Anna-Christin Söhling describes the acquisition of knowledge during the problem-solving process through experimentation and uncovering misconceptions. She utilizes the conceptual framework of deduction, abduction, and induction as proposed by Peirce and Meyer. Mathematical problem-solving processes often involve trial and error approaches that are prone to mistakes. Nevertheless, students do not seem to arrive at a solution purely by chance. In addition to the philosophical-logical reconstruction of such processes, the author addresses the question of learning mathematics through problem-solving.