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Explaining Technical, Social, and Discursive Participation in Online Mathematical Discussions

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Title: Explaining Technical, Social, and Discursive Participation in Online Mathematical Discussions
Language: English
Authors: Bailing Lyu (ORCID 0000-0002-6964-9081), Chenglu Li (ORCID 0000-0002-1782-0457), Hai Li (ORCID 0009-0004-7299-2042), Wangda Zhu (ORCID 0000-0001-9611-4800), Wanli Xing (ORCID 0000-0002-1446-889X)
Source: Distance Education. 2025 46(4):550-573.
Availability: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
Peer Reviewed: Y
Page Count: 24
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Junior High Schools
Middle Schools
Secondary Education
High Schools
Descriptors: Electronic Learning, Discussion (Teaching Technique), Learner Engagement, Interpersonal Relationship, Student Behavior, Middle School Students, High School Students, Student Participation, Technology Uses in Education, Numeracy, Knowledge Level, Mathematics Education
DOI: 10.1080/01587919.2024.2399151
ISSN: 0158-7919
1475-0198
Abstract: Participating in online mathematical discussions is a beneficial strategy to improve online math learning. Research has examined online mathematical discussions from various aspects, focusing on the content discussed, student interaction, and the technical tools facilitating student participation, but few studies have investigated the interplay among these aspects. This study draws on Communicative Ecology Theory (CET, Foth & Hearn, 2007), which conceptualizes the sustainability of online communities as influenced by discursive, social, and technical factors, to explore how students' discursive, social, and technical participation behaviors on an online mathematical discussion board are interacted. Leveraging a dataset including more than 90,000 students and two million online discussion interactions, this study indicated that students' engagement with technical functions, especially a communication tool and a motivation system, within the discussion board significantly facilitated their social interactions and enhanced their demonstration of mathematical knowledge, mathematical literacy, and affective control in the discussions. These findings provide insights for educators and designers of educational applications to enhance student participation in online discussions thereby improving the effectiveness of these discussions in online learning.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1500784
Database: ERIC
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  Value: <anid>AN0189588744;5f001nov.25;2025Nov28.00:21;v2.2.500</anid> <title id="AN0189588744-1">Explaining technical, social, and discursive participation in online mathematical discussions </title> <p>Participating in online mathematical discussions is a beneficial strategy to improve online math learning. Research has examined online mathematical discussions from various aspects, focusing on the content discussed, student interaction, and the technical tools facilitating student participation, but few studies have investigated the interplay among these aspects. This study draws on Communicative Ecology Theory (CET, Foth & Hearn, 2007), which conceptualizes the sustainability of online communities as influenced by discursive, social, and technical factors, to explore how students' discursive, social, and technical participation behaviors on an online mathematical discussion board are interacted. Leveraging a dataset including more than 90,000 students and two million online discussion interactions, this study indicated that students' engagement with technical functions, especially a communication tool and a motivation system, within the discussion board significantly facilitated their social interactions and enhanced their demonstration of mathematical knowledge, mathematical literacy, and affective control in the discussions. These findings provide insights for educators and designers of educational applications to enhance student participation in online discussions thereby improving the effectiveness of these discussions in online learning.</p> <p>Keywords: online discussions; math education; social interaction; education technology; communicative ecology theory</p> <hd id="AN0189588744-2">Introduction</hd> <p>Mathematics plays a critical role in shaping students' academic success, preparing them for careers in science, technology, engineering, and mathematics (STEM), and influencing everyday life (Cirino et al., [<reflink idref="bib9" id="ref1">9</reflink>]; Lee & Mao, [<reflink idref="bib27" id="ref2">27</reflink>]). Nevertheless, data from the National Assessment of Educational Progress (NAEP) in 2019 and 2022 indicated a concerning trend in mathematics learning in the United States. The results showed that only 75% of 4th graders (aged 9–10), 62% of 8th graders (aged 13–14), and 60% of 12th graders (aged 17–18) achieved the NAEP basic achievement level in mathematics, reflecting partial mastery of fundamental mathematics knowledge and skills. Moreover, a much smaller percentage of students (i.e., 36% of 4th graders, 26% of 8th graders, and 24% of 12th graders) reached or surpassed the NAEP proficient achievement level in mathematics, indicating decreasing competency in more complex mathematical concepts as they get older. These statistics underscore the urgent need for improving math education. Learning math online presents a potential solution by offering flexible access to educational materials, thereby making math education more accessible and engaging for all students.</p> <p>An essential component of online mathematics learning is online mathematical discussions. Theoretically grounded in Vygotsky's social constructivist theory, which posits that learning occurs through social interactions wherein learners negotiate the meaning of information and construct a shared understanding with others (Vygotsky, [<reflink idref="bib50" id="ref3">50</reflink>]), online mathematical discussions allow students to exchange ideas about mathematical problems, explore different problem-solving strategies, and justify their thoughts with others (Staples & King, [<reflink idref="bib46" id="ref4">46</reflink>]; Smith & Stein, [<reflink idref="bib45" id="ref5">45</reflink>]; Harbour & Denham, [<reflink idref="bib17" id="ref6">17</reflink>]). Meanwhile, online discussions can help build an online community and foster emotional connections among students, thereby mitigating the sense of isolation often experienced by students in online learning due to physical separation (Aragon, [<reflink idref="bib1" id="ref7">1</reflink>]). Empirical research has shown that participating in online mathematical discussions can significantly enhance mathematics learning (Chen et al., [<reflink idref="bib6" id="ref8">6</reflink>]; Schumacher & Siegel, [<reflink idref="bib43" id="ref9">43</reflink>]; Lee & Recker, [<reflink idref="bib28" id="ref10">28</reflink>]). Thus, we would argue that understanding student participation in online mathematical discussions is crucial for enhancing mathematical education. Previous research has explored online mathematical discussions from multiple aspects, including the content discussed by students, their interactions within these discussions, and the tools they utilized to support their communication during discussions (Grackin et al., [<reflink idref="bib15" id="ref11">15</reflink>]; Wessner et al., [<reflink idref="bib51" id="ref12">51</reflink>]; Broderick, [<reflink idref="bib5" id="ref13">5</reflink>]; Harbour & Denham, [<reflink idref="bib17" id="ref14">17</reflink>]; Banawan et al., [<reflink idref="bib3" id="ref15">3</reflink>]; Mailizar et al., [<reflink idref="bib35" id="ref16">35</reflink>]; Muir, [<reflink idref="bib38" id="ref17">38</reflink>])</p> <p>A theoretical framework that can be used to gain a comprehensive understanding of online mathematical discussions is the Communicative Ecology Theory (CET, Foth & Hearn, [<reflink idref="bib14" id="ref18">14</reflink>]). CET is a theoretical framework commonly used in the fields of sociology, media, and communication. According to CET, an online community, such as an online mathematical discussion board, is composed of three interconnected layers of elements: technical, discursive, and social layers (Foth & Hearn, [<reflink idref="bib14" id="ref19">14</reflink>]). The technical layer concerns the tools used for discussions; the discursive layer pertains to the nature of information exchanged; and the social layer involves the interactions and relationships among discussion participants. These three layers interact with each other to construct a sustained online community. Previous studies using CET as a framework to analyze online communities have examined the associations among the three layers and how each of the three layers influenced user participation. The findings indicated that the three layers were interconnected, with each layer positively correlating with user participation (Hearn et al., [<reflink idref="bib18" id="ref20">18</reflink>]; Seol et al., [<reflink idref="bib44" id="ref21">44</reflink>]; Khan & Dongping, [<reflink idref="bib24" id="ref22">24</reflink>]; Jin et al.,[<reflink idref="bib22" id="ref23">22</reflink>]).</p> <p>However, such studies are rarely conducted in educational settings, particularly within online mathematical discussions. Furthermore, most studies on online mathematical discussions focused on the social (i.e., social behaviors, Lee & Recker, [<reflink idref="bib28" id="ref24">28</reflink>]; Mailizar et al., [<reflink idref="bib35" id="ref25">35</reflink>]) and discursive layers (e.g., content analysis, Sudiarta et al., [<reflink idref="bib47" id="ref26">47</reflink>]), but the technical aspects (i.e., the feature of discussion platform used for online mathematical discussions) have received less attention. These highlight a notable gap in the comprehension of the interactions among the three layers in online mathematical discussions, especially how the technical layer is related to social and discursive layers. Understanding these dynamics is important for educators to grasp the overall structure of online mathematical discussions and to design discussion platforms with features that facilitate student participation. In this study, we apply CET to analyze the interplay among technical, discursive, and social layers in online mathematical discussions. Specifically, we examine how students' engagement with the technical functions of an online mathematical discussion board correlates with their social interactions and the nature of their discussion content, and how social interaction mediates the relationship between students' technical participation behaviors and discussion content.</p> <hd id="AN0189588744-3">Research background</hd> <p></p> <hd id="AN0189588744-4">Communicative Ecology Theory</hd> <p>CET is a conceptual framework commonly used in the fields of sociology and communication to explain interpersonal communication processes within virtual communities (Foth & Hearn, [<reflink idref="bib14" id="ref27">14</reflink>]). It views a virtual community (e.g., an online mathematical discussion board) as a communicative ecology. Three interdependent layers—technical social, and discursive (content) layers—interact to sustain the communicative ecology (Foth & Hearn, [<reflink idref="bib14" id="ref28">14</reflink>]; Bock et al., [<reflink idref="bib4" id="ref29">4</reflink>]; Jin et al., [<reflink idref="bib22" id="ref30">22</reflink>]). The technology layer includes factors concerning the features of the social-technology systems that are used for communication. Systems that provide efficient and easy-to-use communication tools, improve access to information, and encourage participation are crucial for sustaining an online community (Teo et al., [<reflink idref="bib49" id="ref31">49</reflink>]; Lin, [<reflink idref="bib31" id="ref32">31</reflink>]). For instance, on an online mathematical discussion board, drawing tools and information search tools enable students to easily share math-related information (e.g., equations, symbols) and retrieve previously discussed relevant information, thereby facilitating student participation in the discussions. The social layer involves the interactions or connections among members within virtual communities. Within the context of an online mathematical discussion board, students interact with different people and are involved in discussion threads of varying lengths to share their ideas about math learning (Xie et al., [<reflink idref="bib54" id="ref33">54</reflink>]; Bock et al., [<reflink idref="bib4" id="ref34">4</reflink>]; Seol et al., [<reflink idref="bib44" id="ref35">44</reflink>]). The discursive layer pertains to the nature of the information exchanged by members within the online communities. Participants in an online mathematical discussion board can share various types of math-learning content, such as conceptual content or problem-solving (Sudiarta et al., [<reflink idref="bib47" id="ref36">47</reflink>]).</p> <p>Researchers have examined how the technical, social, and discursive layers affect individual participation or willingness to participate in online communities differently. For example, Seol et al. ([<reflink idref="bib44" id="ref37">44</reflink>]) developed a research model to explain the continued use of corporate SNS pages based on CET. They found that SNS platform quality (i.e., technical layer), content quality of corporate SNS pages (i.e., discursive layer), service quality of corporate SNS pages, and the quality of social interactions among members (social layer) significantly predicted users' perceived usefulness and enjoyment of these pages, and in turn, predicted their intention to continue using them. Additionally, several studies have investigated the interactions among the three layers in virtual communities. For example, Bock et al. ([<reflink idref="bib4" id="ref38">4</reflink>]) examined the sustainability of virtual communities by analyzing how users' use of collaborative tools (technical layer) correlates with the strength of emotional connections among them (social layer) and their extent of information sharing (discursive layer). Users from 15 virtual communities participated in this study. The findings demonstrated a positive correlation between the use of collaborative tools with the strength of emotional ties and the amount of information shared, illustrating the interconnectedness of these layers. More recently, Jin et al. ([<reflink idref="bib22" id="ref39">22</reflink>]) examined users' willingness to diffuse healthcare knowledge on social media using CET as a framework. The results indicated that factors related to the discursive (i.e., the interestingness, usefulness, emotionality, and positivity of health content), social (i.e., perception of source credibility given the content creators), and technical layers (i.e., one's perception of the social media environment) all were significant predictors of users' willingness to diffuse healthcare knowledge on social media. Furthermore, the social layer was found to mediate the relationship between the technical layer and users' willingness to disseminate knowledge.</p> <p>These studies have underscored the significance of the technical, social, and discursive layers in maintaining an online community and the interplay among the three layers. However, a common limitation of these studies is their reliance on self-reported measures to assess constructs related to each layer. While self-reported measures offer a direct means to assess users' perceptions, they can be subject to biases, such as participants' potential overreporting or underreporting. There is a need for research to explore the relationships among the three layers using alternative forms of data, such as actual participation behaviors. Additionally, although Communicative Ecology Theory (CET) is well-established in media and sociology, it was less applied in educational settings. The interactions among these layers within educational contexts, such as online mathematical discussions, are under-explored. Therefore, this study aims to analyze the interplay among the technical, social, and discursive layers in online mathematical discussions, assessing each layer based on students' actual participation behaviors. The following section reviews the literature examining these three layers within online mathematical discussions to guide the assessment of each layer in the current study.</p> <hd id="AN0189588744-5">Online mathematical discussions</hd> <p>Mathematical discussion is characterized as a purposeful interchange of mathematical ideas, solutions, and reasoning through various forms of communication, including verbal, written, or visual (National Council of Teachers of Mathematics, [<reflink idref="bib41" id="ref40">41</reflink>]). Engaging in these discussions enables students to express and justify their thoughts and interact with the ideas of others. Importantly, through critically examining others' reasoning and solving disagreements, students monitor their thinking and deepen their understanding of complex mathematical concepts, procedures, and problem-solving strategies (Kramarski & Mizrachi, [<reflink idref="bib25" id="ref41">25</reflink>]; Staples & King, [<reflink idref="bib46" id="ref42">46</reflink>]; Harbour & Denham, [<reflink idref="bib17" id="ref43">17</reflink>]). As online math learning becomes popular, students can participate in online mathematical discussions without the limitations of time and place. There has been an increase in research that focuses on online mathematical discussions (Grackin et al., [<reflink idref="bib15" id="ref44">15</reflink>]; Wessner et al., [<reflink idref="bib51" id="ref45">51</reflink>]; Broderick, [<reflink idref="bib5" id="ref46">5</reflink>]; Harbour & Denham, [<reflink idref="bib17" id="ref47">17</reflink>]; Muir, [<reflink idref="bib38" id="ref48">38</reflink>]). These studies have examined the social, discursive, and technical dimensions of online mathematical discussions to varying degrees, with a primary focus on the social and discursive aspects.</p> <hd id="AN0189588744-6">Social layer</hd> <p>Researchers have explored the social layer of online mathematical discussions by examining social interaction within online mathematical discussions, focusing on both the breadth (i.e., the number of people interacted with) and depth (i.e., the length of discussion threads) of the interaction (Lyu & Li, [<reflink idref="bib33" id="ref49">33</reflink>]; Lyu et al., [<reflink idref="bib34" id="ref50">34</reflink>]; Mailizar et al., [<reflink idref="bib35" id="ref51">35</reflink>]). For instance, Mailizar et al. ([<reflink idref="bib35" id="ref52">35</reflink>]) used social network analysis to examine how secondary school mathematics teachers who participated in a webinar on realistic mathematics education (RME) interacted via WhatsApp to design lesson plans based on RME principles. They found that active participants (i.e., participants who sent the most messages and mostly started a new discussion session) interacted with most of the other participants. Besides the number of people participants interacting with, research has analyzed social interaction through a consideration of the length of the discussion threads they involved in. For example, Lyu & Li ([<reflink idref="bib33" id="ref53">33</reflink>]) categorized students on an online mathematical discussion board into core, periphery, and x-periphery roles given the number of people they communicated with and the length of their discussion threads. Most participants were categorized as x-peripheral participants who indicated loose connections with other members and no dyadic relationship observed, followed by peripheral participants who demonstrated loose connections with some dyadic relationships. Smallest number of participants was the core participants who showed tight connections with other members. The current study assesses students' social participation behaviors in online mathematical discussions by examining the breadth and depth of their social interaction in the discussions.</p> <hd id="AN0189588744-7">Discursive layer</hd> <p>Content analysis and natural language processing methods have been used to analyze the information shared in online mathematical discussions (Banawan et al., [<reflink idref="bib3" id="ref54">3</reflink>]; Sudiarta et al., [<reflink idref="bib47" id="ref55">47</reflink>]; Zou et al., [<reflink idref="bib56" id="ref56">56</reflink>]). Sudiarta et al. ([<reflink idref="bib47" id="ref57">47</reflink>]) analyzed the content of online mathematical discussions in a blended learning environment, identifying significant mathematical proficiency elements, such as conceptual understanding, procedural fluency, and strategic components, within the discussions. Additionally, natural language processing techniques have been used to examine the linguistic features of online mathematical discussions. For example, given that mathematical language typically features high lexical density and precise technical terminology, Banawan et al. ([<reflink idref="bib3" id="ref58">3</reflink>]) investigated linguistic characteristics such as cohesion, language sophistication, and lexical diversity on an online mathematical discussion board using Coh-Metrix. They conducted a Principal Component Analysis (PCA) on these linguistic features, identifying seven Math Discourse Linguistic Components (e.g., referential cohesion). These components explained 49% of the variance of the discussions, highlighting the critical role that understanding and using mathematical language plays in facilitating communication within mathematical discussions. These results emphasize the vital importance of both mathematical knowledge (e.g., conceptual knowledge, procedural knowledge, and strategic knowledge) and mathematical literacy in mathematical discussions.</p> <p>Furthermore, researchers have investigated the influence of online mathematical discussions on students' emotions. For instance, research has demonstrated that such discussions can help reduce math anxiety and improve affective control. Karen Van et al. ([<reflink idref="bib23" id="ref59">23</reflink>]) studied the impact of web-based instruction (WBI), including online discussions, on math anxiety and found that students participating in online discussions reported reduced math anxiety by the end of the course. Similarly, Liu ([<reflink idref="bib32" id="ref60">32</reflink>]) investigated the effect of online mathematical discussions on pre-service teachers' anxiety related to mathematics and teaching mathematics, revealing that such discussions significantly decreased participants' math anxiety stemming from the perception that mathematics is challenging. These findings highlight the beneficial impact of online mathematical discussions on math learning by reducing math anxiety and enhancing affective control, suggesting that affective control may be a key component of online mathematical discussions. In this study, we examine students' discursive (content) participation behaviors in online mathematical discussions by assessing the presence of mathematical knowledge, mathematical literacy, and affective control.</p> <hd id="AN0189588744-8">Technology layer</hd> <p>Prior research has also focused on the features of platforms used for online mathematical discussions (Grackin et al., [<reflink idref="bib15" id="ref61">15</reflink>]; Levonian et al., [<reflink idref="bib29" id="ref62">29</reflink>]; Wessner et al., [<reflink idref="bib51" id="ref63">51</reflink>]). Grackin et al. ([<reflink idref="bib15" id="ref64">15</reflink>]) emphasized the importance of fundamental communication tools that enable students to view, edit, and post diagrams and equations directly, on mathematical discussion platforms. They assessed undergraduates' ease of use with an online math discussion platform called NetTutor, which provided these tools. The majority of students reported finding the platform user-friendly, felt that the tools met their needs, and believed that the tools provided were sufficient, showcasing the importance of communication tools in online mathematical discussions. Also, Wessner et al. ([<reflink idref="bib51" id="ref65">51</reflink>]) examined the design-based research process involved in developing a platform for synchronous math problem-solving discussions. Their observations revealed important tools that support online mathematical discussions, including drawing tools and features for locating and referencing earlier postings. These studies pointed out the critical role of communication and information access tools within online mathematical discussion platforms. However, they did not explore how these tools affect student participation in the discussions. This study examined students' technical participation behaviors in online mathematical discussions by focusing on their use of a communication tool and information access tool. Meanwhile, since diverse learning theories highlight the essential role of motivation in learning (Wigfield, [<reflink idref="bib52" id="ref66">52</reflink>]; Deci & Ryan, [<reflink idref="bib11" id="ref67">11</reflink>]), and empirical research has established associations between motivation and student participation in online mathematical discussions and mathematics learning (Xie et al., [<reflink idref="bib55" id="ref68">55</reflink>]; Cleary & Kitsantas, [<reflink idref="bib10" id="ref69">10</reflink>]; Rutherford et al., [<reflink idref="bib42" id="ref70">42</reflink>]), this study further assesses students' engagement with a motivational system embedded in the online mathematical discussion board as an indicator of their technical participation behaviors, investigating whether engaging in a motivation system on online mathematical discussion board enhance students' social interaction and math learning in the discussions.</p> <p>In summary, in order to build a comprehensive understanding of online mathematical discussions, this study, leveraging CET, examines the interplay between students' technical, social, and discursive participation behaviors in an online mathematical discussion board. Given prior research on online mathematical discussions, we analyze technical participation behaviors by examining students' interaction with a communication tool, an information access tool, and a motivation system. On the social layer, we assess the breadth (i.e., the number of people students communicate with) and depth (i.e., the length of discussion threads) of students' social participation in the discussions. The discursive participation is assessed by evaluating students' demonstration of three types of math-learning knowledge in the discussions: mathematical knowledge, mathematical literacy, and affective control.</p> <hd id="AN0189588744-9">Research model and hypotheses</hd> <p>Based on the communicative ecology theory and the literature reviewed, the hypothesized model explaining the relationship between students' technical, social, and discursive participation behaviors within an online mathematical discussion board was developed (see Figure 1).</p> <p>PHOTO (COLOR): Figure 1. Hypothesized research model. Purple lines represent the hypothesized direct effects of technical layer on social layer; blue lines represent the hypothesized direct effects of social layer on discursive layer; green lines depict the hypothesized direct effect of technical layer on discursive layer.</p> <hd id="AN0189588744-10">Associations between technical and social participation behaviors</hd> <p> <bold>H1.</bold> The extent to which one uses the communication tool, information access tool, and engages with the motivation system would positively predict the breadth and depth of their social interaction within online mathematical discussions.</p> <hd id="AN0189588744-11">Associations between technical and discursive participation behaviors</hd> <p> <bold>H2A.</bold> The extent to which one engages with the motivation system would positively predict the demonstration of mathematical knowledge, mathematical literacy, and affective control.</p> <p> <bold>H2B</bold>. The extent to which one uses the communication tool would positively predict the demonstration of mathematical knowledge.</p> <p> <bold>H2C.</bold> The extent to which one uses the information access tool would positively predict the demonstration of mathematical knowledge and affective control.</p> <hd id="AN0189588744-12">Associations between social and discursive participation behaviors</hd> <p> <bold>H3</bold>. The breadth and depth of social interaction one involves in online mathematical discussion would positively predict their demonstration of mathematical knowledge, mathematical literacy, and affective control.</p> <hd id="AN0189588744-13">The mediation between technical and discursive participation behaviors through social partici...</hd> <p> <bold>H4.</bold> The extent to which one uses the communication tool, the information access tool, and engages with the motivation system would positively predict the demonstration of mathematical knowledge, mathematical literacy, and affective control through social interaction during discussions.</p> <hd id="AN0189588744-14">Method</hd> <p></p> <hd id="AN0189588744-15">Data and context</hd> <p>We analyzed discussion data from Math Nation (MN), a widely adopted online math learning platform for middle and high school students in the United States. This platform supports over a million learners to engage in both hybrid learning within school districts and individual online learning. MN offers various mathematics courses (e.g., Algebra, Geometry). Each course is organized into multiple units that address distinct mathematical topics, and each unit includes several lessons designed to explain the key concepts of the topic. A variety of learning resources are available in each lesson, including instructional videos, self-assessment quizzes, and other educational materials.</p> <p>Meanwhile, students in MN have access to a question-and-answer mathematical discussion board, called "Student Wall". On this board, students post math questions (e.g., questions from school homework, test problems); other students or expert tutors (i.e., paid adult teachers) reply to provide help. The questions can take various forms (e.g., multiple-choice, short answer, or fill-in-the-blank) and cover a range of content areas (e.g., mathematical knowledge, strategies to solve math problems, or other math-learning-related topics). The discussion board is enriched with a variety of tools and functions to help students navigate the discussion content and enhance their participation. For example, students can use a drawing tool to create graphs that aid in articulating their questions (i.e., the use of a communication tool). A search function is embedded in the discussion board, allowing students to easily identify discussion threads relevant to their interests or specific math questions (i.e., an information access tool).</p> <p>Also, the board features a Karma points system, rewarding students for assisting their peers and motivating their learning and participation in the online discussions. Students accumulating significant Karma points appear on the Leaderboard—a ranking derived from these points—and receive recognition, such as the 'student ambassador' badge. Additionally, top students are awarded monthly prizes (e.g., an iPad). This Karma points system employed several gamification elements to improve students' motivation (Toda et al., [<reflink idref="bib48" id="ref71">48</reflink>]). First, students gain points by posting comments to assist peers solve problems, indicating the gamification elements of points (providing feedback to students by awarding points), narrative (giving a small token of appreciation to students who choose to interact with others), and cooperation (students collaborating to achieve a shared goal). Next, the Leaderboard creates an environment where students compete to each other, showing the gamification element of competition. Finally, the badges and prizes awarded to students reflect the gamification element of acknowledgement (a form of extrinsic feedback praising students' actions), such acknowledgements could increase students' reputation (social status that students may gain within the gamification system). Previous studies have demonstrated the positive effect of gamification on students' engagement and motivation (Dichev & Dicheva, [<reflink idref="bib12" id="ref72">12</reflink>]; Hamari & Keronen, [<reflink idref="bib16" id="ref73">16</reflink>])</p> <p>We gathered all discussion posts and replies generated by students and tutors, along with their log data concerning the use of the drawing tool, search function, and checks of the Leaderboard on the discussion board from the MySQL database of MN, spanning from August 15, 2013, to October 22, 2021. This dataset includes a total of 2,453,396 comments from 96,867 students (a total of 3,322,479 comments including those from 3,211 tutors). These comments were generated across 408,351 threads, with each thread averaging 8.14 utterances and 7.14 conversation turns (<emph>SD</emph> = 10.82). The social participation behaviors were measured by considering the interaction among all participants (including both teachers and students), but the technical and discursive participation behaviors were assessed solely based on students' data. MN automatically gathered students' demographic information from students' school districts through a data-sharing agreement when they sign up for MN. The demographic information of the 96,867 students were presented in Figure 2.</p> <p>PHOTO (COLOR): Figure 2. Distribution of demographic information.</p> <hd id="AN0189588744-16">Assessment of technical participation behaviors</hd> <p>MN collected students' log data when students entered the discussion board. Given the log data, students' technical participation behaviors in the discussion board were assessed by evaluating their engagement with the following tools: the communication tool, the information access tool, and the motivation system. Specifically, the three technical participation indicators extracted from the log data are: <bold><emph>a)</emph></bold> the frequency with which students utilized drawing tools for question formulation (i.e., communication tool), <bold><emph>b)</emph></bold> the frequency with which students used the search function (i.e., information search tool), and <bold><emph>c)</emph></bold> the frequency of students checking the leaderboard (i.e., motivation system).</p> <hd id="AN0189588744-17">Assessment of social participation behaviors</hd> <p>Students' social participation patterns were measured by quantifying students' social interactions in two dimensions: breadth and depth. The breadth of the social interaction was examined by counting the number of different participants students posted comments to and received replies from. The depth of interaction was reflected in the average length of discussion threads a student contributed to, including threads they initiated and those they responded to.</p> <hd id="AN0189588744-18">Assessment of discursive participation behaviors</hd> <p>Students' discursive participation behaviors were assessed by coding students' each statement in the discussions for the presence of three types of math-learning knowledge and skill:</p> <p></p> <ulist> <item> mathematical knowledge, identified if students demonstrated their understanding of mathematical concepts, applied computation skills, and formulated plans for solving math problems. This type of knowledge included three sub-categories conceptual knowledge, computational skill, and strategic knowledge.</item> <p></p> <item> mathematical literacy, recognized if students demonstrated their language ability or literacy skills to understand word problems.</item> <p></p> <item> affect control, noted if students exhibited control over their emotions to focus on mathematical tasks.</item> </ulist> <p>Originally, each statement was coded for the presence of conceptual knowledge, computational skill, strategic knowledge, mathematical literacy, and affect control. The conceptual knowledge, computational skill, and strategic knowledge were consolidated into a main category, called mathematical knowledge, reflecting their collective importance as fundamental components of mathematical knowledge when running the path analysis.</p> <p>Four graduate researchers independently coded 257 threads to establish interrater reliability (IRR). To ensure the validity of the coding, the four graduate researchers were trained to code the discussion threads. They first independently coded 50 discussion threads, achieving an interrater reliability of Kappa = 0.81. Then, they discussed the disagreements in groups and resolved the disagreements. Next, they coded an additional 100 discussion threads, obtaining a Kappa = 0.87. After resolving further disagreements, they then coded another 107 threads, reaching an interrater reliability of Kappa = 0.88, which is considered as almost perfect (McHugh, [<reflink idref="bib37" id="ref74">37</reflink>]). After this training process, one faculty member from Educational Technology and one faculty member from Educational Psychology randomly reviewed the coding done by the four graduate researchers. Finally, each of the four researchers independently coded approximately 500 new threads, resulting in a total of 2318 hand-labeled discussion threads (comprising 24,116 comments).</p> <p>An automatic text classification approach was further used to assess the five information types for all discussion threads based on the hand-labeled threads. The number of each label (five information labels) in the coded 24,116 discussion comments (i.e., original data) were presented in Table 1. To address the imbalance in the dataset, we applied an upsampling technique (Barros et al., [<reflink idref="bib2" id="ref75">2</reflink>]) that has been shown to make the dataset distribution more balanced across all constructs and was trained using a standalone model due to its sufficient sample size. This results in a substantial increase in the number of the labeled comments for training, totaling 123,328 in Table 1. Upon acquiring the prediction data and incorporating the training data, the aggregate number of samples amounted to 3,322,479.</p> <p>Table 1. Positive samples for five information type labels.</p> <p> <ephtml> <table><thead><tr><td>Data</td><td>Number</td><td>Math literacy</td><td>Mathematical knowledge</td><td>Affective control</td></tr><tr><td>Computational skill</td><td>Conceptual knowledge</td><td>Strategic knowledge</td></tr></thead><tbody valign="top"><tr><td>Original</td><td char=".">24116</td><td char=".">21</td><td char=".">271</td><td char=".">541</td><td char=".">134</td><td char=".">93</td></tr><tr><td>Upsampling</td><td char=".">123328</td><td char=".">20086</td><td char=".">21777</td><td char=".">2296</td><td char=".">20607</td><td char=".">20160</td></tr></tbody></table> </ephtml> </p> <p>We divided our dataset into an 80% training set and a 20% validation set, avoiding overlap in upsampling data between them. We employed the Transformer model (Lan et al., [<reflink idref="bib26" id="ref76">26</reflink>]), specifically a multi-target BERT-based architecture, which excels in leveraging pre-trained models for transfer learning, and conducted benchmark testing against two machine learning models: Decision Tree and Gaussian Naive Bayes (GNB). The Decision Tree is known for its robust performance in traditional machine learning tasks (Liang et al., [<reflink idref="bib30" id="ref77">30</reflink>]), while GNB is favored for high-dimensional data handling and its simplifying feature independence assumption. During training, we trained a single multi-target model for BERT, while each label had its own model for the traditional algorithms, culminating in five distinct models. We evaluated the models using Accuracy and F1 score, as shown in Table 2, with BERT showing superior performance in classifying five different math-learning knowledge areas.</p> <p>Table 2. Performances for three models' text classification.</p> <p> <ephtml> <table><thead><tr><td>Model</td><td>Metrics</td><td>Math literay</td><td>Mathematical knowledge</td><td>Affective control</td></tr><tr><td>Computational skill</td><td>Conceptual knowledge</td><td>Strategic knowledge</td></tr></thead><tbody valign="top"><tr><td>BERT</td><td>ACC</td><td char=".">0.85</td><td char=".">0.92</td><td char=".">0.88</td><td char=".">0.90</td><td char=".">0.90</td></tr><tr><td>BERT</td><td>F1</td><td char=".">0.87</td><td char=".">0.92</td><td char=".">0.85</td><td char=".">0.87</td><td char=".">0.90</td></tr><tr><td>Tree</td><td>ACC</td><td char=".">0.85</td><td char=".">0.84</td><td char=".">0.82</td><td char=".">0.85</td><td char=".">0.87</td></tr><tr><td>Tree</td><td>F1</td><td char=".">0.80</td><td char=".">0.80</td><td char=".">0.78</td><td char=".">0.79</td><td char=".">0.81</td></tr><tr><td>GNB</td><td>ACC</td><td char=".">0.81</td><td char=".">0.84</td><td char=".">0.82</td><td char=".">0.85</td><td char=".">0.88</td></tr><tr><td>GNB</td><td>F1</td><td char=".">0.72</td><td char=".">0.80</td><td char=".">0.77</td><td char=".">0.79</td><td char=".">0.83</td></tr></tbody></table> </ephtml> </p> <hd id="AN0189588744-19">Data analysis</hd> <p>A path model with the above three technical, two social, and three discursive participation behaviors was conducted using <emph>Mplus</emph> 8 (Muthén & Muthén, [<reflink idref="bib40" id="ref78">40</reflink>]). All possible indirect effects between technical and discursive participation behaviors through social participation behaviors were tested. In addition, residuals of variables within each layer were allowed to covariate in the tested model. For example, the three types of technical participation behaviors (i.e., use of the communication tool, information access tool, and engagement of motivation system) covariate to each other. The breadth and depth of students' social interaction covariate to each other. Maximum-likelihood estimation with non-normality robust standard errors (MLR) was used to assess the model parameters because the data were not normally distributed. MLR adjusts the model chi-square, fit indices, and standard errors of the parameter estimates based on the degree of non-normality observed in the data. Research has demonstrated that MLR provides a more accurate result for continuous non-normal data compared to maximum likelihood (ML) estimation (Chou et al., [<reflink idref="bib8" id="ref79">8</reflink>]).</p> <p>The model chi-square (<emph>x<sups>2</sups></emph>) statistic was employed to assess the overall fit between the model and the data; it tests a null hypothesis that there is no difference between the model-implied and observed covariance matrices. A nonsignificant x<sups>2</sups> indicates a good fit between the model and the data. However, it should be acknowledged that the chi-square statistic is sensitive to the size of the sample. Additional fit indices such as the Comparative Fit Index (CFI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residual (SRMR) were also used for evaluating model fit (Hooper et al., [<reflink idref="bib19" id="ref80">19</reflink>]). It has been recommended to apply a cutoff value of 0.95 for CFI, with values exceeding 0.95 indicating a good fit between the model and data; and cutoff values of 0.06 and 0.08 for RMSEA and SRMR, respectively, with values smaller than 0.06 and 0.08 indicating a good model-data fit (Hu & Bentler, [<reflink idref="bib21" id="ref81">21</reflink>]).</p> <hd id="AN0189588744-20">Results</hd> <p>The overall model was found to have a strong fit, <emph>x</emph><sups>2</sups> = 8.37, <emph>df</emph> = 3, <emph>p</emph> = 0.04, CFI = 0.98, RMSEA = 0.00, SRMR= 0.06. The significant model chi-square may be attributed to the large sample size (n = 96,867), so the model may still be acceptable (Marsh et al., [<reflink idref="bib36" id="ref82">36</reflink>]). The values of CEI, RMSEA, and SRMR showed that the hypothesized model fit the data well. Results regarding direct and indirect (mediational) effects are presented in Table 3. Standardized coefficients were reported for direct effects to enable comparison across predictors, whereas unstandardized coefficients were used for indirect effects to preserve the original scale and interpretability, as indirect effects involve combining multiple paths.</p> <p>Table 3. Hypotheses testing results.</p> <p> <ephtml> <table><thead><tr><td>Hypotheses</td><td>Path coefficient</td><td>SE</td><td><italic>p</italic>-value</td><td>Hypotheses results</td></tr></thead><tbody valign="top"><tr><td><italic>Direct: Technical → social behaviors</italic></td></tr><tr><td>H1a</td><td>Communication tool→Breadth of interaction</td><td char=".">.44</td><td char=".">0.02</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H1b</td><td>Communication tool→Depth of interaction</td><td char=".">.05</td><td char=".">0.01</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H1c</td><td>Information tool→Breadth of interaction</td><td char=".">.11</td><td char=".">0.07</td><td char=".">0.10</td><td /></tr><tr><td>H1d</td><td>Information tool→Depth of interaction</td><td char=".">.02</td><td char=".">0.00</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H1e</td><td>Motivation system→Breadth of interaction</td><td char=".">−.01</td><td char=".">0.02</td><td char=".">0.71</td><td /></tr><tr><td>H1f</td><td>Motivation system→Depth of interaction</td><td char=".">.05</td><td char=".">0.01</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td><italic>Direct: Technical → discursive behaviors</italic></td><td /><td /></tr><tr><td>H2Aa</td><td>Motivation system→Math Knowledge</td><td char=".">.02</td><td char=".">0.03</td><td char=".">0.47</td><td /></tr><tr><td>H2Ab</td><td>Motivation system→Math literacy</td><td char=".">.03</td><td char=".">0.03</td><td char=".">0.25</td><td /></tr><tr><td>H2Ac</td><td>Motivation system→Affective control</td><td char=".">.16</td><td char=".">0.06</td><td char=".">0.01</td><td><italic>Support</italic></td></tr><tr><td>H2B</td><td>Communication tool→Math knowledge</td><td char=".">−.08</td><td char=".">0.10</td><td char=".">0.45</td><td /></tr><tr><td>H2Ca</td><td>Information tool→Math knowledge</td><td char=".">−.02</td><td char=".">0.04</td><td char=".">0.54</td><td /></tr><tr><td>H2Cb</td><td>Information tool→Affective control</td><td char=".">−.01</td><td char=".">0.02</td><td char=".">0.77</td><td /></tr><tr><td><italic>Direct: Social→ discursive behaviors</italic></td></tr><tr><td>H3a</td><td>Breadth of interaction→Math knowledge</td><td char=".">.66</td><td char=".">0.05</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H3b</td><td>Breadth of interaction→Math literacy</td><td char=".">.61</td><td char=".">0.02</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H3c</td><td>Breadth of interaction→Affective control</td><td char=".">.33</td><td char=".">0.06</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H3d</td><td>Depth of interaction→Math knowledge</td><td char=".">.06</td><td char=".">0.01</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H3e</td><td>Depth of interaction→Math literacy</td><td char=".">.02</td><td char=".">0.02</td><td char=".">0.29</td><td /></tr><tr><td>H3f</td><td>Depth of interaction→Affective control</td><td char=".">.01</td><td char=".">0.01</td><td char=".">0.46</td><td /></tr><tr><td><italic>Indirect effect: Technical→ social→ discursive behaviors</italic></td></tr><tr><td>H4a</td><td>Communication tool→Breadth of interaction→Math knowledge</td><td char=".">.19</td><td char=".">0.04</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H4b</td><td>Communication tool→Breadth of interaction→ Math literacy</td><td char=".">.23</td><td char=".">0.06</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H4c</td><td>Communication tool→Breadth of interaction→ Affective control</td><td char=".">.37</td><td char=".">0.11</td><td char=".">0.001</td><td><italic>Support</italic></td></tr><tr><td>H4d</td><td>Communication tool→Depth of interaction→Math knowledge</td><td char=".">.002</td><td char=".">0.001</td><td char=".">0.03</td><td><italic>Support</italic></td></tr><tr><td>H4e</td><td>Communication tool→Depth of interaction→Math literacy</td><td char=".">.001</td><td char=".">0.001</td><td char=".">0.29</td><td /></tr><tr><td>H4f</td><td>Communication tool→Depth of interaction→Affective control</td><td char=".">.001</td><td char=".">0.001</td><td char=".">0.47</td><td /></tr><tr><td>H4g</td><td>Information tool→Breadth of interaction→Math knowledge</td><td char=".">.04</td><td char=".">0.03</td><td char=".">0.22</td><td /></tr><tr><td>H4h</td><td>Information tool→Breadth of interaction→ Math literacy</td><td char=".">.05</td><td char=".">0.04</td><td char=".">0.27</td><td /></tr><tr><td>H4i</td><td>Information tool→Breadth of interaction→ Affective control</td><td char=".">.07</td><td char=".">0.06</td><td char=".">0.20</td><td /></tr><tr><td>H4j</td><td>Information tool→Depth of interaction→Math knowledge</td><td char=".">.000</td><td char=".">0.000</td><td char=".">0.07</td><td /></tr><tr><td>H4k</td><td>Information tool→Depth of interaction→Math literacy</td><td char=".">.000</td><td char=".">0.000</td><td char=".">0.24</td><td /></tr><tr><td>H4l</td><td>Information tool→Depth of interaction→Affective control</td><td char=".">.000</td><td char=".">0.000</td><td char=".">0.47</td><td /></tr><tr><td>H4m</td><td>Motivation system→Breadth of interaction→Math knowledge</td><td char=".">−.004</td><td char=".">0.01</td><td char=".">0.70</td><td /></tr><tr><td>H4n</td><td>Motivation system→Breadth of interaction→ Math literacy</td><td char=".">−.004</td><td char=".">0.01</td><td char=".">0.71</td><td /></tr><tr><td>H4o</td><td>Motivation system→Breadth of interaction→ Affective control</td><td char=".">−.007</td><td char=".">0.02</td><td char=".">0.71</td><td /></tr><tr><td>H4p</td><td>Motivation system→Depth of interaction→Math knowledge</td><td char=".">.002</td><td char=".">0.00</td><td char=".">0.000</td><td><italic>Support</italic></td></tr><tr><td>H4q</td><td>Motivation system→Depth of interaction→Math literacy</td><td char=".">.001</td><td char=".">0.00</td><td char=".">0.17</td><td /></tr><tr><td>H4r</td><td>Motivation system→Depth of interaction→Affective control</td><td char=".">.001</td><td char=".">0.001</td><td char=".">0.438</td><td /></tr></tbody></table> </ephtml> </p> <p>1 <emph>Note</emph>. Standardized path coefficients are reported for direct effects; unstandardized path coefficients are reported for indirect effects.</p> <hd id="AN0189588744-21">Direct effects</hd> <p>Figure 3 summarizes the direct effects. Students' technical participation behaviors were found to predict their social participation behaviors in the online discussions in terms of both breadth and depth aspects, with 21% of the variance in the breadth (number of people students communicated with) and 1% of the variance in depth (i.e., length of the discussion threads they involved) were explained by the three technical participation behaviors. Specifically, students' use of the communication tool positively predicted the number of people they communicated with (Standardized coefficient <emph>β</emph> =.44, <emph>p</emph> < 0.001) and the length of their discussion threads (<emph>β</emph> =.05, <emph>p</emph> < 0.001), thus supporting hypotheses H1a and H1b. Also, students' use of the information access tool was found to positively predict the length of discussion threads they were involved (<emph>β =.</emph>02, <emph>p</emph> < 0.001), supporting hypothesis H1d. Moreover, students' interaction with the motivation system (<emph>β</emph> =.05, <emph>p</emph> < 0.001) also predicted the length of discussion threads they involved, affirming hypothesis H1f. These results indicated that students' engagement with the technical functions on the discussion board directly influenced their social participation, with use of the communication tool being the most significant predictor.</p> <p>PHOTO (COLOR): Figure 3. Full model with significant direct paths and standardized loading. Purple lines represent the hypothesized direct effects of technical layer on social layer; blue lines represent the hypothesized direct effects of social layer on discursive layer; green lines depict the hypothesized direct effect of technical layer on discursive layer.</p> <p>Discursive participation behaviors were predicted by technical and social participation behaviors, with 14.7% of the variance in students' demonstration of affective control, 40.8% of the variance in demonstrated mathematical knowledge, and 37.7% of the variance in mathematical literacy explained by the technical and social participation behaviors. Students' engagement with the motivation system (<emph>β</emph> =.16, <emph>p</emph> = 0.01) and the breadth of their social interaction (<emph>β</emph> =.33, <emph>p</emph> < 0.001) predicted the demonstration of affective control, supporting hypotheses H2Ac and H3c. Students' demonstration of mathematical knowledge was predicted by only their social participation behaviors, the number of people they communicated with (<emph>β</emph> =.66, <emph>p</emph> < 0.001), and the length of the discussion threads they participated in (<emph>β</emph> =.06, <emph>p</emph> < 0.001), supporting hypotheses H3a and H3d, but not by their technical participation behaviors. Furthermore, the presence of mathematical literacy was predicted by the number of people students communicated with (<emph>β</emph> =.61, <emph>p</emph> < 0.001), affirming hypothesis H3b.</p> <hd id="AN0189588744-22">Indirect effect</hd> <p>The indirect effects of students' technical participation behaviors on their discursive participation behaviors through social interaction were identified. Students' use of the communication tool on the online mathematical discussion board predicted their presence of mathematical knowledge, as mediated by the length of discussion threads in which students participated (Unstandardized coefficient <emph>b</emph> =.002, <emph>p</emph> = 0.002), and the number of the people they communicated with (<emph>b</emph> =.19, <emph>p</emph> < 0.001), supporting hypotheses H4a and H4d. That is, frequent use of the communication tool was associated with increased interactions and longer discussions, which in turn, facilitated learning of mathematical knowledge.</p> <p>The relation between students' engagement with the motivation system and their demonstration of mathematical knowledge in the discussions was also significantly mediated by the length of discussion threads they participated in (<emph>b</emph> =.002, <emph>p</emph> < 0.001). This suggested that the motivation system enhanced students' learning of mathematical knowledge by engaging them in longer discussion threads, thus supporting hypothesis H4p.</p> <p>Additionally, students' use of the communication tool in the online mathematical discussions was found to predict their affective control (<emph>b</emph> =.37, <emph>p</emph> < 0.001) and demonstration of mathematical literacy (<emph>b</emph> =.23, <emph>p</emph> < 0.001) during discussions through the number of individuals they communicated with, supporting hypotheses H4b and H4c. The communication tool facilitated broader discussions, contributing to enhanced affective control and the learning of mathematical literacy during the discussions.</p> <hd id="AN0189588744-23">Discussion</hd> <p>This study applied Communicative Ecology Theory to explore the interactions among students' technical, social, and discursive participation behaviors on an online mathematical discussion board. Students' technical participation was measured by their use of three specific functions on the board: a communication tool, an information access tool, and a motivation system. Social participation was assessed through the number of individuals students interacted with and the length of their discussion threads. The assessment of students' discursive participation involved evaluating their demonstration of mathematical knowledge, affective control, and mathematical literacy during these discussions. The research aimed to understand how engagement with technical functions influences social interactions and the content of discussions, and how these social interactions mediate the effects of technical participation on discussion content. Three key findings were drawn from this study.</p> <hd id="AN0189588744-24">Direct effect of technical participation on social and discursive participation</hd> <p>Students' involvement with the communication tool, information access tool, and motivation system was demonstrated to significantly influence their social and discursive participation behaviors. The findings align with the Communicative Ecology Theory (CET), emphasizing the dynamic interactions among technical, social, and discursive layers within an online community (Bock et al., [<reflink idref="bib4" id="ref83">4</reflink>]; Foth & Hearn, [<reflink idref="bib14" id="ref84">14</reflink>]; Jin et al., [<reflink idref="bib22" id="ref85">22</reflink>]). Notably, students' use of the communication tool emerged as the strongest predictor of social participation behaviors, particularly in terms of the number of individuals students interacted with. This corroborates with prior work on online mathematical discussions, which underscores the critical role of basic communication tools that allow students to view, edit, and post diagrams and equations (Grackin et al., [<reflink idref="bib15" id="ref86">15</reflink>]; Wessner et al., [<reflink idref="bib51" id="ref87">51</reflink>]). Moreover, this result indicated the profound influence of communication tools on online mathematical discussions, suggesting a need for future research focused on developing more effective communication tools within the platforms used for online mathematical discussions to potentially boost student participation and facilitate their math learning.</p> <p>Students' use of the information access tool was found to predict the depth but not the breadth of their social interactions. These results support the notion that easy access to information enhances engagement within online communities, highlighting the importance of information access tools in online mathematical discussions (Lin, [<reflink idref="bib31" id="ref88">31</reflink>]; Wessner et al., [<reflink idref="bib51" id="ref89">51</reflink>]). The absence of a significant relationship between the usage of the information access tool and the number of people students interacted with can be attributed to the specific functionalities of the information access tool (i.e., the search function in this study) and nature of the discussions (i.e., question-to-answer discussions). Students probably leveraged the search function to find previous discussions related to their math problems, allowing them to directly address simpler questions. Consequently, they participated in extended discussion threads to tackle more complex math problems. However, finding answers to simpler questions in existing threads might decrease their likelihood of posting new comments on the discussion board, thus they might not have a chance to communicate with a broad range of individuals on the platform.</p> <p>Students' engagement with the motivation system was indicated to predict the depth of their social interaction, consistent with prior work showing a positive correlation between students' motivation and their participation in online mathematical discussions (Cleary & Kitsantas, [<reflink idref="bib10" id="ref90">10</reflink>]; Xie et al., [<reflink idref="bib55" id="ref91">55</reflink>]). However, regarding discursive participation behaviors, engagement with the motivation system was found to predict affective control but not mathematical knowledge and literacy. This result can be explained in two ways. First, the positive correlation between engagement with the motivation system and the demonstration of affective control could reflect the system's impact on students' immediate behaviors, facilitating their participation in discussions and enabling them to regulate their behaviors or emotions to focus on mathematical problems and continue participation. However, unlike affective control, acquiring mathematical knowledge and literacy typically needs a long-term effort, therefore, the motivation system might not have an immediate and direct effect on these aspects. Second, the motivation system encourages students to assist others, which presupposes a pre-existing level of mathematical knowledge and literacy. Thus, their involvement in the motivation system may not significantly enhance their mathematical knowledge and literacy, as they already possessed these skills before the discussions.</p> <hd id="AN0189588744-25">Direct effect of social participation on discursive participation</hd> <p>Students' social interaction was found to positively predict their discursive participation behaviors, corroborating with CET and prior research on online communities that emphasize the interaction between social and discursive layers (Foth & Hearn, [<reflink idref="bib14" id="ref92">14</reflink>]; Jin et al., [<reflink idref="bib22" id="ref93">22</reflink>]). The finding is also consistent with previous studies on mathematical discussions which have demonstrated the beneficial impact of students' participation in online mathematical discussions on their math learning (Chen et al., [<reflink idref="bib6" id="ref94">6</reflink>]; Choi & Walters, [<reflink idref="bib7" id="ref95">7</reflink>]; Lee & Mao, [<reflink idref="bib27" id="ref96">27</reflink>]; Schumacher & Siegel, [<reflink idref="bib43" id="ref97">43</reflink>]). Importantly, while the breadth of social interaction (i.e., the number of people students communicated with) was a strong predictor for all three types of discursive content, the depth of social interaction primarily influenced mathematical knowledge. These outcomes highlight the importance of broad social interactions in online mathematical discussions, suggesting that future research or interventions should aim to encourage students to engage with more individuals to enhance their learning. Furthermore, although both the breadth and depth of social interaction were predictors of students' demonstration of mathematical knowledge, only the breadth predicted affective control and mathematical literacy. This differentiation provides valuable insights for educators and researchers to craft targeted interventions to meet specific educational purposes.</p> <hd id="AN0189588744-26">Indirect effect of technical participation on discursive participation through social partici...</hd> <p>Students' use of the communication tool was found to predict their demonstration of mathematical knowledge, mathematical literacy, and affective control through the breadth of their social interaction on the discussion board. These results specified the interactions among technical, social, and discursive layers in an online mathematical discussion board, suggesting the essential role of communication tools and broad social interaction in online mathematical discussions. Additionally, the lack of direct effect of use of the communication tool on mathematical knowledge demonstration, coupled with the significant indirect effect between them via the breadth of social interaction, suggested that the communication tool primarily facilitated students' learning of mathematical knowledge when they enhanced interactions with others.</p> <p>Moreover, a significant indirect effect of engagement with the motivation system on the demonstration of mathematical knowledge via the depth of social interaction was observed, although no direct effect was found. These findings suggest that the motivation system enhances students' demonstration of mathematical knowledge primarily when it fosters longer discussions. This observation is consistent with earlier suggestions that the immediate impact of the motivation system on learning mathematical knowledge might be limited, as acquiring this knowledge is inherently a long-term process. Instead, the motivation system promotes longer discussion threads, which, over time, contributes to the students' learning.</p> <hd id="AN0189588744-27">Contributions</hd> <p>Overall, this study contributes to prior work in at least three ways. First, by applying the Communicative Ecology Theory (CET), it emerges as one of the first studies to examine the interplay among technical, social, and discursive layers in online mathematical discussions. The results indicated the interaction among the three layers, demonstrating how CET, a framework used in the fields of communication and sociology, can be applied to the context of online educational discussion (although certain limitations need to be acknowledged, see 'Limitation and Future Research' section for a detailed explanation). Moreover, through the lens of CET, this study provided a comprehensive understanding of the dynamics within online mathematical discussions. Second, this study found that students' use of the tools and functions in an online mathematical discussion board, especially the communication tool and motivation system, predicted both their social interaction and mathematical learning in the discussions. These findings underscore the value of these tools and offer practical insights for educational researchers and practitioners in designing discussion forums that enhance student participation and learning in mathematics. Third, the study showed that students' board social interaction was the strongest predictor of their discursive participation behaviors, including demonstrations of mathematical knowledge, affective control, and mathematical literacy. These results emphasized the importance of board social interaction, suggesting that researchers and educators should focus on students' board social interaction when developing interventions and activities facilitating participation in online mathematical discussions.</p> <hd id="AN0189588744-28">Practical implications</hd> <p>The results of this study offer implications for students, tutors, course designers, application developers, and institutional policymakers. First, this study indicated that students' engagement with the technical tools, especially the communication tool and motivation system, predicted their social interaction and discussed content. Given this result, it is recommended that students develop a positive attitude to the technical tools embedded within online discussion platforms and engage with these tools to facilitate their discussions. Additionally, tutors can play an important role by modeling the use of these technical tools during their interactions with students and creating assignments that require students to use these tools. Course designers are encouraged to create targeted activities that support and promote students' effective use of technical tools (e.g., an orientation session to highlight the benefits of these tools and instruct how to use these tools). Moreover, application developers can contribute by designing more efficient communication tools or cooperating with course designers and instructors to develop systems or tools that further support students' communication and motivation during discussions. Based on the evidence regarding the positive correlation between the communication tool and motivation system, and their association with social interaction and learning, application developers can add communication tools within a motivation system or incorporate motivation elements in communication tools to encourage student participation in online discussions. Also, they can establish regular feedback loops with course designers and tutors to refine and improve these technical tools gradually. Institutional policymakers can provide funding to support and sustain such collaborations, such as creating policies to reward the design, piloting, and adoption of these tools. They could also establish guidelines for innovations in these tools.</p> <p>Second, the identified association between social interaction, particularly the breadth of social interaction, and discussed content provides valuable insights for students, tutors, and course designers. Previous work suggests that students' social interaction plays a crucial role in development of their emotional and social ties with others (Hosseini & Caragea, [<reflink idref="bib20" id="ref98">20</reflink>]), which influences their participation in the discussions and learning during the discussions. Therefore, students are recommended to seek assistance from and provide help to various people to support their learning in mathematical discussions. Meanwhile, tutors and course designers are also encouraged to regularly monitor and assess students' interaction patterns, identify the students who are not participating broadly, and develop interventions or design materials for those students to enhance their social interaction. Furthermore, the breadth of social interaction has been shown to predict students' demonstration of mathematics learning more effectively than the depth of social interaction. It is possible that students involved in longer discussion threads (i.e., depth of the social interaction) may hold misconceptions in mathematical concepts (Muldner et al., [<reflink idref="bib39" id="ref99">39</reflink>]) which need addressing, which decreases the effectiveness of deep social interaction. This misconception can even spread to peers, negatively influencing their learning. Therefore, it is recommended that tutors and course designers place greater emphasis on broadening students' social interactions with more peers.</p> <hd id="AN0189588744-29">Limitations and Future research</hd> <p>There are several limitations in this study. First, the limitations of applying CET to understand online educational discussions and interpret our results are noteworthy. Although CET describes the three layers (i.e., discursive, social, and technical layers) in online communities, it also proposes the role of micro factors on each layer and individual participation in a community (Foth & Hearn, [<reflink idref="bib14" id="ref100">14</reflink>]). For example, individuals' backgrounds (e.g., international student status) can influence their engagement with the three layers (e.g., communicating with people with similar backgrounds, using culturally specific technologies, and sharing content that differs from domestic students) and participation in a community. As this study primarily focused on the interrelationship between the three layers within an online community, it did not capture the nuanced micro factors that may underlie the observed patterns, limiting the explanatory power and validity of the findings, particularly in learning situations. Therefore, it is crucial to acknowledge the limitations of applying the CET model in this context. More research is needed to confirm the results from this study by taking into account of the specific contexts behind each student's decision when participating in online communities, thereby providing a more comprehensive understanding of online educational discussions. Meanwhile, future research can further use more historical and established theoretical frameworks (e.g., Community of Inquiry) in online learning communities to analyze and validate the relationship among the three layers of students' participation patterns. Second, it analyzed the interplay among the technical, social, and discursive layers within online mathematical discussions by mainly focusing on students' commenting behaviors and the content of their comments. Prior studies have emphasized that assessing student participation in discussions only based on their written comments is not enough. Students' reading behaviors, such as the time they spend reading others' comments or relevant discussion threads, should be assessed as one type of participation, as well (Du et al., [<reflink idref="bib13" id="ref101">13</reflink>]; Wise et al., [<reflink idref="bib53" id="ref102">53</reflink>]). Future research could investigate the association among technical, social, and discursive factors by evaluating students' social interaction given their reading behaviors. Third, this study only examined students' use of three technical functions on the online mathematical discussion board. Future research should explore the effect of more technical functions, such as calculators or tools for typing symbols and equations, on student's social interaction and mathematics learning in online mathematical discussions. Fourth, we assessed students' social interaction and their technical participation patterns through log data. That is, we quantified their activity and usage (e.g., the frequency) to but did not delve into the quality. Future studies can explore the interplay between the three layers in online discussions by considering the quality of interactions (e.g., are the comments provided by students really helpful to address their peers' questions) and tool usage in online discussions (e.g., how clearly the graphs, students generated using the drawing tool, convey their mathematical ideas). Fifth, the motivation system used in this study includes several gamification elements, which may influence students' social interactions and engagement in the discussions. Future research should be conducted to explore how these gamifications elements interact with students' technical participation patterns and their role in students' social interaction and discussed content.</p> <hd id="AN0189588744-30">Conclusion</hd> <p>This study investigated the interaction among students' technical, social, and discursive participation behaviors on an online mathematical discussion board. The results showed that students' use of the technical functions on the discussion board, especially their use of the communication tool and engagement with the motivation system, directly predicted their social interaction and demonstrations of three types of math-learning knowledge. Additionally, the breadth of social interaction mediated the association between students' use of communication tool with the three types of math-learning knowledge. These results enhance researchers' and educators' understanding of the mechanisms underlying online mathematical discussions, highlighting the critical roles of the communication tool, the motivation system, and broad social interaction in online mathematical discussions.</p> <hd id="AN0189588744-31">Disclosure statement</hd> <p>The authors declare that there are not conflicts of interest with respect to this manuscript.</p> <p>Correction Statement</p> <p>This article was originally published with errors, which have now been corrected in the online version. Please see Correction (<ulink href="http://dx.doi.org/10.1080/01587919.2025.2527458">http://dx.doi.org/10.1080/01587919.2025.2527458</ulink>).</p> <ref id="AN0189588744-32"> <title> References </title> <blist> <bibl id="bib1" idref="ref7" type="bt">1</bibl> <bibtext> Aragon, S. R. (2003). Creating social presence in online environments. New Directions for Adult and Continuing Education, 2003 (100), 57 – 68. https://doi.org/10.1002/ace.119</bibtext> </blist> <blist> <bibl id="bib2" idref="ref75" type="bt">2</bibl> <bibtext> Barros, T. M., Souza Neto, P. A., Silva, I., & Guedes, L. A. (2019). Predictive models for imbalanced data: A school dropout perspective. Education Sciences, 9 (4), 275. https://doi.org/10.3390/educsci9040275</bibtext> </blist> <blist> <bibl id="bib3" idref="ref15" type="bt">3</bibl> <bibtext> Banawan, M., Shin, J., Balyan, R., Leite, W. L., & McNamara, D. S. (2022). Math discourse linguistic components (cohesive cues within a math discussion board discourse). In Proceedings of the Ninth ACM Conference on Learning@ Scale (pp. 389–394). https://doi.org/10.1145/3491140.3528320</bibtext> </blist> <blist> <bibl id="bib4" idref="ref29" type="bt">4</bibl> <bibtext> Bock, G. W., Ahuja, M. K., Suh, A., & Yap, L. X. (2015). Sustainability of a virtual community: Integrating individual and structural dynamics. Journal of the Association for Information Systems, 16 (6), 418 – 447. https://doi.org/10.17705/1jais.00400</bibtext> </blist> <blist> <bibl id="bib5" idref="ref13" type="bt">5</bibl> <bibtext> Broderick, S. D. (2009). A comparison of mathematical discourse in online and face-to-face environments. Unpublished master's thesis. Brigham Young University, USA.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref8" type="bt">6</bibl> <bibtext> Chen, G., Chiu, M. M., & Wang, Z. (2012). Social metacognition and the creation of correct, new ideas: A statistical discourse analysis of online mathematics discussions. Computers in Human Behavior, 28 (3), 868 – 880. https://doi.org/10.1016/j.chb.2011.12.006</bibtext> </blist> <blist> <bibl id="bib7" idref="ref95" type="bt">7</bibl> <bibtext> Choi, J., & Walters, A. (2019). Exploring the impact of small-group synchronous discourse sessions in online math learning. Online Learning, 22 (4), 47 – 64. https://doi.org/10.24059/olj.v22i4.1511</bibtext> </blist> <blist> <bibl id="bib8" idref="ref79" type="bt">8</bibl> <bibtext> Chou, C. P., Bentler, P. M., & Satorra, A. (1991). Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: A Monte Carlo study. The British Journal of Mathematical and Statistical Psychology, 44 (2), 347 – 357. https://doi.org/10.1111/j.2044-8317.1991.tb00966.x</bibtext> </blist> <blist> <bibl id="bib9" idref="ref1" type="bt">9</bibl> <bibtext> Cirino, P. T., Tolar, T. D., & Fuchs, L. S. (2019). Longitudinal algebra prediction for early versus later takers. The Journal of Educational Research, 112 (2), 179 – 191. https://doi.org/10.1080/00220671.2018.1486279</bibtext> </blist> <blist> <bibtext> Cleary, T. J., & Kitsantas, A. (2017). Motivation and self-regulated learning influences on middle school mathematics achievement. School Psychology Review, 46 (1), 88 – 107. https://doi.org/10.1080/02796015.2017.12087607</bibtext> </blist> <blist> <bibtext> Deci, E. L., & Ryan, R. M. (2012). Self-determination theory. Handbook of Theories of Social Psychology, 1 (20), 416 – 436.</bibtext> </blist> <blist> <bibtext> Dichev, C., & Dicheva, D. (2017). Gamifying education: what is known, what is believed and what remains uncertain: a critical review. International Journal of Educational Technology in Higher Education, 14 (1), 1 – 36. https://doi.org/10.1186/s41239-017-0042-5</bibtext> </blist> <blist> <bibtext> Du, Z., Wang, F., Wang, S., & Xiao, X. (2023). Online listening responses and e-learning performance. Information Technology & People, 36 (4), 1509 – 1532. https://doi.org/10.1108/ITP-09-2021-0687</bibtext> </blist> <blist> <bibtext> Foth, M., & Hearn, G. (2007). Networked individualism of urban residents: Discovering the communicative ecology in inner-city apartment buildings. Information, Communication & Society, 10 (5), 749 – 772. https://doi.org/10.1080/13691180701658095</bibtext> </blist> <blist> <bibtext> Grackin, J., Ferguson, D., Izubuchi, R., & Smith, G. (2002). Math and distance learning threaded discussions. In EdMedia + Innovate Learning (pp. 1819 – 1824). Association for the Advancement of Computing in Education (AACE).</bibtext> </blist> <blist> <bibtext> Hamari, J., & Keronen, L. (2017). Why do people play games? A meta-analysis. International Journal of Information Management, 37 (3), 125 – 141. https://doi.org/10.1016/j.ijinfomgt.2017.01.006</bibtext> </blist> <blist> <bibtext> Harbour, K. E., & Denham, A. R. (2021). Supporting all students: Productive mathematical discourse in online environments. Intervention in School and Clinic, 57 (2), 87 – 94. https://doi.org/10.1177/1053451221100184</bibtext> </blist> <blist> <bibtext> Hearn, G., Collie, N., Lyle, P., Choi, J. H. J., & Foth, M. (2014). Using communicative ecology theory to scope the emerging role of social media in the evolution of urban food systems. Futures, 62, 202 – 212. https://doi.org/10.1016/j.futures.2014.04.010</bibtext> </blist> <blist> <bibtext> Hooper, D., Coughlan, J., & Mullen, M. (2008, September). Evaluating model fit: a synthesis of the structural equation modelling literature. In 7th European Conference on research methodology for business and management studies (Vol. 2008, pp. 195–200).</bibtext> </blist> <blist> <bibtext> Hosseini, M., & Caragea, C. (2021). It takes two to empathize: One to seek and one to provide. In. Proceedings of the AAAI Conference on Artificial Intelligence, 35 (14), 13018 – 13026. https://doi.org/10.1609/aaai.v35i14.17539</bibtext> </blist> <blist> <bibtext> Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6 (1), 1 – 55. https://doi.org/10.1080/10705519909540118</bibtext> </blist> <blist> <bibtext> Jin, X. L., Zhou, Z., & Yu, X. (2019). Predicting users' willingness to diffuse healthcare knowledge in social media: a communicative ecology perspective? Information Technology & People, 32 (4), 1044 – 1064. https://doi.org/10.1108/ITP-03-2018-0143</bibtext> </blist> <blist> <bibtext> Karen Van, G., Morton, B. A., Liu, H. Q., & Kline, J. (2006). Effects of web-based instruction on math anxiety, the sense of mastery, and global self-esteem: A quasi-experimental study of undergraduate statistics students. Teaching Sociology, 34 (4), 370 – 388. https://doi.org/10.1177/0092055X0603400404</bibtext> </blist> <blist> <bibtext> Khan, I., & Dongping, H. (2017). Variations in the diffusion of social media content across different cultures: A communicative ecology perspective. Journal of Global Information Technology Management, 20 (3), 156 – 170. https://doi.org/10.1080/1097198X.2017.1354598</bibtext> </blist> <blist> <bibtext> Kramarski, B., & Mizrachi, N. (2006). Online interactions in a mathematical classroom. Educational Media International, 43 (1), 43 – 50. https://doi.org/10.1080/09523980500490778</bibtext> </blist> <blist> <bibtext> Lan, Z., Chen, M., Goodman, S., Gimpel, K., Sharma, P., & Soricut, R. (2019). Albert: A lite bert for self-supervised learning of language representations. arXiv Preprint arXiv:1909.11942. https://doi.org/10.48550/arXiv.1909.11942</bibtext> </blist> <blist> <bibtext> Lee, S. W., & Mao, X. (2021). Algebra by the eighth grade: The association between early study of algebra I and students' academic success. International Journal of Science and Mathematics Education, 19 (6), 1271 – 1289. https://doi.org/10.1007/s10763-020-10116-3</bibtext> </blist> <blist> <bibtext> Lee, J. E., & Recker, M. (2022). Predicting student performance by modeling participation in asynchronous discussions in university online introductory mathematical courses. Educational Technology Research and Development, 70 (6), 1993 – 2015. https://doi.org/10.1007/s11423-022-10153-5</bibtext> </blist> <blist> <bibtext> Levonian, Z., Li, C., Zhu, W., Gade, A., Henkel, O., Postle, M. E., & Xing, W. (2023). Retrieval-augmented generation to improve math question-answering: Trade-offs between groundedness and human preference. arXiv preprint arXiv:2310.03184. https://doi.org/10.48550/arXiv.2310.03184</bibtext> </blist> <blist> <bibtext> Liang, J., Yang, J., Wu, Y., Li, C., & Zheng, L. (2016, April). Big data application in education: dropout prediction in edx MOOCs. In 2016 IEEE second international conference on multimedia big data (BigMM), 440–443. https://doi.org/10.1109/BigMM.2016.70</bibtext> </blist> <blist> <bibtext> Lin, H. F. (2008). Determinants of successful virtual communities: Contributions from system characteristics and social factors. Information & Management, 45 (8), 522 – 527. https://doi.org/10.1016/j.im.2008.08.002</bibtext> </blist> <blist> <bibtext> Liu, F. (2008). Impact of online discussion on elementary teacher candidates' anxiety towards teaching mathematics. Education, 128 (4), 614 – 630.</bibtext> </blist> <blist> <bibtext> Lyu, B., & Li, C. (Under review). Understanding online math learning through knowledge graphs powered by large language models: Insights from core, periphery, xperiphery learners. Submitted to British Journal of Educational Technology.</bibtext> </blist> <blist> <bibtext> Lyu, B., Li, C., Li, H., & Xing, W. (2024, July). Roles of joining time, technology use, and social interaction in sustaining student participation in an online mathematics discussion board [Paper presentation]. In Proceedings of the Eleventh ACM Conference on Learning@ Scale (pp. 398 – 402). https://doi.org/10.1145/3657604.3664672</bibtext> </blist> <blist> <bibtext> Mailizar, M., Johar, R., Sadli, R., & Zubaidah, T. (2022). Mathematics teachers' interactions on online community of practices: A social network analysis. Education and Information Technologies, 27 (5), 6533 – 6551. https://doi.org/10.1007/s10639-022-10895-y</bibtext> </blist> <blist> <bibtext> Marsh, H. W., Hau, K. T., & Wen, Z. (2004). In search of golden rules: Comment on hypothesis-testing approaches to setting cutoff values for fit indexes and dangers in overgeneralizing Hu and Bentler's (1999) findings. Structural Equation Modeling: A Multidisciplinary Journal, 11 (3), 320 – 341. https://doi.org/10.1207/s15328007sem1103_2</bibtext> </blist> <blist> <bibtext> McHugh, M. L. (2012). Interrater reliability: the kappa statistic. Biochemia Medica, 22 (3), 276 – 282. https://doi.org/10.11613/BM.2012.031</bibtext> </blist> <blist> <bibtext> Muir, T. (2022). The influences of social, cognitive, and teaching presence on pre-service teachers' online engagement in productive mathematical discourse. International Journal of Mathematical Education in Science and Technology, 55 (9), 2069 – 2086. https://doi.org/10.1080/0020739X.2022.2119176</bibtext> </blist> <blist> <bibtext> Muldner, K., Wixon, M., Rai, D., Burleson, W., Woolf, B., & Arroyo, I. (2015). Exploring the impact of a learning dashboard on student affect. In Artificial Intelligence in Education: 17th International Conference, AIED 2015, Madrid, Spain, June 22-26, 2015. Proceedings 17 (pp. 307 – 317). Springer International Publishing.</bibtext> </blist> <blist> <bibtext> Muthén, B., & Muthén, L. (2017). Mplus. In Handbook of item response theory (pp. 507 – 518). Chapman and Hall/CRC.</bibtext> </blist> <blist> <bibtext> National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. The National Council of Teachers of Mathematics, Inc.</bibtext> </blist> <blist> <bibtext> Rutherford, T., Lee, H. R., & Duck, K. (2023). Dynamic relations between motivation and performance across content in a mathematics learning technology. Learning and Individual Differences, 107, 102346. https://doi.org/10.1016/j.lindif.2023.102346</bibtext> </blist> <blist> <bibtext> Schumacher, C., & Siegel, M. (2015). 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences. Retrieved April 5th, 2016, from <ulink href="http://www.maa.org/sites/">http://www.maa.org/sites/</ulink> de- fault/files/pdf/CUPM/pdf/CUPMguide print.pdf</bibtext> </blist> <blist> <bibtext> Seol, S., Lee, H., Yu, J., & Zo, H. (2016). Continuance usage of corporate SNS pages: A communicative ecology perspective. Information & Management, 53 (6), 740 – 751. https://doi.org/10.1016/j.im.2016.02.010</bibtext> </blist> <blist> <bibtext> Smith, & Stein, M. K. (2018). 5 Practices for orchestrating productive mathematics discussion. National Council of Teachers of Mathematics.</bibtext> </blist> <blist> <bibtext> Staples, M., & King, S. (2017). Eliciting, supporting and guiding the math: Three key functions of the teacher's role in facilitating meaningful mathematical discourse. In D. A. Spangler & J. J. Wanko (Eds.), Enhancing classroom practice with research behind principles to actions (pp. 25 – 36). National Council of Teachers of Mathematics.</bibtext> </blist> <blist> <bibtext> Sudiarta, I. G. P., Sukajaya, I. N., & Suharta, I. G. P. (2018). Investigation on students' mathematical online discussion: A case study in grade 8 SMPN 1 Denpasar. Journal of Physics: Conference Series, 1040 (1), 12031. https://doi.org/10.1088/1742-6596/1040/1/012031</bibtext> </blist> <blist> <bibtext> Toda, A. M., Klock, A. C., Oliveira, W., Palomino, P. T., Rodrigues, L., Shi, L., Bittencourt, I., Gasparini, I., Isotani, S., & Cristea, A. I. (2019). Analysing gamification elements in educational environments using an existing Gamification taxonomy. Smart Learning Environments, 6 (1), 1 – 14. https://doi.org/10.1186/s40561-019-0106-1</bibtext> </blist> <blist> <bibtext> Teo, H. H., Chan, H. C., Wei, K. K., & Zhang, Z. (2003). Evaluating information accessibility and community adaptivity features for sustaining virtual learning communities. International Journal of Human-Computer Studies, 59 (5), 671 – 697. https://doi.org/10.1016/S1071-5819(03)00087-9</bibtext> </blist> <blist> <bibtext> Vygotsky, L. (1978). Mind in society. The development of higher psychological processes. Harvard University Press.</bibtext> </blist> <blist> <bibtext> Wessner, M., Shumar, W., Stahl, G., Sarmiento, J., Mühlpfordt, M., & Weimar, S. (2006). Designing an online service for a math community. In S. Barab, K. E. Hay, & D. T. Hickey (Eds.), Proceedings of ICLS 2006 (pp. 818 – 824). Lawrence Erlbaum.</bibtext> </blist> <blist> <bibtext> Wigfield, A. (1994). Expectancy-value theory of achievement motivation: A developmental perspective. Educational Psychology Review, 6 (1), 49 – 78. https://doi.org/10.1007/BF02209024</bibtext> </blist> <blist> <bibtext> Wise, A. F., Hausknecht, S. N., & Zhao, Y. (2014). Attending to others' posts in asynchronous discussions: Learners' online "listening" and its relationship to speaking. International Journal of Computer-Supported Collaborative Learning, 9 (2), 185 – 209. https://doi.org/10.1007/s11412-014-9192-9</bibtext> </blist> <blist> <bibtext> Xie, K. U. I., Debacker, T. K., & Ferguson, C. (2006). Extending the traditional classroom through online discussion: The role of student motivation. Journal of Educational Computing Research, 34 (1), 67 – 89. https://doi.org/10.2190/7BAK-EGAH-3MH1-K7C6</bibtext> </blist> <blist> <bibtext> Xie, K., Durrington, V., & Yen, L. L. (2011). Relationship between students' motivation and their participation in asynchronous online discussions. Journal of Online Learning and Teaching, 7 (1), 17 – 29.</bibtext> </blist> <blist> <bibtext> Zou, W., Hu, X., Pan, Z., Li, C., Cai, Y., & Liu, M. (2021). Exploring the relationship between social presence and learners' prestige in MOOC discussion forums using automated content analysis and social network analysis. Computers in Human Behavior, 115, 106582. https://doi.org/10.1016/j.chb.2020.106582</bibtext> </blist> </ref> <aug> <p>By Bailing Lyu; Chenglu Li; Hai Li; Wangda Zhu and Wanli Xing</p> <p>Reported by Author; Author; Author; Author; Author</p> <p></p> <p>Bailing Lyu is a Postdoctoral Researcher in the Department of Educational Psychology at the University of Utah. Her research interests include learning from multiple resources, STEM education, learning analytics, and artificial intelligence in education.</p> <p>Chenglu Li is an Assistant Professor in the Department of Educational Psychology at the University of Utah. His research interests include fair AI for educational use, learning analytics, educational data mining, and educational software design and development.</p> <p>Hai Li is a PhD student of Educational Technology at the University of Florida. His research interest includes learning analytics and educational software design and development.</p> <p>Wangda Zhu is a Postdoctoral Researcher in Educational Technology at the University of Florida. His research interests include AI in education and design education.</p> <p>Wanli Xing is an Associate Professor of Educational Technology at the University of Florida. His research interests are artificial intelligence, learning analytics, STEM education, and online learning.</p> </aug> <nolink nlid="nl1" bibid="bib27" firstref="ref2"></nolink> <nolink nlid="nl2" bibid="bib50" firstref="ref3"></nolink> <nolink nlid="nl3" bibid="bib46" firstref="ref4"></nolink> <nolink nlid="nl4" bibid="bib45" firstref="ref5"></nolink> <nolink nlid="nl5" bibid="bib17" firstref="ref6"></nolink> <nolink nlid="nl6" bibid="bib43" firstref="ref9"></nolink> <nolink nlid="nl7" bibid="bib28" firstref="ref10"></nolink> <nolink nlid="nl8" bibid="bib15" firstref="ref11"></nolink> <nolink nlid="nl9" bibid="bib51" firstref="ref12"></nolink> <nolink nlid="nl10" bibid="bib35" firstref="ref16"></nolink> <nolink nlid="nl11" bibid="bib38" firstref="ref17"></nolink> <nolink nlid="nl12" bibid="bib14" firstref="ref18"></nolink> <nolink nlid="nl13" bibid="bib18" firstref="ref20"></nolink> <nolink nlid="nl14" bibid="bib44" firstref="ref21"></nolink> <nolink nlid="nl15" bibid="bib24" firstref="ref22"></nolink> <nolink nlid="nl16" bibid="bib22" firstref="ref23"></nolink> <nolink nlid="nl17" bibid="bib47" firstref="ref26"></nolink> <nolink nlid="nl18" bibid="bib49" firstref="ref31"></nolink> <nolink nlid="nl19" bibid="bib31" firstref="ref32"></nolink> <nolink nlid="nl20" bibid="bib54" firstref="ref33"></nolink> <nolink nlid="nl21" bibid="bib41" firstref="ref40"></nolink> <nolink nlid="nl22" bibid="bib25" firstref="ref41"></nolink> <nolink nlid="nl23" bibid="bib33" firstref="ref49"></nolink> <nolink nlid="nl24" bibid="bib34" firstref="ref50"></nolink> <nolink nlid="nl25" bibid="bib56" firstref="ref56"></nolink> <nolink nlid="nl26" bibid="bib23" firstref="ref59"></nolink> <nolink nlid="nl27" bibid="bib32" firstref="ref60"></nolink> <nolink nlid="nl28" bibid="bib29" firstref="ref62"></nolink> <nolink nlid="nl29" bibid="bib52" firstref="ref66"></nolink> <nolink nlid="nl30" bibid="bib11" firstref="ref67"></nolink> <nolink nlid="nl31" bibid="bib55" firstref="ref68"></nolink> <nolink nlid="nl32" bibid="bib10" firstref="ref69"></nolink> <nolink nlid="nl33" bibid="bib42" firstref="ref70"></nolink> <nolink nlid="nl34" bibid="bib48" firstref="ref71"></nolink> <nolink nlid="nl35" bibid="bib12" firstref="ref72"></nolink> <nolink nlid="nl36" bibid="bib16" firstref="ref73"></nolink> <nolink nlid="nl37" bibid="bib37" firstref="ref74"></nolink> <nolink nlid="nl38" bibid="bib26" firstref="ref76"></nolink> <nolink nlid="nl39" bibid="bib30" firstref="ref77"></nolink> <nolink nlid="nl40" bibid="bib40" firstref="ref78"></nolink> <nolink nlid="nl41" bibid="bib19" firstref="ref80"></nolink> <nolink nlid="nl42" bibid="bib21" firstref="ref81"></nolink> <nolink nlid="nl43" bibid="bib36" firstref="ref82"></nolink> <nolink nlid="nl44" bibid="bib20" firstref="ref98"></nolink> <nolink nlid="nl45" bibid="bib39" firstref="ref99"></nolink> <nolink nlid="nl46" bibid="bib13" firstref="ref101"></nolink> <nolink nlid="nl47" bibid="bib53" firstref="ref102"></nolink>
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  Label: Title
  Group: Ti
  Data: Explaining Technical, Social, and Discursive Participation in Online Mathematical Discussions
– Name: Language
  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Bailing+Lyu%22">Bailing Lyu</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-6964-9081">0000-0002-6964-9081</externalLink>)<br /><searchLink fieldCode="AR" term="%22Chenglu+Li%22">Chenglu Li</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-1782-0457">0000-0002-1782-0457</externalLink>)<br /><searchLink fieldCode="AR" term="%22Hai+Li%22">Hai Li</searchLink> (ORCID <externalLink term="https://orcid.org/0009-0004-7299-2042">0009-0004-7299-2042</externalLink>)<br /><searchLink fieldCode="AR" term="%22Wangda+Zhu%22">Wangda Zhu</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0001-9611-4800">0000-0001-9611-4800</externalLink>)<br /><searchLink fieldCode="AR" term="%22Wanli+Xing%22">Wanli Xing</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0002-1446-889X">0000-0002-1446-889X</externalLink>)
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="SO" term="%22Distance+Education%22"><i>Distance Education</i></searchLink>. 2025 46(4):550-573.
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  Data: Routledge. Available from: Taylor & Francis, Ltd. 530 Walnut Street Suite 850, Philadelphia, PA 19106. Tel: 800-354-1420; Tel: 215-625-8900; Fax: 215-207-0050; Web site: http://www.tandf.co.uk/journals
– Name: PeerReviewed
  Label: Peer Reviewed
  Group: SrcInfo
  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 24
– Name: DatePubCY
  Label: Publication Date
  Group: Date
  Data: 2025
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  Label: Document Type
  Group: TypDoc
  Data: Journal Articles<br />Reports - Research
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  Label: Education Level
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  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="%22High+Schools%22">High Schools</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Electronic+Learning%22">Electronic Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Discussion+%28Teaching+Technique%29%22">Discussion (Teaching Technique)</searchLink><br /><searchLink fieldCode="DE" term="%22Learner+Engagement%22">Learner Engagement</searchLink><br /><searchLink fieldCode="DE" term="%22Interpersonal+Relationship%22">Interpersonal Relationship</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Behavior%22">Student Behavior</searchLink><br /><searchLink fieldCode="DE" term="%22Middle+School+Students%22">Middle School Students</searchLink><br /><searchLink fieldCode="DE" term="%22High+School+Students%22">High School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Student+Participation%22">Student Participation</searchLink><br /><searchLink fieldCode="DE" term="%22Technology+Uses+in+Education%22">Technology Uses in Education</searchLink><br /><searchLink fieldCode="DE" term="%22Numeracy%22">Numeracy</searchLink><br /><searchLink fieldCode="DE" term="%22Knowledge+Level%22">Knowledge Level</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink>
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  Group: ID
  Data: 10.1080/01587919.2024.2399151
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  Data: 0158-7919<br />1475-0198
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Participating in online mathematical discussions is a beneficial strategy to improve online math learning. Research has examined online mathematical discussions from various aspects, focusing on the content discussed, student interaction, and the technical tools facilitating student participation, but few studies have investigated the interplay among these aspects. This study draws on Communicative Ecology Theory (CET, Foth & Hearn, 2007), which conceptualizes the sustainability of online communities as influenced by discursive, social, and technical factors, to explore how students' discursive, social, and technical participation behaviors on an online mathematical discussion board are interacted. Leveraging a dataset including more than 90,000 students and two million online discussion interactions, this study indicated that students' engagement with technical functions, especially a communication tool and a motivation system, within the discussion board significantly facilitated their social interactions and enhanced their demonstration of mathematical knowledge, mathematical literacy, and affective control in the discussions. These findings provide insights for educators and designers of educational applications to enhance student participation in online discussions thereby improving the effectiveness of these discussions in online learning.
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  Group: Date
  Data: 2026
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  Label: Accession Number
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  Data: EJ1500784
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        Value: 10.1080/01587919.2024.2399151
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        PageCount: 24
        StartPage: 550
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      – SubjectFull: Mathematics Education
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      – TitleFull: Explaining Technical, Social, and Discursive Participation in Online Mathematical Discussions
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