ProductiveMath: A Generative-AI-Powered App to Support Productive Failure Teaching

Synthesis: Rhaimi et al. (2025) present ProductiveMath, a generative-AI-powered tool that helps teachers design high-quality Productive Failure problems — a known challenge in PF pedagogy. Across three studies, they define a rubric for high-quality PF problems, use GPT-4o to generate and evaluate them alongside human raters (finding strong AI-human correlation), and report that seven math teachers rated AI-generated algebra problems as high quality with positive usability perceptions and adoption intent.

The challenge it addresses

Productive Failure engages students in problem-solving before instruction, but designing effective PF problems is challenging (Kapur, 2015). ProductiveMath addresses this by using generative AI to support teachers in creating PF problems — lowering the design burden that otherwise makes PF difficult to implement.

Three studies

• Study 1: A literature review defined high-quality PF problems and produced a rubric; GPT-4o generated and evaluated 30 problems alongside human raters.
• Study 2: Replicated with 60 additional problems, showing strong correlations between AI and human ratings — confirming GPT-4o's capability to produce high-quality PF problems.
• Study 3: Seven math teachers evaluated human- and AI-generated problems via surveys and interviews. They rated AI-generated algebra problems as high-quality, reported positive perceptions of ProductiveMath's usability, and expressed intentions to use it. Teacher feedback included adjusting problem difficulty, simplifying text, enhancing visuals, and providing additional PF support.

Relevance to the wiki

This paper connects Productive Failure to teacher support and Generative AI: AI can lower the barrier to implementing PF by scaffolding the creation of high-quality PF problems. It sits alongside the other productive-failure articles as evidence that AI can support (here, help design) productive-failure pedagogy, complementing the articles that focus on AI preserving struggle during learning.

Connected Concepts

• Productive Failure
• Generative AI
• LLM
• Math Education
• K 12
• Teacher Role
• Instructional Design

Connected Articles

• Kim AI Productive Failure Adult 2026 — Designing AI Systems for Productive Failure
• Puech Pedagogical Steering LLM Productive Failure 2025 — Pedagogical Steering of LLMs for Productive Failure
• Wang Safety Gap Productive Struggle 2026 — The Safety Gap: Restoring Productive Struggle

Citation

Rhaimi, S., Ercan, D., Gao, R., Esmaeiligoujar, S., Babaee, M., Li, H., Zhang, S., Lee, S., Closser, A., & Botelho, A. (2025). ProductiveMath: A Generative-AI-Powered App to Support Productive Failure Teaching. University of Florida. DOI: 10.1007/978-3-031-99264-3_43.