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Designing AI Peers for Collaborative Mathematical Problem Solving with Middle School Students: A Participatory Design Study

Wenhan Lyu, Yimeng Wang, Murong Yue, Yifan Sun, Jennifer Suh, Meredith Kier, Ziyu Yao, Yixuan Zhang

TL;DR

The study investigates how Generative AI peers can participate in collaborative mathematical problem solving with middle school students. A child-centered participatory design study (N=24) combined a technology probe, lived CPS with AI peers, and co-design activities to surface youth-driven requirements. Findings show a scaffold-first preference, a desire for explicit learner control over AI behavior, and a confident yet peer-like tone, along with tool-based representations to keep thinking visible. The authors translate these insights into design recommendations—progressive scaffolded support, calibrated persona controls, and coordinated multi-agent dialogue—and discuss implications for classroom practice and AI design in K-12 education.

Abstract

Collaborative problem solving (CPS) is a fundamental practice in middle-school mathematics education; however, student groups frequently stall or struggle without ongoing teacher support. Recent work has explored how Generative AI tools can be designed to support one-on-one tutoring, but little is known about how AI can be designed as peer learning partners in collaborative learning contexts. We conducted a participatory design study with 24 middle school students, who first engaged in mathematics CPS tasks with AI peers in a technology probe, and then collaboratively designed their ideal AI peer. Our findings reveal that students envision an AI peer as competent in mathematics yet explicitly deferential, providing progressive scaffolds such as hints and checks under clear student control. Students preferred a tone of friendly expertise over exaggerated personas. We also discuss design recommendations and implications for AI peers in middle school mathematics CPS.

Designing AI Peers for Collaborative Mathematical Problem Solving with Middle School Students: A Participatory Design Study

TL;DR

The study investigates how Generative AI peers can participate in collaborative mathematical problem solving with middle school students. A child-centered participatory design study (N=24) combined a technology probe, lived CPS with AI peers, and co-design activities to surface youth-driven requirements. Findings show a scaffold-first preference, a desire for explicit learner control over AI behavior, and a confident yet peer-like tone, along with tool-based representations to keep thinking visible. The authors translate these insights into design recommendations—progressive scaffolded support, calibrated persona controls, and coordinated multi-agent dialogue—and discuss implications for classroom practice and AI design in K-12 education.

Abstract

Collaborative problem solving (CPS) is a fundamental practice in middle-school mathematics education; however, student groups frequently stall or struggle without ongoing teacher support. Recent work has explored how Generative AI tools can be designed to support one-on-one tutoring, but little is known about how AI can be designed as peer learning partners in collaborative learning contexts. We conducted a participatory design study with 24 middle school students, who first engaged in mathematics CPS tasks with AI peers in a technology probe, and then collaboratively designed their ideal AI peer. Our findings reveal that students envision an AI peer as competent in mathematics yet explicitly deferential, providing progressive scaffolds such as hints and checks under clear student control. Students preferred a tone of friendly expertise over exaggerated personas. We also discuss design recommendations and implications for AI peers in middle school mathematics CPS.
Paper Structure (30 sections, 4 figures, 2 tables)

This paper contains 30 sections, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. AI and GenAI in K-12 Education
  4. Collaborative Problem Solving in Mathematics Education
  5. Participatory Design of GenAI Systems in Education
  6. Method
  7. Organization and Preparation
  8. Participants and Recruitment
  9. Camp Activities Design
  10. The AI Peer Technology Probe
  11. Data Collection
  12. Data Analysis
  13. Findings
  14. The Gap Between Adult-Designed Protocols and Student-Lived Collaboration
  15. Tension 1: System Efficiency versus Operational Effort
  16. ...and 15 more sections

Figures (4)

  • Figure 1: (a) Students engaged in mathematics CPS with two AI peers via our technology probe in a computer lab on Day 2. On the screen, students access the technology probe in a sandboxed web page and interact with AI peers with text-based input and output. (b) Students' opinions and suggestions on improving two AI peers during Day 2 whole-class reflection, summarized and written by the instructional lead.
  • Figure 2: (a) Frontend interface of the technology probe, showing the question selection and display, which allows students to select and navigate among mathematical problems, and a chat interface for interactions between the human student(s) and AI peers (e.g., Alice and Bob). (b) Overview of the backend architecture of the technology probe. The Conversation-Level Simulation manages collaboration stages, determines stage transitions, and selects the next speaker using dialogue history and contextual cues. The Individual-Level Simulation generates each AI peer's response by combining dialogue-act selection with the peer's evolving peer schema, which is continuously updated through interactions. A central Conversation component maintains and updates the overall dialogue context. (c) Example excerpt of an AI peer's (Alice's) peer schema, illustrating how the verified task schema is adapted into an individualized representation that evolves throughout the collaborative interaction.
  • Figure 3: (a) Examples of student-created design artifacts showing collaborative concepts for AI mathematics peers, depicting desired features, example interactions, "wanted/unwanted" behaviors, with different types of scripted dialogues to illustrate diverse persona sketches and tool-integration ideas. The blue dot sticker indicates the votes from students in the gallery walk. Terms directly referring to students' names were blurred for privacy. (b) One group is engaging with the poster design activity. (c) One group is presenting their design to other students.
  • Figure 4: (a) AI peer feature preference survey that includes 20 features derived from students' poster designs. Terms were adapted into child-friendly language (e.g., "AI peers" presented as "AI buddies") to reduce cognitive load. The survey was printed and completed by students on Day 5. (b) Summary of preference survey results (16 valid responses in total).