The chapter explores the cognitive challenges students face in understanding mathematics, emphasizing the importance of semiotic representation in mathematical processes. It proposes a classification of semiotic representations into two types: treatment and conversion, which correspond to distinct cognitive processes. Treatment is crucial from a mathematical perspective, while conversion is the key factor for learning. The chapter discusses the nature of representations, including individual beliefs, conceptions, and misconceptions, as well as signs and their associations. It highlights the need to understand the cognitive systems required to access and transform mathematical objects, and the role of these systems in the learning process. The analysis aims to identify the cognitive conditions necessary for comprehension and to uncover the sources of students' difficulties in mathematics.The chapter explores the cognitive challenges students face in understanding mathematics, emphasizing the importance of semiotic representation in mathematical processes. It proposes a classification of semiotic representations into two types: treatment and conversion, which correspond to distinct cognitive processes. Treatment is crucial from a mathematical perspective, while conversion is the key factor for learning. The chapter discusses the nature of representations, including individual beliefs, conceptions, and misconceptions, as well as signs and their associations. It highlights the need to understand the cognitive systems required to access and transform mathematical objects, and the role of these systems in the learning process. The analysis aims to identify the cognitive conditions necessary for comprehension and to uncover the sources of students' difficulties in mathematics.