Digital learning environments produce rich clickstream data that can reveal how students approach learning tasks, yet interpreting these fine-grained traces often requires substantial expert effort. We introduce ClickSight, a framework for interpreting student clickstreams through learning strategies defined in the literature. Given a student clickstream and a predefined set of learning strategies, ClickSight uses a staged LLM-based pipeline to identify strategy-relevant evidence, assess adherence to each strategy, and generate an evidence-grounded interpretation of the student's behavior. We evaluate ClickSight across two learning environments, 365 students, and 12 model backbones using an expert-grounded quality rubric and an LLM judge calibrated with human-expert ratings. Our results show that ClickSight can generate high-quality strategy-based interpretations across different models and environments, with reasoning models performing more consistently than instruction-tuned counterparts. We further find that providing external clickstream-extracted guidance can improve interpretation quality for strategies that require precise quantitative information from the trace. By connecting fine-grained clickstreams with theoretically defined learning strategies and preserving the evidence underlying each judgment, ClickSight provides a flexible approach for studying student behavior in digital learning environments.

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