The growing use of large language models (LLMs) for AI-powered tutors in education highlights the need for reliable evaluation of their pedagogical abilities. In this work, we propose a reasoning-based evaluation methodology that leverages pedagogical domain knowledge to assess LLM-generated feedback in mathematical dialogues while providing insights into why a particular evaluation is given. We design structured prompts to invoke pedagogically-informed reasoning from LLMs and compare base model candidates selected for their strengths in reasoning, mathematics, and overall instruction-following. We employ Group Relative Policy Optimization (GRPO), a reinforcement learning method known to improve reasoning performance, to train models to perform evaluation in four pedagogically motivated dimensions, Mistake Identification, Mistake Location, Providing Guidance, and Actionability. Experimental results show that our GRPO-based models consistently outperform the base model and GPT-4.1, and surpass models trained using supervised fine-tuning in three out of four dimensions. Notably, our method achieved top-ranked performance in Actionability and competitive performance in two other dimensions in the BEA 2025 Shared Task under the team name bea-jh, underscoring the value of generating pedagogically grounded rationales for improving the quality of educational feedback evaluation.