Raymond Duval's cognitive analysis of comprehension problems in mathematics learning explores the cognitive systems required to access mathematical objects and perform transformations. He emphasizes the importance of semiotic representations, which are essential for mathematical activity. These representations are classified into two types: treatment and conversion. Treatment involves processing representations, while conversion involves transforming them, each corresponding to different cognitive processes. These processes can lead to difficulties in understanding mathematics. Empirical data supports the idea that these processes are crucial for learning. The paper discusses the nature of difficulties students face in understanding mathematics, which are influenced by the complexity of mathematical knowledge acquisition. It highlights the need for different approaches to understanding mathematical knowledge, including epistemological and educational perspectives. The concept of representation is central, as it refers to something that stands for something else. Representations can be individual beliefs, schematic productions, or signs and their associations. Semiotic representations, including language, are common tools for producing new knowledge. The paper also discusses the cognitive structures underlying these representations, which enable individuals to perform various knowledge activities. The analysis suggests that understanding the cognitive functioning behind mathematical processes is essential for addressing comprehension difficulties. The paper concludes that the way of thinking is generally the same across different areas of knowledge, even though mathematical knowledge is unique.Raymond Duval's cognitive analysis of comprehension problems in mathematics learning explores the cognitive systems required to access mathematical objects and perform transformations. He emphasizes the importance of semiotic representations, which are essential for mathematical activity. These representations are classified into two types: treatment and conversion. Treatment involves processing representations, while conversion involves transforming them, each corresponding to different cognitive processes. These processes can lead to difficulties in understanding mathematics. Empirical data supports the idea that these processes are crucial for learning. The paper discusses the nature of difficulties students face in understanding mathematics, which are influenced by the complexity of mathematical knowledge acquisition. It highlights the need for different approaches to understanding mathematical knowledge, including epistemological and educational perspectives. The concept of representation is central, as it refers to something that stands for something else. Representations can be individual beliefs, schematic productions, or signs and their associations. Semiotic representations, including language, are common tools for producing new knowledge. The paper also discusses the cognitive structures underlying these representations, which enable individuals to perform various knowledge activities. The analysis suggests that understanding the cognitive functioning behind mathematical processes is essential for addressing comprehension difficulties. The paper concludes that the way of thinking is generally the same across different areas of knowledge, even though mathematical knowledge is unique.