This paper presents an intelligent tutoring system (ITS) for the learning of arithmetical problem solving. This is based on an analysis of a) the cognitive processes that take place during problem solving; and b) the usual tasks performed by a human when supervising a student in a one-to-one tutoring situation. The ITS is able to identify the solving strategy that the student is following and offer adaptive feedback that takes into account both the problem's constraints and the decisions previously made by the user. An observational study shows the ITS's accuracy at emulating expert human supervision, and a randomized experiment reveals that the ITS significantly improves students' learning in arithmetical problem solving.