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Exploring Effective Tutoring Strategies in Asynchronous Online Mathematical Discussions: Insights from Ordered Network Analysis

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Title: Exploring Effective Tutoring Strategies in Asynchronous Online Mathematical Discussions: Insights from Ordered Network Analysis
Language: English
Authors: Yukyeong Song (ORCID 0000-0002-4084-2734), Chenglu Li, Yingbo Ma, Bailing Lyu, Wangda Zhu, Hai Li, Wanli Xing
Source: Journal of Science Education and Technology. 2025 34(5):1143-1163.
Availability: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
Peer Reviewed: Y
Page Count: 21
Publication Date: 2025
Sponsoring Agency: Institute of Education Sciences (ED)
Contract Number: R305C160004
Document Type: Journal Articles
Reports - Research
Education Level: Secondary Education
Descriptors: Tutoring, Asynchronous Communication, Electronic Learning, Mathematics Instruction, Discussion (Teaching Technique), Instructional Effectiveness, Knowledge Level, Problem Solving, Tutors, Secondary School Students, Educational Strategies, Secondary School Mathematics
DOI: 10.1007/s10956-025-10233-0
ISSN: 1059-0145
1573-1839
Abstract: Online mathematical discussions provide numerous educational benefits, such as supporting collaborative knowledge construction, increasing learner engagement, and enhancing students' higher-order thinking. Yet, the effectiveness of these discussions is not always guaranteed; rather, it is highly dependent on the use of tutoring strategies. While previous studies investigated the impact of tutoring strategies on the effectiveness of discussions, they mostly focused on the success of problem-solving, and less attention has been paid to how students represented their knowledge during the discussions. This study investigated the relationship between tutoring strategies and the effectiveness of discussions, operationalized as the level of student knowledge representation as well as the success of problem-solving. We retrieved textual data from 2318 tutor-student discussion threads at a secondary school online math learning platform and annotated them with the coding schemes of problem-solving success, students' knowledge representation, and tutoring strategies. Then, we conducted regression analyses to investigate each strategy's impact on the discussion's success and students' knowledge representation. We also conducted an ordered network analysis (ONA) to visualize the sequential networks of the tutoring strategies among four groups of dialogues categorized by discussion's problem-solving success and knowledge representation. Findings suggest that "motivating and encouraging" and "feedback" are the most effective tutoring strategies for both successful problem-solving and knowledge representation, while "direct intervention" is effective for success but minimally influential for knowledge representation. On the other hand, "questioning" was found to be important in promoting students' knowledge representation while showing minimal impact on problem-solving success. The findings provide theoretical, methodological, and practical implications for promoting effective tutoring strategies in online mathematical discussions.
Abstractor: As Provided
IES Funded: Yes
Entry Date: 2026
Accession Number: EJ1497451
Database: ERIC
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  Value: <anid>AN0189590678;4n601oct.25;2025Nov28.05:32;v2.2.500</anid> <title id="AN0189590678-1">Exploring Effective Tutoring Strategies in Asynchronous Online Mathematical Discussions: Insights from Ordered Network Analysis </title> <p>Online mathematical discussions provide numerous educational benefits, such as supporting collaborative knowledge construction, increasing learner engagement, and enhancing students' higher-order thinking. Yet, the effectiveness of these discussions is not always guaranteed; rather, it is highly dependent on the use of tutoring strategies. While previous studies investigated the impact of tutoring strategies on the effectiveness of discussions, they mostly focused on the success of problem-solving, and less attention has been paid to how students represented their knowledge during the discussions. This study investigated the relationship between tutoring strategies and the effectiveness of discussions, operationalized as the level of student knowledge representation as well as the success of problem-solving. We retrieved textual data from 2318 tutor-student discussion threads at a secondary school online math learning platform and annotated them with the coding schemes of problem-solving success, students' knowledge representation, and tutoring strategies. Then, we conducted regression analyses to investigate each strategy's impact on the discussion's success and students' knowledge representation. We also conducted an ordered network analysis (ONA) to visualize the sequential networks of the tutoring strategies among four groups of dialogues categorized by discussion's problem-solving success and knowledge representation. Findings suggest that "motivating and encouraging" and "feedback" are the most effective tutoring strategies for both successful problem-solving and knowledge representation, while "direct intervention" is effective for success but minimally influential for knowledge representation. On the other hand, "questioning" was found to be important in promoting students' knowledge representation while showing minimal impact on problem-solving success. The findings provide theoretical, methodological, and practical implications for promoting effective tutoring strategies in online mathematical discussions.</p> <p>Keywords: Online math discussion; Tutoring strategies; Problem-solving success; Mathematical knowledge representation; Ordered network analysis; Education Specialist Studies In Education</p> <p>Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</p> <hd id="AN0189590678-2">Introduction</hd> <p>Online math learning platforms have become prevalent in recent years, attributed to increased demand for large-scale learning and distance learning that overcomes time and location restrictions (Papanastasiou et al., [<reflink idref="bib53" id="ref1">53</reflink>]; Mooij et al., [<reflink idref="bib47" id="ref2">47</reflink>]). Despite such benefits, online learning has been criticized for its lack of interaction, personalization, external regulation, and affordances for social, cognitive, and teaching presence (Palloff & Pratt, [<reflink idref="bib51" id="ref3">51</reflink>], [<reflink idref="bib52" id="ref4">52</reflink>]). To overcome these, many online learning platforms are adopting asynchronous online discussion forums to allow interactive and individualized question-and-answer or discussion activities around math problems (Hew & Cheung, [<reflink idref="bib27" id="ref5">27</reflink>]). Such asynchronous online discussions can work as a tutoring platform where students can ask math-related questions individually and receive instruction (Graesser et al., [<reflink idref="bib22" id="ref6">22</reflink>]). Furthermore, students can exchange different perspectives and communicate their solution ideas within the learning community (Lee & Recker, [<reflink idref="bib32" id="ref7">32</reflink>]; Song et al., [<reflink idref="bib70" id="ref8">70</reflink>]).</p> <p>Asynchronous online discussions have shown positive effects on math learning by supporting collaborative knowledge construction (Chen et al., [<reflink idref="bib9" id="ref9">9</reflink>]; Rasmussen & Marrongelle, [<reflink idref="bib58" id="ref10">58</reflink>]), increasing learner engagement and participation (Salter & Conneely, [<reflink idref="bib65" id="ref11">65</reflink>]; Lee & Recker, [<reflink idref="bib32" id="ref12">32</reflink>]), enhancing students' communication skills (Schumacher & Siegel, [<reflink idref="bib66" id="ref13">66</reflink>]; Bell & Pape, [<reflink idref="bib5" id="ref14">5</reflink>]), and improving academic achievement (Lee & Recker, [<reflink idref="bib32" id="ref15">32</reflink>]). While math discussion shows great promise, effective discussions are not always guaranteed (Lee & Recker, [<reflink idref="bib32" id="ref16">32</reflink>]; McFarlane, [<reflink idref="bib39" id="ref17">39</reflink>]; Cohen et al., [<reflink idref="bib12" id="ref18">12</reflink>]; Person & Graesser, [<reflink idref="bib55" id="ref19">55</reflink>]; Topping et al., [<reflink idref="bib76" id="ref20">76</reflink>]). Effective discussions are often dependent on many factors, such as tutors' expertise in the use of tutoring strategies (Cohen et al., [<reflink idref="bib12" id="ref21">12</reflink>]; Person & Graesser, [<reflink idref="bib55" id="ref22">55</reflink>]; Topping et al., [<reflink idref="bib76" id="ref23">76</reflink>]). For example, proficient tutors may actively encourage student participation by posing thought-provoking questions, providing timely and constructive feedback, and creating a supportive and inclusive online learning environment (McKeithan et al., [<reflink idref="bib41" id="ref24">41</reflink>]; Bloomberg, [<reflink idref="bib8" id="ref25">8</reflink>]). On the other hand, novice tutors struggle to effectively scaffold and facilitate discussions, often using primitive strategies, such as directly giving students answers (Topping et al., [<reflink idref="bib76" id="ref26">76</reflink>]).</p> <p>Many researchers have been interested in the use of tutoring strategies and their relationship with the effectiveness of tutoring (Lee & Recker, [<reflink idref="bib32" id="ref27">32</reflink>]; Xu et al., [<reflink idref="bib88" id="ref28">88</reflink>]). One important decision in this line of research is how to define the effectiveness of tutoring. While successful tutoring has mostly been defined by the success of problem-solving (i.e., finding a correct answer) or academic achievement (Alzahrani, [<reflink idref="bib2" id="ref29">2</reflink>]; Wikle & West, [<reflink idref="bib84" id="ref30">84</reflink>]), successful problem-solving is not the only way discussion contributes to student learning (Roscoe & Chi, [<reflink idref="bib61" id="ref31">61</reflink>]). Instead, mathematical discussions should provide valuable opportunities for students to express their knowledge through language, find the knowledge gaps and pitfalls in their problem-solving processes, and communicate their reasoning and justifications with others (Chi et al., [<reflink idref="bib10" id="ref32">10</reflink>]; Roscoe & Chi, [<reflink idref="bib61" id="ref33">61</reflink>]; Pirie & Schwarzenberger, [<reflink idref="bib56" id="ref34">56</reflink>]). Discussions that do not invite knowledge representation are likely to miss this valuable learning opportunity and to yield a misleading evaluation of tutoring effectiveness; students may successfully solve math problems without a deep understanding and representation of the underlying concepts (Berg et al., [<reflink idref="bib6" id="ref35">6</reflink>]; Cho et al., [<reflink idref="bib11" id="ref36">11</reflink>]). Therefore, the effectiveness of discussions should be evaluated not only by successful problem-solving but also by how they elicit students' knowledge representation. Despite the importance of knowledge representation during mathematical discussions, little research has considered knowledge representation within math discussions.</p> <p>Another notable gap here is that prior work in this area has primarily measured the use of tutoring strategies based on frequency analysis, such as "coding-and-counting" (Vogel & Weinberger, [<reflink idref="bib81" id="ref37">81</reflink>]). Such frequency-based methods have been criticized in that they do not provide temporal patterns of learning activities Csanadi et al. [<reflink idref="bib13" id="ref38">13</reflink>]. To better understand this temporal quality of learning interactions, this study adopted ordered network analysis (ONA) to capture, visualize, and quantitatively compare the patterns of tutoring actions Csanadi et al. [<reflink idref="bib13" id="ref39">13</reflink>] as well as provide directional information among those different tutoring actions (Fan et al., [<reflink idref="bib17" id="ref40">17</reflink>]).</p> <p>To fill these gaps, this paper aims to examine the relationship between tutoring strategies and the effectiveness of tutoring discussions, operationalized by both successful problem-solving and knowledge representation, and visualize the ordered networks of tutoring strategies used in the discussion groups differing in the level of effectiveness. The study utilized the discussion threads collected from an online math learning platform called Math Nation. We seek to answer the two following research questions (RQs):</p> <p></p> <ulist> <item> RQ1. To what extent do tutoring strategies explain the effectiveness of tutoring, indicated by the success of problem-solving and students' knowledge representation during the discussion?</item> <p></p> <item> RQ2. What are the ordered networks of the tutoring strategies for four groups of discussions, categorized by the level of effectiveness revealed through ONA?</item> </ulist> <p>We define effective mathematical discussions with two factors: the success of problem-solving (i.e., whether the student successfully found the answer to the math problem or not) and students' knowledge representation (i.e., the level of explicit representation of five mathematical knowledge types in the discussion: <emph>computational skill, linguistic knowledge, conceptual knowledge, strategic knowledge,</emph> and <emph>affective control</emph>). Depending on these two variables, we divide discussion threads into four groups: G1 (successful with high knowledge representation), G2 (successful with low knowledge representation), G3 (unsuccessful with high knowledge representation), and G4 (unsuccessful with low knowledge representation). Based on these groupings, we analyzed and visualized the dynamics of tutoring strategies among the different groups using ONA.</p> <hd id="AN0189590678-3">Background</hd> <p></p> <hd id="AN0189590678-4">Effective Mathematical Discussions: Success and Knowledge Representation</hd> <p>Mathematical discussion, also known as mathematical discourse, is defined by the National Council of Teachers of Mathematics (National Council of Teachers of Mathematics, [<reflink idref="bib49" id="ref41">49</reflink>]) as the purposeful exchange of mathematical ideas, solutions, and reasoning through various forms of communication (e.g., verbal, written, visual). It has been recognized as a crucial component of effective mathematics teaching, supporting students to share and justify their ideas and to make connections to others' ideas (Leinwand, [<reflink idref="bib33" id="ref42">33</reflink>]; Smith & Stein, [<reflink idref="bib69" id="ref43">69</reflink>]). Through such interactions, students actively engage in learning complex math concepts, procedures, problem-solving strategies, representations, and reasoning (Staples & King, [<reflink idref="bib72" id="ref44">72</reflink>]; Harbour & Denham, [<reflink idref="bib25" id="ref45">25</reflink>]).</p> <p>Table 1 Types of mathematical knowledge</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left"><p>Category</p></th><th align="left"><p>Definition</p></th><th align="left"><p>Related literature</p></th></tr></thead><tbody><tr><td align="left"><p>Computational skills</p></td><td align="left"><p>The ability to conduct calculations.</p></td><td align="left"><p>"algorithmic knowledge" (Kaur, <xref ref-type="bibr" rid="bibr29">1997</xref>) "math computation" (Villeneuve et al., <xref ref-type="bibr" rid="bibr80">2019</xref>)</p></td></tr><tr><td align="left"><p>Linguistic knowledge</p></td><td align="left"><p>The language ability and literacy to understand word problems.</p></td><td align="left"><p>"linguistic knowledge" (Kaur, <xref ref-type="bibr" rid="bibr29">1997</xref>) "linguistic skills" "linguistic features" (Banawan et al., <xref ref-type="bibr" rid="bibr4">2021</xref>)</p></td></tr><tr><td align="left"><p>Conceptual knowledge</p></td><td align="left"><p>The ability to identify appropriate math concepts and apply them to solve the problems.</p></td><td align="left"><p>"conceptual knowledge" (Kaur, <xref ref-type="bibr" rid="bibr29">1997</xref>; Rittle-Johnson, <xref ref-type="bibr" rid="bibr60">2017</xref>)</p></td></tr><tr><td align="left"><p>Strategic knowledge</p></td><td align="left"><p>The ability to make plans to solve the problem.</p></td><td align="left"><p>"strategic knowledge" (Kaur, <xref ref-type="bibr" rid="bibr29">1997</xref>) "strategic competence" (Findell et al., <xref ref-type="bibr" rid="bibr18">2001</xref>)</p></td></tr><tr><td align="left"><p>Affective control</p></td><td align="left"><p>The ability to manage one's emotions to focus on the task.</p></td><td align="left"><p>"beliefs and affective factors" (Kaur, <xref ref-type="bibr" rid="bibr29">1997</xref>) "emotion regulation" (Losenno et al., <xref ref-type="bibr" rid="bibr37">2020</xref>)</p></td></tr></tbody></table> </ephtml> </p> <p>One way to examine the effectiveness of mathematical discussions is to assess whether the problems discussed are successfully resolved (i.e., finding a correct answer). A crucial goal of mathematics education is to develop students' ability to solve various complex mathematics problems National Council of Teachers of Mathematics ([<reflink idref="bib49" id="ref46">49</reflink>]). Thus, research in mathematics education has often focused on students' problem-solving performance (Montague et al., [<reflink idref="bib46" id="ref47">46</reflink>]; Guven & Cabakcor, [<reflink idref="bib23" id="ref48">23</reflink>]; Dhlamini, [<reflink idref="bib14" id="ref49">14</reflink>]). For example, when Montague et al. ([<reflink idref="bib46" id="ref50">46</reflink>]) examined the effects of cognitive strategy instruction deployed through their learning platform "Solve It!," they concentrated on how the cognitive strategy instructions influenced students' problem-solving performance through paper-and-pencil tests. Similarly, Guven and Cabakcor ([<reflink idref="bib23" id="ref51">23</reflink>]) investigated multiple factors influencing students' problem-solving achievement as measured through testing. They also assessed affective factors (e.g., mathematics anxiety, mathematical self-efficacy, attitudes, and beliefs towards problem-solving), student gender, academic success, and the educational backgrounds of their families, revealing that students' mathematical problem-solving performance was predicted by their academic success and those affective factors. These studies highlight the importance of problem-solving success, which, in turn, informs the assessment of the effectiveness of online mathematical discussions.</p> <p>However, the effectiveness of online mathematical discussions should not be assessed solely based on the success of problem-solving. Research also shows the importance of the process by which this problem-solving occurs (Guven & Cabakcor, [<reflink idref="bib23" id="ref52">23</reflink>]). Cognitive psychologists and educational researchers view problem-solving as a series of mental operations (Lester, [<reflink idref="bib34" id="ref53">34</reflink>]; Kosiak, [<reflink idref="bib30" id="ref54">30</reflink>]) and recognize that students frequently encounter various cognitive challenges during this process (Kaur, [<reflink idref="bib29" id="ref55">29</reflink>]). Mathematical discussions can provide valuable opportunities for students to internalize and construct their mathematical knowledge during the problem-solving process, such as verbally expressing their knowledge structure and critically debating with others (Vygotsky, [<reflink idref="bib82" id="ref56">82</reflink>]; Roscoe & Chi, [<reflink idref="bib61" id="ref57">61</reflink>]; Pirie & Schwarzenberger, [<reflink idref="bib56" id="ref58">56</reflink>]). Therefore, to achieve a more holistic assessment of effectiveness, discussions should also be measured by how well they support students in representing their knowledge throughout the problem-solving process.</p> <p>In mathematical discussions, students express their ideas in spoken or written language, and this verbal output offers insights into the representation of their knowledge. Students need to possess various types of knowledge to solve problems successfully. For example, Kroll and Miller ([<reflink idref="bib31" id="ref59">31</reflink>]) identified five essential types of knowledge for effective problem-solving in mathematics: <emph>algorithmic knowledge</emph> (i.e., computational skills), <emph>linguistic knowledge, conceptual knowledge, strategic knowledge,</emph> and <emph>affective control</emph>. These five types of knowledge have been corroborated by additional research and have guided the foundation of our framework. Table 1 presents the five categories of mathematical knowledge and definitions. The category names were mostly drawn from Kaur ([<reflink idref="bib29" id="ref60">29</reflink>]), but "computational skills" and "affective control" were modified to deliver the meanings in our research more intuitively.</p> <hd id="AN0189590678-5">Tutoring Strategies in Online Mathematical Discussions</hd> <p>Tutoring is defined as a learning session where an adult or expert helps younger or less expert learners (Wood et al., [<reflink idref="bib86" id="ref61">86</reflink>]). Tutors can utilize different pedagogical strategies to enhance the student learning experience and outcomes across different educational contexts (Du Boulay & Luckin, [<reflink idref="bib15" id="ref62">15</reflink>]). These strategies are crucial for effectively guiding teaching efforts and improving students' problem-solving success or knowledge representation by addressing their cognitive, affective, and metacognitive needs (Woolf, [<reflink idref="bib87" id="ref63">87</reflink>]; Van de Pol et al., [<reflink idref="bib57" id="ref64">57</reflink>]). Accordingly, tutoring strategies can be categorized into three groups: cognitive scaffolding, affective support, and metacognitive support (Van de Pol et al., [<reflink idref="bib57" id="ref65">57</reflink>]).</p> <p>First, cognitive scaffolding facilitates a deeper understanding of content knowledge by enabling students to build on their existing knowledge with guided support from more experienced tutors (Wood et al., [<reflink idref="bib86" id="ref66">86</reflink>]). Research has identified a number of cognitive scaffolding strategies that are effective. First, providing <emph>feedback</emph> has been discussed and widely used as a cognitive scaffolding strategy to provide information regarding students' performance to improve and revise the performance (Van de Pol et al., [<reflink idref="bib57" id="ref67">57</reflink>]; Wood et al., [<reflink idref="bib86" id="ref68">86</reflink>]; Tharp & Gallimore, [<reflink idref="bib75" id="ref69">75</reflink>]). Feedback includes both positive reinforcement to acknowledge correct responses and negative feedback to highlight areas for improvement (Chi et al., [<reflink idref="bib10" id="ref70">10</reflink>]). Another strategy, <emph>instructing</emph>, refers to a tutor telling the students what to do, such as giving detailed steps of problem-solving (Eloff et al., [<reflink idref="bib16" id="ref71">16</reflink>]; Graesser et al., [<reflink idref="bib22" id="ref72">22</reflink>]). In the math learning context, it is important for tutors to decompose a complex task into simpler steps for clearer instruction (Graesser et al., [<reflink idref="bib22" id="ref73">22</reflink>]). Third, <emph>explaining</emph> is effective in enhancing knowledge comprehension by clarifying concepts and providing additional information (Wittwer & Renkl, [<reflink idref="bib85" id="ref74">85</reflink>]; Chi et al., [<reflink idref="bib10" id="ref75">10</reflink>]; Van de Pol et al., [<reflink idref="bib57" id="ref76">57</reflink>]; Eloff et al., [<reflink idref="bib16" id="ref77">16</reflink>]). In online learning, explaining also includes providing additional references, such as other online learning resources. Finally, <emph>questioning</emph> elicits students' knowledge representation (Topping et al., [<reflink idref="bib76" id="ref78">76</reflink>]) and construction of a deeper understanding (Lin et al., [<reflink idref="bib35" id="ref79">35</reflink>]). The literature emphasizes the use of open-ended questions (e.g., "why" or "what") rather than closed-ended questions (e.g., "did you understand?") Topping et al. [<reflink idref="bib76" id="ref80">76</reflink>] to provoke deeper thinking.</p> <p>Next, affective support helps maintain students' motivation and resilience, creating a nurturing learning community (Rosiek, [<reflink idref="bib62" id="ref81">62</reflink>]). <emph>Motivating and encouraging</emph> is one strategy of providing affective support, referring to the actions of praising the students and managing their frustration. This action provides emotional support for students, boosting their confidence and perseverance (Topping et al., [<reflink idref="bib77" id="ref82">77</reflink>]). This strategy has been discussed under different names, such as "praise and encourage" (Topping et al., [<reflink idref="bib76" id="ref83">76</reflink>]) and "frustration control" (Van de Pol et al., [<reflink idref="bib57" id="ref84">57</reflink>]), with all emphasizing the importance of students' emotions and motivation in learning (Kaur, [<reflink idref="bib29" id="ref85">29</reflink>]; Losenno et al., [<reflink idref="bib37" id="ref86">37</reflink>]).</p> <p>Lastly, metacognitive support encourages learners to reflect on and regulate their learning processes (Flavell, [<reflink idref="bib19" id="ref87">19</reflink>]). One of the tutoring strategies for metacognitive support is keeping learners on the right track of learning and maintaining their attention to pursue the learning objective, as referred to as "direct maintenance" in Van de Pol et al. ([<reflink idref="bib57" id="ref88">57</reflink>]). Another strategy is to let students "summarize and generalize" what they learned from the problem-solving and talk about how these concepts or strategies can be applied to other situations (Topping et al., [<reflink idref="bib76" id="ref89">76</reflink>]). Although these strategies are necessary for promoting students' self-regulation, research finds that without intense training, metacognitive support strategies are challenging for both tutors and students to practice in authentic tutoring situations (Topping et al., [<reflink idref="bib76" id="ref90">76</reflink>]). Indeed, these strategies occurred rarely enough in our corpus that only "maintaining discussions" (stemming from Pol, Volman, and Beishuizen (2010) (Van de Pol et al., [<reflink idref="bib57" id="ref91">57</reflink>])'s "direct maintenance") could be identified as metacognitive support during our coding scheme development process.</p> <p>While previous research has highlighted some effective tutoring strategies (e.g., Wittwer and Renkl, [<reflink idref="bib85" id="ref92">85</reflink>]; Lin et al., [<reflink idref="bib35" id="ref93">35</reflink>]; Topping et al., [<reflink idref="bib77" id="ref94">77</reflink>]), research that investigates the effectiveness of specific tutoring strategies in the context of online mathematical discussions is scarce. These previous efforts also analyze discussions with limited context; prior studies mainly used a frequency-based analysis approach, in which tutoring discourse was represented as frequency counts (e.g., Molenaar et al., [<reflink idref="bib45" id="ref95">45</reflink>]; Lin et al., [<reflink idref="bib36" id="ref96">36</reflink>]). This approach is straightforward, but it misses out on the contextual information about the discussion moves surrounding each tutoring utterance. The present study goes beyond those traditional analytic approaches and utilizes ONA to gain a further understanding of the temporal networks among different types of tutoring strategies, and it does so in the less-studied domain of online mathematical discussions.</p> <p>Table 2 Coding scheme for students' knowledge representation</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left"><p>Category</p></th><th align="left"><p>Definition</p></th><th align="left"><p>Lacking (0)</p></th><th align="left"><p>Existing (1)</p></th></tr></thead><tbody><tr><td align="left"><p>Computational skill</p></td><td align="left"><p>The ability to conduct basic calculations</p></td><td align="left"><p>"How do you do 2 times 1/4?" "I added wrong"</p></td><td align="left"><p>"25 divided by 2 is 12.5!"</p></td></tr><tr><td align="left"><p>Linguistic knowledge</p></td><td align="left"><p>The language ability or literacy to understand word problems.</p></td><td align="left"><p>"I don't understand how this potato is related to math."</p></td><td align="left"><p>"Well, for every 2 pounds, the price goes up in 1 dollar."</p></td></tr><tr><td align="left"><p>Conceptual knowledge</p></td><td align="left"><p>The ability to identify appropriate math concepts and apply them to problems.</p></td><td align="left"><p>"I don't know how to isolate the variable."</p></td><td align="left"><p>"It would be skewed left since the left side of the box has less than the right side."</p></td></tr><tr><td align="left"><p>Strategic knowledge</p></td><td align="left"><p>The ability to make plans to solve the problem.</p></td><td align="left"><p>"Where should I start?"</p></td><td align="left"><p>"I know I should start with crossing out C."</p></td></tr><tr><td align="left"><p>Affective control</p></td><td align="left"><p>The ability to manage one's emotion to focus on the task.</p></td><td align="left"><p>"I'm so frustrated."</p></td><td align="left"><p>"It was my bad. I can retry."</p></td></tr></tbody></table> </ephtml> </p> <hd id="AN0189590678-6">Data Collection and Annotation</hd> <p></p> <hd id="AN0189590678-7">Data Collection</hd> <p>We retrieved the discussion data from the question-and-answer board in Math Nation.[<reflink idref="bib1" id="ref97">1</reflink>] Math Nation is an online mathematics learning platform for secondary school (i.e., middle school and high school) students. It is widely used for individual and hybrid learning by over a million students and teachers in the USA. The platform is available to students through district-level partnerships, and students are authenticated through district accounts. Math Nation offers learning resources for mathematics, including Algebra, Geometry, and SAT preparation. The platform offers instructional videos, self-assessment quizzes, and a question-and-answer discussion board. On the discussion board, students upload their questions regarding mathematics (e.g., school homework, test problems) and ask for help. In response, tutors would reply and help the student find the answer, involving multiple turns of conversations. Tutors comprise two types: <emph>study experts</emph> and <emph>peer tutors.</emph> Study expert is the title given to paid adult tutors hired by Math Nation. Prior to working as tutors, they receive online and offline training on effective tutoring strategies, such as scaffolding, higher-order questioning, and not giving direct answers. Study experts are responsible for answering students' questions, facilitating the active exchange of ideas among students, and managing the discussions. Peer tutors are middle school and high school students who voluntarily work as tutors. They do not have obligations to tutor their peers but are highly encouraged to do so by the system, which lets them earn points from fellow students as a reward for their help. Peer tutors who earn the highest points are showcased on a leaderboard and rewarded with prizes (such as a tablet PC) once every few months.</p> <p>This study utilized the language data of 2318 discussion threads consisting of 24,116 posts and replies from Math Nation's discussion board. Those discussions involve 16,391 students (1960 middle school students and 14,431 high school students) and 7725 expert tutors. High school students are over-represented due to the math topics taught in Math Nation (e.g., Algebra) tending to be taught more often at the high school level. We first retrieved 306,784 threads[<reflink idref="bib2" id="ref98">2</reflink>]( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>n</mi><mrow><mi>p</mi><mi>o</mi><mi>s</mi><mi>t</mi><mo>+</mo><mi>r</mi><mi>e</mi><mi>p</mi><mi>l</mi><mi>y</mi></mrow></msub><mo>=</mo><mn>3</mn><mo>,</mo><mn>322</mn><mo>,</mo><mn>479</mn></mrow></math> </ephtml> ) posted between October 2013 and October 2021 from a MySQL database of Math Nation. We ended our data collection period on this date in order to ensure all discussions took place in a consistent context; a major change in the Math Nation interface in November 2021 transformed the characteristics of the discussion board. A benefit of the Math Nation dataset, among online learning discussion datasets, is that student demographics are available. The racial categories include Caucasian, Asian, Black or African American, Native American, Hawaiian or other Pacific Islander, and two or more races. Our dataset does not include information on students' ethnicity, such as Hispanic or Latinx. The demographic information was collected automatically from students' school districts through a data-sharing agreement when they signed up for Math Nation. Such information is only available for students and not available for non-student users (e.g., expert tutors).</p> <p>We filtered the data to keep discussion threads with five or more turns for meaningful analysis. We set a minimum number of turns to help ensure that the discussions would include meaningful tutoring strategies and students' knowledge representation[<reflink idref="bib3" id="ref99">3</reflink>]7. The specific number, five, came from the review of the discussion data and several rounds of experiments that led to the decision that the discussions with five or more conversational turns mostly include at least one of the meaningful utterances, such as tutoring strategies or students' knowledge representation. Our filtered dataset contained 2318 discussion threads ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>n</mi><mrow><mi>p</mi><mi>o</mi><mi>s</mi><mi>t</mi><mo>+</mo><mi>r</mi><mi>e</mi><mi>p</mi><mi>l</mi><mi>y</mi></mrow></msub><mo>=</mo><mn>24</mn><mo>,</mo><mn>116</mn></mrow></math> </ephtml> ). On average, each thread has 10.4 utterances and 9.4 turns of conversation (sd = 7.6), with the maximum number of turns being 115 and the minimum one being 5.</p> <p>Table 3 Coding scheme for tutoring strategies</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left"><p>Category</p></th><th align="left"><p>Strategies</p></th><th align="left"><p>Definition</p></th><th align="left"><p>Example quotes</p></th></tr></thead><tbody><tr><td align="left"><p>Cognitive scaffolding</p></td><td align="left"><p>Feedback (Tharp & Gallimore, <xref ref-type="bibr" rid="bibr75">1991</xref>; Wood et al., <xref ref-type="bibr" rid="bibr86">1976</xref>; Van de Pol et al., <xref ref-type="bibr" rid="bibr57">2010</xref>)</p></td><td align="left"><p>Providing confirmatory, correcting information regarding student's performance.</p></td><td align="left"><p>"Yes, your steps are correct!" "I do not agree with your choice."</p></td></tr><tr><td align="left" /><td align="left"><p>Instructing (Van de Pol et al., <xref ref-type="bibr" rid="bibr57">2010</xref>; Eloff et al., <xref ref-type="bibr" rid="bibr16">2006</xref>; Graesser et al., <xref ref-type="bibr" rid="bibr22">2011</xref>)</p></td><td align="left"><p>Decomposing a complex task into simpler steps and telling students what to do.</p></td><td align="left"><p>"You need to calculate the probability of heads of Group A and do the same for Group B."</p></td></tr><tr><td align="left" /><td align="left"><p>Explaining (Van de Pol et al., <xref ref-type="bibr" rid="bibr57">2010</xref>; Eloff et al., <xref ref-type="bibr" rid="bibr16">2006</xref>; Chi et al., <xref ref-type="bibr" rid="bibr10">2001</xref>)</p></td><td align="left"><p>Providing more detailed information on related concepts and additional resources.</p></td><td align="left"><p>"A graph that has data with points to the left is skewed left." "Check Unit 4 for more information!"</p></td></tr><tr><td align="left" /><td align="left"><p>Questioning (Van de Pol et al., <xref ref-type="bibr" rid="bibr57">2010</xref>; Eloff et al., <xref ref-type="bibr" rid="bibr16">2006</xref>; Hmelo-Silver & Barrows, <xref ref-type="bibr" rid="bibr28">2006</xref>; Topping et al., <xref ref-type="bibr" rid="bibr76">2011</xref>)</p></td><td align="left"><p>Asking questions that require an active answer.</p></td><td align="left"><p>"What do you think you should do?" "Could you elaborate on what you did?"</p></td></tr><tr><td align="left" /><td align="left"><p>Direct intervention [<italic>D</italic>]*</p></td><td align="left"><p>Directly telling the correct answer.</p></td><td align="left"><p>"The answer is 25."</p></td></tr><tr><td align="left"><p>Affective support</p></td><td align="left"><p>Motivating and encouraging Topping et al. <xref ref-type="bibr" rid="bibr76">2011</xref></p></td><td align="left"><p>Praising students and managing frustration.</p></td><td align="left"><p>"Good job! You can do it!" "Don't feel dumb."</p></td></tr><tr><td align="left"><p>Metacognitive support</p></td><td align="left"><p>Managing discussions (Van de Pol et al., <xref ref-type="bibr" rid="bibr57">2010</xref>)</p></td><td align="left"><p>Keeping students' attention on the learning track and reminding them of learning objectives</p></td><td align="left"><p>"Let's focus on solving this quadratic equation first." "Guys, please talk about Algebra!"</p></td></tr></tbody></table> </ephtml> </p> <p>*[<emph>D</emph>] indicates that this code was drawn inductively from our dataset</p> <hd id="AN0189590678-8">Data Annotation</hd> <p>We annotated the discussion data to answer our research questions. The initial coding schemes were developed by the first author on a top-down and bottom-up basis after reviewing the related literature of mathematical knowledge, scaffolding, facilitating, and tutoring, as well as the collected data. Then, the drafted coding schemes were reviewed by two faculty members (i.e., one assistant professor in Educational Psychology and another associate professor in Educational Technology at Research 1 University in the United States) and four graduate researchers. Reviewers applied the coding schemes to some sample conversations and shared their opinions. Review opinions were discussed and reflected in the coding schemes, yielding the final coding schemes. The development of each coding scheme and the annotation processes are detailed below.</p> <p>First, we binary-coded each discussion thread to indicate the problem-solving success of the discussion. The problem-solving success of the discussion was decided by whether the student finally found the correct answer to the math question (i.e., success, coded as 1) or not (i.e., non-success, coded as 0). Annotators determine the success of discussions by the discussion context through a thorough reading of the whole conversation. The success was often indicated by students' utterances like "<emph>I got the answer. Thank you for your help.</emph>" or tutor's utterances like <emph>You got the correct answer.</emph></p> <p>Second, each line of a student's utterances was annotated with a coding scheme for student knowledge representation (Table 2). The coding scheme was developed in a top-down manner based on literature that identifies key cognitive and affective knowledge and skills required for mathematical problem-solving (Kaur, [<reflink idref="bib29" id="ref100">29</reflink>]; Dhlamini, [<reflink idref="bib14" id="ref101">14</reflink>]; Vygotsky, [<reflink idref="bib82" id="ref102">82</reflink>]). Based on this body of literature, we identified five categories of mathematical knowledge, including <emph>computational skill, linguistic knowledge, conceptual knowledge, strategic knowledge,</emph> and <emph>affective control</emph> (see the "Effective Mathematical Discussions: Success and Knowledge Representation" section for details of each category and background literature). This coding scheme was used as a binary code (i.e., 0 or 1) for each construct where each code was used only when applicable; for example, when a student shows evidence of computational skills through a certain utterance, we coded that line of utterance as "<emph>computational skill</emph> = 1," whereas it would be coded as "<emph>computational skill</emph> = 0" when there was evidence that they lack this skill. It is noteworthy that not all lines of utterance were coded. In many cases, if we could not find any evidence of either existing or lacking these skills, we did not annotate that line.</p> <p>Third, each line of the tutors' utterances was annotated with a tutoring strategy coding scheme (Table 3). The tutoring strategy coding scheme was drawn from multiple pieces of literature on scaffolding (Van de Pol et al., [<reflink idref="bib57" id="ref103">57</reflink>]), facilitation (Hmelo-Silver & Barrows, [<reflink idref="bib28" id="ref104">28</reflink>]; Eloff et al., [<reflink idref="bib16" id="ref105">16</reflink>]), and peer tutoring (Chi et al., [<reflink idref="bib10" id="ref106">10</reflink>]; Topping et al., [<reflink idref="bib76" id="ref107">76</reflink>]), as well as inductively from the dataset (e.g., "direct intervention."). Following (Van de Pol et al., [<reflink idref="bib57" id="ref108">57</reflink>])'s scaffolding framework, we categorized the tutoring strategies into cognitive, affective, and metacognitive, under which one or more tutoring strategies are presented. The tutoring strategies were drawn from related literature, such as Van de Pol et al. ([<reflink idref="bib57" id="ref109">57</reflink>]); Rittle-Johnson ([<reflink idref="bib60" id="ref110">60</reflink>]); Garrison et al. ([<reflink idref="bib20" id="ref111">20</reflink>]); Topping et al. ([<reflink idref="bib76" id="ref112">76</reflink>]), to be closely related to our research context (i.e., online mathematical discussions for secondary school students). Based on the coding scheme, we annotated tutors' utterances with one or multiple codes (if multiple codes could apply, we chose all that apply).</p> <p>Table 4 Descriptive statistics for each group</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left" /><th align="left"><p>G1</p></th><th align="left"><p>G2</p></th><th align="left"><p>G3</p></th><th align="left"><p>G4</p></th></tr></thead><tbody><tr><td align="left"><p><italic>Students' background</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Female</p></td><td align="left"><p>2131 (33.01%)</p></td><td align="left"><p>1508 (35.23%)</p></td><td align="left"><p>684 (43.16%)</p></td><td align="left"><p>4,028 (34.11%)</p></td></tr><tr><td align="left"><p>Male</p></td><td align="left"><p>2266 (35.18%)</p></td><td align="left"><p>1164 (27.19%)</p></td><td align="left"><p>425 (26.81%)</p></td><td align="left"><p>3752 (31.78%)</p></td></tr><tr><td align="left"><p>Gender unknown</p></td><td align="left"><p>2045 (31.75%)</p></td><td align="left"><p>1609 (37.59%)</p></td><td align="left"><p>476 (30.03%)</p></td><td align="left"><p>4028 (34.11%)</p></td></tr><tr><td align="left"><p>Race minority</p></td><td align="left"><p>649 (10.08%)</p></td><td align="left"><p>599 (13.99%)</p></td><td align="left"><p>279 (17.60%)</p></td><td align="left"><p>1509 (12.78%)</p></td></tr><tr><td align="left"><p>Race majority</p></td><td align="left"><p>3614 (56.10%)</p></td><td align="left"><p>1930 (45.08%)</p></td><td align="left"><p>792 (49.97%)</p></td><td align="left"><p>5806 (49.17%)</p></td></tr><tr><td align="left"><p>Race unknown</p></td><td align="left"><p>2179 (33.82%)</p></td><td align="left"><p>1752 (40.93%)</p></td><td align="left"><p>514 (32.43%)</p></td><td align="left"><p>4493 (38.05%)</p></td></tr><tr><td align="left"><p><italic>Tutor category</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Is student</p></td><td align="left"><p>2000 (53.45%)</p></td><td align="left"><p>1301 (55.74%)</p></td><td align="left"><p>451 (50.28%)</p></td><td align="left"><p>3306 (54.65%)</p></td></tr><tr><td align="left"><p><italic>Utterance counts</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Students</p></td><td align="left"><p>2700</p></td><td align="left"><p>1947</p></td><td align="left"><p>688</p></td><td align="left"><p>5759</p></td></tr><tr><td align="left"><p>Tutors</p></td><td align="left"><p>3742</p></td><td align="left"><p>2334</p></td><td align="left"><p>897</p></td><td align="left"><p>6049</p></td></tr><tr><td align="left"><p><italic>Total utterances</italic></p></td><td align="left"><p>6442</p></td><td align="left"><p>4281</p></td><td align="left"><p>1585</p></td><td align="left"><p>11,808</p></td></tr></tbody></table> </ephtml> </p> <p>To ensure the reliability of all three types of annotations, four graduate researchers coded 11% of the whole dataset (i.e., 257 threads out of 2,318 threads in total) independently and gathered to discuss the different annotations. To streamline the annotating process, we used an online data labeling platform called Labelbox.[<reflink idref="bib4" id="ref113">4</reflink>] The following is the procedure for our data annotation. First, four doctoral students gathered and reviewed the three types of coding schemes, discussed any points of confusion or lack of clarity, and revised the coding schemes to minimize these issues. After this initial meeting, the four students used the resulting coding schemes and independently coded 50 discussion threads. The initial inter-rater reliability (IRR) for the first 100 threads was 0.695 for tutoring strategies, 0.805 for students' knowledge representation, and 0.83 for discussion success. After reviewing data points of disagreement, the same four graduate students coded 100 more threads independently and calculated the IRR again. The IRR for the next 100 threads improved to 0.7496 for tutoring strategies, 0.8702 for students' knowledge representation, and 0.9131 for discussion success. The students gathered and discussed their discrepancies a second time. Following the discussion, the same four students annotated 107 more threads independently and calculated the IRR again. After this third round of annotation, the IRR scores among the four researchers were 0.7956 for tutoring strategies, 0.8758 for students' knowledge representation, and 0.9202 for discussion success for the 257 discussion threads. These IRR scores were considered substantial ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≥</mo></math> </ephtml> 0.61) or almost perfect ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>≥</mo></math> </ephtml> 0.81) based on the previously established threshold of Cohen's Kappa (McHugh, [<reflink idref="bib40" id="ref114">40</reflink>]). Having reached a satisfactory IRR, each of the four annotators coded approximately 500 new threads independently, forming 2318 hand-labeled discussion threads for further analysis.</p> <hd id="AN0189590678-9">Grouping and Descriptive Statistics</hd> <p>Using the codes for problem-solving success and students' knowledge representation as two variables, we grouped the 2318 discussion threads into four groups. Group 1 (G1) represents the most effective discussion threads, as indicated by the high knowledge representation (over the average) and successful problem-solving (success = 1). Group 2 (G2) includes the discussion threads that are successful but where students do not represent their knowledge acquisition often (below the average). On the other hand, group 3 (G3) contains discussions that were not successful (success = 0) but where students represented their knowledge often. Lastly, group 4 (G4) includes the threads that are neither successful nor represent a high level of students' knowledge. Table 4 showcases the descriptive statistics of each group in terms of students' background (i.e., demographics), participants' tutor type (i.e., student tutor vs. expert tutor), and utterance counts.</p> <hd id="AN0189590678-10">Data Analysis</hd> <p></p> <hd id="AN0189590678-11">Regression Analysis</hd> <p>To answer RQ1 about how tutoring strategies explain the effectiveness of tutoring (i.e., success and knowledge representation), we conducted two regression analyses. First, regarding the success of problem-solving, we conducted a logistic regression using generalized linear models with log odds. Second, regarding students' knowledge representation, we conducted a linear regression using Gaussian link functions. Assumptions for the regression analysis, such as linearity and multicollinearity, have been checked to be met before fitting the models. Specifically, using a threshold of 5, we used variance inflation factor (VIF) to identify and remove potentially problematic independent variables Alin ([<reflink idref="bib1" id="ref115">1</reflink>]). Our VIF analysis showed that no multicollinearity was found among predictors. For the logistic regression, we used students' demographics (race, gender), their expressed knowledge, tutor category, and tutoring strategies (Xs) to analyze the relationship between these variables and discussion success (Ys). Four different models were fit to control the effects of demographics, students' knowledge, and tutor category. Regarding the multiple linear regression, all the aforementioned independent variables were used except for students' knowledge, as this analysis intended to measure the relationship between students' knowledge (Ys) and the predictors. Similarly, three models were fit to control confounding variables. Race was coded by us as follows: the majority (<reflink idref="bib1" id="ref116">1</reflink>, Caucasian and Asian), minority (0, Black or African American, Native American, Hawaiian or Other Pacific Islander, and Two or More Races), and unknown ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math> </ephtml> 1). This categorization of race is based on racial representation in STEM learning, following (National Science Foundation, [<reflink idref="bib50" id="ref117">50</reflink>])'s report. Similarly, we also coded gender as unknown ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math> </ephtml> 1), female (0), and male (<reflink idref="bib1" id="ref118">1</reflink>).</p> <hd id="AN0189590678-12">Ordered Network Analysis</hd> <p>To answer RQ2, about the ordered network of the tutoring strategies for the four groups differing in success and knowledge representation, we conducted an ONA on the four identified groups (G1–G4). ONA is a technique designed to detect and measure specific connections between elements in data, taking into consideration the chronological sequence of events, enabling the visualization of these connections through network models (Tan et al., [<reflink idref="bib74" id="ref119">74</reflink>]). Originating from epistemic network analysis (ENA) (Shaffer et al., [<reflink idref="bib67" id="ref120">67</reflink>]), a widely used data analysis method focusing on identifying and visualizing the connections and dynamics among elements in coded data (e.g., visualizing self-regulated learning processes (Paquette et al., [<reflink idref="bib54" id="ref121">54</reflink>]; Saint et al., [<reflink idref="bib63" id="ref122">63</reflink>]) or modeling discourse during collaborative learning processes (Vandenberg et al., [<reflink idref="bib78" id="ref123">78</reflink>]; Wang et al., [<reflink idref="bib83" id="ref124">83</reflink>])), ONA improves its algorithm by adding more features assisting visualization (Tan et al., [<reflink idref="bib74" id="ref125">74</reflink>]). The ONA algorithm differs from ENA in the way in which the sequential order of coded elements is considered, as well as accounting for how each element interacts with other elements in a given period of time.</p> <p>ONA adds four features assisting visualization by representing the frequency of each code with node size and employing directed arrows connecting nodes to represent the sequences (Fan et al., [<reflink idref="bib17" id="ref126">17</reflink>]). First, ONA represents each coded element with a node whose size is proportional to its frequency of connecting with other coded elements. Second, the size of the colored inner circle represents the frequency of the self-transition of the coded element. Third, an edge with direction connecting pairs of elements indicates a more frequent element transition. Fourth, the position of nodes in the generated network graphs is interpretable, as it represents the location of its network in the 2-dimensional projected space. Figure 1 shows an example ONA plot with four nodes. Information that can be drawn from this figure is as follows: (<reflink idref="bib1" id="ref127">1</reflink>) Node D illustrates the most frequent code (size of the node), followed by node A. (<reflink idref="bib2" id="ref128">2</reflink>) Node D has a bigger frequency of self-transition compared to node A (inner circle). (<reflink idref="bib3" id="ref129">3</reflink>) The tendency to transit from node D to node A is stronger than the transition from node A to node D (chevron). (<reflink idref="bib4" id="ref130">4</reflink>) Nodes A and B are more likely to co-occur and thus could be interpreted to convey similar meanings compared to nodes A and D (node position). This approach aligns well with our goal of investigating tutors' behaviors in a collaborative discourse that involves multiple tutors and a tutee.</p> <p>Graph: Fig. 1 ONA illustration</p> <p>To conduct ONA and reveal the dynamics of tutoring strategies, we first assigned four group labels to discussion interactions of peer and expert tutors ( <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>n</mi><mrow><mi>p</mi><mi>o</mi><mi>s</mi><mi>t</mi><mo>+</mo><mi>r</mi><mi>e</mi><mi>p</mi><mi>l</mi><mi>y</mi></mrow></msub><mo>=</mo><mn>13</mn><mo>,</mo><mn>022</mn></mrow></math> </ephtml> ). The four group labels are based on their tutoring success and students' knowledge (G1–G4, refer to the "Grouping and Descriptive Statistics" section for grouping criteria). We used the assigned group and thread identifiers as units in ONA such that different groups' conversations would be treated independently. Finally, we chose a stanza window size of 9, reflecting the average number of conversational turns observed in our dataset. Utilizing singular value decomposition Golub and Reinsch ([<reflink idref="bib21" id="ref131">21</reflink>]), we then performed dimensional reduction. This approach can effectively maximize the variance explained, allowing for a clearer distinction between the analyzed elements.</p> <p>Table 5 Logistic regression analysis for discussion success. <emph>OR</emph>, odds ratio; <emph>CI</emph>, confidence interval</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left"><p>Predictors</p></th><th align="left" colspan="2"><p>Model 1</p></th><th align="left" colspan="2"><p>Model 2</p></th><th align="left" colspan="2"><p>Model 3</p></th><th align="left" colspan="2"><p>Model 4</p></th></tr><tr><th align="left" /><th align="left"><p><italic>OR</italic></p></th><th align="left"><p><italic>CI</italic></p></th><th align="left"><p><italic>OR</italic></p></th><th align="left"><p><italic>CI</italic></p></th><th align="left"><p><italic>OR</italic></p></th><th align="left"><p><italic>CI</italic></p></th><th align="left"><p><italic>OR</italic></p></th><th align="left"><p><italic>CI</italic></p></th></tr></thead><tbody><tr><td align="left"><p>(Intercept)</p></td><td align="left"><p><bold>0</bold>.<bold>8</bold>**</p></td><td align="left"><p>0.78</p></td><td align="left"><p>0.96</p></td><td align="left"><p>0.89</p></td><td align="left"><p>0.98</p></td><td align="left"><p>0.91</p></td><td align="left"><p><bold>0</bold>.<bold>42</bold>**</p></td><td align="left"><p>0.37</p></td></tr><tr><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.82</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.03</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.05</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.45</p></td></tr><tr><td align="left"><p><italic>Students' background</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Female</p></td><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>95</bold>**</p></td><td align="left"><p>0.90</p></td><td align="left"><p>0.97</p></td><td align="left"><p>0.92</p></td><td align="left"><p>0.95</p></td><td align="left"><p>0.90</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.00</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.02</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.00</p></td></tr><tr><td align="left"><p>Race</p></td><td align="left" /><td align="left" /><td align="left"><p><bold>1</bold>.<bold>16</bold>**</p></td><td align="left"><p>1.11</p></td><td align="left"><p><bold>1</bold>.<bold>16</bold>**</p></td><td align="left"><p>1.11</p></td><td align="left"><p><bold>1</bold>.<bold>10</bold>**</p></td><td align="left"><p>1.05</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.21</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.21</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.15</p></td></tr><tr><td align="left"><p><italic>Tutor category</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Is_student</p></td><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>77</bold>**</p></td><td align="left"><p>0.71</p></td><td align="left"><p><bold>0</bold>.<bold>69</bold>**</p></td><td align="left"><p>0.63</p></td><td align="left"><p><bold>1</bold>.<bold>25</bold>**</p></td><td align="left"><p>1.14</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.84</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.75</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>1.38</p></td></tr><tr><td align="left"><p>Students'</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>5</bold>.<bold>92</bold>**</p></td><td align="left"><p>5.07</p></td><td align="left"><p><bold>7</bold>.<bold>76</bold>**</p></td><td align="left"><p>6.64</p></td></tr><tr><td align="left"><p>knowledge</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>6.95</p></td><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>9.12</p></td></tr><tr><td align="left"><p><italic>Tutoring</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p><italic>strategies</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Feedback</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>6</bold>.<bold>35</bold>**</p></td><td align="left"><p>5.48</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>7.40</p></td></tr><tr><td align="left"><p>Instructing</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>3</bold>.<bold>69</bold>**</p></td><td align="left"><p>3.32</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>4.10</p></td></tr><tr><td align="left"><p>Explaining</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>4</bold>.<bold>07</bold>**</p></td><td align="left"><p>3.65</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>4.54</p></td></tr><tr><td align="left"><p>Questioning</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>2</bold>.<bold>23</bold>**</p></td><td align="left"><p>1.98</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>2.52</p></td></tr><tr><td align="left"><p>Motivating</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>8</bold>.<bold>57</bold>**</p></td><td align="left"><p>6.11</p></td></tr><tr><td align="left"><p>and encouraging</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>12.32</p></td></tr><tr><td align="left"><p>Managing</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>2</bold>.<bold>01</bold>**</p></td><td align="left"><p>1.66</p></td></tr><tr><td align="left"><p>discussions</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>2.42</p></td></tr><tr><td align="left"><p>Direct</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>6</bold>.<bold>55</bold>**</p></td><td align="left"><p>4.71</p></td></tr><tr><td align="left"><p>intervention</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>9.31</p></td></tr><tr><td align="left"><p>Observations</p></td><td align="left" colspan="2"><p>24,116</p></td><td align="left" colspan="2"><p>24,116</p></td><td align="left" colspan="2"><p>24,116</p></td><td align="left" colspan="2"><p>24,116</p></td></tr><tr><td align="left"><p>R-squared Tjur</p></td><td align="left" colspan="2"><p>0.000</p></td><td align="left" colspan="2"><p>0.003</p></td><td align="left" colspan="2"><p>0.028</p></td><td align="left" colspan="2"><p>0.129</p></td></tr></tbody></table> </ephtml> </p> <p>Significant values are bolded **<emph>p</emph> <.001</p> <hd id="AN0189590678-13">Results</hd> <p></p> <hd id="AN0189590678-14">RQ1: To What Extent Do Tutoring Strategies Explain the Effectiveness of Tutoring?</hd> <p>The first research question examined the extent to which tutoring strategies explain the effectiveness of tutoring. The effectiveness of tutoring was defined with two variables: the success of the discussion and the level of student knowledge representation during the discussion. To answer this question, we conducted two separate regression analyses. First, a logistic regression analysis was conducted to investigate how much each of the tutoring strategies explains the success of the discussion (binary variable). Table 5 shows the results of the logistic regression. An odds ratio (OR) is used to determine the strength and direction of the association between an independent and dependent variable. With 1 being a threshold suggesting equal odds of having a(n) (un)successful discussion, an OR greater than 1 indicates greater odds of a successful discussion when increasing one unit of an independent variable with other independent variables held constant, whereas ORs less than 1 suggest a decreasing odds. For example, the OR of 6.35 of "feedback" in Model 4 can be interpreted as the odds of being in a successful discussion are predicted to grow about 6.35 times larger for the presence of the "feedback" tutoring strategy when holding other variables constant. On the other hand, the OR of 0.77 for the "tutor category" in Model 2 suggests that having a peer tutor can shrink the odds of discussion success by a factor of about 0.77 when controlling for other independent variables.</p> <p>Table 6 Multiple linear regression analysis for students' knowledge representation. <emph>Est</emph>, Estimates; <emph>std.</emph><ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>β</mi></math> </ephtml> , standardized Beta</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left" /><th align="left" colspan="4"><p>Model 1</p></th><th align="left" colspan="4"><p>Model 2</p></th><th align="left" colspan="4"><p>Model 3</p></th></tr><tr><th align="left"><p> Predictors</p></th><th align="left"><p><italic>Est</italic></p></th><th align="left"><p><italic>std.</italic><math xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">β</mi></math></p></th><th align="left"><p><italic>CI</italic></p></th><th align="left"><p><italic>std. CI</italic></p></th><th align="left"><p><italic>Est</italic></p></th><th align="left"><p><italic>std.</italic><math xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">β</mi></math></p></th><th align="left"><p><italic>CI</italic></p></th><th align="left"><p><italic>std. CI</italic></p></th><th align="left"><p><italic>Est</italic></p></th><th align="left"><p><italic>std.</italic><math xmlns="http://www.w3.org/1998/Math/MathML"><mi xmlns="">β</mi></math></p></th><th align="left"><p><italic>CI</italic></p></th><th align="left"><p><italic>std. CI</italic></p></th></tr></thead><tbody><tr><td align="left"><p>(Intercept)</p></td><td align="left"><p><bold>0</bold>.<bold>04</bold>**</p></td><td align="left"><p>0.00</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.04</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><bold>0</bold>.<bold>05</bold>**</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.04</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><bold>0</bold>.<bold>02</bold>**</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.02</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.04</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.05</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.03</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td></tr><tr><td align="left"><p><italic>Students'</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p><italic>background</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Female</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math><bold>0.00</bold>**</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.04</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.07</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math><bold>0.01</bold>**</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.05</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.07</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.00</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.02</p></td><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.00</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.04</p></td></tr><tr><td align="left"><p>Race</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>00</bold>**</p></td><td align="left"><p>0.05</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.03</p></td><td align="left"><p><bold>0</bold>.<bold>00</bold>*</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.01</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.07</p></td><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.00</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.05</p></td></tr><tr><td align="left"><p><italic>Tutor category</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Is_student</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math><bold>0.01</bold>**</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.05</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.06</p></td><td align="left"><p><bold>0</bold>.<bold>01</bold>**</p></td><td align="left"><p>0.06</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.04</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.03</p></td><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.08</p></td></tr><tr><td align="left"><p><italic>Conversation</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Turn numbers</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>00</bold>**</p></td><td align="left"><p>0.06</p></td><td align="left"><p>0.01</p></td><td align="left"><p>0.05</p></td><td align="left"><p><bold>0</bold>.<bold>00</bold>**</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.00</p></td><td align="left"><p>0.03</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.00</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.07</p></td><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.05</p></td></tr><tr><td align="left"><p><italic>Tutoring</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p><italic>strategies</italic></p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Feedback</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>05</bold>**</p></td><td align="left"><p>0.17</p></td><td align="left"><p>0.05</p></td><td align="left"><p>0.15</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.06</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.18</p></td></tr><tr><td align="left"><p>Instructing</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>04</bold>**</p></td><td align="left"><p>0.13</p></td><td align="left"><p>0.03</p></td><td align="left"><p>0.11</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.04</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.14</p></td></tr><tr><td align="left"><p>Explaining</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>02</bold>**</p></td><td align="left"><p>0.07</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.06</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.02</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.09</p></td></tr><tr><td align="left"><p>Questioning</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>04</bold>**</p></td><td align="left"><p>0.13</p></td><td align="left"><p>0.04</p></td><td align="left"><p>0.11</p></td></tr><tr><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.05</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.14</p></td></tr><tr><td align="left"><p>Motivating and</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>06</bold>**</p></td><td align="left"><p>0.08</p></td><td align="left"><p>0.05</p></td><td align="left"><p>0.06</p></td></tr><tr><td align="left"><p>encouraging</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.07</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.09</p></td></tr><tr><td align="left"><p>Managing</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.00</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.00</p></td></tr><tr><td align="left"><p>discussions</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p>0.01</p></td><td align="left"><p>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.02</p></td></tr><tr><td align="left"><p>Direct</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><bold>0</bold>.<bold>02</bold>*</p></td><td align="left"><p>0.02</p></td><td align="left"><p>0.01</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.01</p></td></tr><tr><td align="left"><p>intervention</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.03</p></td><td align="left"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo xmlns="">-</mo></math>0.03</p></td></tr><tr><td align="left"><p>Observations</p></td><td align="left" colspan="4"><p>24,116</p></td><td align="left" colspan="4"><p>24,116</p></td><td align="left" colspan="4"><p>24,116</p></td></tr><tr><td align="left"><p>R-squared Tjur</p></td><td align="left" colspan="2"><p>0.000 / 0.000</p></td><td align="left" /><td align="left" /><td align="left" colspan="2"><p>0.007 / 0.007</p></td><td align="left" /><td align="left" /><td align="left" colspan="3"><p>0.076 / 0.075</p></td><td align="left" /></tr></tbody></table> </ephtml> </p> <p>Significant values are bolded *<emph>p</emph> <.01; **<emph>p</emph> <.001</p> <p>All tutoring strategies seem to have significant positive effects, while in varying magnitudes, on the success of discussions. Among them, "motivating and encouraging," "direct intervention," and "feedback" are the strategies that largely influence the success of the discussion. On the other hand, "questioning," "managing discussions," and "tutoring reflection" have relatively small impacts on the discussion's success. The increase of Tjur's <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mn>2</mn></msup></math> </ephtml> (Models 2 vs. 3, and Models 3 vs. 4) demonstrates the explanatory power of students' knowledge and tutoring strategies on discussion success compared to student and tutor background information. Higher Tjur's <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mn>2</mn></msup></math> </ephtml> (ranging from 0 to 1) illustrates better model fit. For instance, a Tjur's <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mn>2</mn></msup></math> </ephtml> of 0.129 means there is a 12.9% difference in the mean predicted probabilities between discussions with and without success.</p> <p>Second, multiple linear regression was used to understand the relationship between the tutoring strategies and students' knowledge representation during the discussion. The result is summarized in Table 6. The Estimates are the coefficients of multiple linear regression models, while standardized (std.) Betas are the standardized coefficients. Given that all predictors are categorical, the regular coefficients (Estimates) may provide more straightforward interpretations. For example, an estimated coefficient of 0.04 of "instructing" (binary) in Model 3 shows that receiving such a tutoring strategy will increase students' demonstrated knowledge by 0.04 when holding other variables constant. "Feedback" and "motivating and encouraging" are still amongst the two biggest influential tutoring strategies for students' knowledge representation, followed by "instructing" and "questioning." On the other hand, "direct intervention" has much less influence on students' knowledge representation, compared to that on the discussion's success. Meanwhile, there is a notable trend of increasing explainability by introducing tutoring strategies as predictors, with a 7% increase in the adjusted <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mn>2</mn></msup></math> </ephtml> values from Model 2 to Model 3.</p> <p>Table 7 Comparison of the frequency of each tutoring strategy among the four groups</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left"><p>Tutoring</p></th><th align="left"><p>G1</p></th><th align="left"><p>G2</p></th><th align="left"><p>G3</p></th><th align="left"><p>G4</p></th><th align="left"><p>Comparison</p></th></tr><tr><th align="left"><p>strategies</p></th><th align="left" /><th align="left" /><th align="left" /><th align="left" /><th align="left" /></tr></thead><tbody><tr><td align="left"><p>Feedback</p></td><td align="left"><p>837 (22.37%)</p></td><td align="left"><p>207 (8.87%)</p></td><td align="left"><p>116 (12.93%)</p></td><td align="left"><p>113 (1.87%)</p></td><td align="left"><p>G1>G3>G2>G4</p></td></tr><tr><td align="left"><p>Instructing</p></td><td align="left"><p>866 (23.14%)</p></td><td align="left"><p>450 (19.28%)</p></td><td align="left"><p>256 (28.54%)</p></td><td align="left"><p>332 (5.49%)</p></td><td align="left"><p>G3>G1>G2>G4</p></td></tr><tr><td align="left"><p>Explaining</p></td><td align="left"><p>647 (17.29%)</p></td><td align="left"><p>587 (25.15%)</p></td><td align="left"><p>185 (20.62%)</p></td><td align="left"><p>342 (5.65%)</p></td><td align="left"><p>G2>G3>G1>G4</p></td></tr><tr><td align="left"><p>Questioning</p></td><td align="left"><p>561 (14.99%)</p></td><td align="left"><p>241 (10.33%)</p></td><td align="left"><p>228 (25.42%)</p></td><td align="left"><p>348 (5.75%)</p></td><td align="left"><p>G3>G1>G2>G4</p></td></tr><tr><td align="left"><p>Direct intervention</p></td><td align="left"><p>96 (2.57%)</p></td><td align="left"><p>89 (3.81%)</p></td><td align="left"><p>17 (1.90%)</p></td><td align="left"><p>26 (0.43%)</p></td><td align="left"><p>G2>G1=G3>G4</p></td></tr><tr><td align="left"><p>Motivating and</p></td><td align="left"><p>159 (4.25%)</p></td><td align="left"><p>60 (2.57%)</p></td><td align="left"><p>24 (2.68%)</p></td><td align="left"><p>16 (0.26%)</p></td><td align="left"><p>G1>G3>G2>G4</p></td></tr><tr><td align="left"><p>encouraging</p></td><td align="left" /><td align="left" /><td align="left" /><td align="left" /><td align="left" /></tr><tr><td align="left"><p>Managing discussion</p></td><td align="left"><p>111 (2.97%)</p></td><td align="left"><p>117 (5.01%)</p></td><td align="left"><p>46 (5.13%)</p></td><td align="left"><p>196 (3.24%)</p></td><td align="left"><p>G3>G2>G1=G4</p></td></tr></tbody></table> </ephtml> </p> <hd id="AN0189590678-15">RQ2: What Are the Ordered Networks of the Tutoring Strategies of Four Groups Differing in the...</hd> <p>To answer RQ2, we conducted an ONA to visualize the dynamics of the tutoring strategies in each group. We applied ONA with data of peer and expert tutors' replies, with each data entry representing the presence (i.e., 0 or 1) of each tutoring strategy. Table 7 shows the descriptive statistics for each tutoring strategy found in the four groups and its statistical comparison using Poisson regression to indicate whether being in a specific group tends to see a tutoring strategy more frequently, considering the differences in the total number of replies among groups. The statistical significance is indicated by the ">" sign with an alpha level of <ephtml> <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo><</mo><mo>.</mo><mn>05</mn><mo>.</mo></mrow></math> </ephtml> "=" indicates there is no significant difference between the pair. The percentage in Table 7 is proportional to the total number of replies in each group.</p> <p>Group 1 characterizes the most effective discussion threads that resulted in successful discussions and a high level of student knowledge representation. Figure 2 visualizes the tutoring strategies and their dynamics shown in G1 discussions. Note that in ONA, node size represents the relative frequency of the codes, rather than absolute frequency values. Thus, comparing the size of a node among different ONA plots might not lead to meaningful insights. "Feedback" is the most notable node, indicating the highest frequency. "Instructing" and "explaining" are the second and the third frequent tutoring strategies. The fourth notable node in G1 is "questioning," followed by "motivating and encouraging," "managing discussions," and "direct intervention." Meanwhile, directed arrows in ONA indicate the direction of the actions. "Feedback" has directed arrows stemming from "instructing," "questioning," and "explaining." That means tutors tend to provide feedback after they provide instructions, ask questions, and explain. Also, there is an arrow directing from "instructing" to "explaining" and from "questioning" to "explaining." That is, tutors tend to provide explanations after they give instructions or ask questions. "Motivating and encouraging" is often followed by "instructing" or "questioning." On the other hand, the colored inner circles in ONA illustrate the self-transition of the code. "Instructing" and "explaining" have relatively big inner circles, indicating a frequent self-transition; tutors tend to continue giving instructions or explanations. In contrast, "feedback" and "motivating and encouraging" have less frequent self-transition. Lastly, in ONA, node positions provide information about the co-occurrence of nodes. "Instructing," "questioning," and "explaining" are distinctively separated from each other, whereas "feedback," "motivating and encouraging," "direct intervention," and "managing discussion" are located close to each other. "Feedback" and "motivating and encouraging" share some overlaps in the visualization, meaning they often co-occur in the dataset, likewise "managing discussion" and "direct intervention."</p> <p>Graph: Fig. 2 Ordered network analysis of group 1 (success = 1, knowledge representation = high)</p> <p>Group 2 characterizes successful discussion threads that lack students' knowledge representation. Figure 3 visualizes the tutoring strategies and their dynamics shown in G2. "Explaining" is the most notable strategy, with "instructing" being the second. "Feedback" and "questioning" follow with a relatively big gap. Other strategies like "managing discussion," "motivating and encouraging," and "direct intervention" are among the three least frequent strategies in G2. Similar to G1, directional relationships could be found from "questioning" to "explaining" and "instructing" to "explaining." This means tutors in G2 tend to provide explanations after they ask questions or provide instructions. There are other similar patterns to G1 regarding "feedback" (e.g., directing arrows from "questioning" to "feedback," and "instructing" to "feedback," and "explaining" to "feedback"). However, the thickness of the directed arrows is considerably smaller, indicating weaker connections between the nodes. Regarding self-transition, "explaining" and "instructing" have relatively big inner circles, indicating frequent transitions to themselves.</p> <p>Graph: Fig. 3 Ordered network analysis of group 2 (success = 1, knowledge representation = low)</p> <p>Graph: Fig. 4 Ordered network analysis of group 3 (success = 0, knowledge representation = high)</p> <p>Graph: Fig. 5 Ordered network analysis of group 4 (success = 0, knowledge representation = low)</p> <p>Table 8 Comparing predictors ranking for discussion success and knowledge representation</p> <p> <ephtml> <table rules="groups"><thead><tr><th align="left" /><th align="left"><p>Discussion success</p></th><th align="left"><p>Knowledge representation</p></th></tr><tr><th align="left" /><th align="left"><p>: predictors (Odds Ratio)</p></th><th align="left"><p>: predictors (Estimate)</p></th></tr></thead><tbody><tr><td align="left"><p>1</p></td><td align="left"><p>Motivating and encouraging (8.57)</p></td><td align="left"><p>Feedback (0.06)</p></td></tr><tr><td align="left"><p>2</p></td><td align="left"><p>Direct intervention (6.55)</p></td><td align="left"><p>Motivating and encouraging (0.06)</p></td></tr><tr><td align="left"><p>3</p></td><td align="left"><p>Feedback (6.35)</p></td><td align="left"><p>Questioning (0.04)</p></td></tr><tr><td align="left"><p>4</p></td><td align="left"><p>Explaining (4.07)</p></td><td align="left"><p>Instructing (0.04)</p></td></tr><tr><td align="left"><p>5</p></td><td align="left"><p>Instructing (3.69)</p></td><td align="left"><p>Explaining (0.02)</p></td></tr><tr><td align="left"><p>6</p></td><td align="left"><p>Questioning (2.23)</p></td><td align="left"><p>Direct intervention (0.02)</p></td></tr><tr><td align="left"><p>7</p></td><td align="left"><p>Managing discussions (2.01)</p></td><td align="left"><p>N/A</p></td></tr></tbody></table> </ephtml> </p> <p>Group 3 characterizes unsuccessful discussion threads with high-level student knowledge representation. Figure 4 visualizes the tutoring strategies and their dynamics shown in G3. The most notable characteristic of G3 is the significantly bigger node size of "questioning" compared to G1 and G2. "Instructig" and "explaining" also illustrate relatively big-sized nodes. "Feedback" is also bigger than G2 but smaller than G1. "Managing discussion" was also found to be more frequent than other groups. "Direct intervention" and "motivating and encouraging" were rarely used. The directed arrows illustrate the sequences from "questioning" to "instruction" and "questioning" to "explaining," meaning the tutors are more likely to give instructions or explanations after asking questions. However, notice that the line segment between the "instructing" and "questioning" nodes tapers to a point in the middle, and that point sits roughly equidistant between the two nodes. This indicates that the nodes had a similar likelihood of sequential transition to one another. In other words, while the transition (shown by the chevron) from questioning to instructing was more likely than the reverse direction, this directionality is not strong. "Questioning" has a big inner circle, meaning tutors in this group tend to continuously ask questions.</p> <p>Lastly, G4 characterizes unsuccessful discussion threads with low-level student knowledge representation. Figure 5 visualizes the tutoring strategies and their dynamics shown in G4. Overall, G4 characterizes small-sized nodes, indicating a small percentage of meaningful tutoring strategies used in G4 (see Table 7). Additionally, the edges between nodes are lighter and thinner, meaning that connections among the nodes are weak. The largest nodes include "instructing," "questioning," and "explaining." It is noteworthy that for G4, "direct intervention" is closer in size to the largest nodes than it is for the other groups. Overall, this group suggests much less frequent use of meaningful tutoring strategies.</p> <hd id="AN0189590678-16">Discussion</hd> <p></p> <hd id="AN0189590678-17">The Impact of Tutoring Strategies on the Effectiveness of Online Discussions</hd> <p>Two regression analyses were conducted to examine the extent to which tutoring strategies explain the effectiveness of tutoring, operationalized as problem-solving success and students' knowledge representation, respectively (Tables 5 and 6). Table 8 compares the tutoring strategy variables as predictors between the two regression analyses: they are ordered from the most influential to the least influential for predicting each measure, problem-solving success, and knowledge representation. We interpreted the importance of variables in logistic and linear regression using Odds Ratio and Estimates, respectively. Given the binary nature of these tutoring strategies, these two model results help us understand the effects on discussion success and knowledge representation when changing one tutoring strategy from absent to present (e.g., from 0 to 1), holding other independent variables constant.</p> <p>First, "motivating and encouraging" was identified as the most important tutoring strategy for both discussion success and knowledge representation. This involves tutors providing affective support, such as praising, encouraging, and managing frustration (Sottilare et al., [<reflink idref="bib71" id="ref132">71</reflink>]). In math education, students' lack of affective control and motivation towards math has been considered one of the biggest challenges of math learning (McLeod, [<reflink idref="bib43" id="ref133">43</reflink>]). Previous studies have emphasized the essential roles of affective support in enhancing self-efficacy (Han & Geng, [<reflink idref="bib24" id="ref134">24</reflink>]), academic efforts (Sakiz et al., [<reflink idref="bib64" id="ref135">64</reflink>]), and learning outcome (Arroyo et al., [<reflink idref="bib3" id="ref136">3</reflink>]). This role seems to be especially emphasized in the current study due to the unique context of online asynchronous discussion, where less sense of teacher presence and external regulation likely leads to students feeling isolated during online discussions (Sheridan & Kelly, [<reflink idref="bib68" id="ref137">68</reflink>]; Palloff & Pratt, [<reflink idref="bib52" id="ref138">52</reflink>]; Ma et al., [<reflink idref="bib38" id="ref139">38</reflink>]); thus, tutors' use of "motivating and encouraging" seems to take an even more important role in effective learning by strengthening emotional connections between tutors and tutees, enhancing the sense of social presence (Swan & Shih, [<reflink idref="bib73" id="ref140">73</reflink>]). In line with this, the ONA results suggest that "motivating and encouraging" was used significantly more often in G1 (successful, high knowledge), followed by G3 (unsuccessful, high knowledge), G2 (successful, low knowledge), and G4 (unsuccessful, low knowledge), in order. However, at the same time, it was among the least frequently used tutoring strategies across all groups (refer to Table 7), indicating a clear gap between the importance of effective support and its use in practice. This gap suggests human tutors or the future design of intelligent tutoring systems (ITS) should be encouraged to use more "motivating and encouraging" to facilitate online mathematical discussions.</p> <p>"Direct intervention" was found to be the second important factor in explaining the discussion's success, while it was the least impactful tutoring strategy for knowledge representation. Aligning with this result, "direct interventions" were used the most in G2, characterizing success with low knowledge representation. This indicates that students were more likely to find the correct answers through the tutors' direct intervention (e.g., direct presentation of answers), yet deprived of opportunities to represent their knowledge during the discussion. In general, the literature does not recommend frequent use of "direct intervention" in tutoring (Richey et al., [<reflink idref="bib59" id="ref141">59</reflink>]), as students gain a deeper understanding of knowledge while actively engaging in working through problems instead of being provided with the answer directly (Chi et al., [<reflink idref="bib10" id="ref142">10</reflink>]; Roscoe & Chi, [<reflink idref="bib61" id="ref143">61</reflink>]; Pirie & Schwarzenberger, [<reflink idref="bib56" id="ref144">56</reflink>]). In addition, we found "direct intervention" to be mostly co-occurring with "managing discussions" as indicated by the close node positions of "direct intervention" and "managing discussion" (see Fig. 3). This might be attributed to the fact that tutors try to hinder other tutors from directly providing answers, which was coded as "managing discussions" in our study.</p> <p>"Feedback" was found to be the third most important factor in explaining better chances of success and the first factor in explaining students' knowledge representation. "Feedback" works as a formative assessment to provide important information about students' progress or performances in the discussion (Van de Pol et al., [<reflink idref="bib57" id="ref145">57</reflink>]; Hattie & Timperley, [<reflink idref="bib26" id="ref146">26</reflink>]). The important roles of feedback in learning have been widely discussed and supported by numerous previous studies, which provide insights such that frequent feedback leads students to find misconceptions in their reasoning and fix them (VanLehn, [<reflink idref="bib79" id="ref147">79</reflink>]; McKendree, [<reflink idref="bib42" id="ref148">42</reflink>]). The importance of "feedback" was also visualized and highlighted in the ONA plot for G1 (Fig. 2), in which "feedback" was the biggest node, notably bigger than those in the ONA plots for other groups (Fig. 3, 4, and 5). This result suggests that "feedback" should be highly encouraged for human tutors or intelligent tutors to support a successful discussion that promotes high knowledge representation.</p> <p>"Explaining" was found to be a relatively important tutoring strategy for discussion success but ranked lower in knowledge representation analysis. Previous studies describe "explaining" as a non-interactive and didactic tutoring strategy (Chi et al., [<reflink idref="bib10" id="ref149">10</reflink>]; Van de Pol et al., [<reflink idref="bib57" id="ref150">57</reflink>]). Interestingly, Chi et al. ([<reflink idref="bib10" id="ref151">10</reflink>]) suggested that such non-interactive tutoring could have a similar effect on students' learning, but it could not lead to students' knowledge construction and the elicitation of their understanding. Aligned with such previous literature, this study also suggests that "explaining" was helpful in leading students to find the correct answer efficiently, but it was not effective in promoting students' knowledge representation.</p> <p>"Instruction" was the fifth important tutoring strategy for discussion success and of similar importance (ranked as fourth) in the knowledge representation analysis. Even though it did not rank high in both success and knowledge, "instructing" was found to be one of the most frequently shown tutoring strategies across the four groups (see Table 7). This means that "instructing" was the most common strategy used by online tutors, even though the effect of it is not as large. This gap urges tutors to move toward taking up the role of facilitators or learning partners instead of mainly working as instructors (Mullen, [<reflink idref="bib48" id="ref152">48</reflink>]).</p> <p>"Questioning," on the other hand, offers different patterns in the two analyses. "Questioning" was found to be one of the most important factors in knowledge representation, ranked third, whereas it was one of the least impactful factors in discussion success, ranked sixth. Aligning with this result, "questioning" was the most notable tutoring strategy in G3, compared to other groups, indicating that it can be helpful with promoting knowledge representation but not as beneficial for successful discussions. While "questioning" has been described as an interactive tutoring strategy that provokes students' deep thinking and engagement Lin et al. [<reflink idref="bib35" id="ref153">35</reflink>], the self-loop of "questioning" without following "feedback" or "explaining" may confuse learners and not guide them in solving the problem. Therefore, there needs to be a balance between open, interactive strategies, such as "questioning" and closed, didactic strategies, such as "instructing" or "explaining" or some "feedback" to support successful problem-solving.</p> <p>Lastly, "managing discussion" was found to have a small impact on discussion success and does not show a significant influence in promoting knowledge representation. ONA plots for G1 and G2 illustrate a relatively bigger node size for this strategy, while it was rarely used in G3 and G4. This result makes sense in that "managing discussions" mainly works as logistical support to help students keep on track, maintain their attention to problem-solving, redirect students from off-topic conversation, and guide tutoring behaviors, and thus, it is barely related to promoting students' knowledge representation.</p> <p>Graph: Fig. 6 Node positioning with interpretation</p> <hd id="AN0189590678-18">The Interpretation of Node Positioning in ONA</hd> <p>In ONA analysis, node positioning on a coordinate plane is a meaningful feature, suggesting nodes located closer to each other carry similar qualitative meanings Tan et al. [<reflink idref="bib74" id="ref154">74</reflink>]. Therefore, node positions of our ONA results could imply qualitative meaning in terms of the roles of each tutoring strategy in relation to the effectiveness of discussions. Figure 6 presents the 2-dimensional space onto which the tutoring strategy nodes are mapped. The summary of each group (the four groups of threads, categorized by the presence or absence of success and knowledge representation) is illustrated on the plane as colored crosses, which showcase the average position of each thread's ONA (the cross's center) with a 95% confidence interval (the cross's arms). The four groups' average positions are distributed across the four quadrants. For example, G3 is mostly located in the first quadrant, whereas G2 is placed in the third quadrant.</p> <p>By considering the main tutoring strategies placed on each quadrant, it is possible to make sense of the plane's axes. We interpret the <emph>X</emph>-axis as characterizing the extent to which the tutoring strategies provoke actions from the students, as opposed to merely delivering the information. For example, the nodes placed on the left side of the <emph>X</emph>-axis, such as "instructing" and "questioning," aim to provoke actions from the students (problem-solving steps, responses) (Eloff et al., [<reflink idref="bib16" id="ref155">16</reflink>]; Graesser et al., [<reflink idref="bib22" id="ref156">22</reflink>]; Topping et al., [<reflink idref="bib76" id="ref157">76</reflink>]). On the other hand, there is "explaining" on the right side of the <emph>X</emph>-axis, which can be understood as focused on direct information delivery (Chi et al., [<reflink idref="bib10" id="ref158">10</reflink>]). Meanwhile, the <emph>Y</emph>-axis could be interpreted to showcase the extent to which the tutoring strategies are one-way and closed, limiting students' responses as opposed to open and interactive. On the far positive side of the <emph>Y</emph>-axis, there are "instructing" and "explaining," which are both provided unidirectionally from the tutors to tutees. On the far negative side of the <emph>Y</emph>-axis is located the node of "questioning," which can be characterized as interactive in nature (Chi et al., [<reflink idref="bib10" id="ref159">10</reflink>]). "Feedback" is also slightly below the <emph>Y</emph>-axis, characterizing the interactive nature, even though it is not as strongly interactive as "questioning." This aligns with previous literature that defines feedback to be applicable only when it is provided as a response to the student's actions (Hattie & Timperley, [<reflink idref="bib26" id="ref160">26</reflink>]).</p> <p>Based on this interpretation of the <emph>X</emph> and <emph>Y</emph> axis, we can interpret the overall characteristics of each thread group. G1 (successful problem-solving, strong knowledge representation) is located on the left side of the <emph>X</emph>-axis, aligned with more action-provoking tutoring strategies. At the same time, ONA shows that G1 has a good balance between closed, one-way strategies and open, interactive strategies, allowing students to have an open discussion through "questioning" and receive "feedback" as well as "instructing" and "explaining." Next, G2's (successful problem-solving, weak knowledge representation) location on the right side of the <emph>X</emph>-axis and upper part of the <emph>Y</emph>-axis reflects that these tutors utilized more closed, one-way, and delivery-based tutoring strategies, enabling efficient discussions to find the answers that could typically lack enough knowledge representation. On the other hand, G3 (unsuccessful problem-solving with strong knowledge representation) is on the opposite side of G2, representing more action-provoking and open, interactive tutoring strategies, allowing students to express their knowledge during the discussions through such tutoring strategies as "questioning," yet not be able to help them find the correct answers as efficiently. Lastly, G4 (unsuccessful problem-solving and weak knowledge representation) lacks any strong tendency toward any direction, not because of the balanced use of different strategies but because of the lack of use of meaningful tutoring strategies. This node positioning provides insights into a new way of categorizing tutoring strategies (i.e., openness and action-provoking) and characterizing tutoring discussions following these categorizations.</p> <hd id="AN0189590678-19">Conclusion</hd> <p>This study aims to examine the relationship between tutoring strategies and the effectiveness of tutoring discussions and visualize the ordered networks of effective discussions. Using textual data from 2318 discussion threads from a secondary school online math learning platform, we identified some gaps in the importance of tutoring strategies pertaining to the effectiveness of asynchronous online mathematical discussions. For purposes of this analysis, we operationalized effectiveness as measured by both problem-solving and students' knowledge representation. Furthermore, ONA provided insights into interactive sequential dynamics among those strategies depending on the level of discussion effectiveness.</p> <p>This study makes three major contributions from theoretical, methodological, and practical perspectives. First, this study provides grounding results for the potential theory of knowledge representation in mathematical discussions. While the importance of knowledge representation in discussions has been mentioned widely in literature (Chi et al., [<reflink idref="bib10" id="ref161">10</reflink>]; Roscoe & Chi, [<reflink idref="bib61" id="ref162">61</reflink>]; Pirie & Schwarzenberger, [<reflink idref="bib56" id="ref163">56</reflink>]), this topic has barely been examined empirically. The comparison of the two regression analyses in this study reveals discrepancies in some strategies (e.g., "questioning") as well as commonalities (e.g., "motivating and encouraging") between the two analyses regarding successful problem-solving and knowledge representation. In addition, the ONA positioning provides a new way of categorizing tutoring strategies in terms of their openness and action provocation. These findings could provide insights into forming a theory of tutoring strategies with respect to students' knowledge representation in asynchronous online mathematical discussions.</p> <p>Second, methodologically, this study is a pioneer work in using ONA, which is a rising methodology that has been advanced from ENA. This study is one of the first few attempts to use ONA to analyze educational data, following after Fan et al. ([<reflink idref="bib17" id="ref164">17</reflink>]), who newly introduced the method by analyzing online learning log data to illustrate self-regulated learning patterns. The present study utilizes annotated language data and provides a comprehensive interpretation of the ONA results from four aspects, including node size (frequency), directed edges (sequences), inner circles (self-transition), and node position (qualitative meaning) (Fan et al., [<reflink idref="bib17" id="ref165">17</reflink>]; Tan et al., [<reflink idref="bib74" id="ref166">74</reflink>]), alongside empirical data analysis of tutoring dynamics in online mathematical discussions.</p> <p>Lastly, this study provides a few practical implications. First, the findings could guide the design of tutoring strategies for human tutors (both adult and peer tutors) as well as pedagogical agents, such as artificially intelligent tutors. By leveraging a large dataset from an online math discussion platform over eight years, the study was able to produce robust findings that highlighted discrepancies between the pedagogical impacts of tutoring strategies and their rate and pattern of application in the educational setting. For example, the study reveals that while "motivating and encouraging" is identified as the most crucial strategy for effective discussions, it is paradoxically underutilized in practice. Such findings could provide insights into the training of novice or peer tutors or designing the conversation of intelligent tutoring systems. Moreover, this research further advances the potential to leverage learning analytics to enhance the learning experiences in online discussions or tutoring. As we found the ordered network patterns of discussions from the most effective (i.e., G1) to the least effective set of discussions (i.e., G4), this study highlights the feasibility of using ONA and its visualizations to evaluate the effectiveness of online tutoring discussions in the real world. This approach could form the basis of a system to deliver real-time information to teachers through a well-designed dashboard, which provides a visualization of the ongoing discussions and suggestions on how to improve the use of tutoring strategies.</p> <hd id="AN0189590678-20">Limitations and Future Directions</hd> <p>This study was carried out with certain limitations. First, this preliminary analysis evaluated a broad range of tutoring strategies; a more granular approach would allow a deeper understanding of which component within each strategy contributes to the discussion success and student's knowledge representation. For example, while we created the label "questioning" to encompass multiple types of questions, questions could further be classified into several levels based on existing taxonomies (Bloom & Krathwohl, [<reflink idref="bib7" id="ref167">7</reflink>]), such as simple questions and higher-order questions (Roscoe & Chi, [<reflink idref="bib61" id="ref168">61</reflink>]). Likewise, "feedback," which is shown to be the most important factor in both success and knowledge representation, actually comprises several different types of feedback, such as simple feedback and elaborated feedback (Meyer et al., [<reflink idref="bib44" id="ref169">44</reflink>]) or goal-directed feedback and reason-for-the-error feedback (McKendree, [<reflink idref="bib42" id="ref170">42</reflink>]). If operationalized within our analysis, these different types might show different educational effects. Therefore, based on the exploratory results from this paper, our future studies will adopt a more granular coding scheme to annotate and analyze each strategy in more detail.</p> <p>In addition, this study focused on tutors' utterances to annotate the tutoring strategies used. However, previous studies such as Van de Pol et al. ([<reflink idref="bib57" id="ref171">57</reflink>]) point out that it is insufficient to only annotate tutors' utterances without considering students' responses. Although our study did include students' utterances in the annotation scheme, our annotation focused on students' knowledge representation rather than how students reacted to the tutors' utterances. Future studies could investigate students' utterances in response to the tutoring strategies to dig deeper into the interactive dynamics. These efforts might also incorporate log data to investigate students' actions taken in response to tutoring strategies within the online learning platform.</p> <p>Third, our dataset did not represent tutors' metacognitive support strategies comprehensively. Metacognitive support refers to the strategies to help learners reflect on and regulate overall learning processes (Flavell, [<reflink idref="bib19" id="ref172">19</reflink>]). Even though it includes regulatory strategies, such as redirecting students from off-topic conversations or reminding students of the learning objectives and problem-solving tasks (coded as "maintaining discussions" in our study) (Van de Pol et al., [<reflink idref="bib57" id="ref173">57</reflink>]), it does not fully encompass tutors' metacognitive support strategies (Molenaar et al., [<reflink idref="bib45" id="ref174">45</reflink>]; Flavell, [<reflink idref="bib19" id="ref175">19</reflink>]). Previous study emphasizes tutors to help learners reflect on what they have learned and how to apply what they have learned to other situations (Topping et al., [<reflink idref="bib76" id="ref176">76</reflink>]). However, as previous research has also admitted, this type of metacognitive support is not easy for tutors to demonstrate in a tutoring situation (Topping et al., [<reflink idref="bib76" id="ref177">76</reflink>]). Along with this discussion, our dataset did not include enough utterances that indicate the use of reflective support. Thus, our study had a limited representation of metacognitive support with "managing discussion" only.</p> <p>Fourth, this study focused on tutoring strategies as the central variables impacting discussions' effectiveness (i.e., success and knowledge representation). However, in reality, there could be many other compounding factors to both dimensions of effectiveness, such as differences in math concepts, problem type, or difficulty level. While we tried to control for students' demographics, knowledge, and tutor's expertise in the regression analysis, we could not consider specific contexts of math problems due to our limited dataset. Future studies can more deeply consider problem context in measuring the effectiveness of mathematical discussions.</p> <p>Lastly, we observed significant effects of students' demographic backgrounds and tutor types on the effectiveness of mathematical discussions. Although these variables were not the primary focus of this study and were controlled for in our regression analysis, the findings suggest noteworthy implications. Future research could further explore the relationship between students' and tutors' characteristics and the effectiveness of mathematical discussions.</p> <hd id="AN0189590678-21">Author Contribution</hd> <p>Yukyeong Song conceived the main conceptual ideas, led the whole process including data analysis, interpretated findings, and wrote the manuscript. Chenglu Li collaboratively conceived the main conceptual ideas, analyzed the data, collaboratively interpretated findings, and wrote the manuscript. Yingbo Ma contributed writing the manuscript and analyzing the data. Bailing Lyu, Wangda Zhu, and Hai Li contributed to writing of the manuscript. Wanli Xing supervised the research process and collaboratively conceived the research ideas. All authors discussed the results and commented on the manuscript. All authors read and approved the final manuscript.</p> <hd id="AN0189590678-22">Funding</hd> <p>The research reported here was supported by the Institute of Education Sciences, US Department of Education, through Grant R305C160004, to University of Florida and UF Presidential Strategic Funding award. The opinions expressed are those of the authors and do not represent the views of the Institute of Education Sciences.</p> <hd id="AN0189590678-23">Availability of Data and Materials</hd> <p>The data set was collected with IRB approval from the University of Florida. These data will only be made available to other researchers if specific requests for amendments are made to the current approvals and will be considered on a case-by-case basis.</p> <hd id="AN0189590678-24">Declarations</hd> <p></p> <hd id="AN0189590678-25">Ethical Approval</hd> <p>This study received ethical approval from the University of Florida's Institutional Review Board (IRB No. IRB202201770.).</p> <hd id="AN0189590678-26">Informed Consent</hd> <p>No personal identifiers were reported in this study.</p> <hd id="AN0189590678-27">Consent to Participate</hd> <p>This study received informed consent from all participants.</p> <hd id="AN0189590678-28">Consent for Publication</hd> <p>The author accepts responsibility for releasing this material to be published.</p> <hd id="AN0189590678-29">Conflict of Interest</hd> <p>The authors declare no competing interests.</p> <hd id="AN0189590678-30">Statement Regarding Research Involving Human Participants and/or Animals</hd> <p>No personal identifiers were reported in this study.</p> <hd id="AN0189590678-31">Publisher's Note</hd> <p>Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p> <ref id="AN0189590678-32"> <title> References </title> <blist> <bibl id="bib1" idref="ref97" type="bt">1</bibl> <bibtext> Alin A. 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  Label: Title
  Group: Ti
  Data: Exploring Effective Tutoring Strategies in Asynchronous Online Mathematical Discussions: Insights from Ordered Network Analysis
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  Label: Language
  Group: Lang
  Data: English
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Yukyeong+Song%22">Yukyeong Song</searchLink> (ORCID <externalLink term="http://orcid.org/0000-0002-4084-2734">0000-0002-4084-2734</externalLink>)<br /><searchLink fieldCode="AR" term="%22Chenglu+Li%22">Chenglu Li</searchLink><br /><searchLink fieldCode="AR" term="%22Yingbo+Ma%22">Yingbo Ma</searchLink><br /><searchLink fieldCode="AR" term="%22Bailing+Lyu%22">Bailing Lyu</searchLink><br /><searchLink fieldCode="AR" term="%22Wangda+Zhu%22">Wangda Zhu</searchLink><br /><searchLink fieldCode="AR" term="%22Hai+Li%22">Hai Li</searchLink><br /><searchLink fieldCode="AR" term="%22Wanli+Xing%22">Wanli Xing</searchLink>
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  Data: <searchLink fieldCode="SO" term="%22Journal+of+Science+Education+and+Technology%22"><i>Journal of Science Education and Technology</i></searchLink>. 2025 34(5):1143-1163.
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  Data: Springer. Available from: Springer Nature. One New York Plaza, Suite 4600, New York, NY 10004. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-460-1700; e-mail: customerservice@springernature.com; Web site: https://link.springer.com/
– Name: PeerReviewed
  Label: Peer Reviewed
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  Data: Y
– Name: Pages
  Label: Page Count
  Group: Src
  Data: 21
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  Label: Publication Date
  Group: Date
  Data: 2025
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  Data: Institute of Education Sciences (ED)
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  Data: R305C160004
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  Data: Journal Articles<br />Reports - Research
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  Data: <searchLink fieldCode="EL" term="%22Secondary+Education%22">Secondary Education</searchLink>
– Name: Subject
  Label: Descriptors
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Tutoring%22">Tutoring</searchLink><br /><searchLink fieldCode="DE" term="%22Asynchronous+Communication%22">Asynchronous Communication</searchLink><br /><searchLink fieldCode="DE" term="%22Electronic+Learning%22">Electronic Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Instruction%22">Mathematics Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Discussion+%28Teaching+Technique%29%22">Discussion (Teaching Technique)</searchLink><br /><searchLink fieldCode="DE" term="%22Instructional+Effectiveness%22">Instructional Effectiveness</searchLink><br /><searchLink fieldCode="DE" term="%22Knowledge+Level%22">Knowledge Level</searchLink><br /><searchLink fieldCode="DE" term="%22Problem+Solving%22">Problem Solving</searchLink><br /><searchLink fieldCode="DE" term="%22Tutors%22">Tutors</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Students%22">Secondary School Students</searchLink><br /><searchLink fieldCode="DE" term="%22Educational+Strategies%22">Educational Strategies</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+School+Mathematics%22">Secondary School Mathematics</searchLink>
– Name: DOI
  Label: DOI
  Group: ID
  Data: 10.1007/s10956-025-10233-0
– Name: ISSN
  Label: ISSN
  Group: ISSN
  Data: 1059-0145<br />1573-1839
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Online mathematical discussions provide numerous educational benefits, such as supporting collaborative knowledge construction, increasing learner engagement, and enhancing students' higher-order thinking. Yet, the effectiveness of these discussions is not always guaranteed; rather, it is highly dependent on the use of tutoring strategies. While previous studies investigated the impact of tutoring strategies on the effectiveness of discussions, they mostly focused on the success of problem-solving, and less attention has been paid to how students represented their knowledge during the discussions. This study investigated the relationship between tutoring strategies and the effectiveness of discussions, operationalized as the level of student knowledge representation as well as the success of problem-solving. We retrieved textual data from 2318 tutor-student discussion threads at a secondary school online math learning platform and annotated them with the coding schemes of problem-solving success, students' knowledge representation, and tutoring strategies. Then, we conducted regression analyses to investigate each strategy's impact on the discussion's success and students' knowledge representation. We also conducted an ordered network analysis (ONA) to visualize the sequential networks of the tutoring strategies among four groups of dialogues categorized by discussion's problem-solving success and knowledge representation. Findings suggest that "motivating and encouraging" and "feedback" are the most effective tutoring strategies for both successful problem-solving and knowledge representation, while "direct intervention" is effective for success but minimally influential for knowledge representation. On the other hand, "questioning" was found to be important in promoting students' knowledge representation while showing minimal impact on problem-solving success. The findings provide theoretical, methodological, and practical implications for promoting effective tutoring strategies in online mathematical discussions.
– Name: AbstractInfo
  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: CodeSource
  Label: IES Funded
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  Data: Yes
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2026
– Name: AN
  Label: Accession Number
  Group: ID
  Data: EJ1497451
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ1497451
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s10956-025-10233-0
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 21
        StartPage: 1143
    Subjects:
      – SubjectFull: Tutoring
        Type: general
      – SubjectFull: Asynchronous Communication
        Type: general
      – SubjectFull: Electronic Learning
        Type: general
      – SubjectFull: Mathematics Instruction
        Type: general
      – SubjectFull: Discussion (Teaching Technique)
        Type: general
      – SubjectFull: Instructional Effectiveness
        Type: general
      – SubjectFull: Knowledge Level
        Type: general
      – SubjectFull: Problem Solving
        Type: general
      – SubjectFull: Tutors
        Type: general
      – SubjectFull: Secondary School Students
        Type: general
      – SubjectFull: Educational Strategies
        Type: general
      – SubjectFull: Secondary School Mathematics
        Type: general
    Titles:
      – TitleFull: Exploring Effective Tutoring Strategies in Asynchronous Online Mathematical Discussions: Insights from Ordered Network Analysis
        Type: main
  BibRelationships:
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      – PersonEntity:
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            NameFull: Yukyeong Song
      – PersonEntity:
          Name:
            NameFull: Chenglu Li
      – PersonEntity:
          Name:
            NameFull: Yingbo Ma
      – PersonEntity:
          Name:
            NameFull: Bailing Lyu
      – PersonEntity:
          Name:
            NameFull: Wangda Zhu
      – PersonEntity:
          Name:
            NameFull: Hai Li
      – PersonEntity:
          Name:
            NameFull: Wanli Xing
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2025
          Identifiers:
            – Type: issn-print
              Value: 1059-0145
            – Type: issn-electronic
              Value: 1573-1839
          Numbering:
            – Type: volume
              Value: 34
            – Type: issue
              Value: 5
          Titles:
            – TitleFull: Journal of Science Education and Technology
              Type: main
ResultId 1