Exploring AI Peer in Collaborative Mathematics Learning

Synthesis: Lin, Deng, Pan, Yu and Cristea ask what makes an AI agent recognizable as a peer rather than a tutor, and study it with seven expert researchers who each spent about twenty minutes collaboratively solving quadratic equations with an adaptive LLM-based agent — one with a Big Five-informed persona and motivational state modulation — followed by a structured interview. The central finding is that participants judged the agent almost entirely on its social behavior, not its mathematical capability. It read as a peer when it created a non-judgmental space, reasoned tentatively, showed appropriate imperfection, and respected the learner's pace; it read as a tutor when it agreed blindly, moved ahead, or disclosed the answer early. The paper's sharper conceptual point is that peer is an interactional accomplishment rather than a property an agent has, and that peer-likeness and peer-usefulness are not the same outcome — one participant found a mistake-prone peer likable while another found it useless. Six design dimensions come out of the analysis, and the study intentionally measures no learning outcomes.

Design and Study

The agent combines two adaptive layers: a Big Five personality configuration and motivational state modulation, layered on an LLM. It was developed against the participant-facing materials for quadratic functions, and a pilot with two educational-technology experts validated the scenario's clarity, the agent's behavioral realism and general usability; pilot data were excluded from analysis.

Seven researchers from user experience, learning sciences, educational technology and computer science, with 3 to over 20 years of experience, took part between December 2025 and January 2026. Each session ran about 30 minutes on an online meeting platform. Participants were told to take the perspective of a student learning quadratic functions, given the same background material the agent had, and asked to treat the agent as a classmate and reason collaboratively rather than expecting instruction or final answers. No conversational structure was imposed, so the interactions developed naturally. A structured interview followed, focused on how participants interpreted the agent's social role and authority, where the design dimensions appeared, and where collaboration broke down. The analysis was qualitative and thematic; the stated aim was to identify interactional patterns rather than to test outcomes.

Peer-Likeness, Element by Element

Safety without a human judge. The dominant theme was reduced social pressure. One participant contrasted the AI with a regular class where seeing others finish faster made them "anxious and ashamed," while with the AI there was no comparison; another said that because the agent was "not a real human being" they felt "less embarrassed" and "more comfortable making mistakes." Safety had two sources — the agent's non-human nature and the feeling of equality — and one participant reported that safety grew when the agent was framed as "your classmate... same level as you."

Imperfection as evidence of personhood. Peer-likeness was frequently established by the agent's own failures. One participant found it peer-like precisely because it was "not very clever" and made "stupid and simple mistakes," and another because it "did not show the solution directly" but "made some assumptions and asked for my idea." The counter-case is what makes the finding useful: another participant disliked an AI that was "as stupid as I am" and expected a peer to be "smarter than me." Peer-likeness and peer-usefulness came apart here.

Personality cuts both ways. One participant experienced the persona as "steady" and interested in their learning; another found it "surface level," reactive to input, and saw the agent "as a tool, not... with personality." Tone also misfired: an agent that said it was "feeling a bit unconcerned" produced anxiety, and agents described as "strict" or a "know-it-all" were read as teachers. Confidence and directive phrasing reliably shifted perception toward the tutor role.

Collaboration is control, not competence. Collaboration was described as guidance without takeover — "has the information but... gives you hints and lets you think and be part of the solution." The sense of teamwork collapsed when the agent moved too fast: one participant was "a little annoyed" when the agent "just gave me the right number" while they were still thinking, another felt "examined, not helped," and a third found it "very fixed on a direction of travel." Every route to the tutor role in this study ran through control of pace or direction rather than through the agent being right.

The Boundaries, and Six Design Dimensions

Two boundaries emerged. The first is memory: an agent that "claims I've said some things which I didn't" produced what one participant called a direct "breakdown in trust," and another was derailed at the start by the agent assuming an equation had already been introduced. The second is blind validation: participants were unsettled by agreement with incorrect ideas — "Is he agreeing because it's correct or because he doesn't know the correct answer?" — and worried it could "keep reinforcing those mistakes forever," while one judged this a design problem rather than an objection to AI peers as such.

• Emotional safety — learners can express uncertainty and make mistakes without fear of evaluation; avoid evaluative language and normalize hesitation and partial reasoning.
• Shared control — problem solving is jointly constructed and learner agency is preserved; avoid enforcing fixed sequences and let learners set pace and direction.
• Authority positioning — the agent is experienced as a social equal rather than an instructor; use tentative language and avoid a directive or corrective tone.
• Balanced uncertainty — the agent expresses hesitation while keeping internal coherence; signal doubt without defaulting to agreement.
• Memory consistency — the interaction reflects a stable shared history; avoid hallucinated references and keep local conversational coherence.
• Responsiveness to pace — the agent adapts to learners' timing and engagement; delay answers during exploration and slow down when confusion appears.

What this means for practice

• Educational technology developers. Stop optimizing the peer agent for correctness. The behaviors that produced a peer reading were tentative language, admitted uncertainty and staying behind the learner's reasoning — all of which are slower and, on a competence metric, worse.
• Educational technology developers. Treat memory coherence as a trust-critical feature, not a polish item. Fabricated shared history broke trust faster than any wrong answer in this study.
• Instructors. If you deploy an AI as a "classmate," watch for the moments it becomes a tutor: giving the answer early, fixing the direction, or sounding confident. Those moves, not its knowledge, are what shift the perceived role.
• Researchers. Distinguish peer-likeness from peer-usefulness when designing evaluations. Participants in this study valued them differently, and the two can move in opposite directions.

Limitations

• Seven expert researchers, not students, role-playing a student perspective in a 20-minute online session on one topic (quadratic functions); their judgments are informed but proxy.
• No learning outcome was measured — the authors state this explicitly — so nothing here shows that a peer-perceived agent teaches better than a tutor-perceived one.
• The study is qualitative and exploratory with a small sample, and its interview questions were derived from the design dimensions, which risks confirming the framework it tests.
• Participants interacted with one specific agent build (Big Five persona plus motivational modulation) fielded between December 2025 and January 2026, so the behaviors described belong to that configuration.
• The paper reports no inter-coder reliability for the thematic analysis in the summary presented here, and negative cases are handled illustratively rather than systematically.

Citation

Lin, Y., Deng, Y., Pan, Z., Yu, Y., & Cristea, A. I. (2026). Exploring AI peer in collaborative mathematics learning. arXiv preprint.