Intelligent tutoring systems (ITSs) aim to deliver personalized learning support to each learner, aligning with the educational aspiration of many countries, including China. ITSs' personalized support is mainly achieved by providing individual prompts to learners when they encounter difficulties in problem-solving. The guiding principles and methods of prompts have been less investigated in previous ITS literatures. Based on relevant learning theories, such as self-regulated learning theory, zone of proximal development, scaffolding and heuristic teaching, we proposed seven guiding principles for designing ITS prompts and designed the guiding and adaptive prompts for the difficult questions in a mathematical ITS, math intelligent assessment and teaching system V2.0. In order to verify the effectiveness of this ITS with the aforementioned prompts, we conducted a 2 × 2 quasi-experiment in a high school, where the experimental group followed a process of "pretest, practice with general prompts and adaptive tutoring, and posttest," while the control group followed a process of "pretest, practice with only general prompts, and posttest." We collected the pre and posttest scores of both the experimental and control groups, and log data from the student model within the ITS for the experimental group students. The data analysis indicated that although the experimental group scored lower than the control group in the pretest, they scored higher in the posttest and spent less completion time. The drilled problems and the prompts provided to the experimental group students were personalized. In conclusion, the design principles for guiding and adaptive prompts in the ITS can provide personalized guidance and support for students, thus effectively improve their performance. Those principles are not only valuable for the subject mathematics but also can contribute significantly to the prompt design of other subjects, thereby bolstering the global pursuit of personalized education.