How generative AI guided-professional development supports teachers’ engagement with mathematical creativity, content knowledge, and pedagogical content knowledge

Synthesis: This embedded case study followed eight in-service teachers from rural and under-resourced districts through a generative AI-guided professional development program of ten interactive modules, asking how teachers engaged with mathematical Creativity (MC), content knowledge (CK), and pedagogical content knowledge (PCK), and which AI features shaped that engagement. Teachers worked on proportional reasoning, interpreted simulated student thinking, and revised instructional decisions; dialogue logs, mathematical artifacts and interviews were analyzed through iterative thematic analysis. The authors report three cross-case themes: creative mathematical exploration, conceptual deepening of proportional reasoning, and expansion of pedagogical reasoning. They name six core AI-mediated mechanisms (adaptive and personalized prompting, real-time feedback, progressive scaffold fading, simulated student reasoning, conversational nonjudgmental tone, flexible pacing) plus two cross-cutting mechanisms, representational nudges and cycles of creative challenge and reflection. Teachers described the AI as a thinking partner rather than a content-delivery tool and credited it with enabling productive struggle in a psychologically safe environment. The study reports engagement patterns, not measurable gains in teacher knowledge or student learning.

Key Findings

1. An embedded case, not a trial. Eight in-service teachers from rural and under-resourced districts completed ten interactive modules, and the authors present findings as patterns of engagement rather than measurable gains.
2. Three cross-case themes. Engagement centered on creative mathematical exploration, conceptual deepening of proportional reasoning, and expansion of pedagogical reasoning, which the authors treat as trajectories unfolding across the modules.
3. MC, CK, and PCK moved together. The authors report that teachers engaged with mathematical creativity, content knowledge, and pedagogical content knowledge as interconnected forms of reasoning rather than as isolated domains.
4. Six core mechanisms, two cutting across. The abstract names six core AI-mediated mechanisms and adds two cross-cutting ones, representational nudges and cycles of creative challenge and reflection, that supported movement among the three domains.
5. Simulated student reasoning anchored PCK. Across Modules 6-10 the AI presented hypothetical student responses or misconceptions and asked teachers to diagnose the reasoning behind them, moving teachers from correcting errors to interpreting students' logic.
6. A nonjudgmental tone enabled productive struggle. Teachers called the AI "patient," "neutral," and "encouraging," saying its non-evaluative conversational feedback reduced performance anxiety and positioned the system as a thinking partner.

What the professional development looked like

The program comprised ten interactive modules completed asynchronously, with the AI designed as a cognitive and instructional partner rather than a delivery mechanism. The AI prompted teachers to solve ratio and proportional reasoning problems in multiple ways, critique and modify instructional scenarios, design and refine open-ended tasks, and reflect on simulated student thinking. Modules were built on Rhodes' 4P framework, with the process dimension carrying creativity-directed practices such as multiple-solution strategies, problem posing, representation use and justification, and the press dimension treating mistakes as learning opportunities. The design answered an access problem: Workplace Learning supporting creativity-directed mathematics instruction is limited in rural and under-resourced regions, and asynchronous provision alone often lacks interactivity, real-time feedback and individualized guidance.

How teachers engaged with creativity, content, and pedagogy

Creative mathematical exploration described teachers generating multiple solution strategies and representations and extending or posing new problems. Conceptual deepening of proportional reasoning captured movement from procedures toward relational understanding of ratio and rate. Expansion of pedagogical reasoning appeared as teachers anticipated and interpreted student misconceptions, adapted tasks, and planned how ideas would be taught. Critically, teachers engaged with Creativity, CK and PCK together: the authors argue that MC does not develop independently of teachers' mathematical knowledge and their knowledge of how to make ideas accessible to students. Teachers first approached tasks procedurally, then reframed them as opportunities for inquiry, describing the change as "pushing the envelope," "slowing me down to think," and "making me see the task differently." Prompts that exceeded comfort zones functioned, in the authors' reading, as productive struggle.

The mechanisms teachers credited

Adaptive prompting kept teachers from "slipping into teacher autopilot"; Teacher F said, "It felt like it knew where I was and nudged me just enough." Scaffolding receded deliberately, with explicit guidance early and requests to justify, generalize and design tasks later: Teacher H recalled, "In the beginning AI would guide me. Later it said, 'extend this' or 'explain your choice'. It trusted me more." Real-time feedback let teachers revise immediately, which Teacher D said helped them internalize reasoning. Simulated student thinking moved teachers from correcting errors to interpreting students' logic, as when the AI asked in Module 7 about a student who "scaled one value but not the other." Representational prompts connected Creativity and content knowledge: Teacher B noted that "seeing ratio in a graph helped me connect it to slope." All eight teachers valued the asynchronous pacing.

What this means for practice

• Instructors. Ask for reasons, not answers: teachers credited adaptive "why" prompts with keeping them out of routine procedural work, so require justification and a second representation.
• Program designers. Plan progressive Scaffolding rather than uniform support, withdrawing guidance so teachers generalize, justify and design tasks independently.
• Faculty developers. Build simulated student responses into teacher learning so participants rehearse diagnosing misconceptions before they meet them in class.
• Leaders in under-resourced districts. Asynchronous pacing was the feature all participants valued around heavy schedules, a practical route where local professional development is scarce.
• Researchers. Treat this as engagement-level evidence: no teacher knowledge or student outcomes were measured, so the next step is designs with pre/post measures and observation.

Limitations

• The design is an embedded case study of eight teachers who completed all ten modules, so it identifies engagement patterns rather than causal effects and uses no comparison group.
• There were no pre/post measures, classroom observations or student outcomes, so findings are not evidence of measurable gains or of transfer to practice.
• Teachers reported design constraints including repetition, notation or formatting glitches, hallucination risk, limited visualization tools, and lack of peer learning.
• The evidence base is qualitative logs, artifacts and interviews from a purposeful sample; the authors call for larger and comparative samples to test transfer.

Citation

Bicer, A., Aldemir, T., Lee, U., Moon, J., Rambo Hernandez, K., & Sanders, M. (2026). How generative AI guided-professional development supports teachers’ engagement with mathematical creativity, content knowledge, and pedagogical content knowledge. ZDM - Mathematics Education, 58, 1027–1039.