The Process of Learning Mathematics

The Process of Learning Mathematics is a collection of essays from a two-term course of intercollegiate lectures for students of B.Ed. degree. This collection starts with two different views on the nature of mathematics. One essay discusses the role of intuition in understanding mathematics, while another paper expounds on the role of logic. This book then discusses the generalization, structure, and approximations used in teaching mathematics, and emphasizes the problems of applied mathematics and technology pertaining to equations of motion, mathematical representation of physical phenomena, or in relations such as conservation of matter. One paper reviews Piaget's studies on the development of children's thinking process, noting that teachers should consider the level of thinking the pupil uses when designing his teaching material. Another essay deals with how the existing knowledge in a student can affect new kinds of learning through assimilation and accommodation. This book then describes the use of symbols and "reflective intelligence," addressing reflective activities, communication, and the contribution of symbols. This text then discusses computer-assisted education and several mathematical teaching or learning experiments. This compendium can prove useful for mathematics majors, educators, school administrators, and math teachers.

ContributorsForewordThe Nature of MathematicsThe Nature of Mathematics - Another ViewThe Role of IntuitionThe Role of LogicGeneralization and StructureAttempts to Investigate the Learning of MathematicsThe Growth of Logical ThinkingSchematic LearningReflective Intelligence, and the Use of SymbolsMotivation, Emotional and Interpersonal FactorsInvestigational MethodsA Note on DiscoveryStructural ApparatusComputer-assisted InstructionThe Uses of Programmed Material in British Schools and CollegesThe Midlands Mathematical ExperimentScottish Mathematics GroupSchool Mathematics Project; the Initial StagesNuffield Foundation Mathematics Teaching Project