This embedded case study examined how eight in-service teachers from rural and under-resourced districts engaged with mathematical creativity (MC), content knowledge (CK), and pedagogical content knowledge (PCK) during an AI-guided professional development program, and how specific AI-mediated mechanisms shaped that engagement. Teachers completed ten interactive modules in which a generative AI system served as a cognitive and instructional partner by prompting problem solving, problem posing, representational reasoning, simulated student interpretation, and reflective instructional decision-making. Data sources included teacher-AI dialogue logs, teacher-generated mathematical artifacts, and interviews, which were analyzed through iterative thematic analysis. Findings showed that teachers engaged with MC, CK, and PCK as interconnected forms of reasoning rather than as isolated domains. Three cross-case themes characterized this engagement: creative mathematical exploration, conceptual deepening of proportional reasoning, and expansion of pedagogical reasoning. These trajectories were shaped by six core AI-mediated mechanisms: adaptive and personalized prompting, real-time feedback, progressive scaffold fading, simulated student reasoning, conversational nonjudgmental tone, and flexible pacing. Two cross-cutting mechanisms, representational nudges and cycles of creative challenge and reflection, further supported teachers’ movement between mathematical exploration, conceptual reasoning, and pedagogical decision-making. Teachers emphasized that these mechanisms enabled productive struggle within a psychologically safe environment and positioned AI as a thinking partner rather than a content-delivery tool. The study contributes to research on AI-supported teacher learning by showing how mathematical creativity-aligned AI scaffolding can support teachers’ integrated engagement with mathematics and pedagogy in rural professional learning contexts where access to sustained professional development is limited.
Ali Bicer, T. Aldemir, Unggi Lee et al.· ZDM: Mathematics Education· 1 citation
Adapting a language model to a task no longer requires training all of its weights, and a line of parameter-efficient methods has driven the trainable count from billions down to a handful of scalars. Gradient-free adaptation, which samples random weight perturbations and keeps the ones that score well, has not followed that trajectory and still perturbs every entry of the weight tensor. It is unknown whether that full-weight search is necessary, and more fundamentally which property of a perturbation makes it work at all, because existing methods vary the search space, the perturbation scale, and the aggregation together. We resolve this by intervening on one factor at a time inside a fixed pipeline, holding candidate scoring and voting constant while we vary the search dimension, the subspace that carries the perturbation, and its norm. Perturbing a frozen frame of 12 to 16 scalars stays 1.8 accuracy points behind full-weight search on average across 49 model-benchmark cells, trailing it in 36 of them. Neither the dimension nor the choice of basis explains that performance. A random frame whose Grassmann overlap with the SVD frame is at chance level performs identically once a single scale factor is matched, and at large scales the SVD directions collapse first. What survives is the perturbation norm, whose usable range closes within a factor of five across seven models and stays flat inside. The perturbation norm is therefore the one factor with a failure mode, and its safe region transfers across scale and family. The design question narrows from which subspace to perturb to how hard to shake.
Taeyeon Kim, Ahhyun Kim, Taehyeon Kim et al.· 0 citations
EduClaw-Bench is introduced, a benchmark that places an agent tutor in a continuous 30-day relationship with a simulated learner grounded in knowledge tracing (KT), whose knowledge-concept mastery, from a KT model trained on real-student data, drives its answers and is probed for learning gain across 55 scenarios.
Unggi Lee, Sookbun Lee, Yeil Jeong et al.· 0 citations