Exploring AI Peer in Collaborative Mathematics Learning

Synthesis: Lin, Deng, Pan, Yu and Cristea (2026) ask what makes a language-model agent recognizable as a peer rather than a tutor, and answer with seven expert interviews rather than with learning outcomes. Their agent combines a Big Five personality profile with motivational-state modulation that shifts across forethought, performance and self-reflection phases, and it was tested on quadratic equations in a mathematics task with researchers who took the student role for twenty minutes each. The central finding is that participants judged the agent by its social behavior, not its mathematics: a non-judgmental space, tentative reasoning, appropriate imperfection and respect for the learner's pace made it a peer, while blind agreement and over-instruction pushed it back toward tutor. The paper proposes design dimensions for Collaborative Learning agents and is explicit that it did not measure learning.

Key Findings

1. Seven experts, twenty minutes each. Participants were researchers in user experience, learning sciences, educational technology and computer science with three to over twenty years of experience, meeting the agent online in 30-minute sessions.
2. Social behavior decided the role. Participants primarily judged the agent through how it behaved socially rather than through its mathematical capability.
3. Safety came partly from non-humanity. Several participants reported less embarrassment making mistakes with the agent than with classmates, because there was no comparison and no human judgment.
4. Tentative reasoning read as peer-like. An agent that expressed uncertainty, offered partial ideas and let the learner set the pace was perceived as a collaborator; one that delivered correct instruction was not.
5. Appropriate imperfection helped. Deliberate fallibility signaled a peer, while the appearance of complete competence signaled an authority.
6. Blind agreement destroyed trust. An agent that simply agreed with everything the learner said shifted perception toward a tool or a tutor rather than a peer.
7. Peer-likeness and peer-usefulness diverged. The authors report that being perceived as a peer and being useful for learning were not always aligned in participants' accounts.

Designing for a role, not a capability

The system's design separates three questions that AI tutors usually conflate: what personality the agent presents, what motivational stance it takes at each phase, and what it does with the mathematics. Personality is drawn from Big Five embeddings; motivation is modulated by phase, with curiosity-driven engagement during forethought, sustained engagement during performance, and consolidation during self-reflection.

The phase structure comes from Self-Regulated Learning, and it is the part that makes the agent more than a persona. In the performance phase it generates ideas, monitors progress, refocuses scattered discussion and proposes tentative next steps; in self-reflection it frames difficulty as task-related and avoids signaling finality. A tutor's job is to close the gap; a peer's job, on this design, is to keep the joint work open.

Why experts rather than students

The study's population is a deliberate choice with a real cost. Domain experts can articulate why an interaction felt peer-like, which is what a design study needs, and they can compare the experience against their own teaching. They are also not the learners the agent is for, and they knew they were evaluating a system.

That means the findings are design-relevant rather than learner-relevant. The paper is candid about the boundary: it examines interactional conditions, not learning gains or mathematical performance, and the authors frame the contribution as design dimensions for future peer-oriented systems rather than as evidence that peers teach better.

The unresolved tension

The most useful observation in the paper is that peer-likeness and usefulness came apart. An agent that is safe, tentative and imperfect may be a better peer and a worse source of correction, which is the classic risk of peer learning itself: peers can reinforce each other's errors.

The paper does not resolve this, and its design dimensions do not say how to. What it does establish is that the trade-off is real and that it is visible to expert users within a single session, which makes it a design question to be specified rather than discovered later in an outcome study.

What this means for practice

• Instructional designers. Decide which role the agent plays before writing prompts. The same model reads as peer or tutor depending on whether it expresses uncertainty and follows the learner's pace.
• Educational technology developers. Build the phase structure, not just the persona. Motivation that changes with forethought, performance and reflection is what makes tentative behavior coherent rather than erratic.
• Instructors. Expect safety to come from the absence of an audience. Students who fear comparison in class may engage more with an agent partly because it cannot judge them, which is a real benefit and a poor substitute for a classroom.
• Researchers. Pair a design study with an outcome study. The peer-like configuration is now specified well enough to test whether it improves mathematics learning relative to a tutor configuration.

Limitations

• The sample is seven domain experts rather than learners, and the agent was evaluated by researchers who knew they were assessing a system.
• Each participant interacted for approximately 20 minutes in a single session, so no claim about sustained use or relationship is possible.
• The study measured perception and interaction, not learning gains or mathematical performance, as the authors state explicitly.
• The agent was tested on one topic (quadratic equations) with a single design configuration, and no comparison condition was run.
• Thematic analysis of interviews with seven participants cannot establish prevalence; the themes describe conditions, not distributions.

Citation

Lin, Y., Deng, Y., Pan, Z., Yu, Y., & Cristea, A. I. (2026). Exploring AI Peer in Collaborative Mathematics Learning. arXiv:2610.38990.