Understanding Mathematical Giftedness: Integrating Self, Action Repertoires and the Environment

Abstract

A modern conceptualization of mathematical giftedness must take into account different cultural views of the nature of mathematics as well as conform to Ziegler and Heller‘s (2000) four postulates of giftedness (temporal precedence, fulfillment of the “inus” condition, personal characteristic and theoretical significance). With the Actiotope Model of Giftedness (Ziegler,2005) as a conceptual framework, this chapter will focus on recent research in neuropsychology, cognition, personal factors, language and the environment as applied to the development of mathematical excellence. The first section will review recent research that examines aspects of self in the development of mathematical thinking. The next section examines the role of the environment in the growth of mathematical expertise, particularly in the selection and adaptation of action repertoires and the possibility for a collective mathematical cognition. Finally, this chapter will expose some of the emerging pedagogical and political issues in the development of mathematical excellence within the context of increasing globalization.