This study investigates the use of infinities and limits during the first 12 years of schooling while a secondary study presents ideas and comments on the observations that were made during the primary study. (MVL)

Reviews and analyzes the number-line metaphor in textbooks. Presents examples to show a way to produce an internal critique of mathematical textbooks, a critique that targets the practices in which the notions are involved within the text. Presents the number-line metaphor as the horizon and the tiller of all the enlargements of the notion of…

Explores the mathematical abilities of human infants compared with various species of animals. Studies indicate that human infants enter the world capable of doing simple mathematical operations. Nonhuman animals can discriminate among sets of objects based on the number of items in each set. Further studies may pinpoint the age at which children…

The purpose of this paper is to identify how the theory and techniques of research in cognitive development can be applied to the study of learning and instruction in mathematics. Five basic research paradigms are characterized; major directions of research on number, measurement, geometry, and adolescent reasoning are identified. Most of the…