This paper proposes a generic methodology and architecture for developing a novel conversational intelligent tutoring system (CITS) called Oscar that leads a tutoring conversation and dynamically predicts and adapts to a student's learning style. Oscar aims to mimic a human tutor by implicitly modelling the learning style during tutoring, and personalising the tutorial to boost confidence and improve the effectiveness of the learning experience. Learners can intuitively explore and discuss topics in natural language, helping to establish a deeper understanding of the topic. The Oscar CITS methodology and architecture are independent of the learning styles model and tutoring subject domain. Oscar CITS was implemented using the Index of Learning Styles (ILS) model (Felder & Silverman, 1988) to deliver an SQL tutorial. Empirical studies involving real students have validated the prediction of learning styles in a real-world teaching/learning environment. The results showed that all learning styles in the ILS model were successfully predicted from a natural language tutoring conversation, with an accuracy of 61-100%. Participants also found Oscar's tutoring helpful and achieved an average learning gain of 13%. (Contains 5 figures and 9 tables.)