One of the greatest challenges Computer Science (CS) teachers face is that of guiding their pupils through problem-solving processes, i.e., the process of constructing a solution for a given problem as an algorithm or a computer program. This paper suggests a tutoring model, to be implemented by prospective CS teachers, that aims at training them to accomplish this challenge. The model is based on one-on-one tutoring sessions, in which the prospective teacher meets a novice undergraduate student taking an introductory CS course and guides him or her through problem-solving processes. The tutoring activity provides the prospective CS teachers with an opportunity to experience teaching situations, especially learners' difficulties with respect to problem-solving processes, and consequently, to improve their teaching skills. The tutoring model was integrated into the Methods of Teaching Computer Science course and was accompanied by a qualitative research. The main research findings indicate that the prospective CS teachers: (a) change their perspective with respect to teaching processes; (b) focus in their teaching on learners' difficulties; (c) increase their awareness to problem-solving processes and to the need to adapt different teaching approaches for different learners; (d) become reflective practitioners; and (e) increase their confidence with respect to teaching processes.