OpenCD: Empowering Diagnosis of Children's Mathematical Cognition through Open-ended Multimodal Tasks

Assessing children’s cognitive development in early mathematics is vital for effective teaching. Compared to closed-ended questions, which may fail to capture nuanced developmental spectrum, open-ended elicitation tasks (e.g., asking students to manipulate objects or draw to represent numbers) serve as a promising approach to reveal deeper cognitive processes. However, their diverse and unstructured nature makes systematic analysis challenging for teachers. We present OpenCD, a teacher-facing system that automatically analyzes multimodal student responses to capture individualized insights. Based on Evidence-Centered Design, it combines Vision-Language Models (VLMs) and expert models to generate interactive diagnostic graphs and reports with traceability back to behavioral evidence. In our two-part evaluation, a validation study found 90.3% of the system’s diagnoses “completely reasonable,” and a user study showed that OpenCD reduced teachers’ analysis burden and enhanced their insights into student thinking. Our work contributes to scalable process-based assessment for mathematical literacy.