Cognitive Processes in Mathematics

The psychology of mathematics is an expanding field of research that presents issues of fundamental importance. The seminar which formed the basis of this volume brought together researchers who are making significant contributions, to examine the present state of the subject. Two areas in particular are reviewed. One is early competence in various areas of mathematical skill: the development of maths skills in infancy, and the acquisition of algebraic and statistical skills in older children and university students. The second area concerns the representation of mathematical information: the relations between imaginal and propositional understandings in children's approaches to arithmetic word problems; the relation between semantic and syntactical knowledge of mathematics; the question of digital form; and the roles of associative and rule-based knowledge. The contributions also indicate future directions for research: the more precise specification of change processes; the integration of early and advanced states of knowledge and the examination of more complex tasks such as algebra and inferential statistics.