Invited Speakers > Robert Siegler

Numerical Development

Robert S. Siegler
Carnegie-Mellon University

In this talk, I attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from nonsymbolic to small symbolic numbers, from smaller to larger whole numbers, and from whole to rational numbers. One reason why this development is important is that precision of numerical magnitude knowledge is correlated with, predictive of, and causally related to both whole and rational number arithmetic. Rational number arithmetic, however, also poses challenges beyond understanding the magnitudes of the individual numbers. Some of these challenges are inherent; they are present for all learners. Other challenges are culturally contingent; they vary from country to country and classroom to classroom. Our findings indicate that a largely ignored culturally contingent variable, distributions of problems in mathematics textbooks, substantially influences learning of rational number arithmetic. Generating theories and data that help children surmount the challenges of rational number arithmetic is an important goal for numerical development research.