Cover -- Understanding in Mathematics -- Copyright -- Contents -- List of Figures -- Acknowledgments -- Preface by Series Editor -- Introduction -- Chapter 1 Understanding and Meaning -- Understanding -- Meaning -- Chapter 2 Components and Conditions of an Act of Understanding -- What Could Be an Act of Understanding? -- Components of an Act of Understanding -- Psychological Conditions of an Act of Understanding -- Social Conditions of an Act of Understanding -- What Understanding Is Not -- Chapter 3 Processes of Understanding -- The Process of Understanding -- Reasonings -- Explanation and Understanding -- The Role of Example and the Medium in Which It Is Presented for Understanding -- The Role of Activity in Understanding -- The Question of Continuity of the Processes of Understanding -- Chapter 4 Good Understanding -- The Relativity of 'Good Understanding' -- Various Approaches to Research on Understanding in Mathematics Education -- Models of Understanding -- The Historico-empirical Approach to Understanding in Mathematics -- 'Good Understanding' in the Historico-empirical Approach: Significant Acts of Understanding -- The Philosophy of Epistemological Obstacles -- Epistemological Obstacles in Mathematics: The Case of the Bolzano Theorem -- The Notion of Epistemological Obstacle as a Category of Thought in Mathematics Education -- Problems of Definition -- Chapter 5 Developmental and Cultural Constraints of Understanding -- The Relationship Between Development and Culture -- The Genesis of Understanding and the Developmental Roots of Epistemological Obstacles -- The Cultural Roots of Epistemological Obstacles -- References -- Index.