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Peers4U: Designing Learner-Centered Virtual Peers for Children's Multimodal Mathematics Learning

Zhi Zheng, Binglin Liu, Weihao Chen, Lan Luo, Yu Mei, Jie Cai, Chun Yu, Yuanchun Shi

arXiv:2610.37238v1cs.HC

TL;DR

Early mathematics learning involves concrete and visual representations, yet virtual peers often center on conversation, and little is known about young children’s participation in open virtual-peer learning. Peers4U combines inspectable multimodal peer solutions with learner-centered, mixed-initiative discussion. In a study with 22 children and two experts, its topic orchestration significantly outperformed a persona-centered baseline, while children also created new artifacts and solutions.

  • Problem

    Conversational virtual peers and limited evidence about young children’s participation leave open how to support multimodal peer learning in early mathematics.

    Source: §1 · p. 2, §2.3 · p. 4

  • Method

    Peers4U assigns a personalized group of peers with inspectable multimodal solutions and supports learner- and peer-initiated discussion along a pedagogical progression.

    Source: §1 · p. 2

  • Results

    Learner-centered topic orchestration received 4.69/5 for pedagogical appropriateness and significantly outperformed a persona-centered baseline.

    Source: §1 · p. 3

  • Takeaways & Limitations

    Children can both learn from and teach virtual peers, including by creating artifacts to share strategies or demonstrate inspired ideas.

    Source: §1 · p. 3, §6.2.2 · p. 19

    The small between-subjects study, without a learning control condition or delayed measures, cannot establish durable learning gains or transfer.

    Source: §8 · p. 24

Abstract

from arXiv · show

In early mathematics, children learn abstract concepts through concrete representations, such as manipulating objects, drawing, and speaking. Learning with peers can enrich this process by exposing children to diverse strategies and enabling them to exchange ideas through interaction. We realized this potential with virtual peers in Peers4U, a multimodal learning system to enhance children's mathematical conceptual understanding. Virtual peers driven by LLMs are personalized to the learner's cognitive level and assigned multimodal solutions with inspectable processes. During learning, peers engage in mixed-initiative interactions by responding, initiating topics, and advancing discussions along a pedagogical progression. A user study with 22 children and two experts showed our learner-centered topic orchestration significantly outperformed a persona-centered baseline, and children spontaneously authored new artifacts to demonstrate inspired ideas or share their own strategies, producing significantly more solutions when grouped with more Leading Peers. We contribute design insights for multimodal, learner-centered virtual peer systems.

1 Introduction

Peers4U addresses the mismatch between conversational virtual peers and early mathematics learning, where children use concrete, visual, and manipulable representations. It combines multimodal peer artifacts with learner-centered interaction, and its study reports stronger pedagogical ratings than a persona-centered baseline.

Motivation

  • Children ground abstract mathematical concepts in concrete experiences, using activities such as bundling objects, drawing quantities, and connecting them to written numerals.Learning across manipulating, drawing, writing, and speaking supports conceptual understanding and representational fluency.Source: §1 · p. 2
  • Peer learning can expose children to diverse strategies and representations, giving them opportunities to explain reasoning, compare approaches, exchange ideas, and build on understanding.These opportunities motivate exploring virtual peers as part of multimodal mathematics learning.Source: §1 · p. 2

Research gap

  • Existing virtual-peer systems often target older learners or other domains and center interaction on text or voice, leaving early mathematics’ visual and manipulable needs poorly served.The paper also identifies limited evidence about how young children participate and learn in open virtual-peer environments.Source: §1 · p. 2

Formative study

  • The system’s design was informed by four challenges identified in probe sessions with eight children and interviews with five experienced teachers.The challenges concerned shareable artifacts, peer difference balanced with understandability, varied participation preferences, and the need for a coherent learning progression.Source: §1 · p. 2

System design

  • Peers4U presents a personalized group of four peers whose inspectable multimodal solutions support mixed-initiative discussion and learner-created artifacts.Learners can discuss specific artifacts and share new solutions, while peers can respond, initiate topics, and advance discussion along a pedagogical trajectory.Source: §1 · p. 2

Study findings

  • In a study with 22 children and two experts, learner-centered topic orchestration received 4.69/5 for pedagogical appropriateness and significantly outperformed a persona-centered baseline.Children also authored new artifacts and produced significantly more additional solutions in a Leading Group; willingness to learn with the same peers again was significantly greater in a Mixed Group.Source: §1 · p. 3

Contributions

  • The paper frames its contributions as threefold, identifying core challenges and deriving four design goals for virtual peers in children’s mathematics learning.The supplied contribution passages also describe the system paradigm, empirical findings, and design implications.Source: §1 · p. 3
  • The paper contributes the design and implementation of an artifact-mediated, multi-peer learning paradigm combining mixed initiative with learner-centered pedagogical orchestration.It also reports children’s interaction patterns and transferable design implications for virtual peer learning systems.Source: §1 · p. 3

2 Related Work

Prior work motivates combining multiple mathematical representations with peer learning, but multimodal systems often lack peer interaction and virtual peers commonly rely on conversation. Peers4U addresses this gap by exploring multimodal virtual peers for children’s mathematics learning.

2.1 Theoretical Foundations: Multiple Representations and Peer Learning in Mathematics

  • Multiple representations support children’s construction of abstract mathematical concepts, while peer learning offers opportunities to observe diverse strategies and acquire them through interaction.The cited frameworks emphasize translating among manipulatives, drawings, spoken language, and written symbols.Source: §2.1 · p. 3

2.2 Multimodal Interactive Systems for Mathematics Learning

  • Digital mathematics systems support interconnected representations and virtual manipulatives, but are predominantly designed for solo learning rather than peer interaction.Physical and XR systems ground learning in embodied experience, but remain constrained by physical artifacts and particular topics.Source: §2.2 · p. 4

2.3 Virtual Peers in Learning Environments

  • Virtual-peer research includes single and multiple peers, but conversation-centered interaction leaves their role in multimodal early mathematics underexplored.The paper explores virtual peers embedded in a multimodal interactive environment to foster cognitive friction and learning opportunities.Source: §2.3 · p. 4, §2.2 · p. 4

3 Formative Study

The formative study combined child probe sessions with teacher interviews to derive design goals for multimodal virtual peers in early mathematics. Its findings emphasize shareable artifacts, calibrated peer differences, flexible participation, and pedagogically progressive interaction.

3 Formative Study

  • The study synthesized child and teacher evidence into four design goals after observing children’s interactions with an exploratory probe and interviewing experienced teachers.The probe kept peer social behaviors simple while offering an open multimodal solution space; the two study components examined children’s interaction and teachers’ pedagogical perspectives.Source: §3 · p. 5, §3.1 · p. 5, §3.2 · p. 5

3.2 Part 1: Child Probe Sessions

  • The probe let children choose mathematics tasks, create multimodal solutions, inspect peer solutions, replay their construction, and chat with associated peers.The sessions used nine tasks across three categories, and researchers observed children’s behavior and occasionally varied peer-solution presentation configurations.Source: §3.2 · pp. 5–6, Figure 2 · p. 5

3.3 Part 2: Teacher Interviews

  • Teacher interviews elicited views on early-math peer interaction, critiques of the probe, and pedagogical interpretations of children’s observed behaviors.Five experienced elementary mathematics teachers participated in semi-structured interviews.Source: §3.3 · p. 6

3.4 Data Collection and Analysis

  • Researchers analyzed child-session and teacher-interview data separately before integrating themes to connect children’s behavior with teachers’ interpretations.The team used codebook thematic analysis, independently open-coded subsets, and reviewed candidate themes against the full datasets.Source: §3.4 · pp. 6–7

3.5 Findings and Design Goals

  • Probe sessions showed that children used multimodal artifacts to observe, question, explain, and respond, and often asked about specific actions in peers’ construction processes.Children also wanted to share their own solutions and sometimes created new ones after viewing peers’ approaches; teachers emphasized making mathematical thinking visible.Source: §3.5 · p. 7
  • Peer solutions that were too similar were often skipped, while novel methods sparked curiosity in seven children; overly large cognitive gaps sometimes led to misinterpretation.Teachers recommended an intermediate ladder from understandable methods toward unfamiliar ones, and peer levels can serve distinct purposes: inspiration, relatability, correction, and confidence-building.Source: §3.5 · p. 7
  • Children differed substantially in participation: some sent over 10 messages per task while others sent no more than one, and teachers noted that listening could suit introverted learners.The resulting goal was flexible initiative and participation roles, allowing peers to respond, initiate topics, move discussion forward, or conclude it when learners are passive.Source: §3.5 · p. 8
  • Teachers cautioned that open peer interaction alone may not yield a learning trajectory, recommending initial idea formation, progressive exposure to methods, and later comparison of approaches.The corresponding goal is to orchestrate topics around learners’ current understanding and deepen discussions progressively according to cognitive levels.Source: §3.5 · p. 8

4 System Design

Peers4U organizes multimodal artifact exchange around each learner’s demonstrated understanding. Its peers respond and initiate discussions that progress through pedagogically structured topics.

4.2 Multimodal Artifact Creation and Peer Interaction (DG1)

  • Learners can create and share multimodal solutions, inspect peers’ artifacts and construction processes, and discuss them in group or private chats.The workspace supports virtual manipulatives, drawing, writing, and speaking.Source: §4.2 · p. 9

4.3.1 Artifact Analysis and Cognitive Mapping.

  • Initial solution artifacts are mapped to task-specific competencies in a cognitive graph, forming a profile of the learner’s demonstrated understanding.The system analyzes the full multimodal problem-solving process to identify behavioral evidence and map it to the graph.Source: §4.3.1 · pp. 9–10

4.3.2 Assigning Artifacts to Peers.

  • The system constructs heterogeneous peer profiles and assigns each peer a diverse set of solutions consistent with its profile.Leading Peers offer strategies the learner has not demonstrated; Struggling Peers have more incomplete or flawed solutions that create opportunities for correction and learning-by-teaching.Source: §4.3.2 · pp. 10–11

4.4 Learning Topic Initiation and Progression (DG3, DG4)

  • Peers4U’s learner-centered orchestration coordinates peer behavior around the learner’s progression rather than letting each peer pursue a persona-driven agenda.The design combines adaptive conversational agency with progressive topic orchestration.Source: §4.4 · p. 12

4.4.1 Adaptive Conversational Agency via Implicit Interaction.

  • Learner activity modulates conversational agency: peers respond to messages, remain silent during engaged activity, and may initiate or advance topics when the learner is idle.Reactive and follow-up agents can also conclude a topic when its goal is reached or it expires.Source: §4.4.1 · p. 12

4.4.2 Orchestrating Progressive Learning Topics.

  • Topic types progress from lower-demand explanation and probing to deeper analysis connecting solutions, then conclude with an evaluation discussion.The Topic Agent selects topics based on the learner’s demonstrated understanding, peer cognitive configurations, and prior chat history; facilitation messages support topics requiring pedagogical orchestration.Source: §4.4.2 · pp. 12–13

5 User Study

The study examined children’s engagement and peer-composition differences in Peers4U, then asked expert teachers to evaluate its generated topics. It combined an in-person between-subjects study with a post-hoc paired-topic assessment.

5 User Study

  • The exploratory study involved 22 children, while two expert teachers assessed the pedagogical appropriateness of generated topics.The study addressed children’s engagement and peer composition; the post-hoc evaluation addressed topic appropriateness.Source: §5 · p. 13, §5.1 · p. 13

5.2 Study Setup

  • Children were assigned to either a Mixed Group with two Leading and two Struggling Peers or a Leading Group with four Leading Peers.Each condition included 11 children, and peer profiles and artifacts were personalized from the child’s initial solutions.Source: §5.2 · p. 14

5.3 Procedure

  • After a tutorial and task-tier selection, each child created initial solutions, explored personalized peers, completed a questionnaire and paired post-test, and took part in an interview.The researcher’s assistance was limited to reading text, correcting speech-recognition transcripts, and answering basic interface questions.Source: §5.3 · p. 14

5.4 Data Collection and Analysis

  • The researchers analyzed logs, questionnaires, messages, artifacts, and interviews using descriptive, statistical, and qualitative methods.Between-condition outcomes used two-sided exact Mann–Whitney U tests, and message-level response comparisons used user-stratified exact permutation tests.Source: §5.4 · p. 15

5.5 Post-hoc Expert Evaluation

  • Two expert mathematics teachers independently and blindly rated paired learner-centered and persona-centered topics, reconciling differences exceeding one point.They rated instructional value and fit with the learner and interaction on a five-point scale; ratings of 3 or below required an inappropriateness reason.Source: §5.5 · p. 15

6 Findings

Children’s participation and artifact creation varied across Peers4U interactions and peer compositions. Experts rated learner-centered topics more appropriate than persona-centered alternatives, while identifying different sources of inappropriateness in each.

6.1 Children’s Engagement and Experience in Multimodal Peer Learning (RQ1)

  • 11 children voluntarily created 29 additional artifacts during peer interaction, often to share a method, respond to help-seeking, or explore an idea raised by peers.Eight artifacts resembled a previously viewed peer solution, two followed chat suggestions, and six improved on the child’s earlier work.Source: §6.1.2 · p. 17
  • Children’s participation styles ranged from passive observation to highly active engagement, and most sent more responsive than self-initiated messages.All 22 children participated; 21 completed all system-orchestrated topics, and 73.8% of messages concerned mathematical learning content.Source: §6.1.1 · p. 16, §6.1.3 · p. 18
  • Across 717 response-eligible messages, the response rate was 33.3%; questions and message framing were associated with differing response rates.Among 106 eligible group topics, adaptive follow-ups raised cumulative participation from 29.2% after the initial message to 68.9% after two follow-ups.Source: Figure 8 · p. 17, §6.1.3 · p. 18

6.2.1 Leading Groups Elicited More Additional Artifact Creation. Children in Condition B (Leading Group)

  • Children in the Leading Group created significantly more additional artifacts than those in the Mixed Group (p = .037).Eight Leading Group children created 22 artifacts, compared with three Mixed Group children who created seven; this pattern was consistent with greater exposure to Leading Peers providing material or motivation for solution creation.Source: §6.2.1 · p. 18

6.2 Engagement and Experience across Peer Compositions (RQ2)

  • Mixed Groups had more system-initiated private topics and private-chat messages, and children were more willing to learn with the same peers again.These differences were significant for private topics (p = .006), private-chat messages (p = .029), and willingness to learn again (p = .015).Source: §6.2.2 · p. 19

6.3 Pedagogical Appropriateness of Generated Learning Topics (RQ3)

  • Learner-centered topics received significantly higher expert appropriateness ratings than persona-centered alternatives.Learner-centered topics averaged 4.69 ± 0.58, and 91.7% were rated appropriate by both experts.Source: §6.3 · p. 20, Figure 10 · p. 20
  • Inappropriate learner-centered topics more often reflected low-quality artifacts or artifact misinterpretation, whereas persona-centered topics often gave learners little role or exceeded their cognitive level.Of 13 inappropriate learner-centered topics, six involved low-quality artifacts and five had artifact misalignments; 72.1% of 43 inappropriate persona-centered topics gave the learner little role.Source: §6.3 · p. 20

7 Discussion

The discussion argues that peer learning should be grounded in shareable mathematical artifacts and adapt to children’s participation styles, while deliberately guiding interaction toward productive learning. It also identifies artifact credibility and cognitive diversity as constraints on extending the approach.

7.1.1 Multimodal Solution Artifacts as the Medium of Peer Interaction. Existing virtual peers are often designed

  • Artifact-mediated interaction supported cycles of observing, explaining, imitating, modifying, and sharing solutions, with children directing inquiries at specific actions, symbols, and strategies.The authors argue that artifacts should be primary shared objects of interaction, not merely additions to a chat interface.Source: §7.1.1 · p. 21

7.1.2 Flexible Participation across Initiating, Responding, and Observing. Our findings highlight multiple

  • Flexible participation means adapting invitations and timing to whether children initiate, respond, or observe; specific follow-ups drew more responses than open group questions.The system remained silent during active learning and increased initiative after sustained operational silence, which the authors caution is ambiguous.Source: §7.1.2 · pp. 21–22

7.1 Supporting Peer Interaction through Multimodal Artifacts and Flexible Participation

  • Children’s emotional reactions varied, including tension, impatience with ongoing messages, and anger after a peer praised another approach.The authors recommend affect-aware interaction and adapting message timing, frequency, and content, while preserving privacy in any external sensing.Source: §7.1.3 · p. 22

7.2 Turning Multi-Peer Interaction into Productive Mathematics Learning

  • Heterogeneous peers can support reciprocal learning, with roles shifting locally as peers offer unfamiliar strategies or ask the learner for help.Children did not always recognize designed Leading Peers as more capable; social signals such as repeated questions could instead make them seem less knowledgeable.Source: §7.2.1 · p. 23, §7.2.2 · p. 23

7.2.3 Orchestrating Peer Interaction along a Cognitive Progression. Pedagogical orchestration remains neces-

  • Persona-led topic generation could sound socially plausible yet fail to give the learner a clear role or match their understanding; orchestration can instead progress from observation toward creation and transfer.The authors frame productive learning as also depending on reciprocity and children recognizing the mathematical value of peers’ methods.Source: §7.2 · p. 22, §7.2.3 · pp. 23–24

7.3 Extending Artifact-Mediated Peer Learning to Broader Educational Contexts

  • Extending artifact-mediated peer learning beyond early mathematics may be constrained by the effort of obtaining credible, cognitively diverse artifacts.Peers4U used authentic child-produced artifacts and researcher-authored supplements after direct LLM generation often yielded overly polished, mature processes.Source: §7.3 · p. 24

8 Limitations and Future Work

The authors identify limits on generalizing the findings, establishing learning effectiveness, and validating peer construction and artifact assignment. The appendix also describes the formative study’s task coverage.

8 Limitations and Future Work

  • Findings are constrained to 22 children aged 6–8 from one Chinese city and one mathematics topic, in a single researcher-present laboratory session.That session cannot reveal how participation, peer relationships, or interest evolve over time; the authors call for longitudinal work across populations, topics, and everyday settings.Source: §8 · p. 24
  • Immediate pre–post tasks and small between-subjects conditions provide limited evidence of learning effectiveness, without a learning control or delayed measures to establish durable gains or transfer.The persona-centered baseline was assessed offline by two experts and was not used in children’s interactions, leaving online effects on participation and learning unknown.Source: §8 · p. 24
  • The pedagogical value of VLM- and rule-based peer profiles and artifact assignments remains unvalidated, and expert-identified low-quality artifacts require stronger curation.Group size and artifact exposure were held at four peers and approximately ten artifacts, so their effects on social presence and cognitive load remain unknown.Source: §8 · p. 24

A.1 Mathematics Content and Tasks

  • The formative study covered three mathematics topics at three difficulty tiers, yielding nine tasks.Table 3 presents the mathematics content and tasks used in that study.Source: §A.1 · p. 29, Table 3 · p. 30

A.2 Probe Implementation

The probe varied peer-solution configurations and used an artifact-grounded chat agent to support children’s exploration and interaction.

A.2 Probe Implementation

  • The probe compared developmental, diversity-maximizing, and researcher-selected configurations for presenting peer solutions.Developmental selection prioritized artifacts near a child’s next steps using a task-specific cognitive graph; diversity selection chose behaviorally dissimilar artifacts; researcher-selected sets could include flawed solutions marked as needing help.Source: §A.2 · p. 30
  • Developmental and diversity configurations initially showed four artifacts and added two when researchers requested more.The developmental estimate updated as children viewed artifacts; researcher-selected flawed solutions opened with a scripted request for assistance.Source: §A.2 · p. 30
  • One Gemini 3 Flash Preview chat agent generated concise persona-aligned replies using the task, peer artifact process and analysis, and conversation history.Children’s speech was transcribed with streaming ASR, while peer replies were spoken using ElevenLabs; original child narration pitch was shifted for de-identification during replay.Source: §A.2 · p. 30

B.1 Artifact Analysis Agents

The appendices describe agents for interpreting mathematical artifacts, constructing personalized peer groups and portfolios, and adapting conversational initiative.

B.1 Artifact Analysis Agents

  • Two VLM agents described each artifact’s solution process and mapped detected mathematical behaviors to competencies in a task-specific cognitive graph.An additional outlier-diagnosis call handled behaviors outside predefined rubrics; the outputs informed peer profiles and artifact assignment.Source: §B.1 · p. 31

B.2 Personalized Peer Construction

  • Peer profiles were generated from prerequisite-consistent cognitive-graph states, while artifact assignment covered mastery boundaries, learning paths, and target competencies.Assignment then added role-consistent incomplete or flawed artifacts and supplemented portfolios to meet minimum coverage and group-size constraints; struggling peers could master foundational competencies the learner had not shown.Source: §B.2 · p. 32

B.3 Adaptive Conversational Agency

  • The activity monitor used four intensity levels to estimate interruption cost, with more intensive activity extending the system’s wait before proactive messaging.Sustained silence could trigger topic-grounded pickup invitations, followed by a brief closing message if silence continued; follow-ups were withheld when unread messages remained.Source: §B.3 · p. 32

C.1 Child Participants

  • Appendix C.1 includes participant demographics and examples of personalized peer construction across tasks and group compositions.The appendix also lists four message-generation agents used in the formal system.Source: Figure 11 · p. 33, Table 8 · p. 34, Table 7 · p. 34

C.2 Mathematics Content and Tasks

The study focused on subtraction with regrouping, using tasks at three content levels and a repository of child- and researcher-contributed solution artifacts. Post-study measures covered peer perceptions, social pressure, learning experience, and children’s reasons for their responses.

C.2 Mathematics Content and Tasks

  • The user study focused on subtraction with regrouping, with each participant completing one of three content levels and an initial task and corresponding quiz task.The artifact repository contained 130 retained and preprocessed artifacts: 92 from OpenCD, 6 from the formative study, and 32 authored by researchers.Source: §C.2 · p. 34
  • Across participants, 62 unique artifacts were assigned to at least one peer portfolio, drawn from the tiered artifact pools.The assigned artifacts included 18 of 45 in Tier 1, 19 of 48 in Tier 2, and 25 of 37 in Tier 3.Source: §C.2 · p. 35

C.3 Post-study Questionnaire and Interview

  • Questionnaire items used labeled five-point pictorial response scales, and researchers could read or clarify items without suggesting answers.Labels were customized to each construct while retaining an ordered negative-to-positive response.Source: §C.3 · p. 35
  • The questionnaire asked children to rate and rank peers’ likability and perceived mathematics level, including their own relative standing.It also asked about social pressure and compared this learning experience with regular classes on relaxation and interest.Source: §C.3 · p. 35
  • Children answered structured interview questions about learning new methods, teaching and seeking help, preferred methods, and how the experience compared with usual mathematics learning.Researchers used brief clarification prompts to elicit reasons or concrete examples.Source: §C.3 · p. 35

C.4 Analysis of Child-study Data

The researchers combined structured coding of messages and artifacts with question-guided interview analysis and descriptive and inferential quantitative analyses. A subset of system-generated messages was coded using GPT-5.6-sol and then reviewed by researchers.

C.4 Analysis of Child-study Data

  • Learner messages were coded for content domain and conversational role, with each response linked to the prior message it answered.Researchers jointly developed and reconciled the codebook, then one researcher coded the remaining messages and the second reviewed the complete coding.Source: §C.4 · p. 35
  • For non-learner messages, GPT-5.6-sol applied researcher-defined categorical codes, and researchers reviewed the resulting classifications.The codes covered learning relevance, question type, and the target of group-chat questions; channel, topic, and follow-up sequence came from system metadata.Source: §C.4 · pp. 35–36
  • Researchers coded pre- and post-test artifacts for representational forms, calculation strategies, and correctness, and classified positive changes between each child’s artifacts.Additional artifacts were analyzed alongside video and system logs to reconstruct preceding events, subsequent actions, and links to earlier artifacts or chat suggestions.Source: §C.4 · p. 36
  • Structured interview responses were organized by question, with recurring explanations and examples grouped within each question.Reported quotations were translated from Chinese into English.Source: §C.4 · p. 36
  • Log-derived behavioral measures and questionnaire responses were summarized descriptively, with between-condition and message-level comparisons analyzed using exact tests.Between-condition comparisons used tie-aware Mann–Whitney U tests and Cliff’s δ; message-level response comparisons used user-stratified permutation tests to account for messages nested within children.Source: §C.4 · p. 36

C.5.1 Evaluation Dataset and Persona-centered Baseline.

The post-hoc expert evaluation paired learner-centered topics from the study with persona-centered alternatives generated from the same preceding interaction context. Two experts independently rated blinded candidates before reviewing subsequent interaction trajectories, then reached consensus on discrepant ratings.

C.5.1 Evaluation Dataset and Persona-centered Baseline.

  • Each learner-centered topic was paired with a persona-centered candidate generated from the state immediately before that intervention, including task, available artifacts, and conversation history.The baseline used two sequential LLM calls: one selected a peer to initiate, and the other generated a topic and attached artifacts from that peer’s perspective.Source: §C.5.1 · p. 36
  • Experts reviewed candidate messages in randomized, blinded order, rating each for pedagogical appropriateness on a five-point scale.For ratings of 3 or below, they had to select a reason tag or provide an explanation; tags included difficulty, participation, profile consistency, misleading content, and repetition.Source: §C.5.2 · p. 36, Figure 12 · p. 37
  • Before independent review, experts calibrated their interpretations of the rating scale and reason tags by reviewing three participant sessions and discussing discrepancies.Researchers clarified criteria and procedural questions during calibration.Source: §C.5.2 · p. 37
  • The independent review covered 19 sessions and 133 intervention points, yielding 266 candidate messages; the experts’ mean absolute rating difference was 0.387.Both experts rated candidates before viewing the subsequent trajectory at each intervention point.Source: §C.5.2 · p. 37
  • In the consensus meeting, experts revisited messages with scores differing by more than one point, adjusted ratings to within one point, and retained all distinct reasons for inappropriateness.The resulting ratings were averaged for each message, and analysis covered all 22 participant sessions.Source: §C.5.2 · pp. 37–38

D.1 Statistical Details for Results Reported in the Main Text

The statistical details report expert ratings, child outcomes, and message response comparisons. Learner-centered topics received higher pedagogical appropriateness ratings than persona-centered alternatives; other reported comparisons include solution creation, peer willingness, and response rates.

D.1 Statistical Details for Results Reported in the Main Text

  • Across the four peer-pressure items, condition means ranged from 3.2 to 3.5 in Condition A and 3.5 to 4.2 in Condition B, with no significant differences.Children’s perceived peer mathematics levels and self-rankings also showed no significant between-condition differences.Source: §D.1 · p. 38
  • Three children in Condition A created 7 additional solutions, compared with 22 solutions created by eight children in Condition B; per-child counts were 0.6 ± 1.5 and 2.0 ± 1.7, respectively.The exact test yielded U_A=31.0, p=.0370, and Cliff’s δ=−.488.Source: §D.1 · p. 38
  • Children in Condition A selected 3.8 ± 0.6 peers to learn with again, compared with 2.5 ± 1.6 in Condition B; the exact test yielded U_A=94.0, p=.0152.Cliff’s δ was .554.Source: §D.1 · p. 38
  • Learner-centered topics scored 4.694 ± 0.585 versus 4.360 ± 0.784 for persona-centered alternatives; the estimated learner-centered advantage was β=0.338 (p=.0013).The paired rating comparison covered 157 topic rounds; the 95% CI for the estimated advantage was [0.148, 0.527].Source: §D.1 · p. 38
  • Among eligible cases, questions received responses in 187 of 442 cases (42.3%, 95% CI [37.8%, 47.0%]), compared with 52 of 275 non-question messages (18.9%, 95% CI [14.7%, 24.0%]).Source: §D.1 · p. 39
  • In group chat, closed-ended questions received responses in 74 of 183 eligible cases (40.4%), compared with 48 of 174 open-ended questions (27.6%).Wilson 95% CIs were message-level descriptive intervals and did not account for within-child clustering.Source: §D.1 · p. 39

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