Large language models (LLMs) present new opportunities for creating pedagogical agents that engage in meaningful dialogue to support student learning. However, current LLM systems used in classrooms often lack the solid theoretical foundations found in earlier intelligent tutoring systems. To bridge this gap, we propose a framework that combines Evidence-Centered Design with Social Cognitive Theory and Zone of Proximal Development for adaptive scaffolding in LLM-based agents focused on STEM+C learning. We instantiate 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 effective guidance that students value. This research demonstrates the potential for theory-driven LLM integration in education, highlighting the ability of these systems to provide adaptive and principled instruction.