Large language models (LLMs) present new opportunities for creating pedagogical agents that engage in meaningful dialogue to support student learning. However, the current use of LLM systems like ChatGPT in classrooms often lacks the solid theoretical foundation found in earlier intelligent tutoring systems. To bridge this gap, we propose a framework that combines Evidence-Centered Design with Social Cognitive Theory for adaptive scaffolding in LLM-based agents focused on STEM+C learning. We illustrate this framework with Inquizzitor, an LLM-based formative assessment agent that integrates human-AI hybrid intelligence and provides feedback grounded in cognitive science principles. Our findings show that Inquizzitor delivers high-quality assessment and interaction aligned with core learning theories, offering teachers effective guidance that students value. This research underscores the potential for theory-driven LLM integration in education, highlighting the ability of these systems to provide adaptive and principled instruction.