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The Socratic teaching method encourages students to solve problems through instructor-guided questioning, rather than providing direct answers. Although this method can enhance learning outcomes, it is both time-consuming and cognitively demanding, limiting instructors' ability to provide individualized attention at scale. Automated Socratic conversational agents offer a promising avenue for supplementing human instruction in programming education, yet their development has been constrained by the lack of appropriate datasets, evaluation frameworks, and principled approaches to dialogue generation. This dissertation presents a computational framework for automated Socratic debugging conversations in novice programming environments. The framework makes three important, interconnected contributions: (1) benchmarks and evaluation standards for Socratic debugging, (2) automated mining of student misconceptions from code submissions, and (3) generation of Socratic dialogue that guides students to discover and correct their errors. First, I introduce the novel task of Socratic debugging and present a benchmark dataset of expert-crafted multi-turn Socratic conversations, which has been used to evaluate various large language models in zero-shot and fine-tuned settings. Second, I describe an automated approach for mining known as well as novel student misconceptions in code submissions, which can provide crucial knowledge for targeted pedagogical interventions. Third, I introduce the concept of Reasoning Trajectories as intermediate representations of Socratic conversations that are designed to guide the student towards statements about code behavior that contradict their misconceptions. The ensuing cognitive dissonance is expected to lead to enduring belief updates that fix the misconception. Overall, the three contributions establish conceptual and computational foundations for automated Socratic agents. While the focus is on programming education, the framework described in this dissertation is generalizable to any domain that can benefit from Socratic teaching of problem-solving skills through guided discovery and correction of misconceptions. Furthermore, this work opens avenues for research on the optimization of personalized Socratic agents.