Includes bibliographical references (pages 208-210).
Introduction and overview -- We still have a problem -- Mental journey around the world -- Mathematics and human intelligence -- School situation -- Formation of mathematical concepts -- Abstracting and classifying -- Naming -- Communication of concepts -- Concepts as cultural heritage -- Power of conceptual thinking -- Learning of mathematical concepts -- Learning and teaching -- Idea of a schema -- Integrative function -- Understanding -- Implications for the learning of mathematics -- Intuitive and reflective knowledge -- Symbols -- Communication -- Recording knowledge -- Communication of new concepts -- Making multiple classification straight forward -- Different kinds of imagery -- Interpersonal and emotional factors -- New model of intelligence -- From theory into action -- Type 1 theories and type 2 theories -- Mathematics as an activity of our intelligence -- Relational understanding and instrumental understanding -- Goals of learning and qualities of understanding -- Communicating mathematics -- Symbolic understanding -- Emotions and survival in the classroom -- Managing the risks in learning -- Silent music of mathematics