Intelligent Tutoring Systems (ITS) have gained popularity due to their ability to provide students with cost-effective and personalized learning experience. The development of Large Language Models (LLMs) offer great potential to revolutionize personalized education to autonomously create effective ITS without relying on manual, labor intensive processes. Our research introduces a novel design framework, named Conversational Learning with Analytical Step-by-Step Strategies (CLASS), which harnesses the potential of high-performance LLMs to construct advanced ITS. The CLASS framework empowers ITS with two critical capabilities. First, through a carefully curated scaffolding dataset, CLASS provides essential problem-solving capabilities, enabling it to provide tutor-like, step-by-step guidance to students. Second, by using a dynamic conversational dataset, CLASS facilitates natural language interactions, which fosters engaging student-tutor conversations. The CLASS framework also enhances the transparency of ITS, offering valuable insights into its internal decision-making process. This interpretability allows seamless integration of user feedback, thus facilitating continuous refinement and improvement. Additionally, we present a practical application of the CLASS framework through a proof-of-concept ITS, with a focus on introductory college-level biology content. A carefully constructed protocol was developed for the biology ITS's preliminary evaluation, examining aspects such as the factual accuracy and relevance of its responses. Experts in the field of biology offered favorable remarks, particularly highlighting its capability to break down questions into manageable subproblems and provide encouraging responses to students.