Problem-solving is central to mathematics education. However, diagnosing where students' reasoning breaks down requires individualized probing and consistent criteria that teachers cannot sustain at classroom scale. We introduce STEP (STage-based Evaluation of Problem-solving skills), co-designed with six mathematics education experts, which operationalizes problem-solving as four stages and eight diagnostic sub-skills. By specifying what evidence to elicit and assess at each stage, STEP enables an LLM pipeline to generate stage-specific questions and rubrics for any math word problem, reducing the manual design of diagnostic materials. An expert review (N=8) assessed the pedagogical validity of the generated materials and informed STEPwise, a teacher-in-the-loop system for diagnostic material generation and process-level assessment. In a classroom study with 5 teachers and 64 students, STEPwise helped teachers and students locate reasoning breakdowns and supported students in reflecting on their reasoning. Together, STEP and STEPwise offer a structured approach to fine-grained diagnosis at classroom scale.

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