldCode="DE" term="%22Young+Children%22">Young Children</searchLink><br /><searchLink fieldCode="DE" term="%22Handheld+Devices%22">Handheld Devices</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Skills%22">Mathematics Skills</searchLink><br /><searchLink fieldCode="DE" term="%22Skill+Development%22">Skill Development</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Achievement%22">Mathematics Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Games%22">Computer Games</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1111/desc.12908
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 1467-7687
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet-based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten-age children. We hypothesized that playing a number-based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; M[subscript age] = 71.87 months) were randomly assigned to either play a number-based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain-specific and domain-general skills can benefit a broad range of kindergarten-aged children.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2020
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1257547
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1257547
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1111/desc.12908
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 17
    Subjects:
      – SubjectFull: Educational Games
        Type: general
      – SubjectFull: Mathematics Education
        Type: general
      – SubjectFull: Number Concepts
        Type: general
      – SubjectFull: Short Term Memory
        Type: general
      – SubjectFull: Kindergarten
        Type: general
      – SubjectFull: Young Children
        Type: general
      – SubjectFull: Handheld Devices
        Type: general
      – SubjectFull: Mathematics Skills
        Type: general
      – SubjectFull: Skill Development
        Type: general
      – SubjectFull: Mathematics Achievement
        Type: general
      – SubjectFull: Computer Games
        Type: general
    Titles:
      – TitleFull: Racing Dragons and Remembering Aliens: Benefits of Playing Number and Working Memory Games on Kindergartners' Numerical Knowledge
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Ramani, Geetha B.
      – PersonEntity:
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            NameFull: Daubert, Emily N.
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            NameFull: Lin, Grace C.
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            NameFull: Kamarsu, Snigdha
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            NameFull: Wodzinski, Alaina
      – PersonEntity:
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            NameFull: Jaeggi, Susanne M.
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          Dates:
            – D: 01
              M: 07
              Type: published
              Y: 2020
          Identifiers:
            – Type: issn-electronic
              Value: 1467-7687
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            – Type: volume
              Value: 23
            – Type: issue
              Value: 4
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            – TitleFull: Developmental Science
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