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Keep DRAGging ON: Is Solving More Problems in DragonBox 12+ Associated with Higher Mathematical Performance during the COVID-19 Pandemic?

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Title: Keep DRAGging ON: Is Solving More Problems in DragonBox 12+ Associated with Higher Mathematical Performance during the COVID-19 Pandemic?
Language: English
Authors: Chan, Jenny Yun-Chen (ORCID 0000-0003-1479-5935), Byrne, Chloe, Jerusal, Janette, Liu, Allison S. (ORCID 0000-0003-1075-2575), Roberts, Justin (ORCID 0000-0001-5906-6336), Ottmar, Erin (ORCID 0000-0002-9487-7967)
Source: British Journal of Educational Technology. Jul 2023 54(4):943-966.
Availability: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
Peer Reviewed: Y
Page Count: 24
Publication Date: 2023
Sponsoring Agency: Institute of Education Sciences (ED)
Contract Number: R305A180401
Document Type: Journal Articles
Reports - Research
Education Level: Junior High Schools
Middle Schools
Secondary Education
Elementary Education
Grade 7
Descriptors: Game Based Learning, Educational Games, Problem Solving, Mathematics Achievement, Middle School Students, Grade 7, Algebra, Prior Learning, Predictor Variables, COVID-19, Pandemics, Secondary School Mathematics, Mathematics Instruction, Supplementary Education
DOI: 10.1111/bjet.13304
ISSN: 0007-1013
1467-8535
Abstract: Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between students' progress within DragonBox and their algebraic knowledge and general mathematics achievement, (b) the moderating effects of students' prior performance on these relations and (c) the potential factors associated with students' in-game progress. Among students with higher prior algebraic knowledge, higher in-game progress was related to higher algebraic knowledge after the intervention. Higher in-game progress was also associated with higher end-of-year mathematics achievement, and this association was stronger among students with lower prior mathematics achievement. Students' demographic characteristics, prior knowledge and prior achievement did not significantly predict in-game progress beyond the number of intervention sessions students completed. These findings advance research on how, for whom and in what contexts game-based interventions, such as DragonBox, support mathematical learning and have implications for practice using game-based technologies to supplement instruction. [For the corresponding grantee submission, see ED626412.]
Abstractor: As Provided
Notes: https://osf.io/nfg4c
IES Funded: Yes
Entry Date: 2023
Accession Number: EJ1380171
Database: ERIC
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  Value: <anid>AN0164202690;58i01jul.23;2023Jun12.07:55;v2.2.500</anid> <title id="AN0164202690-1">Keep DRAGging ON: Is solving more problems in DragonBox 12+ associated with higher mathematical performance during the COVID‐19 pandemic? </title> <p>Prior research has shown that game‐based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in‐game progress positively predicts their later performance. Using data from 253 seventh‐graders (12–13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between students' progress within DragonBox and their algebraic knowledge and general mathematics achievement, (b) the moderating effects of students' prior performance on these relations and (c) the potential factors associated with students' in‐game progress. Among students with higher prior algebraic knowledge, higher in‐game progress was related to higher algebraic knowledge after the intervention. Higher in‐game progress was also associated with higher end‐of‐year mathematics achievement, and this association was stronger among students with lower prior mathematics achievement. Students' demographic characteristics, prior knowledge and prior achievement did not significantly predict in‐game progress beyond the number of intervention sessions students completed. These findings advance research on how, for whom and in what contexts game‐based interventions, such as DragonBox, support mathematical learning and have implications for practice using game‐based technologies to supplement instruction. Practitioner notesWhat is already known about this topicDragonBox 12+ may support students' understanding of algebra but the findings are mixed.Students who solve more problems within math games tend to show higher performance after gameplay.Students' engagement with mathematics is often related to their prior math performance.What this paper addsFor students with higher prior algebraic knowledge, solving more problems in DragonBox 12+ is related to higher algebraic performance after gameplay.Students who make more in‐game progress also have higher mathematics achievement, especially for students with lower prior achievement.Students who spend more time playing DragonBox 12+ make more in‐game progress; their demographic, prior knowledge and prior achievement are not related to in‐game progress.Implications for practice and/or policyDragonBox 12+ can be beneficial as a supplement to algebra instruction for students with some understanding of algebra.DragonBox 12+ can engage students with mathematics across achievement levels.Dedicating time and encouraging students to play DragonBox 12+ may help them make more in‐game progress, and in turn, support math learning.</p> <p>Keywords: algebraic learning; DragonBox 12+; in‐game progress; mathematics achievement</p> <hd id="AN0164202690-2">INTRODUCTION</hd> <p>Algebraic knowledge is defined as the understanding of principles, procedures and strategies of working with generalized mathematical symbols (eg, letters, variables; Kieran, [<reflink idref="bib23" id="ref1">23</reflink>]). It provides an important foundation for higher‐level STEM courses (Chen, [<reflink idref="bib10" id="ref2">10</reflink>]), yet students' often struggle with learning algebra (Kieran, [<reflink idref="bib23" id="ref3">23</reflink>]) and this struggle is even more apparent during the COVID‐19 pandemic. Emerging studies have shown that students are making less progress in mathematics and other domains compared to their peers in prior years (Engzell et al., [<reflink idref="bib15" id="ref4">15</reflink>]; Kuhfeld et al., [<reflink idref="bib24" id="ref5">24</reflink>]). Preliminary research further showed that students' participation and engagement in online learning during the pandemic were lower than typical (Rutherford et al., [<reflink idref="bib45" id="ref6">45</reflink>]). Some research has shown that game‐based learning—a method of learning where students can interact with educational materials in a way that is fun and playful—may support students' engagement with a topic and in turn improve learning (Connolly et al., [<reflink idref="bib11" id="ref7">11</reflink>]). We examine how students' engagement with an educational technology game, as measured by their in‐game progress, may support their algebraic learning and mathematics achievement during the pandemic.</p> <hd id="AN0164202690-3">Game‐based learning and in‐game progress</hd> <p>Theories of game‐based learning posit that learning occurs through playing games that are designed to improve educational outcomes (Plass et al., [<reflink idref="bib40" id="ref8">40</reflink>]). In this theoretical approach, learning is integrated with gameplay so that students acquire the targeted content through play. Some previous studies have shown the positive impacts of game‐based learning (eg, Rowe et al., [<reflink idref="bib43" id="ref9">43</reflink>]; Sun‐Lin & Chiou, [<reflink idref="bib50" id="ref10">50</reflink>]); however, other studies have not (eg, Attali & Arieli‐Attali, [<reflink idref="bib3" id="ref11">3</reflink>]; Wrzesien & Raya, [<reflink idref="bib55" id="ref12">55</reflink>]). The increasing use of educational technology games combined with the mixed findings prompts more research to understand <emph>how</emph>, <emph>for whom</emph> and <emph>in what contexts</emph> these games support learning.</p> <p>One potential mechanism of game‐based learning is engaging students in the content and learning processes through play (Ke, [<reflink idref="bib21" id="ref13">21</reflink>]; Mora et al., [<reflink idref="bib31" id="ref14">31</reflink>]; Samur & Evans, [<reflink idref="bib46" id="ref15">46</reflink>]). Educational technology games often provide an interactive environment that maintains students' active engagement, allowing students to build up their knowledge and skills as they progress through games (Gee, [<reflink idref="bib16" id="ref16">16</reflink>]). Prior research has found that making more progress, which is defined as solving more problems or completing more exercises, within mathematical games positively predicts students' posttest scores on numeracy (Chan & Santos, [<reflink idref="bib9" id="ref17">9</reflink>]) and arithmetic (Hulse et al., [<reflink idref="bib19" id="ref18">19</reflink>]) even after controlling for their prior performance (ie, pretest scores). We contribute to this literature by testing the effects of in‐game progress, as measured by the total number of completed problems, within DragonBox 12+ on students' later algebraic knowledge and mathematics achievement.</p> <hd id="AN0164202690-4">DragonBox 12+</hd> <p>DragonBox 12+ (hereafter DragonBox, https://dragonbox.com/products/algebra‐12; Kahoot!, [<reflink idref="bib20" id="ref19">20</reflink>]) is an educational technology game that supports algebraic learning. In this game, students follow algebraic rules to manipulate digital characters and isolate a box containing a dragon, analogous to solving an equation for <emph>x</emph> (Figure 1). DragonBox has won several awards, including the Best App for Teaching and Learning in 2014 from the American Association of School Librarians. Its design has also been applauded for its research‐backed principles, including embedded gestures and immediate feedback (Cayton‐Hodges et al., [<reflink idref="bib5" id="ref20">5</reflink>]; Torres et al., [<reflink idref="bib53" id="ref21">53</reflink>]). Extensive research has suggested that mathematical learning is inherently perceptual, and students' physical experiences impact their mathematical thinking (Abrahamson et al., [<reflink idref="bib1" id="ref22">1</reflink>]; Alibali & Nathan, [<reflink idref="bib2" id="ref23">2</reflink>]; Goldstone et al., [<reflink idref="bib17" id="ref24">17</reflink>]; Kellman et al., [<reflink idref="bib22" id="ref25">22</reflink>]). In DragonBox, the active manipulation of symbols combined with the immediate feedback on students' actions may help students ground their abstract algebraic knowledge in physical experiences, developing an embodied routine for algebraic reasoning. This notion is supported by prior research examining a similar educational technology game that leverages action and perception in algebraic learning (eg, Chan, Lee, et al., [<reflink idref="bib7" id="ref26">7</reflink>]).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/58I/01jul23/bjet13304-fig-0001.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="bjet13304-fig-0001.jpg" title="1 A sample problem and its problem‐solving process within DragonBox. (a) Multiply the DragonBox by 2; (b) multiply all other terms on both sides by 2; (c) Factor 4 into 2∙2; (d) Combine 2s in the numerator and denominator; (e) subtract both sides by 1/2; (f) The DragonBox is isolated and the user received 3 stars for solving the problem. This image is used with permission from DragonBox (Kahoot!)." /> </p> <p></p> <p>Several studies have found mixed effects of DragonBox on algebraic understanding and engagement. For example, in a sample of K‐12 US students (5–18 years old) from 70 schools across 15 districts, the DragonBox developers and the University of Washington Center for Game Science found that 93% of students could correctly answer three consecutive algebra problems (eg, <emph>d</emph> × <emph>x</emph> + <emph>m</emph> = 8) after 1.5 hours of playing a combined version of DragonBox 5+ and 12+ (Liu et al., [<reflink idref="bib27" id="ref27">27</reflink>]). Compared with a control group receiving typical instruction, eighth‐grade Malaysian students (14 years old) in the DragonBox condition scored higher on assessments of algebraic thinking and mathematics attitudes after 16 hours of teaching and playing (Siew et al., [<reflink idref="bib47" id="ref28">47</reflink>]). Similarly, Indonesian middle‐schoolers (12–15 years old) who used DragonBox as a supplemental activity in a semester‐long algebra course outperformed their peers who did not use DragonBox on conceptual understanding (ie, the knowledge of algebraic principles, such as both sides of the equal sign represent the same quantity) and algebraic equation solving (Supriadi et al., [<reflink idref="bib51" id="ref29">51</reflink>]). Another study with eighth‐graders in Norway (13–14 years old) found that after receiving 4 hours of instruction and using DragonBox in pairs for another 4 hours within 4 weeks, students significantly improved their algebraic performance as measured by items selected from textbooks and standardized assessments (Dolonen & Kluge, [<reflink idref="bib13" id="ref30">13</reflink>]). Although students in that study showed high levels of usage and engagement with DragonBox, their learning gains were smaller compared with those of students who practised textbook‐like algebra problems. Similarly, Long and Aleven ([<reflink idref="bib28" id="ref31">28</reflink>]) found that seventh‐ and eighth‐grade US students (12–14 years old) who played DragonBox for 3.5 hours across five sessions showed no improvements in problem‐solving performance or confidence, although they reported higher enjoyment compared with students using an intelligent tutor system.</p> <p>Prior studies typically involved testing the effects of playing DragonBox for 2–4 hours on algebraic learning and engagement. It remained unclear whether these improvements were associated with how much students played DragonBox, or whether improvements would have emerged regardless of the amount of in‐game progress. Furthermore, to our knowledge, prior studies have only focused on DragonBox's impacts on algebraic performance. Given that algebraic knowledge supports general mathematics performance (eg, National Mathematics Advisory Panel, [<reflink idref="bib34" id="ref32">34</reflink>]), playing DragonBox may also have significant impacts on students' overall mathematics achievement. Finally, prior research did not explore the potential moderating effects of students' prior knowledge on the relation between playing DragonBox and learning outcomes. Addressing these questions is crucial for understanding the ways in which DragonBox supports mathematical learning.</p> <hd id="AN0164202690-6">Moderating effects of prior knowledge</hd> <p>Research has demonstrated that the effects of mathematics interventions vary depending on students' prior knowledge—the knowledge students already have and which interventions build upon. For example, among US first‐graders (6–7 years old) with higher mathematics achievement, those who received an intervention involving peer‐assisted supplemental activities showed greater gains in mathematics compared with those who did not. However, among students with lower mathematics achievement, those who did not receive the intervention showed greater gains compared with those who did (Wood et al., [<reflink idref="bib54" id="ref33">54</reflink>]). Other studies have reported mixed results, with some finding larger benefits of intervention among students with higher prior knowledge (eg, Swanson et al., [<reflink idref="bib52" id="ref34">52</reflink>]) and others finding the opposite (eg, Murphy et al., [<reflink idref="bib32" id="ref35">32</reflink>]). In the context of educational technology games, one study has examined the moderating effects of students' prior knowledge on the relation between in‐game progress and later mathematical performance (Hulse et al., [<reflink idref="bib19" id="ref36">19</reflink>]). Solving more problems within the game was related to higher mathematical performance at posttest among students with lower, but not higher, prior knowledge, suggesting the select benefits of in‐game progress among struggling students. To efficiently support all students in mathematical learning, it is important to understand when and for whom interventions are effective. We test the moderating effect of prior knowledge, as measured by students' algebraic knowledge and mathematics achievement prior to the intervention, on the relation between DragonBox progress and learning outcomes to contribute new findings regarding the role of prior knowledge in mathematical learning.</p> <hd id="AN0164202690-7">Factors associated with in‐game progress</hd> <p>Finally, we explore whether students' characteristics, such as biological sex, race/ethnicity and prior knowledge and achievement are associated with their progress within DragonBox. Although prior studies have reported significant differences in sex and race/ethnicity in students' mathematics achievement, these differences tended to be related to situational contexts, such as educational experience and socioeconomic status (eg, Linn & Hyde, [<reflink idref="bib26" id="ref37">26</reflink>]; Sonnenschein & Galindo, [<reflink idref="bib48" id="ref38">48</reflink>]). For example, gender stereotypes have contributed to female students showing more negativity towards mathematics, less participation and worse achievement compared with their male counterparts (Nosek & Smyth, [<reflink idref="bib36" id="ref39">36</reflink>]). Similarly, Black female students reported lower levels of engagement in mathematics classes compared with other students (Martinez & Guzman, [<reflink idref="bib29" id="ref40">29</reflink>]). However, one study using the process data within an e‐textbook found that female versus male students were more likely to spend more time and provide more detailed responses to mathematical questions, suggesting higher engagement (Reinhold et al., [<reflink idref="bib41" id="ref41">41</reflink>]). Furthermore, students with higher versus lower prior knowledge tend to report higher learning engagement (Dong et al., [<reflink idref="bib14" id="ref42">14</reflink>]) and show higher engagement in the learning process (Pecore et al., [<reflink idref="bib39" id="ref43">39</reflink>]). By examining whether students' in‐game progress varies by their sex, race/ethnicity or prior knowledge or achievement, we aim to provide a starting point for future work that supports learning through games among all students from diverse backgrounds and at different levels.</p> <hd id="AN0164202690-8">The current study</hd> <p>The research questions (RQs) and their corresponding hypothesis are pre‐registered (https://osf.io/eg2bu) and are as follows:</p> <p></p> <ulist> <item> <emph>Does students' in‐game progress within DragonBox predict their later algebraic knowledge?</emph> Based on prior research (Chan & Santos, [<reflink idref="bib9" id="ref44">9</reflink>] ; Hulse et al., [<reflink idref="bib19" id="ref45">19</reflink>]), we hypothesize that students who solve more versus fewer problems in DragonBox may score higher on an algebraic knowledge posttest.</item> <p></p> <item> <emph>Does the relation between in‐game progress and later algebraic knowledge vary by students' prior knowledge?</emph> Due to the mixed findings in prior research, we do not have a directional hypothesis. We explore whether the relation between progress and learning outcome varies by students' prior knowledge.</item> <p></p> <item> <emph>Do the effects of in‐game progress and its interaction with prior knowledge emerge in students' general mathematics achievement?</emph> We explore these effects on students' end‐of‐grade mathematics achievement scores and do not have an a priori hypothesis.</item> <p></p> <item> <emph>Do students' sex, race/ethnicity or prior knowledge or achievement predict their in‐game progress?</emph> We explore these associations to identify potential factors related to students' in‐game progress. We do not have an a priori hypothesis.</item> </ulist> <p>We use the data collected from a randomized controlled trial (RCT) comparing the efficacy of four educational technology conditions to address our RQs. In the RCT, Decker‐Woodrow et al. ([<reflink idref="bib12" id="ref46">12</reflink>]) found that seventh‐grade US students assigned to the DragonBox condition scored significantly higher on the algebraic knowledge post‐test compared with students in the active control condition. Extending that work, we examine the impacts of DragonBox progress on students' mathematics performance and factors associated with in‐game progress.</p> <hd id="AN0164202690-9">METHODS</hd> <p></p> <hd id="AN0164202690-10">Participants</hd> <p>The data were collected as a part of an RCT with seventh‐graders during the 2020–2021 academic year amidst the COVID‐19 pandemic. The students were recruited from a large, suburban school district that consisted of 10 physical schools and one virtual school in the Southeastern US. Due to the COVID‐19 pandemic, the school district provided students and their families with two options for instruction: synchronous in‐person instruction at school or asynchronous virtual instruction at home. Prior to the start of the academic year, the students and families selected their instructional format for the entire academic year, but they could change the format throughout the year. The research team randomly assigned students to one of four intervention conditions prior to the academic year, and the students used their assigned technology throughout the year (see details in Decker‐Woodrow et al., [<reflink idref="bib12" id="ref47">12</reflink>]).</p> <p>The current study included 253 students who started the pretest, played DragonBox and started the post‐test. Because our RQs focused on students' progress within DragonBox, the other three intervention conditions did not provide appropriate data for our RQs. The current sample was somewhat smaller than the original sample of 350 students who were assigned to the DragonBox condition and included in the prior analysis (Decker‐Woodrow et al., [<reflink idref="bib12" id="ref48">12</reflink>]). This discrepancy was due to the missing data in students' DragonBox progress. Because DragonBox is a privately‐owned application that is not freely accessible through web browsers, the research team provided tablets installed with DragonBox for in‐person students. Many virtual students struggled to follow written instructions to download the game for free on their own device and dropped out of the study.</p> <p>We received students' demographic information and standardized achievement scores before and after the intervention directly from the school administrators. Any discrepancies in student information across school years were discussed and resolved with the administrators, ensuring the accuracy of the data. Among the 253 students, 52.2% were male, and 47.8% were female. In terms of race and ethnicity, 64.0% were White, 20.6% were Hispanic and 15.4% were other (8.3% Asian, 3.15% Black, 3.15% Multi‐racial, 0.8% American Indian/Alaska Native). Due to COVID‐19, 92.5% of the sample received in‐person instruction and 7.5% received virtual instruction; however, all students followed the same intervention procedure as detailed below.</p> <hd id="AN0164202690-11">Procedure</hd> <p>This research received approval from the Institutional Review Board at Worcester Polytechnic Institute. This research involved typical educational practices and did not require parental consent. Parents received an informational letter about the research and could opt their child out of the study.</p> <p>In the RCT, students completed a pretest in September 2020, nine 30‐minute intervention sessions (with a 2‐week window to complete each), and a post‐test from March to April 2021. During the pretest and post‐test, students completed assessments on their algebraic knowledge and attitude towards mathematics. During each intervention session, students played DragonBox and reported their in‐game progress. All students, regardless of their instructional format, completed the assessments and intervention sessions individually on a device at their own pace. For in‐person students, teachers were asked to dedicate instructional periods for students to complete their study assignments. For virtual students, teachers assigned the assignments as a part of students' homework.</p> <hd id="AN0164202690-12">DragonBox</hd> <p>DragonBox is a commercially available, phone‐ or tablet‐based application that allows students to interact with algebraic principles through on‐screen actions. For example, students can combine the opposite numbers by dragging, overlapping and dropping one term on top of the other. DragonBox has 10 chapters, each with 20 problems. Students started from the first problem and progressed through simple (eg, arithmetic) and then complex topics (eg, factoring, distribution).</p> <p>At the first intervention session, students followed the instructions provided in the study platform to open their player profile in the game, started a timer in the study platform and then played DragonBox. After 25 minutes, the timer rang; students returned to the study platform and reported their in‐game progress. We asked students to report their progress because we did not have access to the log data within the game. At each subsequent session, students were prompted to report the chapter and problem at which they ended in the previous session to ensure that we obtained the data if students ran out of time in the previous session. Afterwards, they played DragonBox for 25 minutes continuing from where they left off, reported the chapter and problem at which they ended, and then reflected on the connections between DragonBox and their mathematics instruction.</p> <hd id="AN0164202690-13">Measures</hd> <p></p> <hd id="AN0164202690-14">In‐game progress</hd> <p>Informed by the prior literature (eg, Chan & Santos, [<reflink idref="bib9" id="ref49">9</reflink>]; Hulse et al., [<reflink idref="bib19" id="ref50">19</reflink>]), we used the total number of problems in DragonBox that students worked on throughout the nine intervention sessions as a measure of students' in‐game progress. To derive this measure, we computed the total number of completed problems based on students' final chapter and problem. For example, a student who was on Chapter 4 Problem 11 at the end of the intervention would have worked on 71 problems (ie, (4–1) chapters × 20 problems per chapter + 11 problems). The total number of problems was a focal predictor for RQ1, and its interaction with students' pretest algebra scores was a focal predictor for RQ2. Both the main effect of in‐game progress and its interaction with prior mathematics achievement were the focal predictors for RQ3. The total number of problems was a focal outcome for RQ4.</p> <p>For the in‐person students who used the researcher‐provided tablets, we reviewed the tablets after study completion and recorded students' final problem. Even though 92.5% of the students were in person, we could only extract the progress data for 89.7% of students due to various reasons (eg, broken tablet screens, students started the assignments at home and continued using their personal devices). For the remaining students, we used their self‐reported progress in the analyses. The correlation between researcher‐recorded progress and student‐reported progress was <emph>r</emph>(<reflink idref="bib186" id="ref51">186</reflink>) = 0.807, <emph>p</emph> < 0.001, suggesting that students' self‐reported progress was a reliable measure of their in‐game progress.</p> <hd id="AN0164202690-15">Sessions completed</hd> <p>We also recorded the number of intervention sessions students completed out of nine sessions as a proxy for the amount of time they engaged with the intervention. We controlled for this variable to test the unique effect of students' in‐game progress, independent of their time spent with the intervention, on their algebraic performance and mathematics achievement.</p> <hd id="AN0164202690-16">Algebraic knowledge assessment</hd> <p>We selected 10 multiple‐choice items from a previously validated measure (Star et al., [<reflink idref="bib49" id="ref52">49</reflink>]) for our algebraic knowledge assessments (Appendix A, Table A1). The items measured students' conceptual knowledge (eg, understanding equivalence; Items 3, 6, 7, 10), procedural knowledge (eg, solving for a variable; Items 1, 5, 8) and procedural flexibility (eg, evaluating different strategies; items 2, 4, 9) in algebraic equation solving and together tapped a range of students' knowledge targeted by the intervention. The pretest and post‐test items were isomorphic, with different numbers of similar magnitudes in the questions and response options. Each item was scored as correct (<reflink idref="bib1" id="ref53">1</reflink>) or incorrect (0); the reliability of these items was acceptable (pretest: KR‐20 = 0.74; post‐test: KR20 = 0.79; Decker‐Woodrow et al., [<reflink idref="bib12" id="ref54">12</reflink>]). The total score out of 10 on the post‐test was included as the outcome and the pretest as a covariate or moderator for RQs 1 and 2, respectively.</p> <hd id="AN0164202690-17">State standardized assessment on mathematics</hd> <p>Of the 253 students, we obtained 183 students' state standardized mathematics assessment scores at the end of fifth grade (May 2019) and seventh grade (May 2021) from the district. The sample size for the state standardized assessment was smaller than 253 because some students opted out of the assessment due to parental choice and concerns related to the COVID‐19 pandemic. We used the fifth‐grade state scores as the measure of prior achievement because the assessment was not administered at the end of sixth grade (May 2020) due to COVID‐19‐related disruptions.</p> <p>The assessment measured students' mathematical understanding of a broad range of topics, including ratios, equations, geometry and statistics. The assessment included a variety of tasks (eg, computation, word problems) and answer formats (eg, multiple‐choice, graphing). The scores on the assessment ranged between 265 and 740. We used students' seventh‐grade state standardized scores (hereafter seventh‐grade state scores) as the outcome variable and the interaction between fifth‐grade state scores and in‐game progress as a focal predictor for RQ3.</p> <hd id="AN0164202690-18">Analytic approach</hd> <p>We first conducted descriptive and correlational analyses to examine the distribution of, and correlation between, each variable, as well as to inform our primary analyses. To test the effect of in‐game progress on students' later algebraic knowledge (RQ1), we conducted a linear regression with students' post‐test algebra score as the dependent variable, the number of DragonBox problems completed as the focal predictor and the number of intervention sessions completed, instructional format, sex, race/ethnicity and pretest score as the covariates. Next, we added the interaction between students' pretest score and their in‐game progress as the focal predictor of students' post‐test score to test the moderating effect of prior knowledge on the relation between students' in‐game progress and later algebraic knowledge (RQ2). To test the potential effects of in‐game progress on students' general mathematics achievement (RQ3), we repeated the first two models but substituted pretest and post‐test scores with fifth‐grade and seventh‐grade state scores, respectively. Finally, to identify potential factors associated with students' in‐game progress (RQ4), we conducted a linear regression with student's in‐game progress as the dependent variable, sex, race/ethnicity, pretest score and fifth‐grade state score as the focal predictors and the number of intervention sessions completed and instructional format as the covariates.</p> <p>We noted that the analyses for RQ3 only included 183 students, whereas the remaining analyses included 253 students. To ensure that the pattern of the results could not be attributed to the differences between samples, we repeated the remaining analyses using the sample of 183 students and reported the additional findings in Appendix B (see Tables B1–B3 and Figure B1). The pattern of the results was identical for the two samples (<emph>N</emph> = 253 vs. <emph>N</emph> = 183). Therefore, we reported the findings for RQs 1, 2 and 4 based on 253 students in the Results section.</p> <p>For all the linear regression models, we considered the nesting structure of students within teachers. The intra‐class correlations were above 0.07 threshold (Niehaus et al., [<reflink idref="bib35" id="ref55">35</reflink>]) for post‐test algebra scores (0.414), seventh‐grade state scores (0.573) and in‐game progress (0.363); therefore, we modelled the nesting structure. This modelling approach accounts for the variations between students of different teachers, whether known or unknown, improving the accuracy of the estimates. In the multilevel models, all continuous predictors were grand mean centered (ie, sessions completed, pretest scores, fifth‐grade state scores, in‐game progress), and all categorical predictors were dummy coded (ie, sex, race/ethnicity, instructional format). The analyses were conducted in RStudio (RStudio Team, [<reflink idref="bib44" id="ref56">44</reflink>]) using the <emph>lme4</emph> package (Bates et al., [<reflink idref="bib4" id="ref57">4</reflink>]). The final dataset and the R script are available on the Open Science Framework (https://osf.io/nfg4c).</p> <hd id="AN0164202690-19">RESULTS</hd> <p></p> <hd id="AN0164202690-20">Preliminary analyses</hd> <p>Descriptive statistics of, and the correlations between, the focal variables are reported in Table 1. As indicated by the average values of in‐game progress and sessions completed, many students were actively solving problems in DragonBox and engaged with the intervention. The range of the values was large for both variables, suggesting large variability in students' in‐game progress and overall intervention participation.</p> <p>1 TABLE Descriptive statistics of and correlations between each variable.</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left" /><th align="left">In‐game progress</th><th align="left">Sessions completed</th><th align="left">Pretest score</th><th align="left">Post‐test score</th><th align="left">Fifth‐grade state score</th><th align="left">Seventh‐grade state score</th></tr></thead><tbody valign="top"><tr><td>In‐game progress</td><td>–</td><td /><td /><td /><td /><td /></tr><tr><td>Sessions completed</td><td>0.57<xref ref-type="fn" rid="tfn4" /></td><td>–</td><td /><td /><td /><td /></tr><tr><td>Pretest score</td><td>0.24<xref ref-type="fn" rid="tfn4" /></td><td>0.23<xref ref-type="fn" rid="tfn4" /></td><td>–</td><td /><td /><td /></tr><tr><td>Post‐test score</td><td>0.30<xref ref-type="fn" rid="tfn4" /></td><td>0.20<xref ref-type="fn" rid="tfn3" /></td><td>0.51<xref ref-type="fn" rid="tfn4" /></td><td>–</td><td /><td /></tr><tr><td>Fifth‐grade state score</td><td>0.17<xref ref-type="fn" rid="tfn2" /></td><td>0.09</td><td>0.61<xref ref-type="fn" rid="tfn4" /></td><td>0.49<xref ref-type="fn" rid="tfn4" /></td><td>–</td><td /></tr><tr><td>Seventh‐grade state score</td><td>0.33<xref ref-type="fn" rid="tfn4" /></td><td>0.22<xref ref-type="fn" rid="tfn3" /></td><td>0.64<xref ref-type="fn" rid="tfn4" /></td><td>0.60<xref ref-type="fn" rid="tfn4" /></td><td>0.79<xref ref-type="fn" rid="tfn4" /></td><td>–</td></tr><tr><td>Mean</td><td>103.02</td><td>5.16</td><td>4.21</td><td>4.10</td><td>560.97</td><td>549.25</td></tr><tr><td>SD</td><td>49.11</td><td>3.25</td><td>2.16</td><td>2.54</td><td>57.94</td><td>55.55</td></tr><tr><td>Min–Max</td><td>2–200</td><td>0–9</td><td>0–10</td><td>0–10</td><td>446–725</td><td>428–725</td></tr><tr><td>Skewness</td><td>0.06</td><td>−0.34</td><td>0.64</td><td>0.60</td><td>0.59</td><td>0.52</td></tr><tr><td>Kurtosis</td><td>−1.01</td><td>−1.33</td><td>−0.05</td><td>−0.46</td><td>0.36</td><td>−0.34</td></tr></tbody></table> </ephtml> </p> <p>1 Abbreviations: Max, maximum; Min, minimum; SD, standard deviation.</p> <ulist> <item>2 * <emph>p</emph> < 0.05.</item> <item>3 ** <emph>p</emph> < 0.01.</item> <item>4 *** <emph>p</emph> < 0.001.</item> </ulist> <p>Next, students' algebra scores at pretest and post‐test as well as their state standardized scores at fifth and seventh grades were widely distributed, indicating that the sample represented students with a wide range of mathematics performance levels. We noted that students' post‐test scores and seventh‐grade state scores were descriptively lower than students' pretest scores and fifth‐grade state scores, respectively. The decrease was not significant for the algebraic knowledge scores, <emph>p</emph> = 0.455, but significant for the state standardized scores, <emph>p</emph> < 0.001. We discuss these findings and their implications in the Discussion section.</p> <p>Correlation analyses revealed the associations between intervention progress, algebraic knowledge scores and state scores. Specifically, students' in‐game progress and sessions completed were moderately correlated with each other, suggesting that these two variables might have captured related yet distinct aspects of students' participation in the intervention; therefore, it was appropriate to control for the number of sessions completed to test the independent effects of in‐game progress on students' later mathematics performance. Next, students' scores on the algebraic knowledge assessment and state standardized assessment were moderately correlated with each other, warranting the analyses on both types of scores.</p> <hd id="AN0164202690-21">RQ1: In‐game progress did not predict students' post‐test algebra scores</hd> <p>A multilevel model revealed that students' in‐game progress did not significantly predict their post‐test scores on the algebraic knowledge assessment above and beyond the covariates, <emph>p</emph> = 0.065 (Table 2, Model 1.1). As expected, students' pretest scores significantly predicted their post‐test scores, <emph>p</emph> < 0.001. For students scoring one point higher than the average on the pretest, their post‐test scores were estimated to be 0.41 point higher than the post‐test average. The remaining covariates did not significantly predict students' post‐test scores. Together, the predictors accounted for 18% of the variances in students' post‐test scores.</p> <p>2 TABLE Multilevel linear regression models predicting students' post‐test algebra scores (N  = 253).</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Predictors</th><th align="left">Model 1.1 <italic>B</italic> (<italic>SE</italic>) [95%CI]</th><th align="left">Model 1.2 <italic>B</italic> (<italic>SE</italic>) [95%CI]</th></tr></thead><tbody valign="top"><tr><td>Intercept</td><td>4.21 (0.29) [3.66, 4.78]<xref ref-type="fn" rid="tfn7" /></td><td>4.17 (0.28) [3.63, 4.71]<xref ref-type="fn" rid="tfn7" /></td></tr><tr><td>Sessions completed</td><td>0.003 (0.06) [−0.12, 0.12]</td><td>−0.01 (0.06) [−0.12, 0.11]</td></tr><tr><td>Instructional format: virtual</td><td>0.15 (0.58) [−0.96, 1.34]</td><td>0.07 (0.58) [−1.04, 1.23]</td></tr><tr><td>Sex: male</td><td>−0.11 (0.27) [−0.63, 0.42]</td><td>−0.10 (0.27) [−0.62, 0.42]</td></tr><tr><td>Race: Hispanic</td><td>−0.04 (0.36) [−0.74, 0.65]</td><td>−0.06 (0.35) [−0.76, 0.61]</td></tr><tr><td>Race: Other</td><td>0.13 (0.43) [−0.69, 0.98]</td><td>0.04 (0.43) [−0.77, 0.88]</td></tr><tr><td>Pretest algebra scores</td><td>0.41 (0.07) [0.26, 0.58]<xref ref-type="fn" rid="tfn7" /></td><td>0.41 (0.07) [0.27, 0.58]<xref ref-type="fn" rid="tfn7" /></td></tr><tr><td>In‐game progress</td><td>0.01 (0.004) [−0.0003, 0.014]</td><td>0.01 (0.004) [−0.0008, 0.013]</td></tr><tr><td>Pretest × in‐game progress</td><td>–</td><td>0.003 (0.001) [0.0002, 0.005]<xref ref-type="fn" rid="tfn6" /></td></tr><tr><td>Marginal R<sup>2</sup></td><td>0.18</td><td>0.21</td></tr><tr><td>Conditional R<sup>2</sup></td><td>0.32</td><td>0.32</td></tr></tbody></table> </ephtml> </p> <ulist> <item>5 <emph>Note</emph>: Instructional format: virtual = 1, in‐person = 0; sex: male = 1, female = 0; race: Hispanic and Other are binary variables with White as the reference group.</item> <item>6 * <emph>p</emph> < 0.05.</item> <item>7 *** <emph>p</emph> < 0.001.</item> </ulist> <hd id="AN0164202690-22">RQ2: The effect of in‐game progress varies by students' pretest algebra scores</hd> <p>Building on Model 1.1, we added the Pretest × In‐game Progress interaction. The interaction was significant, <emph>p</emph> = 0.036 and accounted for an additional 3% of the variance in students' post‐test algebra scores. For students with higher pretest scores, more progress in DragonBox was associated with higher post‐test scores. This association was not significant among students with lower pretest scores (Table 2, Model 1.2, Figure 2).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/58I/01jul23/bjet13304-fig-0002.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="bjet13304-fig-0002.jpg" title="2 Pretest algebra score by in‐game progress interaction on post‐test algebra score." /> </p> <p></p> <hd id="AN0164202690-24">RQ3: The effects of in‐game progress and prior mathematics achievement</hd> <p>Next, we repeated the models for RQ1 and RQ2 using students' seventh‐grade state score as the outcome variable and fifth‐grade score as a covariate. We found that students' in‐game progress predicted their seventh‐grade state scores above and beyond the covariates, <emph>p</emph> = 0.012. For students with average in‐game progress, increasing their progress by one problem was associated with 0.17 point increase in their seventh‐grade state scores (Table 3, Model 2.1). Adding the Fifth‐grade Score × In‐game Progress interaction revealed that the effect of in‐game progress varied by students' fifth‐grade state score, <emph>p</emph> = 0.035. The positive association between in‐game progress and seventh‐grade state scores was stronger among students with lower versus higher fifth‐grade state scores (Table 3, Model 2.2, Figure 3).</p> <p>3 TABLE Multilevel linear regression models predicting students' seventh‐grade state score (N  = 183).</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Predictors</th><th align="left">Model 2.1 <italic>B</italic> (<italic>SE</italic>) [95%CI]</th><th align="left">Model 2.2 <italic>B</italic> (<italic>SE</italic>) [95%CI]</th></tr></thead><tbody valign="top"><tr><td>Intercept</td><td>550.21 (5.70) [539.26, 561.60]<xref ref-type="fn" rid="tfn11" /></td><td>550.22 (5.77) [539.17, 561.72]<xref ref-type="fn" rid="tfn11" /></td></tr><tr><td>Session completed</td><td>1.64 (1.20) [−0.71, 3.96]</td><td>1.85 (1.20) [−0.51, 4.16]</td></tr><tr><td>Instructional format: virtual</td><td>−11.78 (10.48) [−32.09, 10.49]</td><td>−11.71 (10.36) [−31.85, 10.41]</td></tr><tr><td>Sex: male</td><td>2.81 (4.75) [−6.31, 12.16]</td><td>2.96 (4.69) [−6.02, 12.15]</td></tr><tr><td>Race: Hispanic</td><td>6.99 (5.98) [−5.18, 18.44]</td><td>8.59 (5.94) [−3.39, 19.95]</td></tr><tr><td>Race: Other</td><td>4.92 (7.50) [−9.47, 20.07]</td><td>6.94 (7.50) [−7.40, 21.88]</td></tr><tr><td>Fifth‐grade scores</td><td>0.58 (0.05) [0.47, 0.71]<xref ref-type="fn" rid="tfn11" /></td><td>0.57 (0.05) [0.47, 0.70]<xref ref-type="fn" rid="tfn11" /></td></tr><tr><td>In‐game progress</td><td>0.17 (0.07) [0.04, 0.30]<xref ref-type="fn" rid="tfn9" /></td><td>0.18 (0.07) [0.05, 0.30]<xref ref-type="fn" rid="tfn10" /></td></tr><tr><td>Fifth‐grade score × in‐game progress</td><td>–</td><td>−0.002 (0.001) [−0.003, −0.0001]<xref ref-type="fn" rid="tfn9" /></td></tr><tr><td>Marginal R<sup>2</sup></td><td>0.52</td><td>0.52</td></tr><tr><td>Conditional R<sup>2</sup></td><td>0.66</td><td>0.67</td></tr></tbody></table> </ephtml> </p> <ulist> <item>8 <emph>Note</emph>: Instructional format: virtual = 1, in‐person = 0; sex: male = 1, female = 0; race: Hispanic and Other are binary variables with White as the reference group.</item> <item>9 * <emph>p</emph> < 0.05.</item> <item>10 ** <emph>p</emph> < 0.01.</item> <item>11 *** <emph>p</emph> < 0.001.</item> </ulist> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/58I/01jul23/bjet13304-fig-0003.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="bjet13304-fig-0003.jpg" title="3 Fifth‐grade state score by in‐game progress interaction on seventh‐grade state score." /> </p> <p></p> <hd id="AN0164202690-26">RQ4: Factors associated with students' in‐game progress</hd> <p>After controlling for the number of intervention sessions and instructional format, none of the predictors were significantly associated with students' in‐game progress, <emph>p</emph>s >0.192 (Table 4). For students with an average number of sessions completed, completing one additional session was associated with 8.12 problems increase in their in‐game progress, <emph>p</emph> < 0.001.</p> <p>4 TABLE Multilevel linear regression model predicting students' in‐game progress (N  = 253).</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Predictors</th><th align="left">Model 3 <italic>B</italic> (<italic>SE</italic>) [95%CI]</th></tr></thead><tbody valign="top"><tr><td>Intercept</td><td>97.35 (5.68) [86.33, 108.27]<xref ref-type="fn" rid="tfn13" /></td></tr><tr><td>Sessions completed</td><td>8.12 (1.07) [6.06, 10.19]<xref ref-type="fn" rid="tfn13" /></td></tr><tr><td>Instructional format: virtual</td><td>12.39 (11.20) [−9.16, 34.19]</td></tr><tr><td>Sex: male</td><td>3.95 (5.17) [−6.14, 13.90]</td></tr><tr><td>Race: Hispanic</td><td>−4.24 (6.92) [−17.81, 9.05]</td></tr><tr><td>Race: Other</td><td>8.39 (8.03) [−7.32, 23.83]</td></tr><tr><td>Pretest algebra score</td><td>2.03 (1.55) [−0.97, 5.03]</td></tr><tr><td>Fifth‐grade state scores</td><td>0.02 (0.06) [−0.10, 0.14]</td></tr><tr><td>Marginal R<sup>2</sup></td><td>0.34</td></tr><tr><td>Conditional R<sup>2</sup></td><td>0.46</td></tr></tbody></table> </ephtml> </p> <ulist> <item>12 <emph>Note</emph>: Instructional format: virtual = 1, in‐person = 0; sex: male = 1, female = 0; race: Hispanic and Other are binary variables with White as the reference group.</item> <item>13 *** <emph>p</emph> < 0.001.</item> </ulist> <hd id="AN0164202690-27">DISCUSSION</hd> <p>Three main findings emerged from the current study. First, among students with higher prior knowledge, higher in‐game progress was associated with higher algebraic performance after the intervention. Second, higher in‐game progress was associated with higher mathematics achievement at the end of seventh grade, and this effect was stronger among students with lower versus higher prior achievement. Finally, students who completed more intervention sessions made more in‐game progress; their biological sex, race/ethnicity, prior algebraic knowledge and prior mathematics achievement did not predict in‐game progress beyond the intervention sessions.</p> <p>Although the positive effects of in‐game progress were promising, on average, students' performance on the algebraic assessment did not significantly improve from pretest to post‐test, and their mathematics achievement scores slightly decreased from fifth grade to seventh grade. While surprising, this finding is consistent with the national US report on the decrease of mathematical performance during the COVID‐19 pandemic (Engzell et al., [<reflink idref="bib15" id="ref58">15</reflink>]; Kuhfeld et al., [<reflink idref="bib24" id="ref59">24</reflink>]). The long‐term educational impacts of the pandemic have yet to be seen, but the current study provided a valuable glimpse of its potential impact on algebraic learning. We interpret the findings with caution and in the context of the pandemic disruptions.</p> <hd id="AN0164202690-28">Algebraic performance</hd> <p>Contrary to our hypothesis and prior research (Chan & Santos, [<reflink idref="bib9" id="ref60">9</reflink>]; Hulse et al., [<reflink idref="bib19" id="ref61">19</reflink>]), we did not find an overall positive effect of in‐game progress on students' algebraic performance. However, we observed an interaction such that the positive effect of in‐game progress was only significant among students with higher pretest algebra scores. While beyond the scope of the current study on in‐game progress, we found that, in the larger RCT, students who received either DragonBox or another interactive algebraic game notably improved on all four conceptual knowledge items from pretest (<emph>M</emph> = 46%) to post‐test (<emph>M</emph> = 53%), whereas their improvements over time were inconsistent on other items (Chan et al., [<reflink idref="bib6" id="ref62">6</reflink>]). Given the seemingly stagnant performance on the overall algebraic assessment from pretest to post‐test, it is exciting to observe student improvement in conceptual knowledge, especially during the COVID‐19 pandemic. Together, the findings from the RCT corroborate with prior research reporting the potential benefits of playing games like DragonBox on students' conceptual knowledge of algebra, more specifically understanding of mathematical equivalence (Chan, Lee, et al., [<reflink idref="bib7" id="ref63">7</reflink>]; Supriadi et al., [<reflink idref="bib51" id="ref64">51</reflink>]).</p> <p>The current finding extends the literature on in‐game progress (Chan & Santos, [<reflink idref="bib9" id="ref65">9</reflink>]; Hulse et al., [<reflink idref="bib19" id="ref66">19</reflink>]) and DragonBox (Liu et al., [<reflink idref="bib27" id="ref67">27</reflink>]; Siew et al., [<reflink idref="bib47" id="ref68">47</reflink>]; Supriadi et al., [<reflink idref="bib51" id="ref69">51</reflink>]) in two important ways. First, it provides additional evidence supporting the notion that in‐game progress may be positively related to some students' learning outcomes. Specifically, the active experience of balancing two sides of the screen while isolating the dragon box may help students develop a perceptual‐motor routine of algebraic equation solving, improving their understanding of algebra. Although this potential explanation seems counterintuitive, it is supported by extensive theoretical and empirical work on the perceptual and embodied nature of learning (eg, Abrahamson et al., [<reflink idref="bib1" id="ref70">1</reflink>]; Alibali & Nathan, [<reflink idref="bib2" id="ref71">2</reflink>]; Goldstone et al., [<reflink idref="bib17" id="ref72">17</reflink>]; Kellman et al., [<reflink idref="bib22" id="ref73">22</reflink>]; Supriadi et al., [<reflink idref="bib51" id="ref74">51</reflink>]). For example, performing actions by using one's body to form triangles, even without pedagogical language to connect actions with mathematical concepts, helps undergraduate students gain insights into geometric proofs (Nathan et al., [<reflink idref="bib33" id="ref75">33</reflink>]). Furthermore, the active experience of manipulating and transforming algebraic expressions prior to a formal lesson on mathematical principles, such as the commutative property, improves seventh graders' performance on simplifying algebraic expressions (Ottmar & Landy, [<reflink idref="bib38" id="ref76">38</reflink>]).</p> <p>When asked about the connections between DragonBox and mathematics in the current study, students' anecdotal report after their gameplay suggested that they recognized some of these connections as they described their actions in mathematical terms (eg, fractions, equations, multiply, divide, etc.). For example, one student recognized that they could multiply a term in DragonBox by dragging a number to the term. They further explained that '...just like in math when you do equations you [<emph>sic</emph>] [,] whatever you do to one side you do to the other, which is the case with dragonBox [<emph>sic</emph>]. When I dragged one icon to one side [,] I would have to do the same to the other side. Another connection I could make was that the rules for cancelling out numbers are the same'. One student made a similar comment about balancing equations by saying that, '...when you add something to one side like a[n] animal, you have to also apply it to the other side as well'. Students also connected the action of combining the same pictures at the top and bottom of a fraction in DragonBox to combining like terms in mathematics. The seemingly frivolous procedure of moving pictures and boxes, therefore, may help students discover and practice algebraic concepts, such as equivalence, just as procedural and conceptual knowledge iteratively support each other throughout mathematical development (Rittle‐Johnson, [<reflink idref="bib42" id="ref77">42</reflink>]). However, more qualitative research is needed to test this hypothesis and explore the potential mechanisms through which DragonBox supports algebraic learning.</p> <p>Second, the finding suggests a nuanced dosage effect in that the students with higher prior knowledge may benefit more from solving more problems in the game. A potential explanation for this select benefit of in‐game progress is that students with higher, as opposed to lower, foundational knowledge of algebra may be better equipped to make connections between the mathematical ideas hidden within DragonBox and algebraic concepts taught in classrooms, and in turn benefit more from DragonBox as they progress through the game. This explanation aligns with some prior work demonstrating that students with higher versus lower prior knowledge benefit more from mathematics interventions (Swanson et al., [<reflink idref="bib52" id="ref78">52</reflink>]; Wood et al., [<reflink idref="bib54" id="ref79">54</reflink>]) and that students with higher prior knowledge may be more likely to notice mathematical structures that support learning (Novick, [<reflink idref="bib37" id="ref80">37</reflink>]) and equation solving (Chan, Ottmar, et al., [<reflink idref="bib8" id="ref81">8</reflink>]; Lee et al., [<reflink idref="bib25" id="ref82">25</reflink>]). The moderating effect of students' prior algebraic knowledge, therefore, highlights its importance in the relation between in‐game progress and later algebraic performance. To maximize the potential benefits of playing DragonBox, it may be helpful for students to first establish foundational algebraic knowledge through instruction and then engage with problem solving through game play.</p> <hd id="AN0164202690-29">Mathematics achievement</hd> <p>Given the prior focus on students' algebraic performance (Dolonen & Kluge, [<reflink idref="bib13" id="ref83">13</reflink>]; Liu et al., [<reflink idref="bib27" id="ref84">27</reflink>]; Long & Aleven, [<reflink idref="bib28" id="ref85">28</reflink>]; Siew et al., [<reflink idref="bib47" id="ref86">47</reflink>]; Supriadi et al., [<reflink idref="bib51" id="ref87">51</reflink>]), the current study is the first to report DragonBox's impacts on general mathematics achievement. We found that on average, students' state standardized scores decreased over time, potentially owing to the negative impacts associated with educational disruptions during the COVID‐19 pandemic (Engzell et al., [<reflink idref="bib15" id="ref88">15</reflink>]; Kuhfeld et al., [<reflink idref="bib24" id="ref89">24</reflink>]). Despite the learning loss, we found a positive effect of in‐game progress, suggesting that solving more problems in DragonBox may have mitigated the decrease in students' mathematics achievement. Furthermore, this positive effect was stronger among students with lower mathematics achievement.</p> <p>One potential explanation of this finding is that simply engaging students in mathematics through playing DragonBox may help foster a positive attitude towards mathematics and in turn support their later performance, especially among students with lower mathematics achievement. Prior work has shown that the game‐based approach can increase students' engagement with learning (Mora et al., [<reflink idref="bib31" id="ref90">31</reflink>]) and that playing DragonBox fosters students' positive attitudes towards mathematics (Dolonen & Kluge, [<reflink idref="bib13" id="ref91">13</reflink>]; Long & Aleven, [<reflink idref="bib28" id="ref92">28</reflink>]; Siew et al., [<reflink idref="bib47" id="ref93">47</reflink>]). Focus groups with teachers in the RCT revealed that students were excited and happy when they noticed the connections between DragonBox and classroom instruction, suggesting that the game may foster students' positive attitudes towards learning mathematics (Miyaoka, et al., [<reflink idref="bib30" id="ref94">30</reflink>]). Future work should replicate the current finding and delineate the mechanisms through which in‐game progress and prior knowledge influence students' mathematics attitudes and performance. Doing so will help identify ways that game‐based approaches support different aspects of mathematical learning and inform practices that maximize their benefits across students at varying levels of performance.</p> <hd id="AN0164202690-30">Factors associated with in‐game progress</hd> <p>To identify potential factors related to students' in‐game progress, we tested whether students' biological sex, race/ethnicity, pretest algebraic knowledge and fifth‐grade mathematics achievement were associated with students' in‐game progress. These factors were selected based on prior research reporting their associations with mathematical learning and engagement (Dong et al., [<reflink idref="bib14" id="ref95">14</reflink>]; Martinez & Guzman, [<reflink idref="bib29" id="ref96">29</reflink>]; Nosek & Smyth, [<reflink idref="bib36" id="ref97">36</reflink>]; Pecore et al., [<reflink idref="bib39" id="ref98">39</reflink>]; Reinhold et al., [<reflink idref="bib41" id="ref99">41</reflink>]). Contrary to prior work, we found that none of these factors were significantly associated with students' in‐game progress beyond the number of intervention sessions students completed, implicating that the effects of these factors may be inconsistent or situational (Linn & Hyde, [<reflink idref="bib26" id="ref100">26</reflink>]; Sonnenschein & Galindo, [<reflink idref="bib48" id="ref101">48</reflink>]). We did find that students who completed more intervention sessions made more in‐game progress. A potential implication is that, regardless of students' sex, race/ethnicity or prior knowledge or achievement, dedicating time and encouraging students to solve problems in DragonBox may help them make progress and in turn support mathematical learning.</p> <hd id="AN0164202690-31">Limitations and future directions</hd> <p>The current study had several limitations. First, our definitions and measures of the constructs by no means represented all perspectives in the field, and the study only focused on the effects of in‐game progress within DragonBox, limiting the generalizability of the current findings. However, our definitions and measures were grounded in existing work (eg, Chan & Santos, [<reflink idref="bib9" id="ref102">9</reflink>]; Hulse et al., [<reflink idref="bib19" id="ref103">19</reflink>]; Star et al., [<reflink idref="bib49" id="ref104">49</reflink>]), allowing us to connect with the larger literature on educational technologies, algebraic knowledge and mathematics achievement. Furthermore, the current results contributed novel findings on the effects of in‐game progress, advancing our understanding of how DragonBox supports mathematical learning.</p> <p>Second, the current sample was a subset of students from an RCT conducted in one school district; therefore, the study did not capture a wide range of demographic or socioeconomic diversity, limiting the generalizability of the results. However, the large range of the scores on the pretest and fifth‐grade mathematics achievement indicated that the sample consisted of students at varying performance levels. Furthermore, the current sample was large compared with some prior work (eg, Long & Aleven, [<reflink idref="bib28" id="ref105">28</reflink>]; Siew et al., [<reflink idref="bib47" id="ref106">47</reflink>]; Supriadi et al., [<reflink idref="bib51" id="ref107">51</reflink>]); the study was conducted in an authentic classroom context over an academic school year; and the pattern of results was robust across two subsamples (Appendix B). Future studies should replicate the current findings with participants from a wide range of backgrounds to ensure the generalizability of the results.</p> <p>Third, the study was conducted during the pandemic and many known or unknown factors might have impacted our findings. Despite these challenges, we aimed to contribute to the cumulative understanding of learning by explicitly articulating our study contexts, grounding our work in the literature and triangulating our inferences using available data (Grosz et al., [<reflink idref="bib18" id="ref108">18</reflink>]). For example, while we were not able to collect additional qualitative data or account for all possible factors given the already stressful situation, we quantitatively accounted for students' instructional format and the nesting structure of the data. This approach succinctly accounted for a salient feature of the instruction during the pandemic and the potential systematic variations between students. Furthermore, we discussed some qualitative anecdotes from the larger project to supplement quantitative results and provide additional information on the study context. Although we were unable to capture a comprehensive picture of student learning during the pandemic, our findings nonetheless provide a piece of the puzzle on student learning during this difficult time.</p> <hd id="AN0164202690-32">CONCLUSION</hd> <p>We examined the associations between students' DragonBox progress and two mathematics outcomes. We found that these associations varied depending on students' prior performance. If students' later mathematics performance is related to their engagement with DragonBox and its interaction with students' prior performance, parents and educators may dedicate varying amounts of time for students to play the game depending on their prior performance. Doing so may maximize the efficacy of the game to efficiently support students with varying levels of mathematical knowledge and achievement.</p> <hd id="AN0164202690-33">ACKNOWLEDGEMENTS</hd> <p>The research reported here was supported by the Institute of Education Sciences, US Department of Education, through an Efficacy and Replication Grant (R305A180401) to Worcester Polytechnic Institute. The opinions expressed are those of the authors and do not represent the views of the Institute or the US Department of Education. We thank the participating teachers and students for their support with this study. We also thank Barbara Booker, Craig Mason, Shihfen Tu, Ji‐Eun Lee and members of the Math Abstraction Play Learning and Embodiment Lab for their work on this project.</p> <hd id="AN0164202690-34">CONFLICT OF INTEREST STATEMENT</hd> <p>None.</p> <hd id="AN0164202690-35">DATA AVAILABILITY STATEMENT</hd> <p>The final dataset for the current study is available on the Open Science Framework (https://osf.io/nfg4c).</p> <hd id="AN0164202690-36">ETHICS APPROVAL STATEMENT</hd> <p>This research received approval from the Institutional Review Board at Worcester Polytechnic Institute.</p> <hd id="AN0164202690-37">A APPENDIX</hd> <p>A1 TABLE The items in the algebraic knowledge assessment at post‐test (Star et al., 2015).</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Item</th><th align="left">Type</th><th align="left">Question</th><th align="left">Answer</th></tr></thead><tbody valign="top"><tr><td>1</td><td>Procedural</td><td><p>Solve the equation for <italic>y</italic>.</p><p>3 (<italic>y</italic> − 2) = −1 (<italic>y</italic> − 2) + 2</p><p>a. 10</p><p>b. −2</p><p>c. 10/4</p><p>d. 4</p></td><td>c</td></tr><tr><td>2</td><td>Flexibility</td><td><p>Lynn solved the problem: 1/5 (<italic>x</italic> + 9) = 6</p><p>Lynn's first step was (5) 1/5 (<italic>x</italic> + 9) = 6 (5)</p><p><italic>x</italic> + 9 = 30</p><p>What step did Lynn use to get from the first line to the second line?</p><p>a. combine like terms</p><p>b. add or subtract the same quantity on both sides</p><p>c. distribute across parentheses</p><p>d. multiply or divide the same quantity on both sides</p></td><td>d</td></tr><tr><td><p>3</p></td><td>Conceptual</td><td><p>6 + 2 = 8</p><p>↑ What does this symbol mean?</p><p>a. two quantities on either side have the same value</p><p>b. the total</p><p>c. the problem has been solved</p><p>d. what the answer is</p></td><td>a</td></tr><tr><td><p>4</p></td><td>Flexibility</td><td><p>Imagine you are taking a timed test. You want to use fast (and correct) ways to solve the problems so you can finish as many as possible. Which would be the best way to start the problem 6 (<italic>y</italic> + 3) = 19?</p><p>a. Alice's 'multiply by 6 on both sides' way</p><p>b. Bob's 'divide by 6 on both sides first' way</p><p>c. Channing's 'subtract 19 from both sides first' way</p><p>d. David's 'distribute first' way</p></td><td>d</td></tr><tr><td>5</td><td>Procedural</td><td><p>Solve the equation below for x.</p><p>1 = (6 − 5<italic>x</italic>)/2</p><p>a. 4/5</p><p>b. 0</p><p>c. 1</p><p>d. −4/5</p></td><td>a</td></tr><tr><td>6</td><td>Conceptual</td><td><p>If 12<italic>x</italic> + 18 = 19, which of the following must also be true?</p><p>a. 2<italic>x</italic> + 3 = 19</p><p>b. 12<italic>x</italic> + 18 − 18 = 19 − 18</p><p>c. 12<italic>x</italic> − 12 + 18 − 12 = 19</p><p>d. −12<italic>x</italic> − 18 = 19</p></td><td>b</td></tr><tr><td>7</td><td>Conceptual</td><td><p>Which of the following is equivalent to (the same as)</p><p>(<italic>a</italic> + 2) + (<italic>a</italic> + 2) + (<italic>a</italic> + 2) + (<italic>a</italic> + 2) + (<italic>a</italic> + 2)?</p><p>a. <italic>a</italic> + 10</p><p>b. 5<italic>a</italic> + 2</p><p>c. 5 (<italic>a</italic> + 2)</p><p>d. <italic>a</italic><sup>5</sup> + 10</p></td><td>c</td></tr><tr><td>8</td><td>Procedural</td><td><p>Solve the equation below for <italic>n</italic>.</p><p>10 <italic>n</italic> + 5 = 12 <italic>n</italic> + 17 − 6 <italic>n</italic></p><p>a. 0</p><p>b. 3</p><p>c. 2</p><p>d. 3/2</p></td><td>b</td></tr><tr><td>9</td><td>Flexibility</td><td><p>Imagine you are taking a timed test. You want to use fast (and correct) ways to solve the problems so you can finish as many as possible. Which would be the best way to start the problem? (Choose the letter for the best way to start) 1/5 (3<italic>x</italic> + 2) = 10</p><p>a. Abby's 'divide by 5 on both sides first' way</p><p>b. Blake's 'distribute first' way</p><p>c. Chen's 'subtract 10 from both sides first' way</p><p>d. Dean's 'multiply by 5 on both sides first' way</p></td><td>d</td></tr><tr><td>10</td><td>Conceptual</td><td><p>Which of the following is NOT equivalent to 18 (75 − 16)?</p><p>a. 18 (59)</p><p>b. 18 (−16 + 75)</p><p>c. 18 (75) − 16</p><p>d. 18 (75) − 18 (16)</p></td><td>c</td></tr></tbody></table> </ephtml> </p> <hd id="AN0164202690-38">B APPENDIX</hd> <p>Because the analyses testing the effects of in‐game progress and fifth‐grade state scores on students' seventh‐grade state scores only included 183 students (RQ3), we repeated the analyses for RQs 1, 2 and 4 with these same 183 students. By doing so, we (a) checked the robustness of the results across the two overlapping yet different samples (253 vs. 183 students) and (b) examined whether the pattern of results varied by the analytic samples. We found that the pattern of the results with 183 students was identical to that with 253 students reported in the manuscript. Below, we reported the descriptive statistics, correlations and model estimates for the RQs 1, 2 and 4 with 183 students who had both fifth‐grade and seventh‐grade state scores and, thus, were included in the analyses for RQ3 in the manuscript.</p> <hd id="AN0164202690-39">Descriptive and correlation analyses</hd> <p>B1 TABLE Descriptive statistics of and correlations between each variable (N  = 183).</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left" /><th align="left">In‐game progress</th><th align="left">Sessions completed</th><th align="left">Pretest score</th><th align="left">Post‐test score</th><th align="left">Fifth‐grade state score</th><th align="left">Seventh‐grade state score</th></tr></thead><tbody valign="top"><tr><td>In‐game progress</td><td>–</td><td /><td /><td /><td /><td /></tr><tr><td>Sessions completed</td><td>0.58<xref ref-type="fn" rid="tfn16" /></td><td>–</td><td /><td /><td /><td /></tr><tr><td>Pretest score</td><td>0.32<xref ref-type="fn" rid="tfn16" /></td><td>0.29<xref ref-type="fn" rid="tfn16" /></td><td>–</td><td /><td /><td /></tr><tr><td>Post‐test score</td><td>0.37<xref ref-type="fn" rid="tfn16" /></td><td>0.28<xref ref-type="fn" rid="tfn15" /></td><td>0.52<xref ref-type="fn" rid="tfn16" /></td><td>–</td><td /><td /></tr><tr><td>Fifth‐grade state score</td><td>0.19<xref ref-type="fn" rid="tfn15" /></td><td>0.13</td><td>0.59<xref ref-type="fn" rid="tfn16" /></td><td>0.47<xref ref-type="fn" rid="tfn16" /></td><td>–</td><td /></tr><tr><td>Seventh‐grade state score</td><td>0.32<xref ref-type="fn" rid="tfn16" /></td><td>0.21<xref ref-type="fn" rid="tfn15" /></td><td>0.65<xref ref-type="fn" rid="tfn16" /></td><td>0.59<xref ref-type="fn" rid="tfn16" /></td><td>0.79<xref ref-type="fn" rid="tfn16" /></td><td>–</td></tr><tr><td>Mean</td><td>104.19</td><td>5.27</td><td>4.23</td><td>3.97</td><td>560.33</td><td>550.75</td></tr><tr><td>SD</td><td>48.39</td><td>3.32</td><td>2.14</td><td>2.53</td><td>58.25</td><td>55.38</td></tr><tr><td>Min–Max</td><td>13–200</td><td>0–9</td><td>0–10</td><td>0–10</td><td>446–725</td><td>428–725</td></tr><tr><td>Skewness</td><td>0.13</td><td>−0.37</td><td>0.62</td><td>0.67</td><td>0.58</td><td>0.54</td></tr><tr><td>Kurtosis</td><td>−1.03</td><td>−1.34</td><td>−0.07</td><td>−0.44</td><td>0.38</td><td>−0.27</td></tr></tbody></table> </ephtml> </p> <ulist> <item>14 Abbreviations: Max, maximum; Min, minimum; SD, standard deviation.</item> <item>15 <emph>p</emph> < 0.01.</item> <item>16 <emph>p</emph> < 0.001.</item> </ulist> <hd id="AN0164202690-40">RQs 1 and 2: Effects of in‐game progress and pretest algebra scores on post‐test algebra scor...</hd> <p>B2 TABLE Multilevel linear regression models predicting students' post‐test algebra scores (N  = 183).</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Predictors</th><th align="left">Model 1.1 <italic>B</italic> (<italic>SE</italic>) [95%CI]</th><th align="left">Model 1.2 <italic>B</italic> (<italic>SE</italic>) [95%CI]</th></tr></thead><tbody valign="top"><tr><td>Intercept</td><td>3.93 (0.32) [3.32, 4.55]<xref ref-type="fn" rid="tfn19" /></td><td>3.87 (0.29) [3.31, 4.42]<xref ref-type="fn" rid="tfn19" /></td></tr><tr><td>Sessions completed</td><td>0.06 (0.07) [−0.08, 0.20]</td><td>0.05 (0.07) [−0.08, 0.17]</td></tr><tr><td>Instructional format: virtual</td><td>0.69 (0.67) [−0.59, 2.11]</td><td>0.61 (0.66) [−0.63, 1.94]</td></tr><tr><td>Sex: male</td><td>−0.22 (0.31) [−0.81, 0.37]</td><td>−0.24 (0.30) [−0.82, 0.34]</td></tr><tr><td>Race: Hispanic</td><td>0.10 (0.38) [−0.63, 0.82]</td><td>0.04 (0.37) [−0.68, 0.74]</td></tr><tr><td>Race: Other</td><td>0.37 (0.47) [−0.53, 1.30]</td><td>0.18 (0.47) [−0.71, 1.08]</td></tr><tr><td>Pretest scores</td><td>0.40 (0.08) [0.23, 0.58]<xref ref-type="fn" rid="tfn19" /></td><td>0.39 (0.08) [0.23, 0.57]<xref ref-type="fn" rid="tfn19" /></td></tr><tr><td>In‐game progress</td><td>0.01 (0.004) [−0.001, 0.016]</td><td>0.007 (0.004) [−0.001, 0.015]</td></tr><tr><td>Pretest × in‐game progress</td><td>–</td><td><p>0.004 (0.001)</p><p>[0.002, 0.007]<xref ref-type="fn" rid="tfn18" /></p></td></tr><tr><td><italic>Marginal R</italic><sup>2</sup></td><td>0.24</td><td>0.32</td></tr><tr><td><italic>Conditional R</italic><sup>2</sup></td><td>0.38</td><td>0.39</td></tr></tbody></table> </ephtml> </p> <ulist> <item>17 <emph>Note</emph>: Instructional format: virtual = 1, in‐person = 0; sex: male = 1, female = 0; race: Hispanic and Other are binary variables with White as the reference group.</item> <item>18 <emph>p</emph> < 0.01.</item> <item>19 <emph>p</emph> < 0.001.</item> </ulist> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/58I/01jul23/bjet13304-fig-0004.jpg?ephost1=dGJyMNXb4kSepq84yOvqOLCmsE6epq5Srqa4SK6WxWXS" alt="bjet13304-fig-0004.jpg" title="B1 Pretest algebra score by in‐game progress interaction on post‐test algebra score (N = 183)." /> </p> <p></p> <hd id="AN0164202690-42">RQ4: Predictors of students' in‐game progress</hd> <p>B3 TABLE Multilevel linear regression model predicting students' in‐game progress (N  = 183).</p> <p> <ephtml> <table><thead valign="bottom"><tr><th align="left">Predictors</th><th align="left">Model 3 <italic>B</italic> (<italic>SE</italic>) [95%CI]</th></tr></thead><tbody valign="top"><tr><td>Intercept</td><td>100.37 (6.30) [88.21, 112.47]<xref ref-type="fn" rid="tfn21" /></td></tr><tr><td>Sessions completed</td><td>8.35 (1.19) [6.07, 10.63]<xref ref-type="fn" rid="tfn21" /></td></tr><tr><td>Instructional format: virtual</td><td>5.14 (11.84) [−17.59, 28.51]</td></tr><tr><td>Sex: male</td><td>4.36 (5.37) [−6.02, 14.76]</td></tr><tr><td>Race: Hispanic</td><td>−6.10 (6.75) [−19.27, 6.87]</td></tr><tr><td>Race: Other</td><td>7.60 (8.45) [−8.75, 23.84]</td></tr><tr><td>Pretest algebra score</td><td>2.49 (1.65) [−0.68, 5.69]</td></tr><tr><td>Fifth‐grade state scores</td><td>0.003 (0.06) [−0.12, 0.12]</td></tr><tr><td><italic>Marginal R</italic><sup>2</sup></td><td>0.36</td></tr><tr><td><italic>Conditional R</italic><sup>2</sup></td><td>0.54</td></tr></tbody></table> </ephtml> </p> <ulist> <item>20 <emph>Note</emph>: Instructional format: virtual = 1, in‐person = 0; 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Liu; Justin Roberts and Erin Ottmar</p> <p>Reported by Author; Author; Author; Author; Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib23" firstref="ref1"></nolink> <nolink nlid="nl2" bibid="bib10" firstref="ref2"></nolink> <nolink nlid="nl3" bibid="bib15" firstref="ref4"></nolink> <nolink nlid="nl4" bibid="bib24" firstref="ref5"></nolink> <nolink nlid="nl5" bibid="bib45" firstref="ref6"></nolink> <nolink nlid="nl6" bibid="bib11" firstref="ref7"></nolink> <nolink nlid="nl7" bibid="bib40" firstref="ref8"></nolink> <nolink nlid="nl8" bibid="bib43" firstref="ref9"></nolink> <nolink nlid="nl9" bibid="bib50" firstref="ref10"></nolink> <nolink nlid="nl10" bibid="bib55" firstref="ref12"></nolink> <nolink nlid="nl11" bibid="bib21" firstref="ref13"></nolink> <nolink nlid="nl12" bibid="bib31" firstref="ref14"></nolink> <nolink nlid="nl13" bibid="bib46" firstref="ref15"></nolink> <nolink nlid="nl14" bibid="bib16" firstref="ref16"></nolink> <nolink nlid="nl15" bibid="bib19" firstref="ref18"></nolink> <nolink nlid="nl16" bibid="bib20" firstref="ref19"></nolink> <nolink nlid="nl17" bibid="bib53" firstref="ref21"></nolink> <nolink nlid="nl18" bibid="bib17" firstref="ref24"></nolink> <nolink nlid="nl19" bibid="bib22" firstref="ref25"></nolink> <nolink nlid="nl20" bibid="bib27" firstref="ref27"></nolink> <nolink nlid="nl21" bibid="bib47" firstref="ref28"></nolink> <nolink nlid="nl22" bibid="bib51" firstref="ref29"></nolink> <nolink nlid="nl23" bibid="bib13" firstref="ref30"></nolink> <nolink nlid="nl24" bibid="bib28" firstref="ref31"></nolink> <nolink nlid="nl25" bibid="bib34" firstref="ref32"></nolink> <nolink nlid="nl26" bibid="bib54" firstref="ref33"></nolink> <nolink nlid="nl27" bibid="bib52" firstref="ref34"></nolink> <nolink nlid="nl28" bibid="bib32" firstref="ref35"></nolink> <nolink nlid="nl29" bibid="bib26" firstref="ref37"></nolink> <nolink nlid="nl30" bibid="bib48" firstref="ref38"></nolink> <nolink nlid="nl31" bibid="bib36" firstref="ref39"></nolink> <nolink nlid="nl32" bibid="bib29" firstref="ref40"></nolink> <nolink nlid="nl33" bibid="bib41" firstref="ref41"></nolink> <nolink nlid="nl34" bibid="bib14" firstref="ref42"></nolink> <nolink nlid="nl35" bibid="bib39" firstref="ref43"></nolink> <nolink nlid="nl36" bibid="bib12" firstref="ref46"></nolink> <nolink nlid="nl37" bibid="bib186" firstref="ref51"></nolink> <nolink nlid="nl38" bibid="bib49" firstref="ref52"></nolink> <nolink nlid="nl39" bibid="bib35" firstref="ref55"></nolink> <nolink nlid="nl40" bibid="bib44" firstref="ref56"></nolink> <nolink nlid="nl41" bibid="bib33" firstref="ref75"></nolink> <nolink nlid="nl42" bibid="bib38" firstref="ref76"></nolink> <nolink nlid="nl43" bibid="bib42" firstref="ref77"></nolink> <nolink nlid="nl44" bibid="bib37" firstref="ref80"></nolink> <nolink nlid="nl45" bibid="bib25" firstref="ref82"></nolink> <nolink nlid="nl46" bibid="bib30" firstref="ref94"></nolink> <nolink nlid="nl47" bibid="bib18" firstref="ref108"></nolink>
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  Data: Keep DRAGging ON: Is Solving More Problems in DragonBox 12+ Associated with Higher Mathematical Performance during the COVID-19 Pandemic?
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  Label: Authors
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  Data: <searchLink fieldCode="AR" term="%22Chan%2C+Jenny+Yun-Chen%22">Chan, Jenny Yun-Chen</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-1479-5935">0000-0003-1479-5935</externalLink>)<br /><searchLink fieldCode="AR" term="%22Byrne%2C+Chloe%22">Byrne, Chloe</searchLink><br /><searchLink fieldCode="AR" term="%22Jerusal%2C+Janette%22">Jerusal, Janette</searchLink><br /><searchLink fieldCode="AR" term="%22Liu%2C+Allison+S%2E%22">Liu, Allison S.</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-1075-2575">0000-0003-1075-2575</externalLink>)<br /><searchLink fieldCode="AR" term="%22Roberts%2C+Justin%22">Roberts, Justin</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-5906-6336">0000-0001-5906-6336</externalLink>)<br /><searchLink fieldCode="AR" term="%22Ottmar%2C+Erin%22">Ottmar, Erin</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-9487-7967">0000-0002-9487-7967</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22British+Journal+of+Educational+Technology%22"><i>British Journal of Educational Technology</i></searchLink>. Jul 2023 54(4):943-966.
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  Data: Wiley. Available from: John Wiley & Sons, Inc. 111 River Street, Hoboken, NJ 07030. Tel: 800-835-6770; e-mail: cs-journals@wiley.com; Web site: https://www.wiley.com/en-us
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  Label: Peer Reviewed
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  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 24
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2023
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  Label: Sponsoring Agency
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  Data: Institute of Education Sciences (ED)
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  Label: Contract Number
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  Data: R305A180401
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  Label: Document Type
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  Data: Journal Articles<br />Reports - Research
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  Label: Education Level
  Group: Audnce
  Data: <searchLink fieldCode="EL" term="%22Junior+High+Schools%22">Junior High Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Middle+Schools%22">Middle Schools</searchLink><br /><searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Elementary+Education%22">Elementary Education</searchLink><br /><searchLink fieldCode="EL" term="%22Grade+7%22">Grade 7</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Game+Based+Learning%22">Game Based Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Games%22">Educational Games</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+Solving%22">Problem Solving</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Achievement%22">Mathematics Achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Middle+School+Students%22">Middle School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Grade+7%22">Grade 7</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Prior+Learning%22">Prior Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Predictor+Variables%22">Predictor Variables</searchLink><br /><searchLink fieldCode="DE" term="%22COVID-19%22">COVID-19</searchLink><br /><searchLink fieldCode="DE" term="%22Pandemics%22">Pandemics</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Mathematics%22">Secondary School Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Supplementary+Education%22">Supplementary Education</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1111/bjet.13304
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 0007-1013<br />1467-8535
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between students' progress within DragonBox and their algebraic knowledge and general mathematics achievement, (b) the moderating effects of students' prior performance on these relations and (c) the potential factors associated with students' in-game progress. Among students with higher prior algebraic knowledge, higher in-game progress was related to higher algebraic knowledge after the intervention. Higher in-game progress was also associated with higher end-of-year mathematics achievement, and this association was stronger among students with lower prior mathematics achievement. Students' demographic characteristics, prior knowledge and prior achievement did not significantly predict in-game progress beyond the number of intervention sessions students completed. These findings advance research on how, for whom and in what contexts game-based interventions, such as DragonBox, support mathematical learning and have implications for practice using game-based technologies to supplement instruction. [For the corresponding grantee submission, see ED626412.]
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: Note
  Label: Notes
  Group: Note
  Data: https://osf.io/nfg4c
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  Label: IES Funded
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  Data: Yes
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2023
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  Label: Accession Number
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  Data: EJ1380171
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        Value: 10.1111/bjet.13304
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      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 24
        StartPage: 943
    Subjects:
      – SubjectFull: Game Based Learning
        Type: general
      – SubjectFull: Educational Games
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Mathematics Achievement
        Type: general
      – SubjectFull: Middle School Students
        Type: general
      – SubjectFull: Grade 7
        Type: general
      – SubjectFull: Algebra
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      – SubjectFull: Predictor Variables
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      – SubjectFull: Pandemics
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      – SubjectFull: Secondary School Mathematics
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      – SubjectFull: Mathematics Instruction
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      – SubjectFull: Supplementary Education
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      – TitleFull: Keep DRAGging ON: Is Solving More Problems in DragonBox 12+ Associated with Higher Mathematical Performance during the COVID-19 Pandemic?
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          Numbering:
            – Type: volume
              Value: 54
            – Type: issue
              Value: 4
          Titles:
            – TitleFull: British Journal of Educational Technology
              Type: main
ResultId 1