As online education platforms continue to expand, there is a growing need for assessment methods that not only measure answer accuracy but also capture the depth of students' cognitive processes in alignment with curriculum objectives. This study proposes and evaluates a rubric-based assessment framework powered by a large language model (LLM) for measuring algebraic competence, real-world-context block coding tasks. The problem set, designed by mathematics education experts, aligns each problem segment with five predefined rubric dimensions, enabling the LLM to assess both correctness and quality of students' problem-solving processes. The system was implemented on an online platform that records all intermediate responses and employs the LLM for rubric-aligned achievement evaluation. To examine the practical effectiveness of the proposed framework, we conducted a field study involving 42 middle school students engaged in multi-stage quadratic equation tasks with block coding. The study integrated learner self-assessments and expert ratings to benchmark the system's outputs. The LLM-based rubric evaluation showed strong agreement with expert judgments and consistently produced rubric-aligned, process-oriented feedback. These results demonstrate both the validity and scalability of incorporating LLM-driven rubric assessment into online mathematics and STEM education platforms.