Argumentation-based learning has long been recognised as an effective pedagogical approach for promoting critical thinking and reflection, while deepening students' understanding of the subject matter. Despite its benefits, providing students with consistent access to high-quality argumentation practice at scale is a significant educational challenge. Recent advances in Large Language Models (LLMs) offer a promising solution by enabling new interactive and personalised forms of learning through argumentative dialogues. This work presents ArgueMate, an LLM-powered Pedagogical Conversational Agent (PCA) that serves as an interactive partner for educational argumentation exercises. ArgueMate is built on the principle of constructive disagreement, using structured dialogue to enhance learning.